I think the empirical fact
that we see only nonnegative energy density and nonnegative energy flux
(dominant energy condition conjecture) should be explained in the
first place, along with a proper explanation of another, and also
"obvious", asymptotically flat spacetime conjecture.
But in order to 'explain'
something, you'll have to 'derive' it from 'something else', correct? If
you agree, see
You have an evolving
[lambda], and all quantities are quasi-local from the outset.
Have a nice summer.
Best - Dimi
----
Note: On 17 June 2009 -- three months
and twenty days later than my email printed below
-- Laszlo Szabados
published his updated online review, but chose again to
keep quiet on the LIGO controversy.
But
"let's do our job, science ...", as he suggested.
In his
Introduction,
Laszlo Szabados stated the scope of his
review article (emphasis added):
"... why should
the gravitational energy-momentum and angular momentum, or, more
generally, any observable of the gravitational ‘field’, be
necessarily quasi-local."
Namely, his scope
is to explain "the more ambitious claim to associate energy (or rather
energy-momentum and, ultimately, angular momentum as well) to
extended, but finite, spacetime domains, i.e., at the
quasi-local level. Obviously, the quasi-local quantities could
provide a more detailed characterization of the states of the
gravitational ‘field’ than the global ones, so they (together with more
general quasi-local observables) would be interesting in their own
right."
Two questions
follow. What is 'quasi-local'? And secondly, in exactly what sense is
'quasi-local' related to 'extended but finite spacetime domains'
?
I wish Laszlo Szabados and his
colleagues put aside those "two-surface
observables", and study the mechanism by which Mother Nature
produces the 'extended but finite spacetime domains', in such a
way that we enjoy the fundamental attributes of 3-D space (cf. below).
This is a puzzle
known since the time of Lucretius, as it captures 'the
atom of geometry' (explanation and drawings here) and the mystery of 'the
infinitesimal' in diff calculus -- how come we are able to get
different in size finite things from an uncountably
infinite "number" of infinitesimal "points" ?
As to the first
question, regarding the very notion of 'quasi-local', check out the
arrow of spacetime below, and think of the
trajectory of a fish in a shoal swinging around a coral reef, say. We
have an utterly non-linear, holistic, two-way negotiation between every
fish and 'the whole shoal', such that all physical quantities (the inertial mass included) of any given fish become
necessarily quasi-local.
All these
questions lead to the nature of 3-D space and
the ongoing, as-we-speak mechanism of 'the flatness
problem' (asymptotically
flat spacetime conjecture), producing an extremely precise balance between the two
tug-of-war effects, CDM & DDE, of the geometry
of spacetime at cosmological scale (global properties of spacetime).
Unlike
Laszlo Szabados, I don't
believe that the gravitational energy and spacetime "curvature" can be fully
defined intrinsically, i.e., by "working solely within
the 4-dimensional spacetime in which we find ourselves" (John Baez).
Hence the sufficient condition for gravitational dynamics,
called The Aristotelian Connection.
But instead of introducing some extra dimensions for such additional
extrinsic determination of GR dynamics (e.g., Naresh Dadhich), I speculate that the
hypothetical Aristotelian Connection (global mode of spacetime)
lives ]between[ the "points" of the underlying spacetime manifold, and seek 'gravitational potential
reality' effects, CDM &
DDE, emerging from 'the dark gaps' of The Aristotelian Connection during the arrow of spacetime. If you don't like the
gravitational potential reality, you'll have to live with up to
96% "dark stuff", as calculated under the
current assumption that such form of potential reality doesn't exist.
Surely
Laszlo Szabados and his
colleagues would prefer to deal with math instead of metaphysics.
Only the math isn't available.
But why not explore, faute de mieux,
some "two-surface
observables" ? Because the black cat ain't there.
D. Chakalov
July 30, 2009
Last update: August 17, 2009
----
The hardest thing of all
is to find a black cat in a dark room, especially if there is no cat.
Confucius
===============
Subject:
Schizophrenic behavior of gravity ?
Date: Sat, 28 Mar 2009 04:41:47 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: "Szabados,L." <lbszab@rmki.kfki.hu>
Dear Laszlo,
On Sat, 28 Mar 2009 02:49:13 +0100 (CET), you wrote:
> Let's do our job, science ...
I am under the impression that you are treating GR as a hobby, since
you clearly do not want to be involved in serious science such as the
LSC project.
We *both* know that you can demolish their LIGO project and save
hundreds of million dollars and euro, all taxpayers' money.
The scandal after the failure of the "enhanced" LIGO will be incredible,
Regarding the wristwatch of LIGO's operator (ExplanatoryNote.pdf, p.
8): at an instant t_1 , the + polarization, which "has its own
gravitational-wave field" (Kip Thorne), must be totally shielded from
the neighboring gravitational-wave field of the x polarization, in such
a way that the latter can patiently wait for its turn to wobble the
metric field at t_2 , as recorded by the wristwatch of LIGO's operator.
For if the two "polarizations" interfere in 3-D space, it is completely
unclear what can happen to LIGO's arms, as being simultaneously
stretched and squeezed by the + polarization, and squeezed and
stretched in 45o by the x polarization.
Can you understand such schizophrenic behavior of gravity? If you can,
please do not reply to this email.
Sincerely,
Dimi Chakalov
================
Subject: From Pauli to "GW astronomy"
Date: Wed, 15 Apr 2009 13:11:17 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Mike Turner <mturner@uchicago.edu>
Cc: Josh Frieman <frieman@fnal.gov>,
Dragan Huterer <huterer@umich.edu>,
Norbert Straumann <norbert.straumann@gmail.com>
Eight years ago, on 2 April 2001, you stated that the dark energy "may
be something entirely new and unexpected". Then you added:
"While we don't know what dark energy is, we are certain that
understanding it will provide crucial clues in the quest to unify the
forces and particles in the universe, and that the route to this
understanding involves telescopes, not accelerators."
It refers to Sec. 10.1.4 'Vacuum energy as dark energy' and Sec. 5.1
from your
arXiv:0803.0982v1 [astro-ph], and to the calculation by W. Pauli in
early 1930s (the size of the universe could not even reach to the moon,
W. Pauli, cf. N. Straumann's arXiv:gr-qc/0208027v1).
3. You and your colleagues will continue to keep quiet, as if you've never ever heard of
my work.
Would you please try to prove me wrong?
Regards,
Dimi
The schizophrenic
behavior of gravity(SBG), which is needed for LIGO to achieve its goal,
refers to some shielding (and also metronome-like) mechanism
denoted with / , which separates the two "polarizations"
, denoted with + and x , in such fashion that
the sequence
+ / x / + / x / + / x / + /
x / + / x / + / x / , ...
will have a frequency of N cycles of [+ / x /]per
second, as recorded by the wristwatch of LIGO's operator, reading
h(t) (see below).
This wristwatch is supposed to read
simultaneously the dynamics of the two "waveforms" ("each
polarization has its own gravitational-wave field", says Kip
Thorne), encoded with the mysterious h(t) above, which pertains to the two (presumably) independent
"polarizations": see the slide below, from Kip Thorne's lecture in
January 2001.
And by the way, what is the
dimensionality of the GW amplitude
projected on the x/y plane below ?
Without
some exact metronome-like shielding mechanism (totally absent in
the slide above) separating the two gravitational-wave fields, the two
"polarizations" will inevitably interfere along their common h(t) read
by the wristwatch of LIGO's operator, and it is totally unclear
what might happen to LIGO's arms, as they may, for example, be
simultaneously stretched and squeezed by the +
polarization, and squeezed and stretched
by the x polarization.1
As of today, all members of LIGO
Scientific Collaboration (LSC) -- a
self-governing collaboration2 seeking to detect gravitational
waves, currently made up over 600 members from over 50 institutions
and 11 countries -- deeply believe that such shielding
mechanism exists in Nature.
I disagree, and refer to LSC as 'Jehovah's Witnesses of
GW astronomy'. But instead of repeating the rigorous
proofs by
Angelo Loinger that in the full non-linear GR the
project undertaken by LSC is an absurd (see also Jose
G. Pereira et al.), I opted for the linearized approximation
itself, to show the dead end of their project by
reductio ad absurdum.
Surely GWs exist, but if the GW detector doesn't have access to the
reference
fluid of GR, it cannot in principle "sense" the displacement of
spacetime itself, relative to the reference fluid. The latter cannot be
unveiled in the current GR, and because we
still don't have proper quantum gravity, all we
can say today is that
"if we displace a mass, its gravitational field and the related
curvature of the interested manifold displace themselves along with
the mass." (A. Loinger, physics/0506024 v2,
pp. 2-3)
Moreover, GW
detectors should be designed on the basis of the non-linear
mechanism by which GWs carry energy (Hermann Bondi),
provided one can describe
smooth bi-directional transitions between very strong GWs and
very weak GWs (here Josh Goldberg is keeping
quiet), while LSC members use
linearized approximation
with some fictional "background" (B. Schutz), which produces
ridiculous artifacts (e.g., the h(t)
above). Of course, these artifacts were
not detected during all five LIGO "runs", and will not be detected with
the forthcoming S6 "run" in 2009 either.
Recall that Russell Hulse and Joseph
Taylor
were very lucky to discover the binary system
PSR1913+16, in which one of the stars was a pulsar with period of
orbit just eight hours -- extremely small by astrophysical standards --
hence they used it as a clock, and speculated further that the change in
the period corresponded to the rate by which the binary system
were (supposedly) losing energy. Then Hulse and Taylor decided to explain the inferred
loss of energy with "GW emission".
Namely, they applied the old Tanzanian
saying: "How do we know that Father Christmas has a beard? We know it,
because snow falls when he shakes his beard." But again, the rate of the
"snowfall" was the only evidence in support of their wild guess,
and it can be explained without invoking "GW emission" (e.g.,
Davor
Palle and Fred Cooperstock).
However, in the
case of LIGO and the like, LSC members will have to find a brand new system that
can provide precise shielding and metronome-like
mechanism, as explained above.
What is the price tag of the "advanced" LIGO? Should we allow LSC to produce
more space junk with the three LISA satellites and
waste billions of taxpayers'
money?
All LSC members have
professional knowledge and expertise in gravitational physics, and all
of them should be perfectly aware that LIGO is for the birds.
Yet they keep quiet and ask for more money earned with hard labor by millions of people.
D. Chakalov
March 28, 2009
Last update: October 25, 2009
----
1 Notice that the wristwatch of LIGO's operator
is supposed to read the "response" h(t), which is "only a
certain linear combination" of the two "polarizations", but without
some metronome-like shielding mechanism the two "polarizations"
will conflate and intermingle: see Eq. 1.3 below.
"A laser interferometric or
resonant bar gravitational wave detector measures the local
components of a symmetric 3 x 3 tensor which is composed of the
"electric" components of the Riemann curvature tensor, [XXX], via the
equation of geodesic deviation, given for a pair of freely falling
particles by [XXX], where [XXX] denotes the spatial separation.
"In general there are six independent components, which can be
expressed in terms of polarizations (modes with specific transformation
properties under rotations and boosts). Three are transverse to the
direction of propagation, with two representing quadrupolar
deformations and one representing a monopole
"breathing" deformation. Three modes are longitudinal, with one an
axially symmetric stretching mode in the propagation direction, and one
quadrupolar mode in each of the two orthogonal planes containing the
propagation direction.
...
"Figure 9
shows the displacements induced on a ring of freely falling test
particles by each of these modes. General relativity predicts only the
first two transverse quadrupolar modes (a) and (b) independently of the
source; these correspond to the waveforms h+
and hx discussed earlier (note the
cos[phi] and sin[phi] dependences of the displacements)."
The missing element in this
picture is some metronome-like shielding mechanism, which would
prevent the two "polarizations" to conflate and intermingle, along with
the longitudinal modes (J. G. Pereira et al.).
In addition to these inherent problems of the "transverse" direction of
GW strain, the alleged "longitudinal" direction
of GW propagation cannot be demonstrated in 3-D
space either: check out a simple Gedankenexperiment with the phase
of GWs and the dimensionality of their "amplitude" here. These two
simple examples comply with the linearization approximation of GR
and demonstrate the absurdity of LSC project.
Besides, as two prominent pupils of
Kip Thone, E. Flanagan and S. Hughes, acknowledged in their gr-qc/0501041v3,
p. 12 (emphasis added), the important variables that "have the
advantage of being gauge invariant" have "the disadvantage of being
non-local". Computation of "these variables at a point requires
knowledge of the metric perturbation habeverywhere." In the case of LIGO (cf. Eq 3.13),
"many observations that seek to detect GWs are sensitive only
to the value of the Riemann tensor at a given point in space."
(...) "For example, the Riemann tensor components [XXX], which are
directly observable by detectors such as LIGO, are given in terms of
the gauge invariant variables as [Eq 2.70]. Thus, at least certain
combinations of the gauge invariant variables are locally
observable."
Any observable of the gravitational field
is quasi-local (L. Szabados), so the phrase
"the value of the Riemann tensor at a given point in space" is
sheer poetry; check out the “point particle limit” in Bob Wald's
arXiv:0907.0412, p. 3 and ref [4]
therein.
The poetry in the phrase "at
least certain combinations" is also unacceptable. We are not dealing with
some mixture of distinguishable "non-local" vs. "local" gauge
invariant variables. It is not like dealing with some statistical
mixture of 'unobservable-by-LIGO non-local black balls', as
opposed to 'observable-by-LIGO local white balls', so that LSC
members could hope that LIGO can be tuned to detect "at least certain
combinations" of the white balls, without bothering about the black
ones. The increasing
of sensitivity toward the "white balls" is just ridiculous. And
costs billions.
2 Since LSC does not have
elected President and governing body, similar to the GRG Society
(LSC Member Groups appoint the Collaboration Council, which in turn
elects the LSC Spokesperson, who "leads the LSC, and is empowered to
represent the LSC to the outside world",
LSC Bylaws, Secs 4 and 7.1), all LSC Members are responsible for
authorizing the LSC Spokesperson and Collaboration Council to waste taxpayers' money on their behalves.
Addendum
Fred Cooperstock
and Maurice
Dupré have presented today (April 6, 2009) the notion
of “spacetime energy-momentum” [Ref.
1]. I will ask them, by private email,
to comment on the schizophrenic behavior of gravity, which is needed
for LIGO to achieve its goal (see above).
Notice the localization
hypothesis introduced by Fred Cooperstock below, [Ref. 2],
[Ref. 3], [Ref.
4], [Ref. 5]. I can understand why all members
of LIGO Scientific Colaboration (LSC) ignore my arguments, but to
ignore Fred Cooperstock and his colleagues for full ten years is just ... unbelievable.
If we compare the situation with
the localization of
wegtransformierbar gravitational energy to the localization of
quantum particles, we can claim that all we need for the second case is
a macro-device -- the
double split experiment, for example, is so highly reproducible
that there is at least no argument about the reality of quantum
waves. Thus, in the case of QM we have experiments from which we deduce
the theory, while in the case of the "ripples" of metric called
'gravitational waves' the situation is turned upside-down: LSC members
start with two custom-made approximations, the linearized
approximation and the quadrupole approximation, to
reach the "confirmation" of these
approximations. Their first
crucial assumption is that if GWs are weak, they can be detected as some "ripples"
propagating on some undisturbed background (see the GW lake below).
This crucial assumption made by
LSC members has nothing to do with General Relativity (GR). Unlike
quantum waves, the very reality of GWs is unclear from the start, since
the crux of the matter is whether
GWs can transport energy, and how. In GR, "such transport is a
fundamentally nonlinear phenomenon" (Hermann Bondi).
Which brings up the puzzles of localization of wegtransformierbar
gravitational energy, the reversible conversion of non-tangible
forms of energy into tangible/localized energy (Hermann
Bondi), and the unsolved issue of conservation
of energy in GR.
LSC members are fully aware that
the crucial issue of 'energy conservation in GR' (recall the binary star PSR 1913+16)
is not resolved, nor do they have any working hypothesis for
the non-linear transport of energy by GWs. Instead, they make
a second, also crucial
assumption that there is no difference between (i) inferring
the loss of energy due to emission of GWs, as recorded post factum
(PSR
1913+16), and (ii) detecting GWs online, along the time
read by the wristwatch of LIGO's operator. Then they just ask for more money. Which is
why I accused LSC members of aggressive professional
negligence.
How many hundreds of millions
U.S. Dollars and Euro have been wasted so far? What is the price for
the "advanced" LIGO? How much will cost LISA?
D. Chakalov
April 6, 2009
Last update: April 11, 2009
[Ref. 1] F.I. Cooperstock, M.J. Dupre, Covaraint energy-momentum and an
uncertainty principle for general relativity, arXiv:0904.0469v1 [gr-qc]
"The consequences are immediate: since the Ricci tensor is non-zero
only in the regions where the energy-momentum tensor is non-zero,
gravitational waves, waves of propagating spacetime curvature, are not
carriers of energy-momentum through the vacuum, in conformity with the
localization hypothesis [6]."
[Ref. 2] F.I. Cooperstock, The Role of Energy and a New Approach to
Gravitational Waves in General Relativity, arXiv:gr-qc/9904046v1; Annals
Phys. 282 (2000) 115-137
"The elusive gravitational waves, first proposed by Einstein to be
emitted by accelerated masses in analogy with electromagnetic waves
from accelerated charges in electromagnetism, had escaped all but a
conjectured indirect indication of their presence from the period
variation
of the binary pulsar. If there were to be a direct detection, the
fundamental nature of these waves vis-a-vis energy content would have
to be understood.
...
"However, it is to be emphasized that all particles and fields apart
from gravity exist within spacetime whereas, in essence,
gravity is spacetime. From the general relativity perspective,
gravity assumes a very special role. These and other facts [1] led the
author to hypothesize that in generality, energy and momentum are
localized in regions of the energy-momentum tensor Tk_i . This would
imply that gravitational waves are not carriers of energy and
momentum in vacuum [1]. If correct, this would have far-reaching
consequences.
...
"Thus, while the energy and momentum of electromagnetic waves is
indisputable both theoretically and from solid experimental evidence,
the situation for gravity waves is clearly not on the same footing.
...
"These considerations led the author to the localization hypothesis
[1]. An immediate consequence is that gravitational waves would not
be carriers of energy in vacuum. This is in contradiction to many
previous calculations which have attributed an energy loss to systems
which emit gravitational waves and the
generally prevailing belief.
...
"We began by outlining the unusual role that energy has played in
general relativity and the various ideas which have been expressed
through the years regarding the issue of its localizability. The
reasons which led the present author to hypothesize that energy is most
logically localized in regions of non-vanishing energy-momentum tensor
T_ik were presented. It was noted that if correct, the hypothesis would
lead to a hitherto unprecedented aspect of a wave in the case of
gravitation: waves carrying real curvature through vacuum would
nevertheless be devoid of energy.
"While such a conclusion might at first glance appear untenable, it was
noted that gravity plays a different role in physics from the
perspective of general relativity: all particles and fields exist within
spacetime whereas gravity, in essence, is spacetime [1].
[Ref. 3] F. I. Cooperstock, S. Tieu, The Energy of a Dynamical
Wave-Emitting System in General Relativity, arXiv:gr-qc/0302020v1; Found.
Phys. 33 (2003) 1033-1059
"Various aspects of gravity waves led the first author [2] to the
hypothesis that energy in general relativity is localized in the
regions of the non-vanishing energy-momentum tensor Tk_i (henceforth
the “localization hypothesis”).
...
"If the localization hypothesis should prove to be correct, it would
have fundamental consequences. First, it would imply that gravity waves
in vacuum (assuming that they exist and there are ample reasons to
believe that they do) would not be carriers of energy, in
conformity with the Kerr-Schild aspect. This notion challenges the very
meaning that we give to the word “wave”, as a disturbance that carries
energy.
...
"2. What is the energy of the system during the particularly
interesting gravity-wave emitting phase?
"The standard derivations of the Tolman integral expression for energy
break down when the metric is time-dependent. Therefore the energy at
that point is unknown."
[Ref. 4] F.I. Cooperstock, Does a dynamical system lose energy by
emitting gravitational waves? Mod. Phys. Lett. A14 (1999)
1531-1537 (Received 29 April 1999);
http://dx.doi.org/10.1142/S0217732399001620
Abstract
We note that Eddington's radiation damping calculation of a spinning
rod fails to account for the complete mass integral as given by Tolman.
The missing stress contributions precisely cancel the standard rate
given by the "quadrupole formula". This indicates that while the usual
"kinetic" term can properly account for dynamical changes in the
source, the actual mass is conserved. Hence gravity waves are not
carriers of energy in vacuum. This supports the hypothesis that energy
including the gravitational contribution is confined to regions of
nonvanishing energy-momentum tensor T_ik.
[Ref. 5] Maurice J. Dupré, The Fully Covariant Energy Momentum
Stress Tensor For Gravity and the Einstein Equation in General
Relativity, arXiv:0903.5225v1
[gr-qc]
p. 22: "(I)n the vacuum there is no energy of the gravitational field,
and consequently from this point of view, a gravitational wave carries
no gravitational field energy through the vacuum.
...
p. 23: "In particular, both Carl Brans and Frank Tipler (in personal
communication) have expressed concerns about how the view expressed
here on the gravitational energy momentum stress tensor relates to the
analysis of the energy dissipation from binary pulsars, an issue also
addressed in [7] in relation to the Cooperstock hypothesis.
Particularly relevant here are the calculations in [8] and [9] of the
gravitational radiation due to a rotating rod, showing the general
relativistic calculation to be consistent with the Cooperstock
Hypothesis.
"The idea that gravitational radiation carries energy away may be a
useful idea for keeping track of the various ”energies”, or conserved
quantities, in the system, but the calculations always involve a choice
of reference background metric which produces the
apparent ”energy”.
---
[7] Cooperstock, F. I., Energy localization in general relativity,
Foundations of Phys., vol. 22, No. 8, (1992) 1011-1024.
[8] Cooperstock, F. I., The role of energy and a new approach to
gravitational waves in general relativity, Annals of Physics,
282(2000), 115-137.
[9] Cooperstock, F. I. and Tieu, S., The energy of a dynamical
wave-emitting system in general relativity, Foundations of Physics,
33(7), 1033-1059.
---
"Alternately, it seems that there is no mathematical vacuum in
realistic models of the universe, because of background radiation and
possibly dark energy, so there is background
matter to carry the gravitational energy."
---
Comments: First, the object that
carries the gravitational energy doesn't have to be
necessarily "background matter"; it can be 'potential
reality', as explained below. And secondly
-- we don't know for sure whether "in the vacuum there is no energy of
the gravitational field" (p. 22 above). These
comments pertain to the third option for GW
detection, as well as to the interpretation of "dynamic dark energy" below.
Namely, the "background matter"
is the explicated form of matter such as 'blue stuff', but the object that
actually carries the gravitational energy is the true
cosmological constant that varies in neither
space nor time. The former is an instantaneous explicated
snapshot from the "film reel" (called local
mode of spacetime), in which the "dynamic dark energy" is precisely zero. Nonexistent.
The latter is 'potential reality' kept in the so-called global mode of spacetime. It is totally "dark" or invisible in the local mode. It can
explicate any amount of physical stuff in the local
mode, but because the route toward the global mode cannot be
traced back from the local one, the explicated physical stuff
will inevitably look like "CDM" or
alternatively like "dark energy from empty
space".
Thus, if we take the quantum
vacuum "energy" to be 'undecidable',
it will range in the open interval (0, [infinity]). If we install a
provisional (yet reasonable) cutoff from the Planck scale, the maximum
untraceable or "dark" mass density of the vacuum, stored in the global
mode, will be about 1096 kilograms per cubic meter, so
replace [infinity] in the open interval above with this value.
Subsequently, the minimum untraceable or "dark" mass density
of the vacuum will not be zero but 'less than one
part in 10120', so replace [zero] in the open interval
above with this value.
Now you're safe: the so-called
"cancellation mechanism" is due to the nature of 'potential
reality', as it can explicate any amount of untraceable or
"dark" mass density in the local mode of spacetime from the
open interval above, depending on the cosmological stage ("the energy
density is determined by what is called the effective potential, and
this is dynamically determined", N.
Straumann, arXiv:gr-qc/0208027v1).
Which resolves the coincidence problem (S. Weinberg) as well.
No "multiverse", no multidimensional
superstitions like "extra dimensions of the embedding
space", and no "anthropic"
parapsychology are needed.
Of course, many people will consistently ignore such proposals, but this is a
different subject.
Subject:
arXiv:0909.4408v1 [gr-qc], p. 10
Date: Fri, 25 Sep 2009 04:36:38 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: José Geraldo Pereira <jpereira@ift.unesp.br>, jpereira2@mac.com
Cc: yo@ift.unesp.br, grubilar@udec.cl, cordac.galilei@gmail.com
Dear José,
You and your co-authors wrote (p. 10): "One can wonder whether the
inability to transport energy and momentum is a property of this
specific exact solution, or is a general property of any linear
gravitational waves."
I've been hoping to learn the opinion of Christian
Corda on this crucial issue since February (cf. my email printed
below, and Hans-Jürgen Schmidt,
gr-qc/0407095, Sec. 4.2, 'Why do all the curvature invariants of a
gravitational wave vanish'). Also, he has offered some "waves
overlapping principle", but hasn't commented on your
arXiv:0809.2911v1 [gr-qc], nor to my suggestion to convert LIGO and
VIRGO tunnels to wine cellars.
Would you and your colleagues be interested to learn how
Christian Corda will defend "GW astronomy"?
On Thu, Sep 24, 2009 at 4:58 PM, Dimi Chakalov <dchakalov@gmail.com>
wrote:
>
> P.S. On Wed, 18 Feb 2009 12:42:29 +0200, I
replied to your suggestion
> to read your arXiv:0806.3397 (about "the proper duration" of the
> round-trip of a photon (Eq. 48, p. 11) along the x arm of the
> interferometer), and explained why your paper is *not relevant* to my
> objections at
>
> http://www.god-does-not-play-dice.net/Szabados.html#SBG
>
> Does the "waves overlapping principle" resolve your problem at the
> link above? And how?
>
> D.
==========================
Subject: Re: In Defense of Leslie
Date: Wed, 8 Apr 2009 03:50:10 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Cliff <cmw@wuphys.wustl.edu>
Cc: K G Arun <arun@physics.wustl.edu>,
Richard H Price <rprice@phys.utb.edu>,
David Garfinkle <garfinkl@oakland.edu>,
Warren Johnson <johnson@ligo.phys.lsu.edu>,
Bernard.Schutz@aei.mpg.de,
kip@tapir.caltech.edu,
office-hannover@aei.mpg.de,
m.a.h.maccallum@qmul.ac.uk
"At the end of Bernie’s talk, a member of the audience asked whether
Cliff had ever been known to be wrong on a serious issue. Bernie
answered that to his knowledge, this had never happened. At this moment
Leslie, Cliff’s wife, raised an eager hand and offered to present many
examples of Cliff being in error."
B. Schutz, "Will and Testament", MATTERS OF GRAVITY, Number 29,
Winter 2007
----
Here's another serious error, on a *very* serious issue.
In your latest arXiv:0904.1190v1 [gr-qc],
you wrote: "We consider the bounds that could be achieved using
advanced LIGO, ..."
You won't get the "advanced LIGO" though, for some very simple reasons
explained at
Would you please consider responding professionally? Because keeping
quiet won't help you nor your LSC colleagues.
A HUGE scandal is just around the corner.
Do not ever say you knew nothing about it.
D. Chakalov
==========================
Subject: Re: In Defense of Leslie
Date: Thu, 9 Apr 2009 02:35:03 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Clifford Will
<cmw@wuphys.wustl.edu>
Cc: K G Arun <arun@physics.wustl.edu>,
Richard H Price <rprice@phys.utb.edu>,
David Garfinkle <garfinkl@oakland.edu>,
Warren Johnson <johnson@ligo.phys.lsu.edu>,
Bernard.Schutz@aei.mpg.de,
kip@tapir.caltech.edu,
office-hannover@aei.mpg.de,
m.a.h.maccallum@qmul.ac.uk
On Wed, 8 Apr 2009 10:51:41 -0500, Message-Id:
<4192DFEC-A883-43EC-A233-A0F5F83C1913@wuphys.wustl.edu>, Clifford
Will <cmw@wuphys.wustl.edu> wrote:
>
> Dear Mr. Chakalov:
>
> I once asked you politely to remove my name from your email lists.
This isn't "spam". I am not advertising cat food, Clifford.
> You responded in a very insulting way and refused to do so.
Also, I am talking about hundreds of millions U.S. Dollars and Euro
wasted by LSC, and even more scheduled to be wasted with the "enhanced"
and "advanced" LIGO and LISA.
All these taxpayers' money could have been used for real scientific
research (e.g., stem cell research), for the benefit of people in your
country and all over the world.
You have no idea of whom you have been dealing with.
D. Chakalov
==========================
Subject: arXiv:0908.0286v1 [gr-qc],
Table 1
Date: Tue, 4 Aug 2009 13:35:04 +0100
From: Dimi Chakalov <dchakalov@gmail.com>
To: Saeed Mirshekari <smirshekari@wustl.edu>,
smirshekari@ut.ac.ir,
Amir M Abbassi <amabasi@khayam.ut.ac.ir>
Cc: Kirk McKenzie <kirk.mckenzie@jpl.nasa.gov>,
LSC Spokesperson <reitze@phys.ufl.edu>,
Beverly Berger <bberger@nsf.gov>,
Tom Carruthers <tcarruth@nsf.gov>,
Denise S Henry <dshenry@nsf.gov>,
Ramona Winkelbauer <rwinkelb@nsf.gov>,
Peggy Fischer <pfischer@nsf.gov>
Dear colleagues,
Regarding your Table 1, 'Energy densities related to gravitational
wave’s general line element': please check out my objections to LIGO
project at
Can you solve the problems at the link above, hence save LIGO tunnels
from being converted to wine cellars ?
Kindest regards,
Dimi Chakalov
35 Sutherland St
London SW1V 4JU
U.K.
==========================
Subject: Re: SBG
Date: Mon, 27 Jul 2009 16:12:12 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Stephen Crothers <thenarmis@gmail.com>
Dear Steve,
Thank you for your very nice article.
> Attached is a non-mathematical article. I hope it meets
requirements.
I was hoping that you will take their own "linearized approximation"
and expose their tacit assumptions, as I tried with SBG.
You quoted Weyl's 1944 article, which is very dense,
while LIGO mafia (e.g., Clifford
Will) says about PSR 1913+16: "If we assume that the orbital period
of the system is decreasing due to the emission of gravitational waves,
then theory and experiment agree to within 0.2%."
So, they will insist on the linearized "theory". Angelo Loinger's
papers, as well as yours, are targeting the full non-linear GR. The
mafia doesn't care.
IMHO the only way to crash it is to expose their errors from their own
"theory".
Best regards,
Dimi
=============
Subject: Re: supermassive black
hole at Sagittarius A*
Date: Tue, 4 Aug 2009 12:50:00 +0100
From: Dimi Chakalov <dchakalov@gmail.com>
To: Stephen Crothers <thenarmis@gmail.com>
Cc: Stefan Gillessen <ste@mpe.mpg.de>,
Reinhard Genzel <genzel@mpe.mpg.de>,
Frank Eisenhauer <eisenhau@mpe.mpg.de>,
Jonathan Thornburg <jthorn@astro.indiana.edu>,
Michael Cohen <mcohen@caltech.edu>
Perhaps the reason why your colleagues won't reply is purely
psychological. Surely you are right about "black holes" and their
"apparent horizons" (cf. Jonathan Thornburg and Michael Cohen et al.
below), yet you don't offer any ideas to account for GRBs, say
I trust your colleagues are aware that this whole "black hole" business
is crap, but do they have a better deal? Maybe their situation is
'faute de mieux on couche avec sa belle-mère' :-)
Best regards,
Dimi
-------------
Jonathan Thornburg, Event and Apparent Horizon Finders for 3+1
Numerical Relativity, arXiv:gr-qc/0512169v2,
http://arxiv.org/abs/gr-qc/0512169
"The event horizon is defined
nonlocally in time: it’s a global property of the entire spacetime, ...
"
"There are two useful concepts
to describe the location of black holes in a spacetime, apparent
horizons (AH) and event horizons (EH). An EH is the true surface of a
black hole: it is defined as the boundary of the region of the
spacetime that is causally connected to future null infinity.
"Because the definition of the EH involves global properties of the
spacetime, one must know the full future evolution of the spacetime
before the EH can be determined exactly. This difficulty has led
researchers to instead identify black holes with apparent horizons,
(...)."
===============
Subject: Re: supermassive black
hole at Sagittarius A*
Date: Fri, 7 Aug 2009 13:12:36 +0100
From: Dimi Chakalov <dchakalov@gmail.com>
To: Stephen Crothers <thenarmis@gmail.com>
Cc: Stefan Gillessen <ste@mpe.mpg.de>,
Reinhard Genzel <genzel@mpe.mpg.de>,
Frank Eisenhauer <eisenhau@mpe.mpg.de>,
Jonathan Thornburg <jthorn@astro.indiana.edu>,
Michael Cohen <mcohen@caltech.edu>
Dear Steve,
> I have no ideas about GRB's. My research is restricted to what is
and
> what is not consistent with General Relativity, and the
foundations of
> GR itself.
GR has been a 'work in progress' since 1915; as Einstein stressed in
1949, "a field-theory may not contain any singularities, i.e., any
positions or parts in space in which the field-laws are not valid", and
then he acknowledged:
"Not for a moment, of course, did I doubt that this formulation (the
field equations of GR) was merely a makeshift in order to give the
general principle of relativity a preliminary closed expression. For it
was essentially not anything more than a theory of the gravitational
field, which was somewhat artificially isolated from a total field of
as yet unknown structure."
I think that avoiding singularities and revealing the reference fluid
in GR is a bundle.
> Certainly black holes, big bangs, Einstein gravitational waves, and
> associated phantasmagoria are phantasmagoria, not science. My view
> is that GR fails because a spacetime that by construction contains
no
> matter (Ric = 0) can't contain matter, from which it immediately
follows
> that the total energy of Einstein's gravitational field is always
zero. The
> black hole is in addition a violation of geometry, assuming the
validity of
> Ric = 0 for the sake of argument. So the black hole is not just a
dog but
> a dog with fleas.
Okay, but 'besser ein Laus im Kraut als gar kein Fleisch' :-)
> Thanks for the links. I'll take a look.
Thank you for your time. Please send me your ideas about GRB's energy
source.
BTW I mentioned your Ric = 0 paper at the GR section of
Didn't elaborate much, but will be happy to do so, in case you're
interested.
Regards,
Dimi
==========================
Subject: A future directed, time-like unit vector field
Date: Tue, 31 Mar 2009 05:46:18 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Helmut Friedrich <hef@aei.mpg.de>
Cc: Hermann.Nicolai@aei.mpg.de, Curt.Cutler@aei.mpg.de
Dear Dr. Friedrich,
You acknowledged that a future directed, time-like unit vector field,
for which no natural choice exists in general, is characterized
indirectly and becomes explicitly available only after solving
the equations (arXiv:0903.5160v1
[gr-qc], p. 17).
I've been trying to argue that this problem can only be solved by
recovering the reference fluid in GR. In the context of "GW
astronomy", an outline of my proposal can be read at
I wonder if you and/or your colleagues may be interested.
Kindest regards,
Dimi Chakalov
----
Note: Notice above the tacit assumption
made by LSC members, that there is no difference between (i) inferring
the loss of energy due to emission of GWs, as recorded post factum
(PSR
1913+16), and (ii) detecting GWs online,
along the time read by the wristwatch of LIGO's operator. The presupposition (i) is wrong (check out F. Cooperstock), because GWs cannot propagate
along that linearized time variable, which becomes explicitly available
only after solving the equations (H.
Friedrich). If they could, their energy will be perfectly localized
along a continual trajectory of perfectly localized instants/events
from that linearized (and highly deceptive) time variable. In
no physical theory can we disentangle energy from time: if 'time in GR'
is somehow made to look like the variable read by your wristwatch,
so should be 'energy', in blatant contradiction to GR (cf.
L. Szabados).
In order to detect GWs online,
LIGO will have to read the "proper time [tau] along spacetime
trajectories", but the latter "cannot be used as an independent
variable either, as [tau] is a complicated non-local function of the
gravitational field itself" (Carlo Rovelli).
The genuine dynamics of GWs is not known: without the reference fluid of GR, GWs
will have to propagate 'within themselves and with respect to
themselves' (email from 16 May 2004).
All we can say is that GWs need not "calculate" some 'future directed,
time-like unit vector field' in order to carry their quasi-local energy across the entire universe.
Subject: Re: Let's get the job
done.
Date: Mon, 30 Mar 2009 16:30:49 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: zyfang@cqu.edu.cn, hglee@163.com, cqstarv@yahoo.com.cn,
cqufangyuli@hotmail.com, lixiaozhou818@ayahoo.com.cn,
junluo@mail.hust.edu.cn, mawg@ustc.edu.cn, phwen@ust.hk,
wzhao7@mail.ustc.edu.cn, drrobertbaker@gravwave.com
P.S. Once I receive your professional response (cf. my email from Mon,
30 Mar 2009 01:21:29 +0300 below), I will comment on the first-order
perturbative photon flux (PPF), in Slide 9, "The Synchro-Resonance
Solution", from "Li-Baker Detector Development Powerpoint Presentation",
If you ignore my proposal to
exchange opinions on our work, it may cost you approximately 41 Million
Yuan (cf. Slide 2 above).
Best regards,
Dimi Chakalov
On Mon, Mar 30, 2009 at 4:05 PM, Dimi Chakalov
<dchakalov@gmail.com> wrote:
>
> Dear Colleagues,
>
> Again, try to find Beckwith at UH People Search
>
>
http://www.uh.edu/search/directory/
>
> No match found.
>
> Andrew Beckwith has papers listed there, but he is *not* on UH web
> site. That is a fact.
>
> I don't care who is behind Andrew Beckwith, nor what face he is
trying
> to show to you. I am only interested in HFGW detectors.
>
> Let's get the job done. Please see my email from Mon, 30 Mar 2009
> 01:21:29 +0300 (printed below).
>
> Kindest regards,
>
> Dimi Chakalov
>
>
> ========
>
> Subject: Re: Stop spamming to Chinese researchers I know, DIMI.
> Message-ID:
<bed37360903291521v641e2612y2695b25945d995ba@mail.gmail.com>
> Date: Mon, 30 Mar 2009 01:21:29 +0300
> From: Dimi Chakalov <dchakalov@gmail.com>
> To: zyfang@cqu.edu.cn, hglee@163.com, cqstarv@yahoo.com.cn,
> lixiaozhou818@ayahoo.com.cn, junluo@mail.hust.edu.cn,
> mawg@ustc.edu.cn, phwen@ust.hk, wzhao7@mail.ustc.edu.cn,
> drrobertbaker@gravwave.com
> Cc: abeckwith@uh.edu, Andrew.Beckwith@mail.uh.edu
>
> Dear Colleagues,
>
> Andy Beckwith doesn't know how to behave professionally, so may I
> offer you the following:
>
> Please check out the arguments at
>
> http://www.god-does-not-play-dice.net/Szabados.html#SBG
>
>
http://www.god-does-not-play-dice.net/Szabados.html#wine_cellars
>
> and send me your professional opinions.
>
> Once I receive your professional response, I promise to do the same
> for your HFGW detectors.
>
> Yours sincerely,
>
> Dimi Chakalov
>
===============
Subject: Re: HFGW Communications Study
Date: Tue, 31 Mar 2009 14:29:34 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Giorgio Fontana <giorgio.fontana@unitn.it>
Cc: Robert M L Baker Jr <drrobertbaker@gravwave.com>,
Christian <christian.corda@ego-gw.it>,
Gloria Garcia-Cuadrado <gloria.garcia@ctae.org>
Giorgio,
Nice to hear from you.
> Because the gravitational force is an experimental fact like the
electric
> force, let' say that gravitational waves do exist like
electromagnetic
> waves.
Only they don't. It is a *very* crude analogy.
> Gravity is like electromagnetism in higher dimensions, that it is
in this
> model.
OK. With these two hypotheses (the latter is from 1914), your model will
work like the way I can explain to my wife the first law of Ohm with a
hosepipe and water running in it. It too is amazingly effective. But if
I wish to extend the crude analogy and explain QED to my wife, it will
fail.
So, at what point will your model produce artifacts?
> Dimi, if you want to reply, keep you focus on this subject.
Please keep focus on the question above, and keep in mind that the
dynamics of GWs may require (i) the reference
fluid of GR (it cannot be found in GR because of the general
covariance principle, as Einstein realized from 1913 to 1915), and (ii)
some viable hypothesis to account for the need for D>4 ,
If you agree to comment on my work, I will happily do the same for
yours (cf. my initial email printed below). These are just preliminary,
and very general, comments.
Best regards,
Dimi
> ----- Original Message -----
> From: "Dimi Chakalov" <dchakalov@gmail.com>
> To: "Robert Baker" <drrobertbaker@gravwave.com>
> Cc: "Christian" <christian.corda@ego-gw.it>; "Giorgio
Fontana"
> <fontana@science.unitn.it>; "Gloria Garcia-Cuadrado"
> <gloria.garcia@ctae.org>; "Gary V Stephenson"
<seculine@gmail.com>;
> <HFGWmedia@gmail.com>
> Sent: Monday, March 30, 2009 7:31 PM
> Subject: Re: HFGW Communications Study
>
>
>>> HFGW Communications study that you might find of interest.
>>
>> Thank you very much, Dr. Baker. Just two preliminary comments.
>>
>> 1. While the "fabric" of GR is indeed four-dimensional (com
study
>> composite.pdf, p. 5), it is not at all clear what is the
fabric of
>> spacetime of Nature. We need quantum gravity to answer this
crucial
>> question.
>>
>> 2. I refute the possibility for detecting GWs with *any*
frequencies
>> -- higher or lower than 100 kHz; it doesn't matter.
>>
>> Please tell me if you agree to exchange opinions on our work,
as
>> offered to you and to your Chinese colleagues at
>>
>>
http://www.god-does-not-play-dice.net/Szabados.html#Beckwith
>>
>> Let's get the job done.
>>
>> http://www.god-does-not-play-dice.net/Szabados.html#SBG
>>
>> Sincerely,
>>
>> Dimi Chakalov
>
===============
Subject: Re: The double role of
the metric... at the same time.
Date: Wed, 8 Apr 2009 16:48:13 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Szabados Laszlo <lbszab@rmki.kfki.hu>
Cc: Fred Cooperstock <cooperst@uvic.ca>,
Dupre, Maurice J <mdupre@tulane.edu>,
Adam D Helfer <adam@math.missouri.edu>,
Jörg Frauendiener <joergf@maths.otago.ac.nz>
Dear Laszlo,
On Wed, 23 Feb 2005 17:37:02 +0100 (CET), you wrote:
> What I say in may review is *not* that GR is a non-local theory,
> I say only that the gravitational energy-momentum and angular
> momentum, i.e. the gravitational analogs of the classical conserved
> quantities and observables are non-local. Non-local in the sense
> that they should be associated to *extended* domains rather than
> to points.
These *extended* domains may require a new formulation of 'isolated
system': check out the third approach at
Subject: Re: The double role of
the metric.... at the same time.
Date: Mon, 23 Feb 2009 16:34:57 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: "Szabados,L." <lbszab@rmki.kfki.hu>
Cc: Jörg Frauendiener <joerg.frauendiener@uni-tuebingen.de>
Dear Laszlo,
>> Regarding your arXiv:0902.3199v1 [gr-qc]:
perhaps 'ultimate' boundary
>> conditions for canonical variables cannot exist due to the
inherent
>> problems of the canonical formulation -- "the split into three
spatial
>> dimensions and one time dimension seems to be contrary to the
whole
>> spirit of relativity", S. Hawking.
>
> That is about a different problem in a different context...
Many years ago, Mercedes Benz announced that they had seven different
solutions to the requirements for the new suspension module in the new
E Class, and they choose the one that they considered to be better
than the rest.
In our case, I believe we're
seeking *the unique solution* of Mother Nature.
I hope you will agree that there
is a crucial problem with those quasi-local *variables* of the
gravitational energy-momentum and angular momentum: 'observables' are
local, and we don't know how they "should be associated to *extended*
domains rather than to points", as you put it four years ago (Wed, 23
Feb 2005).
First of all, the recipe advocated by Jörg doesn't work -- see the link from my initial email.
Secondly, the canonical formulation itself produces severe problems
when applied to the global properties of spacetime (if needed,
references are immediately available).
Besides, the conceptual solution to your problem has been offered at
your dedicated web page. All you need is to cast it in math ans see if
it works, instead of trying to improve the suspension of Lada Niva ...
Best,
Dimi
On Wed, 23 Feb 2005 17:37:02 +0100 (CET), Szabados Laszlo
<lbszab@rmki.kfki.hu> wrote:
> What I say in may review is *not* that GR is a non-local theory,
> I say only that the gravitational energy-momentum and angular
> momentum, i.e. the gravitational analogs of the classical conserved
> quantities and observables are non-local. Non-local in the sense
> that they should be associated to *extended* domains rather than
> to points.
=================
Subject: Typo in arXiv:0902.3923v1 [gr-qc]
+ more
Date: Tue, 24 Feb 2009 21:06:36 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Domenico Giulini <domenico.giulini@aei.mpg.de>
Cc: Stanley Deser <deser@brandeis.edu>,
Norbert Straumann <norbert.straumann@gmail.com>,
"Szabados,L." <lbszab@rmki.kfki.hu>,
Claus Kiefer <kiefer@thp.uni-koeln.de>,
Hermann Nicolai <Hermann.Nicolai@aei.mpg.de>
Dear Dr. Giulini,
I hope all my email messages sent since Thu, 23 Jun 2005 have been
safely received.
I appreciate the quote from J.
Wheeler's article in Harper’s Magazine (July
1974, p. 9), which I didn't know. Thank you.
It seems to me that there is a typo on p. 2, "... automorphisms could
be be understood in any depth."
You also wrote (p. 3) about "those E which
are connected and closed (compact without boundary)", which I think is
a big can of worms,
It is my opinion that we cannot define 'spacetime' unless there are
well-defined values of the gravitational energy-momentum and angular
momentum of all physical stuff in such 'spacetime' -- from any given
"point" up to its "boundaries". But this task is not feasible with the
3+1 split of Einstein's equations, and here your quote from John
Wheeler may be very elucidating:
“The stage on which the space of the Universe moves is certainly not
space itself. Nobody can be a stage for
himself; he has to have a larger arena in which to move. The arena
in which space does its changing is not even the spacetime of Einstein,
for space-time is the history of space changing with time. The arena
must be a larger object: ..."
This 'larger object' can only be the *unique* object of 'the whole
universe as ONE',
The only choice you have is to ignore my email notes, as you and Claus
have been doing in the past four years.
Kindest regards,
Dimi Chakalov
=================
Subject: The double role of the metric... at the same time.
Date: Tue, 09 Aug 2005 20:01:14 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Szabados Laszlo <lbszab@rmki.kfki.hu>
Dear Laszlo,
Thank you, once more, for your very
informative reply from Wed, 23 Feb 2005 17:37:02 +0100 (CET), regarding
my inquiries and request for references prompted by your review article
"Quasi-Local Energy-Momentum and Angular Momentum in GR", Living
Rev. Relativity 7, (2004) 4.
You wrote:
> In subsection 3.3.1 I argued that this
phenomenon is not
> accidental, a consequence of an unfortunate
choice for the field
> variables, but this is a consequence of a
much deeper fact, namely
> that the metric has a double role: it is a
field variable and defines
> the geometry at the same time. Or, in other
words, GR is a
> completely diffeomorphism invariant theory,
which
> diffeomorphisms form an incredibly huge set.
I consider the phrase 'at the same time'
crucially important for
amending Einstein's GR with a hypothetical
parameter, which might
account for all "dark" effects, labeled with
'dark energy' and 'dark
matter',
I've been trying to introduce two modes of
spacetime, local and global. The former can be poetically explained as
'the end result' from the bi-directional talk of matter and space (J.A.
Wheeler), which can never be actually reached. Regarding the metric
"field", it is being thought as 'the end result' from a dynamic process
of cancellation of two fluxes [Ref. 1], but I suspect
that this so-called 'end result' cannot be *actually* reached. Rather,
it should resemble the dynamic nature of the infinitesimal, which
produces dimensionless "points" (and strictly zero cosmological
constant) only if we instruct it to run toward infinity. Thus, we need
something that can take care of 'running toward infinity', and I call
it (poetically again) 'global mode of spacetime'.
Can you ride a bike?
Imagine the bi-directional talk of matter and space as a constant run
of the infinitesimal toward a geometrical "point" of tµv = 0 [Ref. 1], which can never be actually reached, because
the bike always moves ahead. On the other hand, you need to 'stop the
bike' in order to solve the field equations for a frozen, static
hypersurface, and then you discover all sorts of pathologies in it,
such as shielded (event horizon) and naked singularities, CTCs, and
geodesic incompleteness (Cauchy problem).
So, how does Mother Nature
run the bike? There is an invisible or "dark" process in the global
mode of spacetime, which I call 'potential reality'; please see NB on
p. 12 from
In the local mode of spacetime, all values of
physical quantities are *already* localized (hence the term 'local mode
of spacetime') by the time we look at them in our past light cone. If
we stop the bike, they will be strictly zero, but the bike never stops.
> What I say in may
review is *not* that GR is a non-local theory,
> I say only that the gravitational
energy-momentum and angular
> momentum, i.e. the gravitational analogs of
the classical conserved
> quantities and observables are non-local.
Non-local in the sense
> that they should be associated to *extended*
domains rather than
> to points. The field equations are still
genuine partial differential
> equations.
We can think of an *extended* domain as a
shoal of fish (see paper.doc above, p. 14),
hence each individual fish would follow a strictly local geodesic, only
the non-local influences on it would be negotiated in the global mode
of spacetime, hence each and every fish will be EPR-like correlated
with 'the rest of the fish': think globally, act locally.
> As far as I can see the non-locality in
QM is a completely different
> business. The root of this is that the basic
object, the wave
> function, by means of which the elementary
states are described is
> already an "extended" mathematical objects.
This comes from the
> different nature of the notion of the states
and the dynamics of the
> two theories.
Sure, but we need to find their joint
dynamics. Please see my efforts at
[Ref. 1] Merced Montesinos,
The double role of Einstein's equations: as equations of motion and as
vanishing energy-momentum tensor, gr-qc/0311001
v1.
"This means that for this type of observers,
there is a balance between the 'content' of energy and momentum
densities and stress associated with the matter fields [psi] (which is
characterized in Tµv) and the 'content' of energy and momentum
densities and stress associated with the gravitational field (which is
characterized in [XXX])
--->--->--->--->
<---<---<---<---
(23)
in a precise form such that both fluxes
cancel, and thus leading to a
vanishing 'flux', i.e., tµv = 0. Once
again, the vanishing property of
tµv for the system of gravity coupled to
matter fields is just a
reflection of the fact that the background metric is
dynamical.
"More precisely, tµv = 0 tells us that
the 'reaction' of the dynamical
background metric is such that it just cancels
the effect of 'flux'
associated with the matter fields. It is
impossible (and makes no
sense) to have a locally non-vanishing 'flux' in
this situation. If this
were the case, there would be no explanation for
the origin of that
non-vanishing 'flux'. Moreover, that hypothetic
non-vanishing 'flux'
would define privileged observers associated with
it (the ether would
come back!)."
Note: I
mentioned above the conjecture about an invisible
or "dark" process in the global mode of spacetime, which I call
'potential reality'. To explain how it became "dark", I'll use again
the dark room metaphor.
Suppose you stay in a
pitch-dark room with a camera in your hands, and take snapshots which
you record with your camera clock placing time stamps on your photos,
at tn , n=0,1,..., which are events in your dark room
and belong to the (global) time read by your wristwatch. The latter
includes all time stamps placed on your photos as well. Any time you
take a snapshot, you're wiping out the darkness (global time mode)
completely: you get a frozen picture of the room.
Now, consider only the events
marked with the your camera clock (local time stamps), which constitute
the 'elements of physical reality'
of the local mode of spacetime: you're confined in a 3-D space
and have a new clock that can read only and exclusively only tn
, n=0,1,..., . If you do classical physics and GR at length scales not
larger than our solar system, you have no problems whatsoever: you
cannot detect the effects of the 'dark room', and can happily use partial diff equations.
The fun begins when you take a
closer look at the dynamics of the embedding of a quantum event
into your local mode of spacetime, as explained here and here. You also find out that you
live in a "block universe" that is completely frozen [Ref.
2], and recall the 1929 paper by Nevill
Mott. Briefly, you cannot use some 'film
reel' metaphor, because in your local mode of spacetime the size
of the "dark strips" separating your tn ,
n=0,1,..., is zero. You
can only talk about some timeless probability for transition between the "points" of your
local mode of spacetime. The idea is very old, after Chuang-Tzu: Before
Zen, a tree is a tree and a mountain is a mountain. During Zen, a tree
is not a tree and a mountain is not a mountain. After Zen, a tree is
again a tree and a mountain is again a mountain. Only Zen is very well
hidden [Ref. 3], and the Zen state of the tree and the
mountain is completely "dark", being a quantum-gravitational atemporal potential reality. Viewed from the
local mode of spacetime, it is is both "outside" the cosmological
horizon and "inside" the instant 'now', hence it serves as the
"absolute" reference frame which 3-D Flatlanders, such as LIGO
Scientific Collaboration (LSC),
need to detect GWs.
To explain the nature of
'potential reality' of the global mode of spacetime and its "dark"
effects, the cosmic equator included, we
need new ideas. I tried to suggest the place where we can "insert"
these new ideas: the double role of the metric in Einstein's GR. My
email to Laszlo Szabados was based on the presumption that he is
acquainted with the main ideas, hence was very brief and perhaps
eclectic. I hope it can now be understood. If not, please do write me
back, and I'll try to do better.
D. Chakalov
August 10, 2005
[Ref. 2] Julian
Barbour, The End of Time, Phoenix, London, 2000.
"I think that if the collapse
of the wave function could be demonstrated to be a real physical
phenomenon, that would be a true demonstration of something one might
call transience" (p. 359). "That would kill my idea" (p. 358).
[Ref. 3] Roman
Buniy et al., Is Hilbert space discrete? hep-th/0508039
v1.
"In a universe with a minimal
length (for example, due to quantum gravity), no experiment can exclude
the possibility that Hilbert space is discrete. (...) In conclusion, it
appears that the traditional assumption of continuous Hilbert space is
rather strong: minimal length precludes any experiment showing that the
discreteness parameter e is exactly zero."
=======
Subject:
Conserved quantities of massive point particles and of extended bodies
Date: Fri, 19 Aug 2005 15:30:37
+0300
From: Dimi Chakalov
<dimi@chakalov.net>
To: David B Malament
<dmalamen@uci.edu>
CC: Katherine Brading
<kbrading@nd.edu>,
Elena
Castellani <castella@philos.unifi.it>,
Leonardo
Castellani <castellani@to.infn.it>,
Jeremy
Butterfield <jb56@cus.cam.ac.uk>,
John D
Norton <jdnorton@pitt.edu>,
John Earman <jearman@pitt.edu>,
Erik
Curiel <encuriel@gab.stanford.edu>,
Robert
Rynasiewicz <ryno@lorentz.phl.jhu.edu>,
Szabados
Laszlo <lbszab@rmki.kfki.hu>
Dear Professor Malament,
I think there is a big can of
worms in the so-called 'asymptotic behavior' [Ref. 1].
Please see my efforts to
explain the issue to my 12-year old daughter at
[Ref. 1] David
B. Malament, Classical Relativity Theory, Version 2.4, gr-qc/0506065 v2. To
appear in: Handlbook of the Philosophy of Physics,
eds. J. Butterfield and J. Earman,
Elsevier.
Footnote 40, p. 33: "But
sometimes a Killing field in a curved spacetime resembles a Killing
field in Minkowski spacetime in certain respects, and then the
terminology may carry over naturally. For example, in the case of
asymptotically flat spacetimes, one can classify Killing fields by
their asymptotic behavior."
...
"For further discussion of
symmetry and conservation principles in general relativity, see Brading
and Castellani (this volume, chapter 13)."
Note 2: See
Refs. [11, Ch. 3.12], [12], [27], and [28] in paper.doc.
Then there is another problem in Einstein's GR: the so-called geodesic
incompleteness. All we have to do is to solve these two problems and
leave room for 96 per cent "dark" stuff in GR from
the outset, bearing in mind the "dark" potential reality in QM as well.
Mother Nature doesn't suffer
from Cauchy problems, closed time
curves (CTCs), or "singularities", neither
shielded by some "horizon" nor naked, because the physical content of each
and every "point" is being re-created in the dark gaps, along the "vertical" line of the global mode
of spacetime. We need to 'stop the bike' to do our
calculations, sure. That's what David
Malament [Ref. 1] does remarkably well.
D. Chakalov
August 19, 2005
============
Subject: Re: Request for references
Date: Sat, 25 Mar 2006 16:57:49 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Szabados Laszlo <lbszab@rmki.kfki.hu>
On Wed, 23 Feb 2005 17:37:02 +0100 (CET), Szabados Laszlo wrote:
[snip]
> Thus, to summarize: even if we start with genuine tensorial
variables,
> then certain important physical quantities turn out to be
non-tensorial.
I tried to explain the origin of this peculiar feature of GR at
Note: How come it happens that,
as Laszlo Szabados said, "even if we
start with genuine tensorial variables, then certain important physical
quantities turn out to be non-tensorial"?
Because "Dirac observable"
cannot exist in GR: the set of Diff(M)-related
configurations, which is supposed to represent the complete
gauge invariant information, cannot exist in
principle, just as the complete (or global) presentation of
a quantum system by a set
of observable (or local) states of that quantum system -- for Hilbert
space dimension greater than two -- cannot exist in principle, as we know after Ernst Specker.
In the context of the ideas from
Plato, the Kochen-Specker Theorem
says that "the observed characteristics of a quantum system" (cf. Charles G. Torre) cannot fully represent
their Platonic idea (=potential reality)
from which they emanate as 'QM observables'. To quote Erwin
Schrödinger:
"In general, a variable has no definite value before
I measure it; then measuring it does not mean ascertaining the
value that it has."
The same kind of situation holds
for present-day GR: until
we determine ("measure") the "definite values" of the physical stuff
from Einstein field equations to obtain their case-specific spacetime,
we don't have any 'spacetime' nor 'physical stuff' (e.g., some scalar field \phi).
We are not allowed to introduce some 'reference fluid' or 'pre-geometric plenum', which would
be "external" to such case-specific
spacetime, and would facilitate
the transition from a given case-specific spacetime to the "next" one: the dynamics of 'spacetime' and its
physical stuff are totally frozen (cf. Karel Kuchar below), and we end
up in the same kind of situation explained by Erwin
Schrödinger.
The solution to the dynamics of
spacetime, after Plato, would be as
follows: 'the observed characteristics of a gravitational system' are
defined with their invariance under "active"
diffeomorphisms -- the field equations are "invariant under all
differentiable diffeomorphisms (the group Diff(M)) of the underlying
manifold M, which have no spatio-temporal significance until the dynamical fields are
specified" (cf. Mihaela Iftime; emphasis added). Thus, until the
dynamical fields are specified -- after which we may "observe" a
snapshot of the gravitational system cast on particular 'spacetime'
(the shadows on Plato's cave), -- the gravitational system per se
exists as 'potential reality'. To
paraphrase Charles G. Torre, the observed characteristics of a
gravitational system do not "reside in" or "be a part of" that system,
in the sense that they cannot fully describe it. Namely, the
'gravitational system' has some holistic "contextual"
properties that cannot be reduced to the properties of its
Diff(M)-invariant states, as Plato
would have probably said.
NB: These holistic contextual properties (another example here) will show up as "non-tensorial quantities" (see the
'second option' here), so even if we
start with genuine tensorial variables, certain important physical
quantities, at some stage, will inevitably turn out to be
"non-tensorial", as Laszlo Szabados noticed above.
In QM, we elucidate the profound
meaning of KS Theorem by comparing 'the observed characteristics of a
quantum system' to the observed characteristics of a macro-system in
its phase space: "In classical
mechanics, a dynamical variable indeed has a definite value at each point
of phase space. Specifying a point in phase space is the
standard way of indicating the state of a physical system" (Asher
Peres; emphasis added).
In GR, we elucidate the profound meaning of active diffeomorphisms by comparing
'the observed characteristics of a gravitational system' to 'the
observed characteristics of a classical system without gravity' in the
case of a fixed background of flat Minkowski space, used to
parameterize the dynamics of such classical system without gravity, and
uniquely define its state at each "point" from that fixed flat
background spacetime.
So, what's the difference? There
are no abstract "bare spacetime points"
in GR, because the point-like "events" are not locked on a fixed flat
background spacetime. The brand new "points" are defined with, and
depend on, their non-tensorial and
quasi-local "energy" as well.
Instead of 'one point from the phase space of classical
mechanics', we have in GR infinitely many "potential point-like states"
resembling 'gravitational context'
(quasi-local or rather quasi-localizable states), hence the observed
characteristics of a gravitational system do not "reside in" or "be a
part of" the potential reality, in the sense that these 'observables'
cannot fully describe the source from which they emanate, by anyset (cf. below) of
'observables': the whole is more than the sum of its parts.
Consider Georg Cantor's
definition of ‘set’ from 1895 (quoted after D. Giulini, arXiv:0802.4341v1,
p. 11):
By a ‘set’ we understand any
gathering-together M of determined well-distinguished objects m
of our intuition or of our thinking (which are called the ‘elements’ of
M) into a whole.
However, the potential
reality, which provides the set-forming 'whole', is itself rooted on
'the ideal monad without windows'
from which totally new things ('the unknown unknown'; cf. David Batchelor) may emerge in a totally
creative, non-unitary fashion (creatio ex nihilo). Thus, if we
wish to construct a "set" which could fully describe the potential
reality and its source, we should introduce a unique "element"
with absolutely no content (resembling 'hidden zero'), to match 'the ideal monad without windows', but such unique
"element" cannot belong to any set, because its nature contradicts the
very definition of 'set' from Georg Cantor: our intuition or thinking
cannot possibly "define" this unique element. In other words, the
"set" of all sets refers to the whole universe as ONE, and cannot
be a set.
The phase space of present-day GR is obviously inadequate for such
task. Nor is the Hilbert space capable of
accommodating the potential reality
in the quantum realm. We simply have two different forms of reality in
QM and GR -- potential reality, and physical reality explicated from
potential reality. If we ignore the former and push GR into 'objective reality out there', we
will have to find some GR phase space that would match the
unique point-like determination of the state of a physical system in
the phase space of classical mechanics, then "discover" some "Dirac
observable" in GR, and finally prove Charles G. Torre wrong, by showing
that GR is indeed some "parametrized field theory".
Hence any such possible
map/presentation of the building would be a perfectly legitimate
(compare with "legitimate definition of (global) time", Butterfield & Isham) and
indistinguishable presentation of such absolute spacetime of the real building 'out there'. But
because 'absolute spacetime' of 'potential reality' (called here global mode of spacetime) is
expelled from present-day GR, the alleged Dirac observable will
inevitably be "contaminated" with non-tensorial quantities (see the
'second option' here), and
will never gain the status of a genuine Dirac observable.
Alternatively, if we update the present-day GR with 'potential reality', a hypothetical
"Dirac observable" would have to be defined one-at-a-time, on a brand
new dynamical phase space. But
then it won't be a Dirac observableeither.
As Karel Kuchar stressed in May 1991: "In general relativity,
dynamics is entirely generated by constraints. The dynamical data do
not explicitly include a time variable." This is as it should be,
because the Perennials of GR should not show up in GR,
for reasons explained here; more
from Aristotle here.
Einstein was not aware of 'potential
reality' and was struggling with the problem of objective reality vs. general covariance from 1913 to 1915.
Yet some people show thriving
optimism for some "approximation scheme for Dirac observables" that can
be extracted from "infinitely many gauge
invariant degrees of freedom" [Ref. 1], by some
putative mechanism that embodies gravity as an inherently self interactive force,
although such approximation scheme for Dirac observables cannot be
constructed even by using flat Minkowski background (reference here).
No way. Fuhgeddaboudit.
D. Chakalov
April 5, 2008
Last update: April 14, 2008
pp. 1-2: If one wants to
quantize a theory with gauge symmetries one has to look for physical
observables, also called Dirac observables, i.e. phase space functions
which are invariant under gauge transformations. For general relativity
this is a very difficult problem since here also translations in time are gauge
transformations. This means that one has to solve at least partially
the dynamics of general relativity in order to obtain gauge invariant
quantities. Because this dynamics is described by a complicated system
of highly non–linear partial differential
equations it is not surprising that there are almost no gauge
invariant phase space functions known. [footnote 1]
--
Footnote 1: For the case of gravity in four space–time dimensions and
for asymptotically flat boundary conditions there are 10 gauge
invariant phase space functions known. These are the ADM charges [4]
given by the generators of the Poincare transformations at spatial infinty. Additionally an observable
is known, which takes only a few discrete values and is trivial on
almost all points in phase space [5]. For gravity coupled to matter, in
some cases gauge invariant functions describing matter are known but in
general no phase space functions which describe the
gravitational degrees of freedom (with the exception of the ADM charges). Yet there are infinitely
many gauge invariant degrees of freedom.
--
p. 2: "Therefore the hope is that one can at least develop an
approximation scheme for Dirac observables."
B. Dittrich, Partial and Complete Observables for Hamiltonian
Constrained Systems, gr-qc/0411013 v1
"To define a complete observable
we will need infinitly many clocks which describe the embedding of the
spatial hypersurface into the space-time manifold. A complete
observable is then a phase space function evaluated on an embedding
which is fixed by prescribing certain values for the infinitly many
clock variables."
T. Thiemann, Reduced Phase Space
Quantization and Dirac Observables, arXiv:gr-qc/0411031v1
"There are even obstruction
theorems available in the literature [1] which state the non existence of local
Dirac observables (depending on a finite number of spatial derivatives)
for GR."
"If one could integrate the
Einstein equations and find an internal time, then in principle
a complete set of observables could be found [5]."
C. G. Torre, The Problems of
Time and Observables: Some Recent Mathematical Results, arXiv:gr-qc/9404029v1
"To summarize, we have ruled out
the simplest putative resolutions of the problems of time and
observables. We cannot use parametrized field theory to solve the
problem of time because, strictly speaking, general relativity is not a
parametrized field theory."
C. G. Torre, Is general
relativity an ‘already parametrized’ theory? Phys. Rev. D 46
(1993) 3231-3234
"And this is why it is not generally appropriate to think of the
observed characteristics of a quantum system to somehow "reside in" or
"be a part of the reality of" that
system. That's just not how nature works."
"From this discussion it is clear that -- according to the description
provided by quantum mechanics -- one cannot assert that the spin
observables were a part of the reality of each particle independent of
the measurements. That's just how nature works (according to quantum mechanics)."
Regarding the Kochen-Specker
Theorem, Zeeya Merali (FQXi) wrote on Jul.
24, 2008 @ 19:40 GMT (the link on _cheating at "twenty questions"_
added by me - D.C.):
"The crux of the proof rests on
the fact that if you measure the square of the spin of so-called “spin
1” particles along three perpendicular axes, you always uncover the
same three values—1,0,1—in various orders. Just over 40 years
ago, Kochen and his colleague Ernst Specker showed that with this
restriction in place, it's impossible for the particle to have
consistently defined spins along every direction you might choose to
measure, before the game begins. Even if you just look at 33 possible
directions, the particle can't set spin values along each of the 33
direction such that you get you 1, 0, 1, no matter which three
perpendicular directions you choose to poke. You can set consistent
spins for 30 directions, but the final three must paradoxically be both
1 and 0.
"That's fine for quantum mechanics, where the particle sets its spin
on-the-fly. This corresponds to cheating
at "twenty questions", where you can keep changing the object in
mind, as the questions are being asked."
"This “101 property” is
paradoxical because it already implies that the quantity that is
supposedly being measured cannot in fact exist before its
“measurement.”" Watch John Conway's lecture on
April 27, 2009, and pay special attention to what he says during
11:30-14:03 and 45:30-45:57.
Hence the title of this essay, 'Quantum Mechanics 101'. It is not
intended to induce associations with those introductory-level courses
offered in some U.S. universities (e.g., 'Flowers and Gardening 101').
NB: In a nutshell, the
failure of '101 property' implies that the properties "possessed"
by quantum particles (e.g., spin orientation projected in 3-D space)
cannot exist as 'objective reality'
neither before nor after their alleged
“measurement” (see Schrödinger's 1935 article below). Surely
quantum particles have context-dependant actualized-able
"projections" at the length scale of tables and chairs, which can be
fitted into a Hilbert space. These "projections" are "governed" by a
totally incomprehensible, shut-up-and-calculate postulate known as the
Born Rule. But we also have a totally different phenomenon
revealed with Ernst Specker's tripod
and KS Theorem, which exposes the intrinsic UNdecidable
quantum stateinterwoven with the context-dependant
actualized-able "projections".
This is the dual nature
of 'quantum state': it is partly explicable
in terms of context-dependant actualized-able "projections", and
partly explicable as an UNdecidable,
in terms of binary truth-valued statements ("paradoxically be both 1
and 0"), quantum state (never in plural).
Regarding the latter: even the weakest possible "objectification"
conjecture, such as the one offered by Peter Mittelstaedt below (P.
Mittelstaedt, The Interpretation of Quantum Mechanics and the
Measurement Process, Cambridge University Press, 2004 (ISBN
0521602815), Ch. 4, p. 67) is not applicable.
All we can say about the UNdecidable quantum state is what this unique quantum
state is not: it has nothing to do with 'probabilities'.
Period.
Check out the letter by Erwin
Schrödinger dated 18 November 1950 below. He was implying
precisely the UNdecidable quantum state. Think of
it as an implication of
Gödel's incompleteness theorems to quantum theory: we should
expect to encounter an assertion that cannot be proven (=is not a
theorem) within quantum theory, as well as the negation of this
assertion that cannot be proven either, simply because the UNdecidable quantum state belongs to a 'meta theory'.
If any reasonable formulation of mathematics contains undecidable
propositions within it (details from Bob
Geroch), how could quantum theory avoid such undecidable
propositions?
All this is totally missing in
the forthcoming Compendium of Quantum Physics (April
16, 2009), although one of the editors, Daniel Greenberger,
certainly knows this web site and has replied to my email.
There is nothing essentially new
in this essay; it could have been written in November 1950. In order to
“measure” an object in the quantum world, the only option we have is to
squeeze it to a "point" from the spacetime in STR, but by imposing such
"filter" onto the quantum world we inevitably see a wrong picture.
Should a quantum particle been localized to a "point" in its natural
habitat, its momentum would have to be infinite.
Therefore, we don't have
sufficient reason to claim that "god plays dice" in the quantum world,
given that fact that we are imposing a "filter" from STR -- the 'time of facts' -- which is
totally alien to QM, and will inevitably introduce severe artifacts
to the "projection" of the quantum world on the scale of tables and
chairs. Just recall the deceptive picture of localized paths in Wilson
cloud chambers (Nevill Mott; see Alessandro Teta,
arXiv:0905.1467v1
[math-ph], pp. 9-10).
All this is well-known; I only
tried to add more evidence in support of what Schrödinger wrote on
18 November 1950. In order to understand QM, we should keep 'the
quantum state' intact before, during, and after its
“measurement” -- the "collapse" from the "eigenvalue-eigenstate link"
is an artifact from imposing the wrong (albeit inevitable) "filter" of
Minkowski spacetime.
The question of "when" (watch the clip
below) belongs to the theory of relativity; it is wrong to be
directed to the UNdecidable quantum state (not shown in the video). The
animated object in the video below do not "move" into any relativistic
space, nor can their "dynamics" be recorded with any physical clock.
There is no 'flow of events' coming from the
quantum world and ending up -- irreversibly -- at the scale
of tables and chairs. Instead, I suggest reversible quantum-classical transitions, and a new kind of
retarded causality (biocausality), to
accommodate the quasi-local nature of both quantum and
gravitational realms. The time irreversibility and the flow of time are
not "already built into quantum mechanics through the
quantum measurement process" (George F R Ellis),
and there is no such thing as "quantum mechanical arrow of time" (Jonathan Dowling) either.
NB: In the light of the
“101 property”, the Heisenberg Relations do not refer to anything
"uncertain" in the quantum realm, but to the inherent flexibility
("formally undecidable", cf. C. Weedbrook)
of quantum objects to negotiate their next state relationally, in line with a new form of retarded
causality, called biocausality. According
to W. Heisenberg (Physik und Philosophie, S. Hirzel Verlag,
Stuttgart, 2000; translated by M. Kober):
"The Copenhagen interpretation
of quantum theory begins with a paradox. Every physical experiment, no
matter if it refers to phenomena of daily live or to atomic physics,
has to be described by the concepts of classical physics. The concepts
of classical physics represent the language in which we describe the
configuration of our experiments and determine the results. We cannot
replace them by other concepts."
Yes we can. The puzzle of the double-slit
experiment -- "the only mystery" of quantum theory, according to
Richard Feynman -- is resolved from the outset: Feynman's
"uncertainty" principle claiming that "any determination of the
alternative taken by a process capable of following more than one
alternative destroys the interference between alternatives" refers to a
single indivisible pathway connecting the "initial" and
"final" states of 'the quantum state'. The latter is interpreted
as 'quantum presentation of Platonic ideas' (see below), which does not
destroy the "interference" because it contains all classical
alternatives en bloc. To be specific, the quantum
presentation of Platonic ideas reveals itself by two reversible
pathways: from 'quantum being' to 'context-dependent quantum becoming',
and back to 'quantum being'. The actualized-able
'context-dependent quantum becoming' unfolds from its source,
the 'quantum being', and can indeed be modeled with 'rays
in a Hilbert space' (compare the latter with Ashtekar and Schilling).
But the source itself can't, because it is
rooted on 'the ideal monad without windows' (Döring and Isham).
If we model the universe as a brain,
all the pieces from the jigsaw puzzle of quantum
gravity snap to their places -- effortlessly.
NB: The only way
to solve the measurement (macro-objectification)
problem in QM stems from Henry Margenau:
you have a perfect continuum of already
explicated projections from 'potential reality' (quantum presentation
of Platonic ideas), at all length scales . All
these already-explicated states (cf. the colored states below)
show up with 'carpe diem' unit probability in the local
mode of spacetime, where their common source, called 'potential
reality' (global mode of spacetime), is already vanished completely.
Stated differently, the only
way to avoid the non-unitary
"collapse" is to endow the potential reality (the ONE
meta-qubit state) with a new (to some people) ontological status,
as known since Plato: it
has nothing to do with 'probabilities'. There is no other way to solve the problems of QM.
Dead matter makes quantum
jumps; the living-and-quantum matter is smarter.
Just don't miss the
explanation of 'already'
below (notice the atemporal "hand-shaking"
mechanism), as well as the discussions of "quantum
computing" and Thompson's lamp; summary here.
As to GR, the world of
'potential reality' (=gravitational presentation of Platonic ideas)
shows up as some kind of luxonic world; cf. Max Tegmark,
gr-qc/9702052, footnote 4: "The only
remaining possibility is the rather contrived case where data is
specified on a null hypersurface. To measure such data, an observer
would need to "live on the light cone", i.e., travel with the speed of
light, which means that it would subjectively not perceive any time at
all (its proper time would stand still)."
In GR, such luxonic world is
perhaps equivalent to a point object (Rµv = 0,
cf.
Stephen J. Crothers) "inside" which there is no real mass
nor real energy whatsoever (just like the quantum vacuum) -- mass and energy are in the
form of 'potential reality'. Perhaps Cartan's "extrinsic curvature" and
the torsion degrees of freedom (Luca Fabbri) may
reveal this broader form of 'potential reality'. It isn't some
Euclidean tangent space or "fiducial space" at each point of the
Riemann manifold, but 'the universe as ONE' acting as 'the ultimate cutoff'.
From this perspective,
Einstein's dictum 'God casts the die, not the dice' can be restored as
the guiding principle in quantum and gravitational physics, while the
picture below ("spacetime foam") is considered 'not even wrong'.
------
Let me try to offer my opinion
on Conway-Kochen
(more here) and Kochen-Specker
theorems, with a little help from Claudia
Schiffer: suppose you obtain "observed characteristics of a quantum
system" (see Charles G. Torre's Lectures 6 and 32 above), in a case in
which the quantum system is (presumably) fully described with a Hilbert space (cf. Diederik Aerts,
p. 2) of three or more dimensions (cf. N. Brunner). Suppose the observable
characteristics are presented with three possible colors:
blue,
red, and green.
The notion of 'color' is like
the notions of 'energy' or 'spacetime': we should answer the question
of 'color of what?', or else we would be talking like
parapsychologists. So, we shall consider some 'colorizable stuff' (=a leg of
tripod, after Ernst Specker), in three
observable colors:
blue
stuff, red stuff, and green stuff.
Now, suppose you've made an
observation on the 3-colored quantum system, and the latter showed up
its blue stuff , say. You're
very pleased with the outcome from your observation, and decide to make
the following statement: 'the quantum system showed its intrinsicblue stuff.'
According to the usual,
two-valued logic of propositions, your statement can be either
true or false. And if you subscribe to the alleged
"scientific", Marxist-Leninist philosophy, you will be dead certain
that you have captured all possible degrees of freedom of the
quantum beast, so you can safely push it into a Hilbert space with dimension 3.
Well, it isn't that simple,
sources say. Neither the blue nor
the blue stuff are 'intrinsic
properties of the quantum system'.
The difference between the two
modes of spacetime can be made as clear as a whistle by providing the
truth-values to the proposition 'the quantum system showed its (intrinsic?)
blue stuff.'
1. In the local
mode of spacetime, the Aristotelian logic, the Born Rule, and
the unitarity
principle hold, so we can claim that the quantum system can
indeed be blue , but only
to the extent to which it can indeed show up as blue , in the particular experimental
context set by 'all the rest in the universe'. To explain this
proposition, which is the essence of my talk on September
21, 2008, notice that there are two "orthogonal" evolutions of the
universe (see the drawing below): the vertical red arrow stands for the
arrow of spacetime, driven by DDE (recall the
lake metaphor here), while the two
horizontal black arrows represent the local mode of spacetime, as
time-symmetric snapshot which, from the perspective of an ideal
observer in the global mode, would "look" like an now-at-a-distance
slice of a transcendental tachyon. The ONE state of the whole universe,
and subsequently The Aristotelian Connection, are briefly explained here and here.
A very important idea, which I
tried to express with the drawing above, is that the evolution of the
universe in the hypothetical 'local mode of spacetime' consists of
fully legitimate and already-correlated
"block universes" (think of them as snapshots from a movie reel)
stacked on top of each other along the "vertical"
arrow of spacetime. An observer cannot notice
any violation of the Aristotelian logic, the Born Rule, and
the unitarity
principle by examining the "horizontal" block universe (never in
plural), because the latter is one single, and perfectly correlated (relational ontology), state of all constituents of
the universe, in line with the Machian-like rule 'thing globally, act
locally'. Thus, no "dynamical dark energy" (DDE)
can be "traced back" in this frozen instantaneous slice called 'local
mode of spacetime' -- DDE remains totally
hidden in the global mode of spacetime. The latter is non-existent
in the local mode, thanks to which the local mode stands as a perfect continuum. Perhaps this is the
reason why our calculations in QM (the projection postulate) and GR
(linearized approximation) work well FAPP. The implications regarding
cosmology are outlined here. Notice that in ADM hypothesis the "vertical" & "horizontal"
evolution inevitably conflates (which may produce terrible
confusion), while in our model the spacetime is "quantized" along
its two modes from the outset.
Going back to the observed
blue stuff , notice that none
of the colors is 'an intrinsic property of the quantum
system'. Moreover, the colored-able
(colorizable) stuff itself is not 'an intrinsic
property of the quantum system' either.
Here comes 'Quantum Mechanics
101': After you observed a blue stuff
, you may call that stuff A and claim that 'stuff A
is indeed blue in the
particular experimental context', but to quote Erwin
Schrödinger:
"... measuring it does not
mean ascertaining the value (of the
intrinsic property - D.C.) that it (the
quantum system - D.C.) has."
Namely, the very stuff that you
just called A might as well be colored, in another
experimental context, in any of the other two available colors.
(Notice that you can't have such quantum
flexibility in Hilbert space with dimension lower than three, and a
"vast, unexplored territory" for qutrits renders
the so-called quantum computingunfeasible.)
You may also claim that, at the instant
in which you made the claim above, there are two more available
colorizable stuff, called B and C ,
only you can't say anything about their actual colors at the instant
in which stuff A turned out to be blue: it would be an indecidable
and counterfactual proposition. And of course you can't employ the latter to run your "quantum
computer" when "no one is looking at it", like T.S. Eliot's cat Macavity.
Also, you shouldn't claim that,
"after the preparation, the system is in a precise and known
state, and it can be treated as isolated from the rest of the
universe, at least until the measurement process begins" (cf. Bassi & Ghirardi, footnote 8): due to the
global mode of spacetime, we can't have any genuine "isolated"
sub-system, but only a context-evoked propensity of the
quantum system to display its possible "colorizable stuff" -- one-at-a-time only, and only to the
extent to which the Aristotelian logic holds for the local mode of
spacetime.
The prerequisites for this
opinion have been laid out by John Conway and Simon Kochen (the Strong
Free Will Theorem, arXiv:0807.3286v1 [quant-ph];
emphasis and links added): "... if indeed we
humans have free will, then elementary particles already have their
own small share of this valuable commodity. More precisely, if the
experimenter can freely choose the directions in which to orient his
apparatus in a certain measurement, then the particle’s response (to be
pedantic – the universe’s response near the particle) is not
determined by the entire previous history of the universe."
Let's be pedantic, as much as
possible: "near" is a crucial issue. It could encapsulate the feedback
from 'everything else in the universe', by means of a confirmation (advanced) wave. Also, the crucial
fact that particle’s response is not determined by the entire
previous history of the universe refers to the genuine flexibility
of quantum and gravitational realms: the concept of Final
Cause ("the end (telos), that for which a thing is done",
Aristotle, Physics 194b33) complements the relativistic
causality, but can only be revealed in the arrow of
spacetime.
NB: Notice the new form
of retarded causality (called biocausality): particle’s response is determined by both
the entire previous history of the universe and its potential
states determined relationally -- relational
ontology -- by 'everything else in the universe'. This is how
Aristotelian Final Cause complements the relativistic causality, in
both quantum and gravitational realms. In the inanimate world of tables
and chairs, the effect of 'potential reality' is vanishing small and
can be safely ignored. Wolfgang Pauli wrote about this new form of
causality in 1953.
2. In the global mode of
spacetime, the intrinsic properties of the quantum
system can be elucidated with their non-Boolean property structure
(Kent Peacock, Aristotle's Sea Battle and the Kochen-Specker Theorem, p.
4), namely, a set of three questions and their answer:
Is the quantum system
itself blue stuff ?
Is the quantum system itself red stuff ?
Is the quantum system itself green
stuff ?
The sole answer is YAIN
(both yes and no -- recall
Gödel's incompleteness theorems), because the quantum
system itself is UNspeakable by means of its 'observable
characteristics' in the local mode of spacetime. It is simply a Noumenon
rooted on the 'monad without windows'
and the Aristotelian First Cause.
All efforts to reveal 'the quantum system' would be akin to
demonstrating the "darkness" (global mode) of a room with a flashlight
(local mode). Or to talking about some totally "uncolored"
Kochen-Specker sphere, under the conditions that every statement
about it must be "colored", like finger
nails.
To grasp the notion of 'totally uncolored Kochen-Specker sphere', all you need is
a brain. Consider, for example, the Platonic idea of 'corner per se'
(more examples here and here). In English, one of its
'observable characteristics' is the word "corner", but in a different
context it can be explicated also with
The Platonic idea of 'corner per
se' will not be changed if I decide to explicate it in Hindi or
Chinese, and, most importantly, it is "open" to be associated with
brand new things that could emerge (cf. John Wheeler) during the cosmological
evolution of the universe.
As Alexandre Grothendieck put
it, "These “probability clouds”, replacing the reassuring material
particles of before, remind me strangely of the elusive “open
neighborhoods” that populate the topoi, like evanescent phantoms, to
surround the imaginary “points”."
Here, the elusive “open
neighborhoods” come from the quantum version of Platonic ideas, with
their truth value YAIN. (No, you
can't achieve this with separable Hilbert spaces and the
"proto-measures" in the topos-formulation of quantum theory, as
advocated by C. Isham and A. Döring, 0809.4847v1 [quant-ph], Sec.
V and Eq. 48.)
To understand the truth value YAIN , read the Shadow Interpretation
(SI) of Warren Leffler (arXiv:0906.4992v1 [quant-ph]),
and recall the Schrödinger
cat state(s) in Wigner presentation, exhibiting an additional,
highly nonclassical feature: a fine structured interference pattern
with negative regions, called here UNdecidable quantum
state or 'quantum version of
Platonic ideas'.
For Hilbert space of three or more dimensions, we don't even
have cat states (or "qubits") anymore (following Wolfgang
Pauli, this should be klassisch nicht beschreibbaren Art von
Dreideutigkeit), and cannot apply the unitary requirement: the
UNdecidale states that can be "both 1 and 0" are
not definable in any probabilistic fashion whatsoever
(cf. Schrödinger's letter from 18 November 1950 below).
To cut the long story short,
if your brain can hold Platonic
ideas, Mother Nature should do it as well. In the context of QM, the
example with "corner" above suggests that 'the quantum state',
which carries its latent non-commuting measure-ables
(see Claudia Schiffer), remainsintact before,
during, and after its observation: Dead matter makes quantum jumps; the
living-and-quantum matter is smarter.
Regarding GR, replace
'observable characteristics' with 'Diff(M)-invariant
characteristics', and check out the text above,
bearing in mind the basic postulates of present-day GR here. Notice that in the local
mode of spacetime the "singularities" are expelled from the outset,
since they would be equivalent to non-contextual values of quantum
observables hanging 'out there' (classical
determinism). Hence the problems with the localization of energy
and vanishing of the four-divergence of matter energy-momentum tensor,
after Equivalence Principle (e.g., Murli Verma, arXiv:0906.4933v1
[gr-qc], Eq. 11), cannot occur in principle.
The underling rule of the
dynamics of GR is as follows: the 'real universe' (local mode) is emerging
from an uncountably infinite set of potential "copies" (like
the "color" of Ernst Specker's tripod) kept in the global mode of spacetime. Then the active diffeomorphism freedom enables us
to move around this uncountably infinite set, only one
element of which becomes real -- one-at-a-time,
along the arrow of spacetime. Obviously, in order
to "move around" and produce the arrow of spacetime,
you need to 'hold onto something' -- the global mode of spacetime.
In other words, the
spatio-temporal structure of our universe is not "underdetermined" (M.
Iftime, 0809.3596v1
[gr-qc], p. 14) but flexible;
the necessary flexibility to produce 'relational ontology' is camouflaged as Cauchy
problem for the Einstein filed equations being not
"well-posed", and the input from 'potential reality' is camouflaged as "gauge-dependent".
To understand the notion of
flexibility in both quantum and gravitational context, recall that the
human arm is not pre-determined to any specific movement
(unlike the arm of a robot, say), thanks to which the human brain can
perform any movement with it. In our case, the "brain" is 'the
whole universe in its ONE state', which "chooses" one explication of
its potential states in the local mode of spacetime.
I suppose Charles
G. Torre holds different views on QM and GR, and will not tell his
students about this web page. One thing for sure -- I haven't yet
received his reply (if any) to my email from 25 July 2006.
And by the way, nothing said
here is new(e.g., recall the Heraclitian time of W.G. Unruh -- an "explicit (but
unmeasureable) time"). The landmark article by Ernst Specker
is from 1960. Ten years earlier, in a letter to Einstein dated 18 November 1950,
Schrödinger wrote (emphasis added):
“It seems to me that the concept
of probability is terribly mishandled these days. Probability surely
has as its substance a statement as to whether something is or is not
the case — an uncertain statement, to be sure. But nevertheless it has
meaning only if one is indeed convinced that the something in
question quite definitely is or is not the case. A
probabilistic assertion presupposes the full reality of its
subject.”
If you agree with
Schrödinger, and understand the theorems mentioned above, then you can't squeeze 'the quantum system'
into any Hilbert space: its full
reality includes both probabilistic assertions modeled with
Aristotelian logic (local mode of spacetime), and the potential
reality "outside" the Hilbert
space, with its negative "probabilities"
(R. W. Spekkens, arXiv:0710.5549v2 [quant-ph]).
In simple words, in we replace
'corner per se' (see above) with 'cat per se', we have
|live cat> + |dead
cat> << [cat per se]
From this perspective, "quantum
theory would be an effective theory which arises from modding out over
the gauge transformations" (Steven Weinstein, arXiv:0812.0349v2 [quant-ph];
see also footnote 5 and notice the interpretation of KS Theorem on p.
11 therein, and compare it with 'potential reality' interpreted as
"gauge-dependent" stuff here).
To the best of my knowledge, the
non-Boolean logic of propositions is acknowledged in all published (on
paper) interpretations of QM (cf. Josef M. Jauch's Foundations of
Quantum Mechanics, pp. 97-101), but none of them can employ both
"quantum logic" (Isham-Döring
toposification of quantum theory included) and the Aristotelian
logic. Notice that in the interpretation of QM proposed here, these two kinds of logic are
considered complementary, since they reflect two 'modes of
spacetime'.
This new (to theoretical
physicists at least) ontology can be elucidated with reversible
being <--> becoming transition:
If we wish to talk about 'modal
interpretations of QM', or about the superposition of |cat>
& |dog> (E. Joos, quant-ph/9908008
v1, Sec. 3.1), or about the polarization of the quantum vacuum (cf.
Robert L. Jaffe, "the deeper question", hep-th/0503158, p. 7),
we refer to the quantum becoming only. The full quantum reality
includes the quantum being,
which is of course "outside" the Hilbert space: see the new "number" phi.
For additional arguments, check out the Gedankenexperiment aimed at deriving the classical limit of QM from STR, bearing
in mind that there are no time operators in QM -- the only "time
parameter" we can use is from STR, but it corresponds to 'classical reality out there', which
in turn contradicts all we know about QM since 1935 Schrödinger
paper quoted above. Ergo, we need two kinds of time.
In short, the PR2 interpretation of QM
suggests that the quantum being and quantum becoming
constitute the potential reality
in the quantum realm, and are rooted on the ultimate reality of 'the
monad without windows' and the
Aristotelian First Cause. In the
standard interpretation of QM, there is no "chooser" (QM is a theory of
choices without a "chooser", cf. P. Pearle, arXiv:quant-ph/9901077v1).
The "chooser" is interwoven in the fabric of spacetime from The
Beginning -- the whole universe as ONE (cf. The Aristotelian Connection
here) -- and the spacetime is
being "quantized" from the outset, with two "modes" of spacetime,
called 'global' and 'local'. In the latter mode, the spacetime is a perfect
continuum, and there is no problem to recover the world of tables and
chairs -- no "semiclassical approximation" is needed. The "problem of
time", as it appears in canonical quantum gravity, is solved with the
Hilbert space problem (cf. C. Kiefer, arXiv:0812.0295v1 [gr-qc])
en bloc, because the pitfalls of the Hamiltonian
formulation of GRare avoided from the
outset. In my "just another crank"
opinion, there is no other way to proceed.
In philosophical terms, we
follow the Bootstrap Principle of Geoffrey Chew (Science161
(1968) 762), "Nature is as it is because it is the only possible Nature
consistent with itself", and advocate the relational
ontology and non-linear dynamics of 'part' and 'whole', namely,
the nature of any one thing is determined by the universe as a
whole, and vice versa. In metaphysical terms, we model the
universe as a brain, and put
aside the theological question of whether some sort of "mental
reflection" (resembling the human mind, cf. John 1:1) may, or may not,
emanate from 'the universe as a brain' (theology deals with 'The
Universe', while we make just a model of it, called 'universe').
As Edward Harrison rightly noticed, "So far, science has failed to make
sense of the bootstrap theory." (Edward R. Harrison, Cosmology: The
Science of the Universe, Cambridge University Press, 2000, ISBN
052166148X, p. 5 and pp. 159-161.)
NB:
We need two kinds of time to explain the holistic phenomenon producing quantum (as well as gravitational) waves, without any "quantum jumps". Hence the title of this
brief essay, 'Quantum Mechanics 101'. As to GR,
the necessary condition to produce a 'spacetime' is the
physical stuff in it ("Space-time does not claim existence on its own,
but only as a structural quality of the field", A.
Einstein), but the sufficient condition for fixing
'spacetime' is The Aristotelian Connection
from 'the whole universe as ONE'.
That's the difference between
people who respect their field of research, and those who just play with their hobby.
D. Chakalov
April 8, 2008
Last update: Christmas 2008
===============
November 26, 2008: Another startling example of those people who do not
respect their field of research but just play with it like a hobby is Sean Carroll (never replied to my email sent
in the past five years).
Five
years ago, he honestly acknowledged that, "In trying to understand
the universe in which we apparently live, we are faced with a problem,
a puzzle, and a scandal."
"What if Time Really Exists?"
-- asked Sean Carroll in his latest essay arXiv:0811.3772v1 [gr-qc],
and then elaborated: "What if time exists, and is eternal, and the
state of the universe evolves with time obeying something like (notice
the poetry - D.C.) Schrödinger's
equation?"
Further, he wrote (p. 3): "What
we are not worrying about, for the moment, is what that wave function
means -- its interpretation in terms of things we observe around us in
the world."
Erwin Schrödinger worried about "that wave function"
from the first days of Quantum Mechanics, and during a visit to Bohr's
institute in September 1926, he stated the following: "If all this
damned quantum jumping (verdammte Quantenspringerei) were really
to stay, I should be sorry I ever got involved with quantum theory".
The reason is simple: you can't keep track on the quantum system if
those verdammte Quantenspringerei were indeed 'a fact of
Nature'. No way.
Regarding quantum evolution in
terms of energy eigenstates, notice the crucially important imaginary
unit in Eq. 4, p.
6 -- "all of the time evolution is encoded in the phases ...".
(Although these "phases" are considered "time dependent", it is
completely unclear what kind of time they
refer to, and the conventional approach is to declare this "time
dependent phase" unobservable, just as the
wave amplitude is unobservable -- recall the "negative amplitude" in Wigner presentation.) S. Carroll
acknowledged that "we don't actually know what the energy eigenstates
are, in terms of easily observable quantities." But you can' t observe any
energy eigenstate -- you need some brand new QM in which the imaginary unit in the phase would be preserved at
the scale of tables and chairs, or somehow gradually (?)
recovered during the classical-to-quantum transition. In the real world
governed by the arrow of spacetime (the
Heraclitean time), this transition is perfectly smooth, bi-directional,
and reversible -- Nature doesn't employ the verdammte
Quantenspringerei.
Notice also footnote 4 on p. 7,
regarding "the Heraclitean property of non-recurrent change throughout
all of eternity" (p. 8), and check out the
text here and here.
If S.
Carroll wishes to 'invent the wheel' known since Plato
-- that's fine with me. But if he isn't telling his students at Caltech
anything about what he has learned from this web site -- that's not
fair. Hell NO!
Kids have the right to know
everything we know. I will be happy to explain the global mode
of time, starting from an exercise explained in Wiki here. The 'test bed', as usual, was the brain of
my teenage daughter, and -- yes, she got it.
By the way, if you trust the
so-called "block universe", as explained by George
F.R. Ellis and Robert Geroch, the
closest match would be the famous story about a multifingered Angel
(reference here):
"Jibrael replied that the Angel
had been appointed by Allah to count the drops of rain, so that it may
be known as to how many drops have fallen down to the earth. I turned
towards the Angel and asked him, "Do you know the total amount of the
rain-drops which have fallen down on the earth from the day Allah
created this world till now"? To which he replied. "O prophet of Allah
I swear by my Lord who has chosen You (as a blessing) for mankind,
verily I know the total amount of rain-drops fallen on the earth till
now. Even to the extent that how many drops have fallen in the
wilds, in the prosperous lands, in the gardens and also in the
cemetery".
Notice that GR
textbooks are far more religious: the total number of rain
drops fallen on a Cauchy surface is dead-fixed up to future null
infinity (I+ or Scri), or rather "up to the Cauchy horizon" (George F R Ellis). No matter where you go,
you will always ‘cross the same river’, because the Heraclitean time
from the arrow of spacetime is absent there.
However, no living brain can operate in a
"block universe", because it will have to function as a Turing machine
installed in some IGUS, and the perpetual "encoding
of information", by any conceivable "code", will require decreasing
of the entropy of the "hard drive", until the
poor Turing machine develops severe structural damages and breaks down
with a stroke. There are many more examples which demonstrate, by reductio
ad absurdum, how desperately hopeless (and misleading)
are the current GR textbooks, but who cares?
Certainly not Prof. Sean Carroll, so let's leave him at Caltech,
musing on "a problem, a puzzle, and a scandal."
D. Chakalov
November 28, 2008
===============
"According to the general theory of relativity space is endowed with
physical qualities; in this sense, therefore, there exists an ether. But this ether may not be thought of as
endowed with the quality characteristic of ponderable media, as
consisting of parts which may be tracked through time."
A. Einstein, Äther und Relativitätstheorie, May 5,
1920
(Lisa M. Dolling et al., The Tests of Time: Readings in the
Development of Physical Theory, Princeton University Press,
Princeton, 2003, p. 346)
Note: Einstein's ether is
interpreted here as the reference fluid in GR, which exists in
the "dark gaps" ]between[ the
points of the underlying manifold. Once we treat spacetime as 'one
entity', after Hermann Minkowski, the local mode
of time is indissolubly linked to the local mode of space: the 3-D
space. The "points" from this 3-D space are made of already-localized
propensities (such as blue stuff -- see above), while the additional degree of freedom -- the
global mode of spacetime -- refers to a genuine "ether" which cannot be
"tracked through time", as noticed by Einstein.
What, then, could be the global mode of time of the ether? It pertains
to the realm of 'potential reality' (see above),
for which the generic restrictions on motion in 3-D space -- 'inside vs
outside' and 'left vs right' -- do not hold. Stated differently, a
'global observer' would have the kind of 'global view' on objects in
3-D space, similar (but not identical!) to the abilities of a 3-D
observer to monitor the dynamics of Flatlanders, as explained in Wikipedia. And since in the local mode
of time, which corresponds to the local mode of 3-D space, the simultaneous
dynamics along all possible directions in 3-D space is inconceivable,
an inanimate clock like your wristwatch will inevitably "read" the
global mode of time as "frozen" (cf. the
Buridan donkey paradox depicted with the famous Esher drawing below).
Since physical bodies can move
in 3-D space only and exclusively only along the local
(also teleological and anti-relativistic) mode of time, the ultimate
"direction" along which 3-D space "expands", producing the
elementary timelike displacement of the arrow of spacetime, will
be omnipresent, hence your poor
wristwatch will inevitably halt and "read" such global mode of
time as "frozen". Don't trust your wristwatch; it can't read the genuine nonlinear time in GR either.
Perhaps the global mode of
spacetime will introduce brand new symmetry groups to GR (cf. M. Iftime), such as (but not limited to)
'space inversion' (notice the
possibility for a radical reformulation of George F R
Ellis' finite infinity idea).
From the perspective of the
local mode of time -- the only kind of time readable by a physical
(inanimate) clock -- the global mode of time will look omnipresent and "stand still", like the proper time of a photon "during" its
flight (cf. the question of Nicolas Gisin below). One way to obtain the kinematics of such
spacetime is to replace the fictitious "4th spatial dimension" (Ned Wright) with
the "unite timelike vector" of Matthew Frank,
and place this global degree of
freedom in the "dark gaps" ]between[ the points of local 3-D
space. The dynamics, due to the arrow of spacetime,
will completely seal off the "dark
gaps", rendering the local mode of spacetime a perfect continuum, and will produce
a pocket of quantum-gravitational propensities -- potential
reality -- placed in the potential future of this spacetime arrow.
Sorry for repeating this all over again. These ideas are not at all
original; recall Charles Howard Hinton's essay of 1880, “What is the
fourth dimension?” (reference here).
The subjective presentation of
such global mode of time, produced by the human brain, is well known. In the context of the train metaphor, every instant 'now'
from the local mode of time keeps an infinite (actual infinity) number of instants
'now' from the global mode of time, but when we "stop
the bike" we can see only a kinematical snapshot from the arrow of spacetime, in which the global mode of
spacetime has been completely obliterated; hence its effects are "dark". More from Gustav Strömberg.
D. Chakalov
September 6, 2008
Last update: November 30, 2008
===============
Subject: Categorifying Fundamental Physics, $131,865
Date: Tue, 12 Aug 2008 03:13:33 +0100
From: Dimi Chakalov <dchakalov@gmail.com>
To: John Baez <baez@math.ucr.edu>
Categorifying Fundamental Physics, $131,865: "Our program has three
components. First, we are developing a version of quantum mechanics in
which Hilbert spaces are replaced by purely combinatorial structures." http://www.fqxi.org/large-grants/awardee/details/2008/baez
Then you recall a letter by Schrödinger dated 18 November 1950,
... and start from scratch, which in turn may ruin the whole project.
So, if you wish to enjoy the money from FQXi, do NOT click the link
above, and never tell anyone that you know this web site since 14 Jan
2002.
D.C.
------
Note: In January of 2002, John
Baez sent me his last email. On Mon, 14 Jan 2002 16:37:33 -0800 (PST),
Subject: Re: Feedback? Message-ID:
<200201150037.g0F0bXg06772@math-lw-n01.ucr.edu>,
baez@math.ucr.edu wrote:
[snip]
> I've repeatedly requested that you not send me email.
> You can save both of us some trouble by taking me off your list.
In January of 2006, he repeated
an "argument" against the ether [Ref. 1], which
goes back to 1934 [Ref. 2]. But if the quantum
vacuum is 'potential reality', it will not
pick out a preferred notion of 'rest' -- the only observable effects
are "energy differences" [Ref. 3] -- yet it
could be a perfect ether (“Lichtäther”)
in the hypothetical global mode of spacetime. No need to speculate
about some stress-energy tensor of the vacuum [Ref. 1];
think deeply about QM instead.
The same applies to the
confusion with "measuring the curvature of spacetime" [Ref.
3]: it could be a "blue stuff" (more on DDE below). Notice also that the "coincidence" problem is solved from the
outset (see also A. Ashtekar), without the
need for any anthropic parapsychology (Steven Weinberg). For if you
interpret the vacuum energy density as some 'objective reality with positive energy density', its mass density will be about 1096
kilograms per cubic meter [Ref. 3]. As Richard Feynman
said in 1987, "it suggests that we're missing
something in our formulation of the theory of gravity."
Back in 1925, when Goudsmit and
Uhlenbeck discovered electron spin, they imagined that the electron
would be configured as a sphere in permanent rotation, but then they
immediately realized that, given the mass of the electron, a spin
momentum of [X] would require the tangential velocity at its "equator"
to be many times the speed of light. Regarding the notion of 'spin',
Wolfgang Pauli explained it as "eigentümlichen, klassisch nicht
beschreibbaren Art von Zweideutigkeit" (quoted from N. Straumann, physics/0010003,
p. 7). To understand the quantum vacuum, replace the word
"Zweideutigkeit" with Wheeler's
"cloud", and kindly -- very kindly -- ask John Baez for his
professional comments.
Perhaps the geodesic incompleteness, the "black
holes" (D. Christodoulou), and other
pathologies (Cattoen & Visser) are
nothing but artifacts from the current incomplete
version of GR: "What general relativity does not do is to
provide any natural way of imposing global constraints on the
spacetime — certainly the Einstein equations provide no such nonlocal
constraint" (Matt Visser).
Besides, if you agree with Naresh Dadhic that "dynamics of gravity
resides in spacetime curvature which must fully and entirely determine
it", you should either look for some "extra dimensions" in GR
(try also "branes"),
or work with the potential reality in QM, as suggested at
the link above. More from John Coleman.
"Still more shocking, it seems that the expansion of the universe may
be accelerating rather than slowing down! One possibility is that the
energy density and pressure are nonzero even for the vacuum. For the
vacuum to not pick out a preferred notion of 'rest', its stress-energy
tensor must be proportional to the metric."
[Ref. 2] P.J.E. Peebles and Bharat Ratra, The Cosmological Constant and
Dark Energy, astro-ph/0207347v2,
p. 16:
"If the physics of the vacuum
looks the same to any inertial observer its contribution to the
stress-energy tensor is the same as Einstein’s cosmological constant
(Eq. [19]). Lemaître (1934) notes this: “in order that absolute
motion, i.e., motion relative to the vacuum, may not be detected, we
must associate a pressure [X] to the energy density [X] of vacuum”."
See also the "preferred frame" problem in footnote 19, p. 15.
"... quantum field theory only
cares about energy differences. If you can only measure energy
differences, you can't determine the energy density of the vacuum -
it's just a matter of convention.
...
"... without measuring the curvature of spacetime, one can only measure
energy differences. (...) If we take advantage of this fact we are free
to redefine energy density by subtracting off the zero-point energy,
leaving an energy density of ZERO (see an elephant on a tightrope below - D.C.). In fact this is what is ordinarily
done in quantum field theory."
===============
Subject: arXiv:0802.4155v2
[quant-ph]
Date: Mon, 22 Sep 2008 06:40:58 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Nicolas Cerf <ncerf@ulb.ac.be>
Cc: Christoph Adami <adami@krl.caltech.edu>
Dear Dr. Cerf,
RE the three arguments in Sec. 2, 'The origin of security', see
Seems to me that the so-called "unconditional security, i.e. the
possibility of guaranteeing security without imposing any restriction
on the power of the eavesdropper", is a joke.
Regards,
Dimi Chakalov
===============
Subject: Counterfactual definiteness ?
Date: Tue, 24 Feb 2009 20:03:48 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Guy Blaylock <blaylock@physics.umass.edu>
Cc: Barry Holstein <holstein@physics.umass.edu>,
William J Mullin <mullin@physics.umass.edu>,
Robert Krotkov <krotkov@physics.umass.edu>
Dear Dr. Blaylock,
Regarding footnote 25 in your recent paper,
please see
I will appreciate your comments, as well as those by your colleagues.
Kindest regards,
Dimi Chakalov
Note: James
Franson mentioned that, as a graduate student at Caltech, "one of
the students asked Feynman if he would explain Bell’s inequality.
Feynman’s reply was “There is nothing to it – I will explain it all
later”. But he never did."
Many physicists have tried to explain
Bell’s inequality, and one very good effort is the article by Guy
Blaylock [Ref. 1], submitted to The
American Journal of Physics.
Regarding counterfactual definiteness,
check out Bill Unruh [Ref. 2]; otherwise you
may develop real headache from reading Anton Zeilinger [Ref. 3] and the like.
The first off headache is
produced by the counterfactual notion of (i) 'contextual
realism' -- the belief that, after the stage of 'preparation',
the attributes of a quantum system should have "gathered" well-defined classical
values "out there", which the measurements will just reveal statistically
-- and (ii) the counterfactual definiteness [Ref. 1]. Students are led to believe that in
both cases the Born Rule is being
applied to things possessing full reality (cf.
Schrödinger's letter from 18 November 1950 above),
hence the outcomes from observing such things "out there" can be
endowed with definite truth values -- either true or
false.
To explain the deceitful
notion of 'contextual realism', from the perspective of the
PR2 interpretation of QM suggested above,
replace the Schrödinger cat with a squeezable ketchup tube which you keep
upside down in your fridge door, such that it has 50% chance to fall
off upon opening the door (spin/tube up denoted with
+ , spin/tube down with - ). Then imagine that
'the tube per se' -- the quantum
presentation of Platonic ideas -- can be filled with paste from
green tomatoes, such that its color can be green,
but with the same quality of 50% chance to fall off upon opening the
door. Thus, you've completed the stage of 'preparation' of 'the tube per
se' as two latent observables (Henry
Margenau) -- either 'red
ketchup' or 'green tomato paste',
with 50% chance for the two "eigenvalues", tube down or tube up,
depending on the colors (see below) inherited from the "two" (in fact,
ONE) tube(s). To expose the deceitful counterfactual definiteness
( e.g., Karl Svozil),
consider two fridges with the same 'tube per se' --
open fridge 1 and look what you got there (say, red
tube + ), and then
you can infer what might have been "prepared" in fridge 2 "out
there" (green tube - ).
It is this definite
truth value inferred from 'contextual realism', which induces
the delusory flavor of some 'probabilistic realism'. It has been
implemented with yes/no structure of Hilbert space
dimensions. But if this Hilbert space is taken to have dimensions
greater than two, it cannot provide answer to any 'realist'
question whatsoever, as Erwin Schrödinger anticipated in 1935 and Ernst
Specker demonstrated in 1960.
Obviously, something essential is missing, perhaps "invisible"
with the Born Rule, yet many people choose to ignore this puzzle and
endorse the slogan "god plays dice". But then none of them could understand
Quantum Mechanics, as they could only 'shut up and calculate', hoping
that "if we get really deep insight into why the world has quantum
mechanics, we might go beyond" (A.
Zeilinger). We might go beyond if we understand all possible artifacts
from the measuring devices working in the realm of
STR (the point-like "window" to which an inanimate measuring device --
not the human brain -- is limited to
take a glimpse at the quantum world), instead of repeating the mantra "the background Newtonian time appears
explicitly in the time-dependent Schroedinger equation" (C. Isham).
May I offer my 'experimental
test of non-local realism in 2-D Hilbert space'. I will flip a quantum coin, call A ,
which has been 'prepared' to display two alternative classical
outcomes, + and - . Quantum
Mechanics says that (i) I will obtain a random sequence of +
and - , and (ii) if I've had an infinite time for this
exercise, I would have found that the two outcomes have equal
probabilities, which nicely sum up to unity. Fine.
Now, suppose I have my quantum
coin A "shared" (entangled) with Claudia Schiffer. She is also
flipping it in her home (causally disconnected from mine) and, due to
some conservation law (cf. Karl Svozil), the
signs obtained by flipping the "two" (in fact, ONE) entangled coins
will have to be opposite.
Here some people might say that
if Claudia observes + with
"her part" from the entangled coin A , I will
definitely observe - with
"my part" from the entangled coin A , hence
speculate about some "non-local realism" [Ref. 3].
Wrong. One can accept some
form of 'realism' iff Claudia could somehow force
"her part" from the entangled coin to produce a distinctive "ketchup"
pattern, +++---+++ , which
will in turn force "my part" from the same entangled coin to
produce instantaneously the opposite "green tomato"
pattern, ---+++--- ,
which will be counterfactual elements of physical
reality to Claudia, while her pattern will be counterfactual
elements of physical reality to me. It is of course impossible to
look at the two patterns simultaneously (see John Polkinghorne), hence any statement
that implies, or explicitly depends on, such simultaneous observation
is 'not even wrong'.
The first and only email I got
from Anton Zeilinger was in
April 2000, then he decided to ignore my comments and continued to
explore his murky philosophy. How many of his students got headaches
from it, I wonder.
I hope to hear from Guy Blaylock
and his colleagues. I can't imagine how Richard Feynman would have
explained the counterfactual pitfalls in Bell's inequality and in the
Gedankenexperiment from 1935 [Ref. 1]. But I
sincerely hope the interpretation of QM outlined above
is headache-free. It also allows quantum systems to have properties
that are not "extrinsic" [Ref. 4],
such as the formally undecidablequantum
presentation of Platonic ideas (cf. the example of 'corner per se'
above, and use your
brain to grasp it).
NB: Notice that with the
so-called PR2 interpretation of QM
there is no need to define QM observables with respect to some
'classical world of tables and chairs', hence we can use it in quantum cosmology (Marco Genovese, arXiv:0904.2300v1),
firstly, and secondly -- the measurement problem is solved from the
outset, by providing smooth bi-directional transitions between the
quantum (Chen Ning
Yang) and classical realms:
the "back bone" to hold onto is the formally
undecidable, in the sense of KS Theorem, quantum presentation of
Platonic ideas or 'potential reality'.
All this may sound like sheer
philosophy, but notice that the absolute value of energy
stored in the quantum vacuum [Ref. 5] is also
'potential reality', which may be neutral to both "charges" of
mass, and if the human brain uses the
same 'potential reality' and 'nondynamical
time parameter' (Unruh &
Wald), a (topological?) bridge between the brain and the
quantum presentation of Platonic ideas may be possible to establish,
with vast technological implications.
There are far too many hypotheses involved with this "bridge", and at
this point I am only trying
to gather indirect evidence in support of it, by proving the
alternative hypothesis wrong. Stay tuned.
D. Chakalov
February 25, 2009
Last update: May 17, 2009
References
[Ref. 1]
Guy Blaylock, A pedagogical study of the Einstein-Podolsky-Rosen
paradox and Bell's inequality, arXiv:0902.3827v1 [quant-ph]
"25 An example of counterfactual reasoning is a statement of the form
“If we had made a certain alternative measurement (rather than the one
we did make) we would have obtained such-and-such result”. Counter
factual definiteness implies that a statement such as the
former has a definite truth value (is either true or
false)."
[Ref. 2] W.
Unruh, Nonlocality, counterfactuals, and quantum mechanics, Phys.
Rev. A59, 126-130 (1999); arXiv:quant-ph/9710032v2,
p. 3.
"Locality prohibits any influences between events in space-like
separated regions, while realism claims that all measurement outcomes
depend on pre-existing properties of objects that are independent of
the measurement. (...) The logical conclusion one can draw from the
violation of local realism is that at least one of its
assumptions fails. Specifically, either locality or realism or both
(here comes the real big mess - D.C.) cannot provide a foundational
basis for quantum theory. (...) It is sufficient for our purposes to
discuss two-dimensional (the implications from KS Theorem are automatically excluded - D.C.)
quantum systems."
"All examples that have been listed show that the intrinsic and
extrinsic properties are physically inseparably entangled with each
other. (...) Still, both kinds of properties are logically clearly
distinguished, and we conjecture that the physical in-and-extrinsic
tangle does not lead to any logical contradictions.
...
"There are intrinsic properties of Sq that are not classical properties
of Sc, e.g., the set of all quantum observables measurable on
Sq. Hence, classical properties must be some specific intrinsic
properties and the question is, which.
...
p. 17, footnote 12: "In the decoherence theory,
another component, the environment, is added at the beginning and
traced out at the end. The result is again an improper mixture and the
problem remains exactly the same.
...
"To summarize: Our interpretation suggests a new approach to quantum
theory of classical properties and of measurement because it allows
quantum systems to have also properties that are not extrinsic.
"Provided we only measure energy differences, we
can subtract this type of contributions and we do not need to worry
when performing calculations (technically we call it normal ordering).
However, this procedure is no longer possible in the presence of
gravitation for in this case the absolute value of energy
matters.
"One expects then a net cosmological constant from the zero-point field
fluctuations [2]. It has been known for many years that these
contributions exceed the observed value (1) by many orders of
magnitude. To solve this problem is one of the present challenges for
Physics [3].
The problem presupposes that vacuum fluctuations have the same
gravitational properties (positive energy density
-- D.C.) as all other forms of matter."
===============
Subject: Formally UNdecidable (arXiv:0809.0151v1)
Date: Mon, 5 Jan 2009 01:38:39 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Christian Weedbrook <christian.weedbrook@gmail.com>,
mgu@physics.uq.edu.au, alvaro.perales@uah.es,
mnielsen@perimeterinstitute.ca
Cc: A.P.A.Kent@damtp.cam.ac.uk, rlaflamme@perimeterinstitute.ca,
dgottesman@perimeterinstitute.ca
Dear Dr. Weedbrook,
I greatly admire your article. Please notice that, from the perspective
of KS Theorem, 'the quantum state' is 'formally undecidable' as well,
This may have devastating consequences for "quantum computing", since
it isn't possible to control 'the quantum state' locally, at the scale
of tables and chairs. I hope you are not connected to this "quantum
computing" community, and may have the freedom to face the bold facts
of QM, as known since 1935.
If you or any of the recipients of this email disagree, please don't
hesitate to write me back.
Kindest regards,
Dimi Chakalov
===============
Subject: Re: Bohmian Mechanics vs KS Theorem
Date: Tue, 17 Mar 2009 17:42:02 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Roderich Tumulka <tumulka@math.rutgers.edu>
Cc: duerr@mathematik.uni-muenchen.de,
oldstein@math.rutgers.edu,
zanghi@ge.infn.it
On Tue, Mar 17, 2009 at 4:46 PM, Roderich Tumulka
<tumulka@math.rutgers.edu> wrote:
>
>
> Because different experiments can be associated with the same
> observable, and the outcome depends on the experiment, not just
> the observable.
>
> Best, Rod
Rod, this is sheer jabberwocky. Please get professional. I know you can
do it.
In the deterministic Bohmian Mechanics, if "the outcome depends on the
experiment, not just the observable" (as you put it) and "the entire
history is fixed by the equations (1) and (2)" (arXiv:0903.2601v1 [quant-ph],
p. 2), what is the value of the "observable" in the case of Specker's
colored tripod?
Check out Ernst Specker, Die
Logik nicht gleichzeitig entscheidbarer Aussagen, Dialectica 14 (1960)
239-246,
To be specific: How is the *absence* of two-valued probability measure
(standard QM + KS Theorem) encoded/presented in your Bohmian Mechanics?
If it isn't, what is "Bohmian Mechanics", actually?
I've been trying to understand Bohm's ideas since 1986, and it seems to
me that with Bohmian Mechanics one can only replace the old puzzles of
QM with new ones, a bit like the quiz below.
Hope you and/or your colleagues will elaborate on the questions above.
Best - Dimi
----
Q: What is green, lives underground, has one eye, and eats stones?
A: The One-Eyed Green Underground Stone Eating Monster!
> On Tue, 17 Mar 2009 03:30:38 +0200, Dimi Chakalov wrote:
>
>> Dear Rod,
>>
>> May I ask you and your colleagues to help me understand your
ideas
>> about Bohmian Mechanics. You stressed that it is
deterministic, in the
>> sense of Eq. 3 in arXiv:0903.2601v1 [quant-ph],
yet claim that "the
>> term “hidden variables theory” is often used to convey the
idea that
>> every “quantum measurement” of an “observable” reveals a
>> pre-existing value of that observable, which is not
the case in
>> Bohmian mechanics."
>>
>> I wonder how does the Bohmian mechanics *not* fix pre-existing
>> values of its observables, as compared to KS Theorem,
>>
>> http://www.god-does-not-play-dice.net/Szabados.html#Hilbert
>>
>> I will highly appreciate the opinion of your colleagues, too.
>>
>> Regards,
>>
>> Dimi
>>
===============
Subject: "There is something beyond my control", Chris Fuchs, arXiv:quant-ph/0505187v4,
p. 2
Date: Wed, 17 Dec 2008 03:45:29 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Chris Fuchs <cfuchs@perimeterinstitute.ca>
Cc: Nicolas Cerf <ncerf@ulb.ac.be>,
Christoph Adami <adami@krl.caltech.edu>,
Carlton Caves <caves@info.phys.unm.edu>,
Jonathan Dowling <jdowling@lsu.edu>
Dear Dr. Fuchs,
Regarding your startling statement quoted in the subject line, may I
offer you an essay on QM at
I'm afraid he will try to borrow some ideas from Nicolas Cerf and
Christoph Adami, and push them well beyond their applicable limits.
The main reason for this email is to correct your statement printed
below. I don't believe my road is distinct from yours, and I never
claimed that "distinct new kinds of physics arise in our brain
processes". Please check out my actual claims at the first URL above.
Should you and any of your colleagues find errors in my essay, please
do write me back.
"Thank you for all the interest you've shown in the papers I have been
involved with. I commend you in your efforts to get to the bottom of
what's going on in our world. But I cannot believe it very likely that
distinct new kinds of physics arise in our brain processes. Instead the
road I have chosen to develop is making sense of quantum mechanics (as
a theory predominantly of inference) from within quantum mechanics. I
understand that your road is distinct: but life is short, and one has
to make a cut or one will certainly never get anywhere. My own
direction may turn out to be completely wrong, but I have decided to
pursue it with dogged determination and not to get derailed. I wish you
luck in your own pursuits."
===============
Subject: Quantum Mechanics 101
Date: Tue, 14 Oct 2008 03:59:13 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: J Tolar <jiri.tolar@fjfi.cvut.cz>
Cc: P Hajicek
<hajicek@itp.unibe.ch>,
Jürg Gasser <gasser@itp.unibe.ch>,
Uwe-Jens Wiese <wiese@itp.unibe.ch>
Dear Dr. Tolar,
In your latest update of "Intrinsic properties of quantum systems", arXiv:0806.4437v2
[quant-ph], you and Petr wrote:
"Our main achievement is the formulation of real existence of quantum
systems
that does not lead to well-known logical problems."
If your claim corresponds to facts, I think the 'proof of the pudding'
is to solve the measurement problem,
Notice the quote from Schrödinger, dated November 18, 1950 (I
believe all this is well known to Petr,
but he has been stubbornly ignoring it).
Should you and/or your colleagues have questions, please don't hesitate
to write me back.
Kindest regards,
Dimi Chakalov
===============
Subject: The reversible, quantum <--> classical transitions
Date: Mon, 29 Sep 2008 05:25:24 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Renato Moreira Angelo <renato@fisica.ufpr.br>
Cc: Eleanor G Rieffel <rieffel@fxpal.com>
Dear Dr. Angelo,
It is a pleasure to read your latest article [Ref. 1].
Regarding the subject line and the issue of "decoherence"
(the last paragraph of Sec. 3.2, p. 10), may I draw your attention to
my essay at
Dimi Chakalov
----
[Ref. 1] R. M. Angelo, Low-resolution measurements induced
classicality, arXiv:0809.4616v1 [quant-ph], http://arxiv.org/abs/0809.4616
"The limit h --> 0 and the
Ehrenfest theorem [1] have recurrently been proved not to be sufficient
to guarantee the classical limit both mathematically and conceptually
[2, 3, 4, 5, 6, 7, 8]. More modern approaches such as the environment induced decoherence (EID) program
also have been claimed to present some conceptual difficulties (see [8,
9] and references therein for more detailed discussions), as for
instance: i-) The incapability of diffusive EID in restraining the wave
function spreading and hence recovering the classical determinism and
ii-) the apparently paradoxical presence of entanglement -- an
exclusively quantum resource -- in semiclassical
regimes.
...
p. 10: "Of course, for those who interpret the wave function as
describing physical reality, the particle delocalization problem would
keep existing (before the measurement is performed) even when we are
not allowed to experimentally observe it. In this case, decoherence would be mandatorily invoked to
destroy quantum coherences and hence settle the problem. However, one
must realize that decoherence is proved to
be associated with an exponential (in some cases Gaussian) death of
quantum coherences, not with the exactly (and instantaneous, as with
the "collapse" postulate - D.C.) disappearance of them. Then, from a
formal point of view, delocalization is always there and the
interpretational difficulties remain.
...
"We then conclude that classical physics, which here is claimed to be
an approximative description of nature, well succeeds in explain
macroscopic motion for several reasons, among which we have to include
the low-resolution power of our spectacles."
---
Q: How would you keep
the complex phase of quantum waves [Ref. 2] intact,
to make reversible quantum <--> classical transitions?
Notice that, to match the
classical realm, you need to obtain an arbitrarily small (approaching
the Plank time) "duration" of an event, while with the "decoherence"
you get a finite duration (10-19
s) for such infinitesimal
timelike displacement, hence the
resulting classical spacetime manifold will be severely discrete. And
if you embrace the convenient view that the world at the length scale
of tables and chairs were "semi-classical" (e.g., IGUS
Jim Hartle), and then try to merge QM with GR, the world of tables
and chairs will be even more elusive and difficult to recover. Hence the
question above remains open.
I don't know the answer, and
can only suggest some very general ideas about
a hypothetical "back bone" of the
whole quantum-gravitational realm, in the form of 'local mode of
spacetime', at all length scales.
This is the only logical possibility which hasn't, to the best of my
knowledge, been explored yet.
[Ref. 2] Chen Ning Yang, Square root of minus one, complex phases and
Erwin Schrödinger, in: Schrödinger: Centenary Celebration
of a Polymath, ed. by C. W. Kilmister, Cambridge University Press,
1989, Ch. 5.
===============
Subject: The Hilbert space dimension and Ernst Specker's tripod
Date: Mon, 12 May 2008 13:56:17 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Nicolas Brunner <nicolas.brunner@physics.unige.ch>
Note: By definition, a Hilbert
space admits and requires an orthonormal
basis, so we can "attach" to it some well-defined dimensionality
iff the case under consideration admits two-valued probability measure (e.g.,
the statement "the URL at ref. [8] seems to be invalid" is "orthogonal"
-- either true or false), which is of course inapplicable for Ernst
Specker's tripod (cf. Ernst Specker, Die Logik nicht gleichzeitig
entscheidbarer Aussagen, Dialectica14 (1960) 239-246).
It is like asking what would be the dimensionality of Hilbert space of
some totally "uncolored" Kochen-Specker
sphere, and subsequently how many dimensions are needed to fit, say, 32
per cent of "uncolored" sphere (cf. H.
Granström). Obviously, we can't pose such questions with
Hilbert space, nor within the geometric
formulation of QM.
As John von Neumann acknowledged (13 November 1935): "I would like to make a
confession which may seem immoral: I do not believe in Hilbert space
anymore". Yet many
people still believe in Hilbert space, and also claim that "the background Newtonian time appears
explicitly in the time-dependent
Schroedinger equation", as if
they could picture the quantum state
evolving happily in some non-relativistic configuration
space, until it gets hit by the "collapse".
Hope Nicolas Brunner will help. Then I'll try to elaborate on the tantalizing
question posed by his colleague Nicolas Gisin (quant-ph/0512168v1):
"Does relativity hold a place for non-signaling nonlocal correlations?"
Does relativity
hold a place for the human brain? Of course it
does. Only the flow of time, pertaining
to the holistic ensemble of non-signaling quasi-local correlata, is called
here 'global mode of time'. From the perspective of the (local mode of)
time in the theory of relativity, the global mode will look "stand
still", like the proper time of a photon "during" its flight. Hence in
the local mode of time, the global mode is unobservable (compare it
with John Cramer's atemporal "handshaking"):
physically, we can observe only the event of joint emission/absorption,
but not the "intermediate" flight of the photon (cf. Kevin Brown).
Subject: Quantum Mechanics 101
Date: Tue, 26 Aug 2008 14:23:07 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: nicolas.gisin@physics.unige.ch, daniel.salart@physics.unige.ch
arXiv:0808.3316v1 [quant-ph]:
"From these observations we conclude that the nonlocal correlations
observed here and in previous experiments[1] are indeed truly nonlocal."
Dear colleagues,
I'm afraid you and your colleagues are ignoring the basic basics of QM,
Dimi
-----
Dimi Chakalov
35 Sutherland St
London SW1V 4JU
Note: If we think of the
measurement in QM as 'physical process' -- and we simply don't have any
choice -- then we have to "accept the conclusion of von Neumann that, at a certain
level, one has to give up the linear structure of the theory, one has
to take into account that in nature nonlinear processes must occur"
(GianCarlo Ghirardi, arXiv:0806.0647v1 [quant-ph],
pp. 1-2).
Welcome aboard! The only way --
and we simply don't have any choice -- to reconcile the nonlinear
processes with the linear ones is to place the former in the global
mode of time, and the latter in the local mode of time. Then you'll be
ready to face the task of deriving the classical
limit of QM from STR, and recover the smooth
and reversible transition between the classical and quantum realms.
It isn't very likely that
GianCarlo Ghirardi would be able to attend the meeting in Munich on September 21st this year, but I hope Angelo Bassi and
Detlef Dürr will accept my invitation.
D. Chakalov
June 10, 2008
===============
Subject: The single whole, arXiv:0707.4539v5 [math-ph]
Date: Mon, 19 May 2008 11:31:45 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Vikram Zaveri <zaverivik@hotmail.com>
Cc: José Pereira <jpereira@ift.unesp.br>
Dear Dr. Zaveri,
I greatly admire your work [Ref. 1], and hope you can
elaborate on 'the single whole' in the context of Quantum Theory,
========== [Ref. 1] Vikram H. Zaveri, Periodic invariant,
general relativity predictions and origin of universe, arXiv:0707.4539v5
[math-ph]
"Hence this single whole does not have a second and mathematical
concepts of zero, one, two, infinity does not apply to this single
whole. (...) What applies to the single whole does not apply to
manifested energies of this universe.
...
"This unmanifest energy could be thought of as the cause behind:
• the vacuum energy of inflation field [47, 48];
• the dark energy field, responsible for the accelerating
universe [38, 39, 74, 75];
• quintessence and phantom energy of the quantum
field theories [40];
• scalar Higgs field, responsible for Higgs boson in
standard model [41, 42];
• strings and branes in the string theories [43, 44];
• microwave background radiation field [45, 46];
• vacuum fluctuations and virtual particles;
"The single whole which does not have a boundary does not form a closed
system from the point of view of the second law of thermodynamics.
...
"No one ever considered a possibility that ether could be a fundamental form
of energy and the only form that is completely free from any vibration,
which means no motion."
---
As to the current
interpretations of 'the single whole' or 'ether', see Friedwardt
Winterberg, The clouds of physics and Einstein's last query: Can
quantum mechanics be derived from general relativity? arXiv:0805.3184v1
[physics.gen-ph]: you may safely place any amount of "negative
mass" in the global mode of spacetime, since there it is not physical
but 'potential reality' (cf. above).
Recall also the dubious
interpretation of the energy-momentum pseudotensor in GR (“the right answer to the wrong question”, MTW,
§20.4, p. 467), and consider
the binary star PSR 1913+16: if
its kinetic energy were 'objective reality out there',
you would, at least in principle, be able to propose some brand new
energy conservation law for GR [Ref. 2], which
is, as far as I understand GR, truly impossible -- not just because
nobody has found it since November 1915, but because such "conservation
law" would require some recipe for mapping the proper time [tau] along
spacetime trajectories (C. Rovelli) to the
time read by your wristwatch, and GR
would become a bona fide parameterized field theory (C. G. Torre).
Alternatively, consider the
following conjecture: what if the binary
star PSR 1913+16 was not
losing kinetic energy by dumping it into "the apparently empty
gravitational field" [Ref. 2]? Perhaps its
kinetic energy was "dissipated" back into the global mode of spacetime,
being back-converted into 'potential
reality'; just like the context-dependent blue
stuffabove, or "a matter of
opinion" [Ref. 2] cast from the global mode. The
process may be reversible: think of the binary star PSR 1913+16 as "charging the battery" of
the global mode of spacetime, and of GRBs as
"discharging the battery".
Then you may discover the
conservation law for all the "dark stuff" in
GR (the "dark energy" of GRBs included),
and even derive QM from GR, but many people from LIGO Scientific Collaboration
will really hate you. And you may never hear from the
theoretical physics community -- they all will
ignore you, or else will have to drop their obsessions with "GW astronomy", convert the LIGO
tunnels to wine cellars,
and start from scratch.
Recall that the principle of equivalence selects an
"object" that cannot be a tensor, since it is capable of being
switched off and set to zero "at a point" (the Wegtransformierbarkeit
of gravitational energy) so the nature of this "object-at-a-point" can
only be the 'potential reality' producing what
Tullio Levi-Civita dubbed “congruences of privileged lines” [Ref. 3], resembling the "privileged lines"
chosen by all fish in a shoal: every fish follows its quasi-local
geodesic that has been pre-correlated with the rest of the fish --
think globally, act locally. There is no other choice but to introduce
the "global mode", after Plato.
Anyway.
The issues raised above are far too serious to be discussed in a web
page, so I will have to stop here. The five paragraphs above were very
dense, and somehow eclectic. Sorry. More on September
21, 2008.
p. 2: "Belief in the production
of gravitational radiation is bound up with the binary star PSR
1913+16, which is considered in §3.14 and supposed to lose kinetic
energy as it spirals inwards; if energy is conserved, the energy lost
in one form must be converted, into a perturbation of the surrounding
spacetime one presumes.
"But the conservation law is flawed (§3.9), involving, in its
integral form, a distant comparison of directions which cannot be both
generally covariant and unambiguously integrable. Even the ‘spiral’
behaviour itself, the loss of kinetic energy, and perhaps the
oscillation on which detection (§3.15) is based can be transformed
away; as can the energy of the gravitational field, which is
customarily assigned using the pseudotensor t_xx : while an observer in
free fall sees nothing at all, an acceleration would produce energy out
of nowhere, out of a mere transformation to another ‘point of view’
or rather state of motion.
p. 12: "Is the physical meaning of [energy-momentum pseudotensor] t_ab
compromised by its troubling susceptibility to disappear, and reappear
under acceleration?
...
p. 7: "The gravitational matter-mass-energy would be "a matter of
opinion" (John Earman and John Norton “What price spacetime
substantivalism? The hole story” British Journal for the Philosophy of
Science 38 (1987) 515-525, p. 519).
pp. 17-18: "We can now turn from the reality of gravitational waves to
their very generation, about which the relationalist can also wonder,
given the shortcomings of the conservation law: if a belief in the
production of radiation rests on the conservation of energy, how can
that belief remain indifferent to such shortcomings?
"If the conservation law is
suspicious enough to make us wonder whether the lost energy is really
radiated into the apparently empty gravitational field, why take the
polarization of that radiation -- which corresponds to the
underdetermination of inertia by matter -- seriously? Couldn’t it be no more
than a purely decorative gauge, without reality or physical meaning?
The binary star’s behaviour and emission of gravitational waves can
admittedly be calculated with great accuracy, but the calculations are
not
generally covariant and only work in certain coordinate
systems.
p. 23: "So a clean separation
into space (across which the integral is taken) and time (in the course
of which the integral remains unchanged) seems to be presupposed when
one speaks of conservation.
p. 27: "Vanishing is an
important criterion: a complex whose components are wegtransformierbar
cannot be physically real -- one whose
components all vanish cannot ‘coincide’ with one whose components don’t.
p. 32: "Belief in gravitational
radiation rests chiefly on the binary star PSR 1913+16, which loses
kinetic energy as it spirals inwards (with respect to popular
coordinates at any rate). If the kinetic energy is not to disappear
without trace, it has to be converted, presumably into radiation. Since
its disappearance is only ruled out by the conservation law,
however, the very generation of gravitational waves must be subject to
the perplexities surrounding conservation.
"Even the ‘spiral’ behaviour, associated so intimately with the loss of
kinetic energy, is wegtransformierbar. A coordinate system leaving the
two pulsars at the constant positions (t, 1, 0, 0) and (t, 0, 0, 0) is
easily found.
"If the pulsars don’t move, if they have no ‘kinesis,’ why should they
lose a kinetic energy they never had in the first place?"
[Ref.
3] S. Capozziello, M. Francaviglia, S. Mercadante, From Dark Energy and
Dark Matter to Dark Metric, arXiv:0805.3642v1 [gr-qc]
"What we present here is a completely new approach to the mathematical
objects in terms of which a theory of Gravitation may be written. At
the end we shall conclude that although the gravitational field is a
linear connection defined on spacetime, the fundamental field of
Gravity is still a metric ... but not the “obvious” one given from the
very beginning (which we shall call “apparent”). Rather we shall show
the importance of another metric, that we shall call dark metric.
...
"In 1919, working on the theory of “parallelism” in manifolds, Tullio
Levi-Civita understands that parallelism and curvature are not metric
properties of space, but rather properties of “affine” type, having to
do with “congruences of privileged lines” [4].
...
"(T)he dynamics of the connection [X] forces [X] itself to be the
Levi-Civita connection of a metric, but not of the “original” metric g,
which we prefer to call the apparent metric for a reason we clarify in
a moment. Instead, the dynamics of [X] identifyies a new metric h,
conformally related to the apparent one, which we call the dark metric.
"Now, the apparent metric is the one by means of which we perform
measurements. In other words, the metric g is the one we have to use
every day to construct and read instruments (rods & clocks). This
is why we like to call it the “apparent” metric. But we claim that the
right metric we have to use as the fundamental object to describe
Gravity is the dark
metric.
"In other words, in our laboratories we have to use the apparent
metric, but in our theories the dark one. (...) Let us notice
explicitly that this in particular implies that if a certain metric h
is expected as a solution of a problem, from a theoretical point of
view, it is wrong looking for h in experiments. The conformally related
metric g has to be searched instead!"
===============
Date: Fri, 11 Apr 2008 19:27:10 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Maximilian Schlosshauer <m.schlosshauer@unimelb.edu.au>
Subject: Neglecting the interference terms in the global density
matrix: t_n
Cc: Kristian Camilleri <kcam@unimelb.edu.au>,
Jonathan Halliwell <j.halliwell@imperial.ac.uk>
Hi Max,
Regarding the statements in your latest manuscript [Ref. 1], let me offer you and your
colleagues 'the proof of the pudding'.
Consider Blue Gene/L, a 130,000 processor supercomputer capable of
performing 478.2 trillion floating operations per second,
Think of the timing of operations in these 130,000 processors as the
pistons of your car: there is an instant at which an operation must stop,
in order to initiate the next operation.
Denote this stop-instant with t_n , and calculate the chance
for error due to "neglecting the interference terms in the global
density matrix" [Ref. 1], and then
calculate "the probability for a history of positions, p( 1, t1, 2, t2
· · · ) and then see if it is strongly peaked
about the classical evolution equations" ...
Notice that t_n is a *crucial* instant: it got to be dead
classical *from the outset*, because it serves as the "chooser" of your
"at least one preferred basis" [Ref. 1],
http://www.god-does-not-play-dice.net/Maximilian.html#2
If you can prove that Blue Gene/L does indeed work as some
"quantum-to-classical" system, and can also resolve the Catch 22
logical contradiction with the chooser of "at least one preferred
basis" in quantum cosmology,
please write me back. I have a second 'proof of the pudding' for you,
based on the wet soft gray "quantum-to-classical" stuff right above
your neck, which operates with 100 billion
neurons and 60 trillion synapses.
Also, there is a simple, and widely known, story about QM, which I
believe should be included in every 'Quantum Mechanics 101',
Some people at the Imperial College (e.g., C. Isham) don't like it, so if you
or any of your colleagues can find an error at the link above, please
write me back, too.
Meanwhile, I will treat "decoherence" with Murphy's Law No. 15: Complex
problems have simple, easy-to-understand wrong answers.
Regards,
Dimi
---- [Ref. 1] Maximilian Schlosshauer,
Kristian Camilleri, The quantum-to-classical transition,
arXiv:0804.1609v1 [quant-ph]; Submitted to Studies in History and
Philosophy of Modern Physics on 10 April 2008. http://arxiv.org/abs/0804.1609v1
p. 19: "As a consequence of decoherence, there will be at least one
preferred basis in which the interference terms between different
one-to-one quantum-correlated system-apparatus states in the reduced
system-apparatus density matrix will be sufficiently small in order to
be neglected in practice. We thus arrive at a system-apparatus density
matrix that is formally identical to (7).
...
p. 31: "Decoherence allows us to analyze, in precise formal and
quantitative terms and wholly from within the quantum-mechanical
formalism, when and how the quantum-to-classical transition happens.
(...) To our knowledge, there are no experimental observations of
quantum-to-classical processes that could not be accounted for, at
least in principle, by decoherence.[footnote 10]
Footnote 10, p. 31: "We emphasize that this statement is independent of
any assessment of whether and how decoherence may help solve the
measurement problem, especially in the sense of the
"macro-objectification" problem (Jammer, 1974; Bassi and Ghirardi,
2000; Adler, 2003; Schlosshauer, 2004; Zurek, 2007)."
----
Note: Jorge Pullin posted
today a new article [Ref. 2], which suggests some
"fundamental mechanism of
decoherence", and I hope some day he will try the first proof of
"decoherence" above.
Recall that the "instant" of
"decoherence" cannot be made arbitrarily short -- its estimated value
is about 10-19 s, so in addition to the first proof of
"decoherence" above, the proponents (Jorge Pullin, IGUS Jim Hartle, Wojciech Zurek,
etc.) will have to explain the paths in Wilson cloud chambers (Nevill Mott) and discover the elementary timelike displacement in the continuum of
events employed in GR. For if the hypothesis of "decoherence" is not
falsifiable, all their fancy equations will be like discussing the
number of angels that can be placed on a tip of a needle.
Regarding the second
'proof of the pudding' of the so-called decoherence, I will quote Matthew Donald (emphasis added):
"If every synaptic transmission
is an uncertain event with probability significantly distinct from 0 or
1 (note: the correct biological term is not "uncertain" but flexible -
D.C.), then there will be at least 1014 such events per
second in the brain.
...
"This seems almost inevitably to lead to the idea that the timings of
neural events need to be defined to sufficient precision that changes
in the time-orderings of each pair of spatially distinct events
can be distinguished. But since this involves an ordering of, say, 1011
events in a second, or at least an ordering of the timelike
separations among those events..."
To cut the long story short, if
your brain were some "decohered" system, you wouldn't be reading these
lines.
Moreover, Matthew Donald missed
the bindingphenomenon: all
these events are not just flexible
("uncertain"), but correlated by the binding phenomenon: read 'Neurophysiology 101 for Quantum Physicists' here.
But are the events in the human
brain timelike or EPR-like correlated?
If they were timelike correlated, we would have immediately discovered
some correlating center (a.k.a. "homunculus")
and its anatomical structure in 19th century, if not earlier. More
about the human brain here.
I will stop here, because it's
just the right time for a large, decohered, just-another-crank
gin tonic!
D. Chakalov
April 12, 2008
Last update: September 25, 2008
"... if one chooses a
one-parameter family of observables such that their value coincides
with the value of a dynamical variable when the parameter takes
the value of another dynamical variable, which one uses to characterize
the evolution, such observables can be used in the Page-Wootters
construction. They have the advantage that there is a sense in which
they “evolve”. That is, unlike the proposal of Rovelli, we will not
consider the “parameter” to be the physical time, but we will use it to
make sense of the conditional probabilities that arise in the
Page-Wootters formulation when one introduces a real quantum clock.
...
"The resulting theory also predicts a fundamental mechanism of
decoherence similarly as the one originally discussed in [6]."
==================
Subject: Re: arXiv:0805.3178v1
[quant-ph]
Date: Thu, 22 May 2008 15:47:42 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: John Gamble <jgamble08@wooster.edu>
P.S. I am puzzled by the footnote 2 on p. 92: does this "e-folding
time" pertain to "zeroing the off-diagonal elements" ONLY? I mean, is
the duration of the paths in Wilson cloud chamber (as read by my wristwatch) composed of some
decorered instants of 10^-19 s (ibid., footnote 3)? Sir Nevill Mott
knew nothing about "decoherence", so I hope you can help me understand
your ideas.
D.C.
On Thu, May 22, 2008 at 3:26 PM, Dimi Chakalov
<dchakalov@gmail.com> wrote:
>
> Dear Dr. Gamble,
>
> I wonder if you could help me understand the generation of
observable
> paths in Wilson cloud chambers (cf. Nevill Mott) with
"decoherence".
>
> Kindest regards,
>
> Dimi Chakalov
---------------
Subject: Re: arXiv:0805.3178v1 [quant-ph]
Date: Sat, 24 May 2008 04:13:58 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: John Gamble <jgamble08@wooster.edu>
Dear John,
Thank you for your efforts.
> Decoherence deals with the reduction of a quantum measurement to
> a classical measurement, not the reduction of a probability
distribution
> to a single value (in Mott's case a single track). In that sense,
> decoherence explains the emergence of definite paths, but does not
> explain the selection of one from the ensemble of possible paths.
Are you saying that "decoherence" can explain the emergence of
definite path(s) ONLY "during" 10^-19 s, as in the case in footnote 3?
> With regard to the footnote, remember that the state operator is
is a
> representation of all possible superposition and product states of
a
> given system. Due to the probability normalization condition
imposed
> on a system, the state operator must always have unit trace. In
Mott's
> case, each track corresponds to a diagonal element of the state
> operator of the particle, while the superpositions of multiple
tracks
> correspond to off-diagonal elements, which decoherence destroys.
Do you have "decoherence" in the case examined by Mott?
Thank you for your time.
Regards,
Dimi
----
Note: To quote from Simon
Saunders' web site
(emphasis added):
"When one introduces
hidden-variables or state reduction, certain kinds of physical
quantities (the “preferred” ones) get to be value-definite - among them
the observed quantities (quantities like position, which are
well-localized in space). Eschewing hidden-variables or
state-reduction, still we have to pick out preferred quantities. How?
And precisely which ones?
This is the preferred basis
problem. The tightrope that must be walked (if we are to make sense
of quantum mechanics without hidden-variables or state reduction) is to
show first, how certain sorts of quantities get to be preferred (the preferred basis problem),
and second, how particular values get to be
assigned to such quantities (...).
...
"But decoherence theory does not solve the preferred-basis problem on
its own. One question that remains is why, even given that
such-and-such a basis decoheres, should that be the basis that
we see?"
What entity chooses "the basis"
(if any) or, in Mott's case, the "decohered history space" (if any)?
D.C.
May 25, 2008
==================
Subject: Will scalable quantum computers ever be built? No. No way. Fuhgeddaboudit.
Date: Wed, 16 Apr 2008 16:47:59 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Eleanor G Rieffel <rieffel@fxpal.com>
Cc: Michael <nielsen@physics.uq.edu.au>, Scott
<aaronson@csail.mit.edu>,
Seth <slloyd@mit.edu>, Adrian <a.p.a.kent@damtp.cam.ac.uk>,
Peter <p.knight@imperial.ac.uk>, John
<preskill@theory.caltech.edu>,
Artur <artur.ekert@qubit.org>
Dear Dr. Rieffel,
Regarding Sec. 11.3 (What if quantum mechanics is not quite correct?)
from your arXiv:0804.2264v1
[quant-ph], as well as your report FXPAL-PR-06-396,
perhaps you may wish to see
Michael, Scott, Seth,
Adrian, and Peter
ignored my email (search my web site for
details), while John and Artur didn't even bother to respond. I
consider such behavior utterly unprofessional.
[snip]
Kindest regards,
Dimi Chakalov
----
Note: People from "quantum computing" community often
complain that reading this web site is difficult, and utterly refuse to
examine the arguments from Schrödinger here, and derive the classical limit of
QM from STR, as explained with a simple Gedankenexperiment here.
To explain their delusion, let's
take just one crucial notion, which they use to promote their efforts: "simultaneously".
Quantum Superposition;
if an event can be realized in two or more indistinguishable ways, the
state of the system is a superposition of each way simultaneously.
Entanglement: the
superposition principle applied to certain nonlocal correlations, if a
correlation can be realized in two or more indistinguishable ways, the
state of the system is a superposition of all such correlations simultaneously.
Karl Svozil raised the issue whether one could "either measure or
counterfactually infer all required entities simultaneously",
and stressed (quant-ph/0206076 v6,
p. 4):
This ambiguity gets worse as
the number of particles increases.
This "ambiguity" is from KS Theorem; see Fig. 1b online here.
Last words from Karl Svozil, replacing "ambiguity" with
"non-uniqueness":
We therefore conclude that it
is impossible to construct quantum states of four or more particles
with the uniqueness property for four or more directions. Likewise,
because of non-uniqueness, the observables involved in a
Kochen-Specker-type argument cannot be measured simultaneously.
I wonder if someone from "qubit" community can prove that the ambiguity
(non-uniqueness), demonstrated by Karl Svozil, is indeed irrelevant
to their efforts.
Look what happens with some
bright students. Indrani Chattopadhyay, from the Department of Applied
Mathematics at the University of Calcutta, has just completed his Ph.D.
Thesis (arXiv:0805.2056v1
[quant-ph]), but didn't mention anything about KS Theorem. It won't
be fair to blame him, because the professional academic researches, who
are supposed to teach their students, consistently ignore 'Quantum
Mechanics 101' above.
Just two examples: Prof. Martin Plenio and Prof. Scott
Cohen. The latter produced an essay entitled "Visualizing
Teleportation", with the ambition to make "teleportation
understandable to undergraduate physics majors (and possibly others)", arXiv:0704.0051v2
[physics.ed-ph], yet conspicuously ignored KS Theorem and its
implications. Even more alarming is his ad posted at his academic
web page: "As quantum information is a relatively new field, it
offers numerous opportunities for innovation, as well as many
fascinating problems for advanced undergraduates to sink their teeth
into. Interested students are encouraged to contact me about possible
research involvement."
And the kids will "sink their
teeth" into a dead end.
Can you outsmart Nature by
'sweeping the garbage under the rug' with those "qubits"? Or with some
"quantum Bayesian picture" [Ref. 1]? Choose anything
you want, then please write down your arguments for "qutrits" [Ref. 2], post them on ArXiv.org server, and I will
get professional -- with utmost pleasure.
D. Chakalov
April 17, 2008
Last update: September 2, 2008
----
pp. 8-9: "[The process of
collapse] is simply an updating of one’s beliefs about what the results
of future measurements on the system will be; an updating that occurs
whenever one has data to update upon.
...
"If Wigner strolls into the lab to see what the result is, then he will
update his beliefs and assign a product state; but there is no question
of his friend hanging in limbo until Wigner does so. There is no
relevant change in anything physical when he does so; the only changes
are internal to the agent ascribing the
state. Given this lack of conflict between state assignments, no
measurement problem arises."
[Ref. 2] Andreas Keil, Proof of the Orthogonal Measurement Conjecture
for Qubit States, arXiv:0809.0232v1 [quant-ph]
"Already for qutrits we are facing serious difficulties. Two qutrits
can in general not be transformed to real matrices with only one
unitary transformation. Restricting ourselves to real qutrit or qunit
matrices we can derive equations of similar type as equations (8).
Performing a similar expansions of the vectors in a basis as in (9)
does not give us, as in this paper, functions of one real variable but
gives rise to intersections of
transcendental curves in projective space, leading us into a vast,
unexplored territory."
==================
Subject: Absolute map of objective reality?
Date: Tue, 6 May 2008 16:36:07 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Angelo Loinger <angelo.loinger@mi.infn.it>
Cc: Silvia Penati <silvia.penati@mib.infn.it>
Dear Angelo,
I read with great interest your latest article [Ref. 1],
and would like to comment on it.
Consider the main building of the University of Milan, Via Giovanni
Celoria 16, where Dr. Silvia Penati currently teaches GR.
The building has some provisional, map-dependent coordinates, and
because it has a "real physical meaning", its properties
(Eigenschaften) are invariant under any transformation of general
coordinates [Ref. 1]: there are infinitely many
possible maps in which *the same
building* will be faithfully displayed as 'objective reality out
there'.
However, if the latter form of reality were the only possible in GR,
the building at Via Giovanni Celoria 16, as well as all objects
displayed on these infinitely many maps, would fix an *absolute map of objective reality*. Then all
geometrical points from this absolute map would acquire a *unique*
physical content as 'objective reality out there', such that all these
points would be identifiable by their unique physical content.
I wonder if this is your vision of GR, and would also be happy to learn
about your understanding of the implications from Einstein's Hole
Argument.
p. 11: "Finally, I wish to recall a significant remark by Hilbert [9]
on the physical meaning of any statement (Aussage) in general
relativity. He emphasized that in GR a given statement has a real
physical meaning only if it has an invariant character under any
whatever transformation of general coordinates. An analogous criterion
holds obviously for the properties (Eigenschaften)."
...
"A geometric comparison: in the differential geometry of curves and
surfaces a given statement, or a given property, have a real geometric
meaning *only if* they are independent of the choice of the coordinates.
...
D. Hilbert: "... so müssen wir auch in der Physik eine Aussage,
die nicht gegenüber jeder beliebigen Transformation des
Koordinatensystems
invariant bleibt, als *physikalisch sinnlos* bezeichnen."
---
Note: This story boils down to
the nature of the "remnant" from the two fluxes in Merced Montesinos'
article above. If the geometrical points from such
'absolute map of objective reality' were identifiable by their unique
physical content of 'objective reality out there', there would be a real
physical "remnant" from the two fluxes, and ultimately "the ether would
come back!" (M. Montesinos). There would be infinitely
many, and equally "genuine", maps/presentations of such ether
pertaining to some 'absolute map of objective reality'. Bad idea. If
this was the case chosen by Nature, the time parameter in each such map
could be regarded as a legitimate definition of time, contrary to what
we know about 'time in GR'.
Alternatively, if the
geometrical points from the spacetime/map are presented as 'the
quantum system' (potential reality), their fleeting 'observable
characteristics' will fill out the spacetime/map with point-like,
context-dependent (relational ontology!)
projections in the local mode of spacetime,
just like the observable characteristics of the three-color quantum
system above. Then the ether in Einstein's GR
will be residing in the global mode
of spacetime only. Stated differently, the ether/reference fluid of
GR should not show up in GR, but only in the full theory of quantum gravity.
It is highly unlikely that Prof. Angelo Loinger
would respond, but this is a different subject. Very briefly: there are
currently three opinions on the alleged GW astronomy: the official, and
hugely advertised, opinion of a large group of GR "experts" (I call
them Jehovah's Witnesses of GW
astronomy), then comes the opinion of Prof. A. Loinger [Ref. 1], and finally the opinion of the author of these
lines. The first opinion is 'GWs exist, therefore they can and
ultimately will be detected', the second one is 'GWs do not exist,
therefore they cannot be detected in principle', and the third opinion
is that GWs exist, but they can never be detected with LIGO, LISA, and
the like, because the GW detector should be able to "sense" the
quasi-localized GW energy, which in turn means that such GW detector
should operate also at the global mode of spacetime, much like
a human brain. Hence the catchword of the
third option (endorsed only by the author of these lines): le Roi
est mort, vive le Roi!
To sum up, let me again quote
David Hilert (Grundsätzliche Fragen der modernen Physik,
Lecture I, Hamburg, 26 July 1923): "A sentence about nature, expressed
in coordinates, is only then a proposition about the objects in nature,
if the sentence has a content which is independent of the coordinates."
("Ein in Koordinaten ausgedrüuckter Satz über die Natur ist
nur dann eine Aussage über die Gegenstände in der Natur wenn
er von den Koordinaten unabhängig einen Inhalt hat.")
We fully agree. But if we
confine ourselves only to the kind of reality from classical physics, 'objective reality out there', we
would be brought back to the problems encountered by Einstein from 1913 to 1915. Let's recall his firm
opinion that singularities must be excluded from GR (The
Meaning of Relativity, 5th ed.): "It does not seem reasonable to me
to introduce into a continuum theory points (or lines etc.) for which
the field equations do not hold."
"That looks as if general
relativity carries within its conceptual belly the seeds of its own
destruction", said Peter G. Bergmann (The 1979 Berlin Einstein
Symposium, Lecture Notes in Physics, Vol. 100, Springer-Verlag, New
York, 1979), after he tried just to elucidate the problem of finding a complete set of diffeomorphism-invariant
quantities (those that would have vanishing Poisson brackets with the
canonical constraints) in 1961 (Observables in general relativity, Rev.
Mod. Phys. 33 (1961) 510-514).
I mean, all problems of GR are
interconnected, so perhaps the time has come to move forward, with some help from Aristotle and Plato.
In 1952, Einstein added a fifth
appendix, "Relativity and the Problem of Space", to his famous book Relativity:
The Special and the General Theory (15 ed., Methuen, London, 1952,
p. 155), in which he wrote:
On the basis of the general
theory of relativity ... space as opposed to "what fills space" ... has
no separate existence. There is no such thing as an empty space, i.e.,
a space without [a gravitational] field. Space-time does not claim
existence on its own, but only as a structural quality of the field.
Given Einstein's
opinion on his GR and the opinions of Peter G. Bergmann (above) and
Arthur Komar, may I suggest a
correction to the text from Einstein above: there is indeed such thing
as "empty space" (called here 'global
mode of spacetime'), in which the 3-D space "moves into", hence producing an arrow of spacetime and holistic
("dark") effects in the local mode of
spacetime. These effects of "empty space" constitute up to 96 per cent
from the observable stuff in the universe.
To be precise, the scholastic
axiom by Michael Faraday, "matter cannot act where it is not", is not
applicable for the quantum and gravitational realms: in the first case,
matter (physical reality) should not be always present (cf. the
discussion of KS Theorem above), while in the
second case matter (physical reality) cannot be always present,
or else we face the paradox of having 96 per
cent of the universe in some "dark" form, and can never resolve the
problem of (teleological)
cosmological time (Rugh & Zinkernagel, arXiv:0805.1947v1 [gr-qc],
p. 40).
The only possible solution seems
to allow matter (physical reality) to be acted upon by something
ontologically different -- potential reality.
It stores the 'sameness' of objects (cf. Kurt Lewin's Genidentität
principle).
Note: Tatyana Shestakova's
"extended phase space" approach has been recently presented in arXiv:0810.4031v1
[gr-qc]. Notice the discussion of "properties of a medium to be
necessary to fix a reference frame" therein. I hope Tatyana Shestakova
has Internet access, and will read the proposal at this web site: the
"medium" playing the role of 'the reference
fluid' (cf. Einstein's "mollusc" and Hilbert's realistic fluid in kvk.pdf,
p. 32) was explained at the first link above, while the case of
'asymptotically flat spacetime' was examined here.
After studying Karel Kuchar [Ref. 1], perhaps the reader will also consider the
putative hidden background structure (global mode
of spacetime), "filling the space time with a fluid which plays the
role of real reference frame" [Ref. 2], to be the
most important unresolved issue in GR.
Why? Because there is nothing
in GR itself, from which one could derive the spacelike and
timelike "directions" (introduced by hand from the outset), just as
there is nothing in QM itself, which would allow you to derive
the "projection" conjecture. In the case of GR, all we can say is that
the physical world couldn't be what it is if spacetime were not 4-D.
Which explains nothing.
In both GR and QM, the most
fundamental action is introduced by hand. People like ADM,
who start with some already-selected Cauchy "surface", or postulate
some spacetime manifold (cf. Robert Geroch)
that would be equipped, at some later stage, with Lorentzian signature [Ref. 3], are already implying -- tacitly,
of course -- the action of the reference fluid in GR.
It goes without saying that the action
of the reference fluid in GR is inevitably "dark",
in the sense that it fixes the global properties of spacetime,
such as its time-orientability, asymptotic
boundaries, and quasi-local energy. Every
infinitesimal domain of spacetime encapsulates all the blueprints from
its global properties.
In my just-another-crank opinion, this is the
only possible way to go forward. In order to address the problems
of GR (Thomas Sotiriou et al., arXiv:0707.2748v2
[gr-qc], Sec. 3), we need to examine its underlying assumptions and
postulates.
But what do the academic
scholars say?
Robert
Geroch and Karel Kuchar haven't responded to my email sent in the
past five years. Two and a half years ago, on 30 March 2006, Stanley Deser
declared that he understands the dynamics of GR, but I still haven't
heard from him. If the brain of Stanley Deser is functioning, ADM viewpoint
on the dynamics of GR will be proven wrong, because only some fully
deterministic Turing machine (but not the human
brain) might operate on the "time surface" (cf. below) in the
"block world" of textbook's GR.
Six years ago, on 23
October 2002, another
prominent scholar, Chris Isham, declared that I "do not know enough theoretical physics to
help with any research in that area."
No efforts has been made on
behalf of Britain's leading expert in quantum gravity to defend his
statement with facts. Moreover, just one approach toward quantum
gravity, which is different from the one explored at this web site, and
also shows some prospects for eventual success, will immediately
ruin my theory.
There is no need to read this
web site to prove me wrong. Just show me anything that you
believe might work. Chris Isham has been keeping quiet for
six years now. I trust other physicists can do better.
Just a hint: have you noticed that the cosmological "presentation" of
expanding spacetime is based on a terribly misleading non-relativistic
picture, in which some meta-observer had taken an absolute snapshot
'now' (see below) of the dimensions of the spacetime "balloon"
at some instant from the cosmological time?
Can you correct the picture
above, by offering a relativistic presentation of the 3-D
snapshot and its instant 'now' from the cosmological time arrow,
as driven by DDE of empty space? Perhaps your
reasoning will be along the following lines: consider two observations
of the "diameter" of the expanding universe, made by one
observer at two instants A and B, separated by an interval [A, B] of,
say, 8 min. Think of it as expanding
"diameter" of the 3-D space of the universe. To grasp the intricacies
of such Gedankenexperiment, compare it to a simple textbook exercise
from STR [Ref. 4], bearing in mind that in GR you
don't have any background metric, nor the privileged, non-relativistic
viewpoint of 'an observer placed outside the expanding
balloon', as in the picture above.
Can you eliminate the tantalizing " ? " section from the "beginning" of the
cosmological time arrow (see also the vacuum
cleaner paradox)? According to some philosophers, such as Andrei Linde,
Notice that the estimate of "the
total duration of inflation" presupposes some absolute clock
pertaining to the whole universe en bloc, which could "count"
the elementary increments of 'the size of the balloon'
per some finite unit of absolute time (say, 'absolute
second'), so that A. Linde and his distinguished colleagues can measure
the number of such elementary increments per 'absolute second'
throughout the whole cosmological time, hence claim that, in the
initial 10-30 seconds, there were many-many-many-many more
elementary increments of the volume of 3-D space per 'absolute second'
-- as compared to the first 10-30 seconds from the time
interval needed to read these lines -- then after these 'initial 10-30
seconds' the "accelerated" expansion of space settled down for a while,
but it is currently again in some accelerated stage, only not so
vicious as it were in the initial 10-30 seconds. Surely A. Linde can decorate this story with
some advanced math, to make it publishable.
Also, have you noticed that
there is 'problem of time' in classical GR
and in canonical quantum gravity, but there isn't any problem of 3-D space?
How would you correct such anti-relativistic
presentation of 3-D space in today's GR? Contrary to what you've
learned from Hermann Minkowski, you apply double
standards to time and space: you kill the nature of time with some "block universe", but leave the 3-D space
intact, like an 'absolute structure' (James Anderson). Namely, there
is no absolute difference between past, present and future,
hence this key feature of 'absolute time' is eliminated, but the key
attributes of 'absolute space' -- inside vs. outside, Large vs. Small
-- are kept absolute, providing an absolute "medium" for 3-D
space in present-day GR. Contrary to the opinion of Karel Kuchar (see
below), it acts as a global fixed structure that is not dynamical.
Notice that the task for
correcting today's GR ("the grave
injustice to space-time covariance that underlies general relativity", A. Ashtekar)
is highly non-trivial, because such global properties of
spacetime cannot be downgraded to the usual Diff(M) observables (cf. Mihaela Iftime above); more here.
The solutions proposed at this
web site (for example, the scale relativity principle)
originate from a very old and simple idea: not everything
should exist as physical reality. As John Wheeler put it, "Time is
Nature's way to keep everything from happening all at once" (he didn't
provide any math though). In this sense, we need potential reality (I don't offer the math either).
To quote Karel Kuchar (emphasis and
links added), "the profound message of general relativity is that
spacetime does not have any fixed structure which is not dynamical but
governs dynamics from outside as an unmoved mover." (The mathematical
description of this well-known 'unmoved
mover' wasn't offered by Karel Kuchar either.)
NB:
But what is the meaning of the phrase "governs dynamics from outside" (global mode of spacetime)? A simple argument from
Wikipedia [Ref. 5] suggests that an inanimate
physical clock will record such "global time" as frozen (recall
Wheeler-DeWitt equation and Karel Kuchar's multifingered
time), simply because it cannot read such infinite-dimensional global time.
Hence the so-called problem of time in canonical quantum gravity is
nothing but an artefact from a very limited notion of time
produced by an inanimate physical clock. The human brain can "read"
such global mode of time (cf. L. Szabados and J. Baez "at the same time"here), and will produce the mental image (qualia)
of 'self-reference'. Then we put aside
all issues related to psychology and theology, and model the universe
as a brain equipped with 'potential reality' produced by the
arrow of spacetime. Just think of all EPR-like correlations across
the entire universe as being negotiated in the realm of 'potential
reality' -- "at the same time" of the global mode of time (compare with
[Ref. 5]).
All pieces of the jigsaw puzzle
of quantum gravity snap to their places -- effortlessly.
Regrettably, Karel Kuchar didn't make any comments on my
ideas offered to solve the problems identified by him in 1991: "The
problem of functional evolution, the multiple choice problem, and the
Hilbert space problem are the three major classes of problems which
quantum geometrodynamics encounters because classical geometrodynamics does not seem to possess a natural (Sic! -
D.C.) time variable, while standard quantum theory relies quite heavily
on a preferred time."
In my just-another-crank opinion, the only
"time variable" natural to both GR and QM is the one read by 'the universe as a brain'.
Hence the need for The Aristotelian
Connection, which acts as 'the unmoved mover' and 'reference fluid
in GR' (see above), is obvious. Ignore it at
your peril.
In practical terms, this lesson
from Aristotle, translated into the languages of GR
and QM, means that you've been wasting hundreds
of millions of U.S. dollars and Euro -- taxpayer's money -- for GW parapsychology.
Unless, of course, Chris Isham was right six years ago. I
don't know. He's still keeping quiet.
D. Chakalov
October 23, 2008
Last update: November 11, 2008
[Ref. 1] Sean Gryb, Quantum Machian Time in Newtonian Mechanics and
Beyond, arXiv:0810.4152v1
[gr-qc]
p. 21: "First, is there a way to introduce a background structure into
GR? This is not a new question and has been raised most notably by
Kuchar after noting the similarities between the ADM action and the
action of PPM [15, 14]. He conjectured that GR might have a hidden
background structure and that solving the problem of time would involve
finding a way to write the theory in terms of this background structure
and quantize it."
[Ref. 2] Simone Mercuri and Giovanni Montani, On the Frame Fixing in
Quantum Gravity, arXiv:gr-qc/0401127v1
"Now the following question arises: how is it possible to speak of a unit time-like normal field for a quantum
space-time?
"Indeed such a notion can be
recognized, in quantum regime, at most in the sense of
expectation values (recall KS Theorem above -
D.C.); therefore assuming the existence of nμ before quantizing
the system dynamics makes the WDW approach physically ill defined.
...
"A more physical manner to ensure the existence of a time-like vector
consists of filling the space time with a fluid which plays the role of
real reference frame."
Sec. 9.3, 'Musings on the Euclidean nature of nature'
"It is difficult to describe, in everyday language, the physics of
spacetime and phase space in Euclidean terms, because so much of our
thought and language include elements of time. For example, a careful
description of events in a Euclidean world must avoid the use of active
verbs!
...
"However, this leads us to the conclusion that the original world we
are measuring has signature zero or is Euclidean. In the Euclidean
case, we must ask what it means to make a measurement at all. Doesn’t
measurement presuppose a time sequence?
"We hasten to point out that the problem is no worse here than in any
deterministic theory. In general relativity, for example, we have an
initial value formulation, but can also find global solutions. In the
initial value formulation, we can specify the configuration of the
world at a given time, then integrate forward to predict how things
will evolve. However, in the case of a global solution such as a
cosmological model, we are presented a complete description of past,
present and future all at once. In this
view, the outcomes of measurements are already fixed. The best we can
do is to think of consciousness as sequentially illuminating certain
fixed events, then others, with all the events already right there in
the solution.
...
"The difficulty we experience at trying to state or digest these ideas
may be seen as an indication of just how much our understanding of the
world hinges on living in a metric phase space. Once we have that
arena, our physical description falls into place. In order to correctly
describe the world from a Euclidean, or even a fully biconformal,
perspective, we need to map backwards from known processes in metric
phase space to a descriptoin of the same processes in the underlying
Euclidean space."
[Ref. 4] Vesselin
Petkov, Can the Growing Block Model of the Universe Save the
Objectivity of Becoming?
"Take as an example length
contraction. Two observers A and B measure the length of a rod that is
at rest in A's reference frame. Due to relativity of simultaneity and
the fact that the rod, as an extended three-dimensional body, is
defined in terms of simultaneity (as all parts of the rod which exist
simultaneously at a given moment), it inescapably follows that having
different sets of simultaneous events A and B measure two different
three-dimensional rods. It is evident (if existence is absolute) that
three-dimensionalism is immediately ruled out -- the worldtube of the
rod must be a real four-dimensional object in a block universe in order
that two three-dimensional rods (that are different three-dimensional cross-sections
of the rod's worldtube) exist for A and B."
"Being three-dimensional, we are
only able to see the world with our eyes in two dimensions. A
four-dimensional being would be able to see the world in three
dimensions. For example, it would be able to see all six sides of an
opaque box simultaneously, and in fact, what is inside the box at
the same time. It would be able to see all points in 3-dimensional
space simultaneously, including the inner structure of solid
objects and things obscured from our three-dimensional viewpoint."
Note about "the 4th dimension w":
Make a fibre
bundle formulation of GR (cf. Robert
Geroch), such that it could provide simultaneous connections from
such 4-D "global mode", to account for the atemporal "hand-shaking"
needed to fix the event horizon and inertial forces. Make sure, however, that (in the
local mode of spacetime) the dimensions of physical bodies along such
"4th dimension w" are non-existent
or zero (the
"dark gaps"). Then try to introduce a brand
new connection to the base manifold:
instead of attaching a vector space at each point (cf. Matt Frank), try a brand new spinor space, such that
two opposite, tug-of-war effects of gravity, CDM and DDE, will be cast on the base manifold.
Of course all this sounds like
a Jabberwocky. We need new math.
D.C.
November 1, 2008
Last update: November 3, 2008
===================
Subject: Eschatology from a Cosmic Perspective
Date: Tue, 11 Nov 2008 15:03:44 +0000
From: Dimi Chakalov <dchakalov@gmail.com>
To: George F R Ellis <george.ellis@uct.ac.za>
The last time I heard from you was eight years ago (you kindly
responded to my request and e-mailed me a manuscript on the same
subject). At that time, I was living in Vienna, and since you were
planning to visit ESI (The Erwin Schrödinger International
Institute for Mathematical Physics, Vienna), I respectfully asked you
to contact me by phone or email, hoping to meet you in person. Never
heard from you.
In case you plan to update your book, may I suggest to check out the NB section at
Please don't treat me as a dead man,
and respond to this email. I hope to hear from you by your 70th
birthday on August 11, 2009.
Regards,
Dimi
----
Dimi Chakalov
35 Sutherland St
London SW1V 4JU
-------
Note: George F R Ellis submitted
yesterday (1 Dec 2008) an outlook of his idea about "an evolving block
universe", but didn't even mention the driving force of 'the
flow of time' [Ref. 1], which is known as
'dynamic dark energy' (DDE).
The fact that the readers have
indeed the ability to read his latest philosophical essay [Ref. 1] does not constitute even an evidence
in support of his "evolving block universe", because the undisputed
observational fact -- "a unique classical space-time structure does
indeed emerge at macro scales from the underlying physics" -- hasn't
been explained. Which is one of the reasons why I sent him the link to
my philosophical essay 'Quantum Mechanics 101' above.
The challenges are widely know since 1935, when
George F R Ellis was ... -4 year old, right?
Well, if you read George F R
Ellis [Ref. 1], that's a tricky question,
because in the framework of "evolving block universe" it is not clear
whether his "negative age 4" was indeed fixed in 1935, or at the
instant of his birth on August 11, 1939. To address this question, he
will have to laid out his opinion on Cosmological
Synchronicity and the temporal organization
of 'potential reality', which would require reading the essay above, and responding to my last
email.
Here are the main questions
which remained untouched in [Ref. 1]:
Q1: Does Nature employ
some irreversible act to fix "unique classical space-time structure"
which emerges at macro scales? Read about the reversible
classical-to-quantum transition above.
Q2: Was the birth of
little George fixed in 1935, four years prior to his actual birth on
August 11, 1939? Or was it just an undecidable propensity with an
answer YAIN? If the latter, was the feedback
from potential future (cf. the arrow of spacetime)
influencing the worldlines of George's parents in 1935? For if we wish
to talk about 'the flow of time', the past should not be
sufficient to fix the present (cf. Conway-Kochen Theorem above), and we have to consider the possibility
that the Aristotelian 'final cause' may complement the
relativistic causality, as stated above.
Q3: Does Nature employ the verdammte
Quantenspringerei ? Eight years ago, while I was living in Vienna
(cf. above), I suggested a tentative answer to
this truly fundamental question, and respectfully asked George F R Ellis to contact me by phone or
email, hoping to meet him during his stay in Vienna. Never heard from
him.
The fact of the matter is in the
past, namely, George F R Ellis managed to meet the deadline (2008-12-01)
for submitting his essay to FQXi Contest "THE NATURE OF
TIME". I didn't. Nobody told me about it. Hence I missed the chance
to become rich and famous -- up to 21 prizes will be awarded, with
amounts ranging from $1000 to $10,000 per prize.
It remains to be seen what
event, still in the future, "was" influencing me to write these lines
today, 2 December 2008. Or maybe I am creating such event right now.
You just never know. The future could be open up to 'the unknown
unknown', and brand new things may emerge,
breaking the dull unitarity principle.
- In the real universe domain
we actually inhabit, a unique classical space-time structure does
indeed emerge at macro scales from the underlying physics
"Hence whatever integrability
conditions are needed for this to happen, they do indeed occur in our
universe domain, and we are able to describe what happens via an
evolving block universe picture.
...
"You would not exist and have the ability to read this article if the
view proposed here (and expounded in more detail in Ref. [6]) was not a
correct description of the way things are."
--
[6] G F R Ellis (2006): “Physics in the Real Universe: Time and
Spacetime”. Gen. Rel. Grav. 38: 1797-1824 [Arxiv:gr-qc/0605049].
Cape Town
2008-12-01
===================
Subject: Feedback to FQXi Essay
Contest
Date: Sun, 14 Dec 2008 00:28:48 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: George F R Ellis <george.ellis@uct.ac.za>,
Julian Barbour <julian@platonia.com>,
Sean Carroll <seancarroll@gmail.com>,
Carlo Rovelli <rovelli@cpt.univ-mrs.fr>,
Claus Kiefer <kiefer@thp.uni-koeln.de>,
Fotini Markopoulou <fmarkopoulou@perimeterinstitute.ca>,
Adam Helfer <adam@math.missouri.edu>,
Gavin Crooks <gecrooks@lbl.gov>
Cc: Anthony Aguirre <aguirre@scipp.ucsc.edu>, Kavita Rajanna
<mail@fqxi.org>,
Chris Isham <c.isham@imperial.ac.uk>
Dear colleagues,
I didn't learn about the FQXi Essay Contest until December 2nd. My
feedback to
1. George Ellis
2. Julian Barbour
3. Chi Ming Hung
4. Sean Carroll
5. Carlo Rovelli
6. Claus Kiefer
7. Fotini Markopoulou
8. Adam Helfer
9. Gavin Crooks
10. Dean Rickles
As Chris Isham declared six years ago (Wed, 23 Oct 2002 19:24:15 +0100):
"You do not know enough theoretical physics to help with any research
in that area."
Wishing you a very merry Christmas,
Dimi
----
Dimi Chakalov
35 Sutherland St
London SW1V 4JU
Notice that the quasi-local
component from The Aristotelian Connection (the 'sufficient condition' from the global
mode of spacetime) is interwoven into the local mode of time dynamically,
as being linearized and "read by a wristwatch" (cf. my posting to David
Wiltshire below), so in my proposal the "block universe" (BU) and
"evolving block universe" (EBU) are united by the two mode of
spacetime. I believe BU and EBU contain some, and of course different,
pieces of truth, and therefore should be united. The end result will be
something quite different from the textbook GR, because, as David
Wiltshire noticed below, the idea of introducing quasi-local variables
"is not something that is being done on top of general relativity."
"Dimi - should you read my work and have any further questions - then
since George has closed his discussion, I guess you should continue
over at my not-so-active thread."
Thanks a lot for your suggestion. I downloaded your essay and tried to
read it, but was struck by a very unclear -- to me -- introduction, and
couldn't proceed.
I am asking you to help me understand the following.
In your essay, you wrote: "A simple way to understand this (quasilocal
quantities - D.C.) is to recall that in the absence of gravity energy,
momentum and angular momentum of objects obey conservation laws. A
conservation law simply means that some quantity is not changing with
time."
Let's find out what kind of 'time' is involved in GR. George Ellis did
not answer any of my arguments posted at his thread. Hope
you can do better.
Please correct me if I'm wrong: The time read by a wristwatch is
assumed to be a linear variable, and it is this linear variable that
enters the conservation laws in the absence of gravity (Minkowski
spacetime).
Q1: What -- if any -- should be the change or alteration to this linear
variable, as introduced by quasi-local variables?
Further, you wrote: "General relativity is entirely local in the sense
of propagation of the gravitational interaction, which is causal."
Q2: What -- if any -- should be the change or alteration to the
propagation of the gravitational interaction, as introduced by
quasi-local variables?
For if you mix apples (local theories) with oranges (quasi-local
variables in these same theories), the confusion may be enormous, which
is perhaps the reason why I couldn't finish reading your essay. Hope
you can help.
My tentative answers to the questions posed above were provided in a
link to my web site, in my first posting to George Ellis from Dec.
2, 2008 @ 07:02 GMT. Regrettably, your mentor neither replied to my
critical comments on his proposal, nor said anything on mine.
>Please correct me if I'm wrong: The time read by a wristwatch is
assumed to be a linear variable, and it is this linear variable that
enters the conservation laws in the absence of gravity (Minkowski
spacetime).
Individual variables themselves are neither linear nor nonlinear. So
time is not "linear" (apart from being a parameter on the real line
which is not what I mean here). Linearity is a property of combinations
of variables in equations. In Minkowski space it is the Lorentz
transformations which relate inertial frames that are linear.
Conservation laws are described by divergence-free currents, which via
Gauss's law give conserved charges when doing the relevant integrals on
hypersurfaces. The time-direction is hypersurface orthogonal in
formulating such conservation laws.
BTW In relativity one also has to be always careful to distinguish
between arbitrary coordinate variables, and proper lengths and proper
times which are invariants. Your watch measures your proper time. If
you are talking about your proper time, say it; "variable" is too vague
as it can also refer to non-measurable things.
>Q1: What -- if any -- should be the change or alteration to this
linear variable, as introduced by quasi-local variables?
Since any "quasilocal" quantity is an integrated regional thing, not a
local quantity like a proper time measured by a clock, in any
formulation one will never replace any proper time by a
quasilocal variable. It is gravitational energy that is quasilocal not
time; proper time is a locally measured quantity on the worldline of a
particle, gravitational energy is not. Gravitational energy
comes into the relative calibration of clocks at widely separated
events.
Why is energy conservation difficult in GR? Well, in the absence of
exact symmetries one cannot do the same procedure of a Gauss law style
integration to extract a conserved 4-momentum and conserved covariant
angular-momentum from the divergence-free energy-momentum tensor as you
can in Minkowksi space. In general relativity one can in general define
conservation laws for completely antisymmetry tensor densities.
However, one cannot do this for the rank 2 symmetric energy-momentum
tensor. If you try to integrate it, in the manner of Gauss's law there
is an extra bit involving the
connection which is in a sense "the work done by gravity".
In the presence of exact
symmetries of the background spacetime, described by a Killing vector,
it is possible to contract the Killing vector with the energy-momentum
tensor to get rid of the extra bit and get conservation laws.
Just symmetries of the background are required, and to get a conserved
energy you need a timelike symmetry of the background. What I am
talking about here is the "energy of the spacetime" but the same is
true for geodesic motion; if you have a timelike Killing vector you can
contract it with a particle 4-velocity to get a conserved energy of the
particle in motion. Without a timelike Killing
vector you cannot do that.
Timelike symmetries describe bound solutions extremely well, but since
the universe is expanding there is no absolute time symmetry, and so
the time symmetry is approximate. Since the timelike Killing vector is
normalised to unity at "spatial infinity", defining the equivalent of
the zero of the Newtonian gravitational potential; in the actual
universe this non-existent spatial infinity has to be replaced by
something like "finite infinity", as first discussed by George
Ellis in the 1984.
Since spacetime is intrinsically dynamical in GR, the "work done by
gravity" enters into energy-momentum conservation in an inextricable
way in general, when there are no time symmetries.
>Q2: What -- if any -- should be the change or alteration to the
propagation of the gravitational interaction, as introduced by
quasi-local variables?
Nothing changes because the idea of "introducing quasilocal variables"
is not something that is being done on top of general
relativity. We are simply discussing known properties of
Einstein's theory. It is a property of his theory that propagation of
the gravitational interaction is causal. It is also a property of his
theory that "the work done by gravity" cannot be separated out
in general, making energy conservation an intrinsically different
problem from the same problem in flat spacetime. This is a consequence
of the equivalence principle; you can always get rid of gravity near a point, and gravity is a property
of spacetime structure. Gravitational energy involves the calibration
of clocks at different points (via the connection), and can only
be regionally refined; so it is at best quasi-local.
Thank you for your professional reply. I believe we have at least one
thing in common: we both want to develop and modify George Ellis'
notion of 'finite infinity', but from entirely different perspectives
(I will be happy to explain mine, if you're interested).
You wrote above: "Your watch measures your proper time. If you are
talking about your proper time, say it."
Yes, I am talking about the proper time in STR, as read by my
wristwatch. Glad you agreed that it is a local quantity.
But in GR we have a formidable conundrum: the metric has a "double
role" (Laszlo Szabados, private communication), namely, it is a field
variable and defines the geometry *at the same time.*
It seems to me -- please correct me if I'm wrong -- that the metric in
GR is treated as a field which not only affects, but also -- at the
same time -- is affected by the other fields.
If you agree, would you please elaborate on the dynamics of GR, as
encoded in the phrase "at the same time"?
In STR, the proper time read by my wristwatch is a local quantity, so
it seems impossible to borrow this kind of time for the dynamics of GR.
The latter does include the extra "work done by gravity" (which is is
absent in STR).
As you put it, energy conservation is "an intrinsically different
problem from the same problem in flat spacetime."
What kind of "time" might be implied in GR, if every instant from it (a
"point" in Euclidean 1-D space) is a nexus of an *already* completed --
at this same instant -- negotiation between the two sides of
Einstein field equation?
I'll come back to you, after Christmas, about your efforts to tweak
George Ellis' finite infinity (FI), as
presented in New Journal of Physics 9 (2007) 377, and will ask
you to test your vision of FI by recasting the positive mass theorems.
If you succeed in replacing the conformal infinity with FI, please try
to eliminate the geodesic incompleteness and the Cauchy problems for
Einstein field equations, as the ultimate 'test of the pudding' for
your vision of FI and the dynamics of GR.
"Since any "quasilocal" quantity is an integrated regional thing, not a
local quantity like a proper time measured by a clock, in any
formulation one will never replace any proper time by a quasilocal
variable. It is gravitational energy that is quasilocal not time;
proper time is a locally measured quantity on the worldline of a
particle, gravitational energy is not."
I am indeed trying to suggest that the proper time, as measured by a
clock, can be replaced by a new quasi-local variable: please see my
postings from Dec. 4, 2008 @ 01:30 GMT and Dec. 10, 2008 @ 14:31 GMT at
Dean Rickles' thread.
The aim is to bridge GR and QM with a new form of retarded causality,
and to open a "window" in GR for the energy density of the so-called empty
space. My opinion on GR matches that of Einstein: "... not anything
more than a theory of the gravitational field, which was somewhat
artificially isolated from a total field of as yet unknown structure."
Since you agree that the geometry both affects and is affected by the
other fields, please notice that I am trying to suggest, with the
so-called Buridan donkey paradox, two kinds of time: "global" time for
the negotiations of all particles, and "local" time for the end-result
of this negotiation. Then the proper time on a particle clock, as a
measurable quantity *at a point on a timelike worldline*, is being
created (i) dynamically, and (ii) relationally (Machian type relational
ontology), and corresponds to its "local" time. The "global" time is
something that belongs to 'the whole universe en bloc'. To define the
latter, I am trying to modify George Ellis' Finite Infinity with some
well-known ideas from Aristotle.
All this comes from the solution of the measurement problem, which was
suggested at the link from my first posting to George Ellis' thread
(Dec. 2, 2008 @ 07:02 GMT).
In my opinion, ADM hypothesis is seriously flawed (I've elaborated
extensively on my web site, with many references).
I don't like *any* coarse-graining whatsoever, since I can't see how
one could approach the Hilbert space problem in quantum gravity. Will
be happy to elaborate, by quoting from Claus Kiefer's research and of
course Karel Kuchar's articles.
You wrote: "I would not attempt anything like a positive mass theorem
based on finite infinity, until I had a better grasp of these sorts of
issues."
To me the main puzzle is that we see only one "charge", called
'positive mass'. The positive mass theorems need a precise cut-off at
spatial infinity, which is the crux of my efforts to modify FI with
some help from Aristotle (cf. my two postings mentioned on Dec. 25,
2008 @ 03:41 GMT).
You say: "I think it is likely that there is no vacuum energy." I
suggest the answer YAIN (both yes and no, in German). It's a whole new
ball game, as I tried to explain here.
Sorry about my stupid remark about "white Christmas".
I agree with the first paragraph from Larry's comment above (Dec. 25,
2008 @ 14:14 GMT). In addition to Hawking's statement that "the split
into three spatial dimensions and one time dimension seems to be
contrary to the whole spirit of relativity", there is a very
interesting, in my opinion, paper by Kiriushcheva and Kuzmin,
arXiv:0809.0097v1 [gr-qc], pp. 7-9, which brings
specific arguments against such "slicing" of spacetime.
My personal (and certainly biased, if not wrong) attitude toward
'spacetime' is that it is *one* object which might be "disentangled"
into '3-D space and its time' for illustrative purposes only, while its
genuine dynamics -- if any -- is not traceable to anything in this
*one* object: we have only constraints, and also the dubious "freedom"
to choose the lapse and the shift by hand, since the latter are gauge
functions (M. Alcubierre, gr-qc/0412019v1, Sec. 5).
In a way, ADM hypothesis is like showing the moving parts of a piano,
but we can't "see" the player. But this is as it should be, since if we
were able to "see" the player with the present-day GR (say, the source
of the so-called dynamic dark energy), the latter must be some bona
fide 'observable in GR', and we would be able to trace back The Beginning or the Aristotelian Unmoved Mover,
whichever comes first :-)
In
connection with the last paragraph from Larry's posting (Dec. 26, 2008
@ 14:01 GMT), it seems to me that the problem of time in canonical
quantum gravity should be solved along with the Hilbert space problem
en bloc, since the latter is 'the test of the pudding' for the former.
More in my latest posting at Claus Kiefer's thread
from Dec. 26, 2008 @ 17:01 GMT.
David: Please excuse my violent curiosity. If you prefer, I will quit.
"The issue of time is a bit slippery. I am not out to deny the
existence of time, but it is something which appears to be geometrical
and as such "relational." It relates kinematic entities to dynamical
ones. As I see it the important question is not whether time exists,
but as a relational quantity "what does it tell us?""
I believe the so-called Buridan donkey paradox
mentioned above (Dec. 25, 2008 @ 11:29 GMT and Dec. 25, 2008 @ 03:41
GMT) offers a tentative answer to your very important question: time as
a geometrical entity "tells us" that the world is fundamentally
relational (relational ontology), in line with the Bootstrap Principle
of Geoffrey Chew (Science 161 (1968) 762).
And here at David Wiltshire's thread, you wrote (Dec. 26, 2008 @ 14:01
GMT): "There are two notions of time at work here. General relativity
only defines a physical time according to the invariant interval or
proper time of a particle. Coordinate time as an element of spacetime
is a gauge dependent (a gauge theory for an external symmetry)
quantity, which ultimately has nothing to do with any evolution. Hence
the nature of block time."
It seems to me that the "block time" and "block universe" (BU) are
artifacts from the current incomplete GR. I've been trying to suggest,
in my two postings mentioned above, the notion of 'quasi-local time'
with two components, "global" and "local". The latter corresponds to
'physical time in GR', each event from which is *already negotiated* in
the "global" component of time. Just try to think of this 'already
negotiated' as the "duration" of the flight of a photon, from its
emission to its absorption: it is zero. It's like clapping your hands
by which you produce one event of joint emission/absorption.
Hence the "dark gaps" of negotiation in the "global" component of time
are completely and totally extinguished in the 'physical time in GR'
(the "local" component of time), rendering the latter a *perfect
continuum* that is being created dynamically and relationally. Hence we
may have the "quantization" of spacetime installed from the outset.
I regret that learned about this FQXi Contest too late, on December
2nd, and haven't submitted my essay here. I can only hope that my ideas
might be of some interest to David and to you.
Thank you for your precise and thoughtful reply from Dec. 27, 2008 @
08:35 GMT. In the last paragraph, regarding positive mass theorems, you
wrote: "It would require a very tight definition of finite infinity
first, however."
You hit the nail on the head. If we employ the Aristotelian First Cause
and Unmover Mover, we may have a precise "boundary" in the so-called
"global" component of time, while in the "local" time this same
"boundary" would look like an ever-sliding horizon extendable to
infinity. The underlying motivation here is that we shall sort out the
ambiguities with our notion of '3-D space', and then approach the
nature of time, pertaining to this 3-D space.
You said: "Something cannot be both local and quasilocal." I believe it
depends on how you understand Quantum Theory (please check out my essay on QM). Which brings me to your comment that
I talk about "negotiation" in the global component of time, without
defining what "negotiation" is. EPR correlations are just one example
of "negotiation", but the really difficult task, to me at least, is to
*derive* the Equivalence Principle -- the focus of your essay -- from
some broader perspective based on Machian-type relational ontology (cf.
the Buridan donkey paradox). At the end of the day, we should be able
to understand the origin of the positive mass, and the
mechanism by which inertial reaction forces are being generated
"instantaneously" (in the "global" component of time, perhaps).
As of today, the Equivalence Principle gives us the dubious "freedom"
to eliminate the energy-components of the gravitational field *at a
point* (Hermann Weyl, Space-Time-Matter, Dover Publications, New York,
1951, 1922, p. 270). I cannot accept this, and neither did Einstein
(quote from Dec. 25, 2008 @ 03:41 GMT above).
You are right that I should produce a "focused paper on just one
topic". I will do that by the end of 2009, and will comment on your
Essay extensively.
Thank you, once more, for inviting me to your thread.
"Of course the question of initial conditions is vitally important on
cosmological scales. Dimi, when you talk about "the Aristotelian First
Cause and Unmover" then no doubt you are talking conceptually in such
terms, though to me me such phrases do not mean anything until you can
write down a physical model which somehow quantitatively matches
reality."
The challenge I face with the Aristotelian First Cause and Unmoved
Mover is first and foremost mathematical: it is not clear to me what
particular blueprint from these notions should be sought in quantum
gravity, yet I think it should be presented with pure math only, or
else the First Cause and Unmoved Mover will be *physically* reachable.
I will be very difficult to provide compelling evidence that the whole
physical world may be grounded on some Aristotelian "cutoff" that is
nothing but 'pure math'. Not to mention the UNspeakable 'cat per se'
(cf. my essay on QM mentioned above), which is
also unclear in mathematical terms. But if some day I make progress,
will get in touch with you.
I left three comments at George Ellis' thread on Dec. 31, 2008 @ 14:32
GMT. Please notice Comment #1, regarding the
missing definition of the non-tensorial gravitational energy in a
"fraction DT of time", as George put it.
Reading your Essay is a joy. You have this utterly professional skill
to elaborate on the most intricate issues in GR -- the obvious, and
deeply puzzling, fact that we observe mass with one "charge" only.
May I ask a question. You wrote: "Instead, only massless particles make
sense, and thus the concept of non-singularity must be expressed from
the ‘point of view’ of massless particles."
I wonder how you would explain the absence of Closed Timelike Curves
(CTCs) from the ‘point of view’ of massless particles. CTCs are exactly
what we should expect from GR (cf. W.B. Bonnor, Closed timelike curves
in general relativity, Int. J. Mod. Phys. D12 (2003) 1705-1708;
gr-qc/0211051 v1). It seems to me that CTCs (and timelike naked
singularities, cf. R. Goswami et al., gr-qc/0410041v1) are just like
the ultraviolet catastrophe from 1905, which too has never happened.
It seems to me that, in order to talk about 'the flow of time', the
past should not be sufficient to determine the present (cf.
Conway-Kochen 'Strong Free Will Theorem', arXiv:0807.3286v1
[quant-ph]), and we have to consider the possibility that the
Aristotelian 'final cause' may complement the relativistic causality,
as elaborated here.
A penny for your thoughts!
------
Dimi Chakalov wrote on Dec. 10,
2008 @ 20:36 GMT
Dear George,
In response to my first posting from Dec. 2, 2008 @ 07:02 GMT above, on
Dec. 3, 2008 @ 16:47
GMT, you wrote:
"... the outcome of quantum events is unknown until they happen. That
is a key feature on which I build my proposal; so there is no conflict."
I'm glad to notice that you can surf the Web, so please check out the
link to my essay 'Quantum Mechanics 101', in my
first posting above. The crucial issue is *not* that the outcome of
quantum events is "unknown until they happen".
We aren't talking epistemology here. The puzzle is know since 1935. To
quote from Erwin Schrödinger's "Die gegenwärtige Situation in
der Quantenmechanik":
"... measuring it does not mean ascertaining the value that it (the
quantum system - D.C.) has."
As to whether there is conflict in your reasoning, I think it is too
early to say anything conclusive. You haven't yet elaborated on the
so-called Dynamic Dark Energy -- the driving
force of 'the flow of time'.
I wish you best of luck in placing this perfectly
smooth "dark stuff" on some Cauchy surface.
Dimi
------
Dimi Chakalov wrote on Dec. 11,
2008 @ 23:31 GMT
Dear George,
Regarding the so-called dark energy, you wrote (Dec. 10, 2008 @ 21:41
GMT):
"I do indeed have views on that issue, but see no reason to post them
here."
Please do not impoverish your readers, and shed some light on all that
"dark" stuff, Cold Dark Matter included.
Thank you very much in advance.
As ever yours,
Dimi
------
Dimi Chakalov wrote on Dec. 12,
2008 @ 19:56 GMT
George Ellis wrote on Dec. 12, 2008 @ 17:31 GMT:
"The current topic is The Nature of Time."
Exactly. Such as its origin and driving force, as in the case of the
cosmological time arrow.
Which brings us to the "dynamic dark energy" and -- inevitably -- to
the "non-tangible" (Sir Hermann Bondi) gravitational energy, without
which we cannot say anything on its "dark" counterpart, in both DDE and
CDM.
But if you've found a way to disentangle time from energy, then I would
agree with you.
I stated above (Dec. 15, 2008 @ 18:44 GMT) that the objectives of your
essay are not clear, and expressed my hope that you can do better than
Carlo Rovelli.
Let me try to explain, by quoting from your postings and inserting my
comments.
1. George Ellis (Dec. 11, 2008 @ 12:05 GMT):
"On this view, infinities are mathematical entities that never occur in
physical reality; this may be taken as applying to the nature of space
in a profound way."
2. George Ellis (Dec. 9, 2008 @ 22:41 GMT)
"The whole point of my article is that there do not exist any
completely isolated systems in the real world (except perhaps the
universe itself)."
-----------
Comment #1: You quoted David Hilbert in [1] above, so please show that
infinities do not, and cannot occur in describing 'the only truly
isolated system' -- the universe itself. It is ONE single system, and
it should require "infinities" for its description.
----------
3. George Ellis (Dec. 4, 2008 @ 10:00 GMT):
"So a key element is how proper time relates to coordinate time as we
move to the future, ... "
4. On Carlo Rovelli's thread,
http://fqxi.org/community/forum/topic/237
George Ellis wrote (Dec. 12, 2008 @ 20:27 GMT):
"But proper time along world lines is indeed a preferred time variable
in GR."
5. On Carlo Rovelli's thread,
http://fqxi.org/community/forum/topic/237
George Ellis wrote (Dec. 15, 2008 @ 05:16 GMT)
"Objectively privileged hypersurfaces do indeed exist in standard
cosmology, and in all physically realistic solutions."
6. George Ellis (Dec. 12, 2008 @ 06:18 GMT):
"Perhaps this is because all these equations are effective equations
deriving from a single deeper unified theory, and it is this common
origin that leads to the different times being being consistent. How
this could all arise from a unified theory of quantum gravity and
fundamental interactions is then what needs clarity."
7. George Ellis (Dec. 4, 2008 @ 05:21 GMT)
"You can't talk about time at all without using the concept of time. My
paper is based on how standard quantum theory in fact implies
the flow of time in an irreversible way. This is one of the best tested
theories in physics."
---------
Comment #2.1: If you wish to talk quantum cosmology, by applying
quantum theory to 'the universe itself' (cf. your note [2] above), then
I might agree with your conjecture in note [6]. But you will need some
brand new quantum theory, not the textbook one, mentioned in [7].
Comment #2.2: If you do not wish to talk quantum cosmology, the task of
your whole essay is ultimately focused on your note [3], "how proper
time relates to coordinate time as we move to the future", given some
"preferred time variable in GR" (note [4]) on some "objectively
privileged hypersurfaces" (note [5]).
---------
8. On Carlo Rovelli's thread,
http://fqxi.org/community/forum/topic/237
George Ellis wrote (Dec. 16, 2008 @ 12:01 GMT)
"... enabling the physical states of our neurons to succeed each other
in timelike succession in a suitable causally patterned way, there is
no way that consciousness can progress from one state to another."
---------
Comment #3:
The Appropriate Content Guidelines for this Forum include "Posts may
not contain language or content that is: [...] Excessively outside of
the scope of the current topic [...]". The current topic is The Nature
of Time, not consciousness.
----------
I wish you best of luck with clarifying the objectives of your essay.
If you wish to suggest, after Bill Unruh,
that there should exist some "explicit (but unmeasureable) time",
please be more specific in its derivation, and then try to imagine how
your ideas might help in understanding the gravitational energy -- the
proof of the pudding, you know.
"... why does the arrow of time of quantum theory (related to collapse
of the wave function, see for example The Emperor’s New Mind) coincide
with the cosmological one (determined by large scale statistical
considerations of a classical kind)? I have no answer but it is
an important question."
Perhaps because there is no such thing as "arrow of time of quantum
theory" in the first place: please check out an essay 'Quantum
Mechanics 101'. The link was also provided in the first posting to your
thread, from Dec. 2, 2008 @ 07:02 GMT.
I am respectfully awaiting for your professional reply.
Regarding your EBU hypothesis, please also read my specific critical
comments from Dec. 16, 2008 @ 14:43 GMT above.
Looking forward to hearing from you,
Dimi
---------
Dimi Chakalov
wrote on Dec. 19, 2008 @ 10:33 GMT
Dear
George,
You wrote (Dec. 15, 2008 @ 15:22 GMT):
"The current topic is The Nature of Time. I am not interested in a
debate on the nature of gravitational energy. Please save us both a lot
of bother by desisting this series of postings."
Since you haven't so far found some spare time to answer any of my
postings at your thread, may I explain the reason why I respectfully
invite you to discuss the nature of gravitational energy as 'the proof
of the pudding' for your EBU hypothesis (as well as BU hypothesis in C.
Rovelli's "forget time" proposal).
It is well known from GR textbooks (cf. MTW, p. 467) that there are
inherent difficulties in defining energy in GR, due to its so-called
non-localizability (cf. L.
Szabados). Once we introduce Lorentzian metric, we're incapable of
capturing the *quasi-local* nature of energy in GR from the outset.
There is nothing quasi-local in splitting the spacetime, as in ADM
hypothesis, either.
The proponents of BU (Rovelli, Barbour, etc.) can 'sweep the garbage
under the rug', because the frozen "block" of spacetime cannot
encapsulate any quasi-local object, in neither time nor space. This is
a kind of Stalinist approach -- kill the time, kill the problem.
But since you claim that can do better, by proposing an Evolving Block
Universe (EBU), I will greatly appreciate your professional explanation
of how you tackle the problem of quasi-local -- in time -- energy in GR.
To be specific: You acknowledged (Dec. 17, 2008 @ 12:54 GMT) that
cannot offer an answer to the question of "why does the arrow of time
of quantum theory (related to collapse of the wave function, see for
example The Emperor’s New Mind) coincide with the cosmological one
(determined by large scale statistical considerations of a classical
kind)?"
Perhaps you can't answer this question because (i) there is no such
thing as "arrow of time of quantum theory", as the "collapse" may be an
artifact from our incomplete presentation of the dynamics of quantum
systems (cf. the first posting to your thread, from Dec. 2, 2008 @
07:02 GMT), and (ii) the cosmological time arrow encapsulates the
quasi-local nature of gravitational energy, which you seem to be very
reluctant to discuss.
Please put your cards on the table: there is very little quasi-local
time left to the contest ending on January 1, 2009.
"I respond to postings that raise questions I find interesting and
relevant to the topic under discussion. I do not respond to postings
that try to tell me what I should do, and (apart from fqxi essays) I
feel no obligation to read any matter on any webpages linked to any
postings."
1. Given the lack of professional response to any of my postings on
your thread, it seems to me that you do not find the issues raised by
me "interesting and relevant to the topic under discussion". You failed
to explain which particular issues raised by me were not relevant,
however.
2. I was not trying to tell you what you should do, George.
I was quoting from your statements for the sole purpose to show you
that they are not better than those produced by your colleagues
supporting the "block universe" viewpoint.
I only wanted to help you do better than your opponents. For example, I
mentioned your notion of finite infinity from 1984 (Dec. 15, 2008 @
18:44 GMT), which I believe can be updated and improved, if only you
could sort out the tasks set by you: check out the quotes from your
numerous postings above (Dec. 16, 2008 @ 14:43 GMT).
3. The fact that you "feel no obligation to read any matter on any
webpages linked to any postings" is very sad, in my opinion. As you
acknowledged (Dec. 3, 2008 @ 16:47 GMT): "I have puzzled over the
Conway-Kochen 'Strong Free Will Theorem' paper, without really
understanding what if anything it has to do with free will".
If you follow the link in my first posting (Dec. 2, 2008 @ 07:02 GMT),
I suppose you will understand the crux of Conway-Kochen argument. If
not, it will be entirely my fault, so please write me back with your
specific questions.
Wishing you and all colleagues at this forum a very merry Christmas,
"please explain carefully to me what was unprofessional about my
posting of Dec. 21, 2008 @ 12:42 GMT."
You ignored my critical remarks -- all of them.
You wrote (Dec. 21, 2008 @ 12:42 GMT): "In my view the key unsolved
problem in classical General Relativity Theory (GRT) is not
gravitational energy, it is the definition and nature of gravitational
entropy, and the related issue of coarse graining in GR."
I respect your viewpoint, but please notice that you completely ignored
all critical remarks in my posting from Dec. 16, 2008 @ 14:43 GMT.
You also wrote (ibid.): "These (pseudotensor definitions - D.C.) have
not yet been used to give a satisfactory definition of gravitational
entropy, as far as I am aware."
Perhaps because it isn't possible to explain one mess (pseudotensor
definitions) with another one (gravitational entropy).
I am not aware of some precise definition of 'low geometric
entropy', but if we trust the calculations by Penrose (cf.
Singularities and Time-Asymmetry, in General Relativity: An Einstein
Centenary Survey, ed. by S W Hawking and W Israel, Cambridge University
Press, 1979), it seems to me that the initial gravitational entropy had
to be *as low as possible*, which in turn means that we cannot begin by
assuming a FRW form for the metric -- even approximately.
See Slide 3 from R. Penrose's talk "Before the Big Bang?" (7 November
2005) here.
Big mess. Which is why I asked you to get to the bottom of this
'gravitational energy' and its quasi-local -- in time? -- nature.
But again, the main puzzle in your EBU idea are produced by your own
statements, as quoted in my posting from Dec. 16, 2008 @ 14:43 GMT
above. As you acknowledged (George Ellis, Dec. 4, 2008 @ 10:00 GMT):
"So a key element is how proper time relates to coordinate time as we
move to the future, ... "
If you believe can resolve this 'key element', please test your
solution with the problem of gravitational energy, from 1918.
On Dec. 22, 2008 @ 01:55 GMT, Vesselin Petkov wrote to Peter Lynds:
"Let me propose something that I think is both constructive and fair -
publish your objections against the BU view."
The BU hypothesis suffers from an incurable logical error: Non sequitur.
Neither STR nor GR can detect the Heraclitean flow of time, because the
latter is supposed to *emerge* along with the *emergence* of 3-D space.
These unresolved issues are clearly outside the applicable limits of GR.
If the flow of time were some 'observable in GR', there should be some
kind of material content left from it as 'observable in GR', and
Einstein’s field equations (EFE) would NOT guarantee "the conservation
of total energy-momentum": see Eq. 2 in [George F R Ellis and Henk van
Elst, arXiv:gr-qc/9812046v5], and notice that it is valid only if the
cosmological constant [lambda] "is constant in time and space" [ibid.]
R. Penrose explicitly stressed (The Road to Reality, p. 777) that "any
non-constancy in [lambda] would have to be accompanied by a
compensating non-conservation of the mass-energy of the matter."
It should be agonizingly clear that GR cannot address these "dynamic
dark energy" (DDE) issues of the Heraclitean flow of time. If GR could
detect DDE as some Dirac observable, the latter would make the
*perfectly smooth* DDE 'observable in GR', and the ether would come
back.
Any definite statement about the flow of time, derived from STR and/or
GR, is logically inconsistent. GR is still too "far away" from quantum
gravity and quantum cosmology.
If you claim that 'fish cannot ride bicycles, therefore we should
"forget" about bicycles', you will make the same logical error, non
sequitur. C. Rovelli, J. Barbour, and many other people already made it
in their publications.
If you, Peter, or anyone else at this forum cannot understand the text
above, it will be entirely my fault, so please don't hesitate to ask
questions. Then please tell your students all about the logical error
in BU: kids have the right to know everything we know. I hope you all
agree.
Vesselin Petkov wrote (Dec. 22, 2008 @ 06:02 GMT): "If you really think
you have something to say professionally, publish it and you will have
my answer."
About twenty years ago, I had a long discussion with two members of
Jehovah's Witnesses, and because it was going nowhere, I asked them to
formulate the conditions under which they will accept my viewpoint and
convert to Catholicism. Never heard from them.
But since Vesselin Petkov is doing science, and is responsible for
teaching students (=kids), I respectfully ask him to formulate the
conditions under which he will accept that the "block universe" (BU)
viewpoint is indeed logically inconsistent, being formulated on the
logical error 'non sequitur'.
To the best of my knowledge, Carlo Rovelli and Julian Barbour haven't
done it. In the context of the fish & bicycles metaphor (cf. my
posting from Dec. 22, 2008 @ 04:51 GMT), they propose to "forget"
bicycles, but fail to acknowledge that the "sea" has to have some kind
of "boundaries" which nobody has so far managed to *derive* from the
"sea" alone (references available upon request).
Stated differently, the first off task toward rejecting the Heraclitean
flow of time is to show rigorously the "boundaries" of spacetime. If
you can't solve it, you have no logical grounds to expand the
applicable limits of STR and GR, and speculate about some "block
universe".
Please put *your* cards on the table, and also promise that if I prove
BU logically inconsistent, you will tell your students all about it --
kids have the right to know everything we know.
I wonder if you have the guts to do it. You will be the first person to
receive my manuscript.
If you can't meet this requirement for scientific research, please note
that I am too tired to discuss issues based solely on faith and
emotions.
I'm afraid we've been tearing apart George Ellis with our very diverse
questions. I for one wish to apologize to George for my violent
curiosity.
Perhaps we can put aside our questions, and focus on one issue, which I
believe is the crux of his EBU proposal:
I look at my wristwatch, and record some linearized variable called
'coordinate time'. How does my wristwatch read it, given the premise
that any finite interval from it belongs to the cosmological time?
"There are a number of different positions held by different people
making postings on this thread; they have been adequately expressed,
and are apparently not going to change."
Please exclude me from this set of people who "are apparently not going
to change." I am ready to change my viewpoint, and am flexible enough
to accept yours, if only you can make it clear by responding to my
critical remarks, hence convince me that I got it wrong.
Merry Christmas to you and all participants in your forum.
I honestly regret that George Ellis choose to leave this Forum. It is
still completely unclear to me how one could falsify his hypothesis
about "evolving block universe" (EBU), as compared to the hypothesis
about some "block universe" (BU).
I was hoping to see some written statement by George, in which he says
something like 'if my conjecture [A] turns out to be wrong, then my EBU
hypothesis will be indistinguishable from BU hypothesis'.
In this context, perhaps it is worth considering his statement from
Dec. 20, 2008 @ 00:42 GMT above, in which he wrote, in response to
Lawrence B Crowell:
"there may not be a timlike Killing vector field, but there is a
conformal timlike Killing vector."
The issue of 'conformal timelike Killing vector' has not been mentioned
in George Ellis' essay. I will refrain from making any comments, and
will instead suggest to the Moderator to ask Claus
Kiefer to pass his professional comments on two issues:
(i) the applicability of the 'conformal timelike Killing vector' in
cosmology, from the perspective of his latest manuscript "Quantum
geometrodynamics: whence, whither?", arXiv:0812.0295v1 [gr-qc],
and
(ii) George Ellis' claims that "proper time along world lines is indeed
a preferred time variable in GR" (Dec. 12, 2008 @ 20:27 GMT) and
"objectively privileged hypersurfaces do indeed exist in standard
cosmology" (Dec. 15, 2008 @ 05:16 GMT).
Thank you, George, for your comprehensive reply, in which you wrote
(Dec. 29, 2008 @ 17:53 GMT):
"... the surfaces S:{s=const} are the globally preferred surfaces of
time (“constant proper time since creation of the universe”) on which
coming into being will take place."
I also notice that you define proper time along all world lines
in "small local neighbourhoods" on which "coming into being will
take place", and I promise that will never ever ask more questions
about your research. Good luck.
Responding to Philip Gibbs, George Ellis wrote (Dec. 31, 2008 @ 05:50
GMT):
[1] "By the way I did not emphasize it, but the choice of world lines I
make is that of the Landau reference frame, representing the velocity
given by the local average of all energy and mass fields in a small
neighbourhood."
Responding to Vesselin Petkov, George Ellis wrote (Dec. 31, 2008 @
05:52 GMT):
[2] "Causality operates as you state it, but only in the EBU region
that already exists. This domain is coming into being at the present
instant; and what is the present instant now will in another fraction
DT of time be in the past.
[3] "As I believe spacetime is quantised, I am happy to assume DT
cannot be taken infinitesimally small but rather has a finite lower
limit (associated with the Planck time); so there are no paradoxes
associated with the present having zero time extent. I am happy if it
has a very small but finite duration.
[4] "As regards the quantum case, say the double-slit experiment, I
have not attempted a description of how particles exist or not in
quantum theory. Whatever works for you in the BU words for me in the
EBU according to principle (A), except for cases involving
entanglement, which I come to in a minute. I hold by the statement that
quantum theory
only predicts probabilities, not specific outcomes.
[5] "Finally, as regards the issue of the EPR-type *experiments*: you
state “those experiments are perfectly explained by the BU because the
future exists there. But they cannot be explained by the EBU since, on
that view, it follows that the non-existing future can determine the
outcome of an experiment.”
[6] "But as already stated in a previous post, the EPR analysis is not
a relativistic analysis: it is based in the Schroedinger equation.
[7] "As long as any experiment whatever gives a future outcome that is
not at present determined even in principle, the EBU description trumps
the BU. And we have plenty of such experiments in quantum theory. The
relativistic interpretation of the EPR experiments will have to adjust
to this fact."
Comment #1: Given the statement [1], about "the local average of all
energy and mass fields in a small neighbourhood", and the statement
[3], I am under the impression that George Ellis should define the
gravitational energy in some 'elementary increment of time' which has
"a very small but finite duration". This will be a daunting task, to
say the least, because it will require a rigorous explanation of how a
"fraction DT of time" [2] is "associated with the Planck time" [3].
Comment #2: By assuming that causality operates "only in the EBU region
that already exists" [2], he presupposes the possibility that some
physical stuff, call it B , fills in "the present instant now"
in a "fraction DT of time", which in turn *implies* that there was
(past perfect) some physical stuff A , whose (potential?)
future was somehow related, or perhaps influenced, by B . Thus,
in order to distinguish EBU from BU, George Ellis has to somehow
eliminate totally A in the "fraction DT of time" in which B is present.
But the very meaning of B is relational, that is, 'with respect
to A and C'. The latter, C , is needed to
define B , just as much as A is needed to define B
.
I am unable to understand the difference between EBU and BU hypotheses.
I'm sure George Ellis can recognize St. Augustine's comments on time in
the puzzle above. In modern language, the puzzle was explained by David
Bohm as follows (Wholeness and the Implicate Order, Ark edition 1983,
p. 204):
"So, if we say that the velocity of a particular *now* (at t_2) is (x_2
- x_1) / (t_2 - t_1) we are trying to relate *what is* (i.e., x_2 and
t_2) to *what is not* (i.e., x_1 and t_1). We can of course do this
*abstractly and symbolically* (as is, indeed, the common practice in
science and mathematics), but the further fact, not comprehended in
this abstract symbolism, is that the velocity *now* is active *now*
(e.g., it determines how a particle will act from now on, in itself,
and in relation to other particles). How are we to understand the
*present activity* of a position (x_1) now non-existent and gone for
ever?"
Comment #3: Regarding statements [4] - [7], they refer to the clash of
STR and QM, which is still unresolved. One of the reasons is that EPR
involves counterfactual reasoning, namely, what could have been the
outcomes of measurements of "two" (in fact, one) entangled
observable(s), had there been some 'now-at-a-distance' reference frame
in which one can verify the alleged "instantaneous" correlation. I
don't think counterfactual reasoning can be used to support EBU or BU.
It is just one big mess.
In response to the anonymous posting from Jan. 1, 2009 @ 10:31 GMT: I
have not posed any questions in my comments from Dec. 31, 2008 @ 14:32
GMT.
I could, for example, ask George Ellis to explain his vision on the
non-tensorial gravitational energy in a "fraction DT of time" (cf.
Comment #1), but I didn't. The task is known since 1918, if not earlier.
Metaphorically speaking, G. Ellis' EBU hypothesis is like opening the
cover of a piano and showing its the moving parts, and then trying to
*derive* the actions of the player from the dynamics of these moving
parts. Only the player is not there: it is "dark", and we can explain
roughly 4 per cent from the composite system 'player + piano'; the rest
if a mixture of cold dark matter (CDM) and dynamic dark energy (DDE).
I cannot agree with George that his EBU hypothesis could be "a
preferable model to the BU" (Jan. 2, 2009 @ 08:13 GMT).
The current BU hypothesis is adopted in basic GR textbooks. Consider,
for example, Robert Geroch (General Relativity from A to B, University
of Chicago Press, Chicago, 1978):
"There is no dynamics within space-time itself: nothing ever moves
therein; nothing happens; nothing changes. [...] In particular, one
does not think of particles as "moving through" space-time, or as
"following along" their world-lines. Rather, particles are just "in"
space-time, once and for all, and the world-line represents, all at
once the complete life history of the particle."
LIGO Scientific Collaboration (LSC) have adopted this "block" view, and
deeply believe that there is no difference between (i) observing the
effects of GW radiation in the *past* (as calculated by Russell Hulse
and Joseph Taylor in the case of the pulsar PSR 1913+16), and (ii) the
detection of GWs "online", as they tweak the interference pattern at
LIGO.
LSC have spend so far hundreds of millions of dollars and euro --
taxpayers' money -- yet all their "runs" have so far produced stunning failures. Yet they are determined to spend
even more, perhaps billions, if the three satellites of LISA are indeed
launched.
I think this is far more important than the flexibility of choosing the
final date for voting. If George Ellis is right, then LSC might have
been on a wrong track from the outset.
Perhaps it will be a good idea if George Ellis proves that EBU
hypothesis could be "a preferable model to the BU" by calculating the
localization of GW energy along the proper time of the wristwatch of
LIGO's operator.
On Jan. 3, 2009 @ 12:51 GMT, Lawrence B. Crowell wrote:
"General relativity gives a meaning to proper time, where coordinate
time is something determined by a gauge choice. A conformal time, or
proper time can lock a choice of coordinate time with proper time, so
called synchronous time. Yet all one has done is to make an appropriate
gauge-like choice so that certain symmetries of the spacetime define a
Killing time vector field. As such the notion of a global time is
something which is observer dependent and not "real." "
Larry: Do you believe all this can help George Ellis? As suggested
previously (Jan. 2, 2009 @ 14:30 GMT):
"Perhaps it will be a good idea if George Ellis proves that EBU
hypothesis could be "a preferable model to the BU" by calculating the
localization of GW energy along the proper time of the wristwatch of
LIGO's operator."
I am only trying to focus the discussion here, at George Ellis' thread,
on this issue of paramount importance.
Perhaps you can help George with his EBU hypothesis, because in the
framework of BU hypothesis the alleged localization of GW energy is
still theoretically unclear. Besides, recall
that LIGO
Scientific Collaboration has failed to detect any GW effect
whatsoever in five "runs" of LIGO, after spending hundreds of million
dollars and euro -- all taxpayers' money.
On Jan. 3, 2009 @ 12:51 GMT, Lawrence B. Crowell wrote:
"That nothing happens in a spacetime or cosmology is due to the fact
that time is a part of the field of gravity. This is what makes time,
or at least coordinate time, something which is similar to vector
potentials, in particular A_t, with internal gauge symmetries. These
things do not exist in a physical sense."
I think your last sentence points to a very tricky issue. The Higgs
boson hypothesis, for example, is introduced by means of a
gauge-breaking "mechanism". As explained by Holger Lyre, Does the Higgs
Mechanism Exist? arXiv:0806.1359v1
[physics.gen-ph], pp. 2-3:
"... the status of the symmetries in question, gauge symmetries, is in
fact a non-empirical or merely conventional one precisely in the sense
that neither global nor local gauge transformations possess any real
instantiations (i.e. realizations in the world). Rather their status is
comparable to the status of coordinate transformations (the status of
gauge symmetries will be addressed in detail in Sec. 3.1).
"How is it then possible to instantiate a mechanism, let alone a
dynamics of mass generation, in the breaking of such a kind of symmetry?
...
"Indeed, how can any physical mechanism arise from the breaking of a
merely conventional symmetry requirement? (Similarly, one would not
think that any physics flows out of the breaking of coordinate
invariance! -- Again this will be addressed in detail in Sec. 3.1.)"
But again, let's focus on George Ellis' EBU hypothesis, because if he
is on the right track, it should be possible to calculate the alleged
localization of GW energy "online", as it tweaks the interference
pattern at LIGO.
As George Ellis explained (cf. my posting from Dec. 31, 2008 @ 14:32
GMT):
"This domain is coming into being at the present instant; and what is
the present instant now will in another fraction DT of time be in the
past."
Can you calculate the localization of GW energy "online", as it is
"coming into being at the present instant", along the proper time of
the wristwatch of LIGO's operator?
A penny for your thoughts! It may be worth of billions.
Thanks a lot for your comment from Jan. 4, 2009 @ 14:41 GMT. I agree
that the past cannot be static, as "it is constantly being added to, as
the present becomes past", as you put it.
The same applies to the future in EBU hypothesis, as hinted in John
Wheeler's statement: "Time is Nature's way to keep everything from
happening all at once". Hence it seems to me that EBU hypothesis should
somehow include 'things that we still don't know that we don't know'.
If this is correct, George Ellis should allow some brand new things to
*emerge* in his EBU, in blatant violation of the unitarity principle.
See how far we can go with philosophy? Let me please go back to the
mundane affairs of GW astronomy, from my
preceding posting from Jan. 4, 2009 @ 12:43 GMT.
Larry: I can't see anything in your latest posting from Jan. 4, 2009 @
15:11 GMT that could be relevant to this ultimate test of George Ellis'
EBU. Please laid out your professional opinion.
Mike
Turner pointed out the accepted theoretical claim that elementary
particles known as the W boson and the Z boson had no mass when the
universe first exploded into being. Modern accelerator experiments have
shown, however, that both are very massive today.
Hence one could argue that the W boson and the Z boson had existed
"during" the inflationary stage as an Aristotelian potentia. As of
today, perhaps the verification of EBU hypothesis (Jan. 4, 2009 @ 12:43
GMT) is also an Aristotelian potentia. I hope Larry will explain his
professional opinion.
D.
===============
Final note: Is there light in the tunnel for George Ellis' EBU
hypothesis? Maybe. His younger colleague David
Wiltshire (University of
Canterbury, NZ) stated recently the following (email from Mon, 29
Dec 2008 18:06:48 +1300 (NZDT) -- emphasis added):
"Our average background
geometry here is close to
Minkowski. Spin-2 waves of characteristic frequencies will alter this average
background in a time-dependent fashion with a
characteristic frequency. That is detectable."
Perhaps he meant the
localization of GW energy "in a time-dependent fashion", along
the proper time of the wristwatch of LIGO's operator. As he explained
today (email from Sun, 04 Jan 2009 09:33:13 +1300 (NZDT) -- emphasis
added):
"I can write down nonlinear GW
solutions, and there is no problem with this. There are a number of
solutions of the full Einstein equations which can be written in
Kerr-Schild form, and thus are exact perturbations of flat space,
with no approximations. This includes Schwarzschild, Kerr and p-p
waves. I am not talking about the linearized approximation, or
the second order approximation, but the full nonlinear theory."
What a startling revelation!
I immediately asked David Wiltshire to write up a research
manuscript on the detection of GWs in the "full nonlinear theory", and
explain the detectors for the localization of GW energy "in a time-dependent
fashion". Perhaps he will somehow manage to disentangle the alleged
localized-on-a-trajectory GW energy from the non-tensorial
gravitational energy that cannot perform such miracle due to the
Equivalence Principle.
David Wiltshire will face a
daunting task: see Hans
Stephani, General Relativity, Cambridge University Press, 1982,
Sec. 15.3, and Hans-Jürgen
Schmidt, gr-qc/0407095, Sec.
4.2, Why do all the curvature invariants of a gravitational wave
vanish?
On the other hand, you never
know with people like David Wiltshire (he proposed recently that there
could be "sections" of the universe in which it is 18.6
billion years old).
Let's wish David L. Wiltshire,
Lawrence B. Crowell, and George F R Ellis best of luck with sorting out
the whole mess of GW "astronomy".
Julian Barbour is again trying to suggest that (quote) "time should be
banished" (end of quote), but the simple proof against his hypothesis
is the fact that his brain is working.
Namely, no living brain can operate in a "block universe", because it
will have to function as a Turing machine installed in some IGUS, and the perpetual "encoding of information", by
any conceivable "code", will lead to decreasing of the entropy of the
"hard drive", until the poor Turing machine develops severe structural
damages and breaks down with a stroke.
Explanatory note: The reason why
Julian Barbour (see below) will never
ever read the text at the link above is that it will kill
his hypotheses by demonstrating the possibility for transience.
But it is not produced by some "collapse", as he expected (p.
359): Dead matter makes quantum jumps; the living-and-quantum
matter is smarter.
You wrote in your essay (p. 8): "So Time has the topology of a linearly
ordered discrete set, isomorphic to the set of integers."
And in your posting from Dec. 3, 2008 @ 01:44
GMT, you expressed your belief that ".. we can define change as
simply the discrete transition from the state at one instant to the
state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."
Do you know the nature of continuum, namely, how many points are there
on a straight line in Euclidean space? (cf. Kurt Gödel, "What is
Cantor's Continuum Problem?", American Mathematical Monthly, Vol. 54,
No. 9, November 1947, pp. 515-525).
I believe the puzzle of these "points" can be explained with Thompson's
lamp paradox: Imagine a lamp that is turned 'on' at some instant
labeled with 0 , and is left 'on' for 1 min, then turned 'off' for 0.5
min, then 'on' for 0.25 min, etc., ad infinitum. Do we have a limit?
Obviously yes: 2 min. Fine, but what is the state of the lamp in the
instant/point labeled with '2 min'? UNdecidable?
Just some musings, prompted by your statement with capital letters.
Regards,
Dimi Chakalov
------
Dimi Chakalov wrote on Dec. 11,
2008 @ 01:46 GMT
Dear Chi,
Thank you for your prompt reply from Dec. 11, 2008 @ 01:07 GMT.
You wrote: "But in order for your argument to hold, you actually need
to assume a physical time continuum (or at least a dense set) from the
start!"
I don't need to assume any additional properties of the continuum,
apart from those identified by Kurt Gödel -- please read his 1947
article. I only object to your belief that ".. we can define change as
simply the discrete transition from the state at one instant to the
state at the next instant, WITHOUT ANYTHING HAPPENING IN BETWEEN."
Nothing can go "in between" two adjacent points, and nothing can verify
the state of the Thompson lamp at the point labeled with '2'. Perhaps
you may wish to think of it as superposition of |on>
+ |off> , which of course will produce even more musings.
To quote from your essay (p. 9), you take "a very reasonable, if far
from unimpeachable, set of assumptions -- a quantum state evolving in
time according to the conventional Schrödinger equation with a
time-independent Hamiltonian", and set your goal (p. 4) as "it is worth
our effort to pursue their ramifications and see where we end up."
I have a simple suggestion. Five years ago, in your
arXiv:astro-ph/0310342v2, you were musing on the “smooth tension” of
the "dark energy", and acknowledged "a problem, a puzzle, and a
scandal".
To clarify what kind of "time" may be implied in the set of assumptions
in your recent essay, try to embed the “smooth tension” into some
Cauchy surface, as explained in your graduate-level textbook "Spacetime
and Geometry".
If you fail, I hope you will have a much better idea of "where we end
up" with your essay, and how to fix your problems.
Your Conclusion #4 is "to forget the notion of time all together, and
to define a quantum theory capable of predicting the possible
correlations between partial observables", which perhaps is related to
your statement that "general relativity challenges strongly our
intuitive notion of a universal flow of time."
But you stressed in gr-qc/0604045 v2 that "the proper time [tau] along
spacetime trajectories cannot be used as an independent variable
either, as [tau] is a complicated non-local function of the
gravitational field itself. Therefore, properly speaking, GR does not
admit a description as a system evolving in terms of an observable time
variable."
Ergo, GR cannot reject something that is beyond it. Perhaps it would be
a good idea if you consult Prof. Karel Kuchar.
------
Dimi Chakalov wrote on Dec. 2, 2008 @ 08:21 GMT
P.S. Following the line of reasoning adopted by C. Rovelli, in a
fundamental description of nature we must "forget" 3-D space as well,
because there is noting in GR to reveal some mechanism producing a
spacelike hypersurface with respect to which people talk about "time",
as in ADM hypothesis on "the dynamics of GR". In this sense, GR cannot
reject something that is beyond it, as stated in my preceding post. Nor
can GR explain the apparent time-orientability of spacetime, which also
is beyond its applicable limits.
It is completely unclear to me how Rovelli's "partial observables" can
shed light on something that is beyond both GR and QM.
It seems to me that Rovelli's recipe for quantum gravity is this: take
Quantum Mechanics and General Relativity in their current formulation,
with all their well-known problems, blend them into some new theory
with "partial observables", and hope that the problems of QM may be
solved from GR, and the problems of GR may be solved from QM. Don't try
to solve any of the initial problems of QM and GR beforehand. Just hope
and pray that the "good parts" from QM and GR will cure all problems.
Picture this: you have a car (QM) which runs quite well on some roads,
but fails miserably on some essential roads, and a helicopter (GR) that
also runs in some favorable weather conditions, but is totally useless
in bad weather. Take the car and the helicopter, and build a brand new
vehicle, which will run better than the car and fly better than the
helicopter, and will also allow you to dive deep into the ocean, as a
perfect submarine.
Is this Rovelli's recipe for quantum gravity?
------
Dimi Chakalov wrote on Dec. 12,
2008 @ 03:58 GMT
Regarding my posting from Dec. 2, 2008 @ 08:21 GMT above: Let's recap
on the facts.
As of today, Carlo Rovelli's essay "Forget time" got 6 Registered
Votes, and 103 Public Votes.
Yet he hasn't made any effort to explain what may happen to 3-D space
in case we choose to "forget time". I do hope he will do this until the
contest ending date, January 1, 2009.
Please correct me if I got it wrong: In the canonical formalism of
today's GR, the foliation of spacetime into 3-D spacelike hypersurfaces
enables the distinction of two infinitesimally neighboured
hypersurfaces, so if we "forget" about [delta]_t, we must "forget"
about the whole 3-D spacelike hypersurface as well. It's a package --
see the drawing attached.
Carlo Rovelli has been manifestly silent on this fundamental issue.
He wrote (Oct. 24, 2008 @ 17:53 GMT): "... I think that in order to
have a clear picture the easiest thing is to "forget space" and "forget
time", and only to talk about relations between observable quantities."
And in his latest posting (Nov. 9, 2008 @ 10:42 GMT), he added even
more confusing remarks: "... the probabilities of all the possible
specific-measurement's outcomes predicted by the theory must sum up to
one. Unitarity in *this* sense must of course be implemented by the
timeless theory, and it is."
It is totally unclear why would the "observable quantities" care about
each other's relational stance, nor what would be the driving force
that implements the unitarity principle.
For if Nature chooses to "forget time", the "observable quantities"
would need human consciousness to get their job done. Or maybe Carlo
Rovelli should re-write his essay?
If he chooses the latter, there is a simple way to convince us that we
should indeed "forget time": The very mechanism which shapes '3-D
space' should be proven non-existent.
Carlo: If you believe can kill the Heraclitean Time, you should first
kill the generation of 3-D space.
Please do not "forget" the event of contest ending, January 1, 2009.
Dimi Chakalov
attachments: adm.jpg
------
anonymously written on Dec. 12, 2008 @ 16:21 GMT
Hi Carlo:
You wrote (Dec. 12, 2008 @ 13:11 GMT): "The result is that some say I
am too radical; others, like Dimi in this post, say I am too
conservative... I don't know what I am; I am just trying to find
tentative solutions to the problems on the table .... "
1. I never said that you are "too conservative". What I actually
suggested (Dec. 12, 2008 @ 03:58 GMT) was this:
If you believe can kill the Heraclitean Time, you should first kill the
generation of 3-D space.
2. We all are trying to find tentative solutions to the problems on the
table, but I'm afraid your approach is logically inconsistent: you
"derive" statements about time and space from a theory -- GR -- that cannot say anything about those same statements.
Your whole essay is tantamount to speculating on the precise conditions
"inside" a singularity, knowing very well that GR cannot be extended
outside its applicable limits.
I also suggested you to consult Prof. Karel Kuchar. If he is busy, I
can quote from his research papers.
I am also going to break in here, because I believe George Ellis made a
crucial remark.
George explained his understanding of your claim that there is no
preferred time variable in GR (George Ellis, Dec. 12, 2008 @ 20:27 GMT):
"This is correct as regards spacelike surfaces that can represent
constant time. But proper time along world lines is indeed a preferred
time variable in GR. The fundamental difference from Newtonian theory
is that the preferred time is defined along world lines, instead of by
spacelike surfaces. Proper times along timelike worldlines is what is
measured by clocks ticking (p.3). So you focus on problems with
surfaces of constant time, I focus on the meaningful nature of proper
time along world lines."
On the other hand, in your arXiv:gr-qc/0604045v2,
p. 4, you explained your understanding of 'no preferred time
variable in GR' in the following fashion:
"In general relativity, when we describe the dynamics of the
gravitational field (not to be confused with the dynamics of matter in
a given gravitational field), there is no external time variable that
can play the role of observable independent evolution variable. The
field equations are written in terms of an evolution parameter, which
is the time coordinate x^0, but this coordinate, does not correspond to
anything directly observable. The proper time [tau] along spacetime
trajectories cannot be used as an independent variable either, as [tau]
is a complicated non-local function of the gravitational field itself.
Therefore, properly speaking, GR does not admit a description as a
system evolving in terms of an observable time variable.
...
"This weakening of the notion of time in classical GR is rarely
emphasized: After all, in classical GR we may disregard the full
dynamical structure of the theory and consider only individual
solutions of its equations of motion. A single solution of the GR
equations of motion determines “a spacetime”, where a notion of proper
time is associated to each timelike worldline (notice the remark by
George above - D.C.).
"But in the quantum context a single solution of the dynamical equation
is like a single “trajectory” of a quantum particle: in quantum theory
there are no physical individual trajectories: there are only
transition probabilities between observable eigenvalues. Therefore in
quantum gravity it is likely to be impossible to describe the world in
terms of a
spacetime, in the same sense in which the motion of a quantum electron
cannot be described in terms of a single trajectory."
It seems to me that you and George are discussing 'apples and oranges':
you are discussing the problem of time in classical GR, while he was
(tacitly?) implying some yet-to-be discovered quantum gravity in which
the "meaningful nature of proper time along world lines" (George Ellis,
Dec. 12, 2008 @ 20:27 GMT) would be akin to "a single trajectory" (arXiv:gr-qc/0604045v2, p. 4).
May I ask you to sort out this issue with 'scrupulous intellectual
honesty' (C. Rovelli, arXiv:gr-qc/0109034v2, p. 9).
Please also notice my criticism of your Essay, posted earlier (Dec. 12,
2008 @ 03:58 GMT and Dec. 12, 2008 @ 16:21 GMT): the Heraclitean Time,
which corresponds to the very *generation of 3-D space*, is absent in
GR.
Again, if you really believe, with scrupulous intellectual honesty,
that we should "forget" time, you have to demonstrate the emergence of
3-D space from some primitive (Borel?) set of abstract mathematical
points, and then prove that this *emergence* is indeed timeless.
Please act promptly: the Heraclitean Time you have by the contest
ending (January 1, 2009) is running out.
Dimi
------
Dimi Chakalov wrote on Dec. 14, 2008 @ 14:01 GMT
Addendum to my request for clarification, posted on Dec. 13, 2008 @
13:01 GMT:
George wrote (George Ellis, Dec. 12, 2008 @ 20:27 GMT):
"But proper time along world lines is indeed a preferred time variable
in GR."
May I ask you to clarify the exact meaning of your "preferred time
variable in GR" by elaborating on the affine connection. Let me quote
from Wikipedia:
"... parallel transport along the curve preserves the tangent
vector to the curve, so
nabla_{dotgamma} dotgamma= 0
at each point along the curve, where dotgamma is the derivative
with respect to t."
George: Is your "preferred time variable in GR" keeping track on *each
point along the curve*? If yes, what is the mechanism of this tracking?
Also, is dotgamma the derivative with respect to some gauge-dependent
coordinate time, t, or is it with respect to the proper time
[tau] along spacetime trajectories?
"The proper time [tau] along spacetime trajectories cannot be used as
an independent variable either, as [tau] is a complicated non-local
function of the gravitational field itself. Therefore, properly
speaking, GR does not admit a description as a system evolving in terms
of an observable time variable."
I trust Carlo will elaborate on the (timeless?) affine connection as
well.
"In elementary textbooks on general relativity we read that the
Einstein equations imply that small bodies move on geodesics of the
spacetime metric. It is very hard to make this into a mathematically
precise statement which refers to actual solutions of the Einstein
equations (and not just to some formal approximations)."
Perhaps Carlo Rovelli's suggestion to "forget" time and space is rooted
on some 'formal approximations'. Recall Murphy's Law No. 15: Complex
problems have simple, easy-to-understand wrong answers.
Dimi Chakalov
------
Dimi Chakalov wrote on Dec. 15,
2008 @ 20:05 GMT
On Dec. 12, 2008 @ 13:11 GMT, Carlo Rovelli wrote:
"I apologize for the posts I am not answering to. I am tryng to catch
up..."
No rush, please take your time. I believe have showed that your
approach is logically inconsistent -- please check out my postings
above from Dec. 12, 2008 @ 16:21 GMT, Dec. 13, 2008 @ 13:01 GMT, and
Dec. 14, 2008 @ 14:01 GMT, and follow the links.
In a nutshell, your logical error would be similar to the following
claim: Fish cannot ride bicycles, therefore we should "forget" about
bicycles.
More on the intrinsic limitations of GR in my posting to Gavin
Crooks from Dec. 13, 2008 @ 20:55 GMT.
Dimi Chakalov
-------
Dimi Chakalov wrote on Dec. 16,
2008 @ 15:56 GMT
[My apologies to Carlo for breaking into his thread]
On Dec. 16, 2008 @ 02:58 GMT, Vesselin Petkov wrote:
"Yes, of course, the evidence that time flows is indeed overwhelming,
but that evidence is not physical."
If the evidence were physical, there would be some bona fide (Dirac)
observable in GR, which would reveal the source and the origin of the
"dynamic dark energy", and the ether will come back.
Therefore, we should not expect to catch any *physical* evidence for
the flow of time.
You also wrote (ibid.): "... the macro scale evidence supporting the
block universe view is overwhelming."
Please see a startling confession by Thomas Thiemann in
astro-ph/0607380 v1:
"The puzzle here is that these observed quantities are mathematically
described by functions on the phase space which do not Poisson commute
with the constraints! Hence they are not gauge invariant and therefore
should not be observable in obvious contradiction to reality."
More in my post to Gavin Crooks from
Dec. 13, 2008 @ 20:55 GMT.
Dimi Chakalov
------
Note: I believe the confusion between George Ellis and Carlo Rovelli
can be explained with a modified picture of the foliation of spacetime,
which I will borrow from C. Kiefer and B. Sandhöfer, arXiv:0804.0672v1
[gr-qc], Fig. 1.
Perhaps George Ellis was implying the picture on the left (as he put
it, "the fundamental difference from Newtonian theory is that the
preferred time is defined along world lines, instead of by spacelike
surfaces"), while Carlo Rovelli (arXiv:gr-qc/0604045v2, p. 4)
was talking about the picture on the right, "where a notion of
proper time (but not "preferred time", as George Ellis claims -
D.C.) is associated to each timelike worldline", depicted with three
coordinate-dependent points A, B, and C, projected on the upper
3-D hypersurface.
But these coordinate-dependent
"points" A, B, and C are nothing but the "local coordinates on
M", at "each point along the curve, where dotgamma is the
derivative with respect to t", as explained in Wikipedia.
We cannot employ the proper time [tau] along spacetime
trajectories, to write the geodesic equation, so we have to replace it
with its linearized (if available), and highly misleading,
"projection", t , left on a Cauchy
surface.
This "projection", t ,
is highly misleading and causes great confusion even to experts in GR,
because it is an already-linearized, and gauge-dependant, 'time
in GR' that your poor wristwatch (cf. Chris
Isham) does read very well. The dynamics of this linearization
procedure is what is missing in GR, to resolve the Cauchy problem
for Einstein field equations.
Any time you look at your
wristwatch and talk about GR, you enter this huge unresolved task in
GR. More from Graham Nerlich.
You may need quantum gravity to
actually "see", from the viewpoint of some absolute
meta-observer, the "proper time [tau] along spacetime
trajectories" -- it "cannot be used as an independent variable
either, as [tau] is a complicated non-local function of the
gravitational field itself", says Carlo Rovelli.
A lot more can be said about the
difference between some "single solution of the GR equations" (C.
Rovelli) and the hypothesis of George Ellis, as well as about the very dynamics
of selecting a single solutions from all potential
"eigenvalues" -- one-at-a-time only, along The Heraclitean Time
(cf. the arrow of spacetime).
Check out my posting No. 9 to
Gavin Crooks below.
As to George Ellis' hypothesis,
he summarized it in the following fashion (Dec. 12, 2008 @
20:27 GMT): "But proper time along world lines is indeed a
preferred time variable in GR." A brief explanation was offered to
Lawrence B. Crowell (George Ellis wrote on Dec. 12, 2008 @ 04:24
GMT; links added to explain my viewpoint):
"Time in GR is represented as
integrals along particle world lines, related to measurement and
physics by ideal clocks (which of course being physical objects move
along timelike world lines). The underlying assumption is different
such clocks (atomic, electromagnetic, mechanical, etc) will all concur on one universal concept of time
('proper time') along the world line."
And on Dec. 12, 2008 @ 06:18 GMT, he added:
"The additional comment is that there are 'times' that occur in each of
the fundamental equations of physics: Newton's equation, Maxwell's
equations, the Schroedinger equation, the Dirac equation, general
relativity when expressed in the 1+3 covariant formalism. Now these
different times along an arbitrary world line could have been
incommensurate, but in fact they turn out to be the same (up to a
constant that can be normalised to unity by choice of units). That is
the deep feature that leads to a consistent concept
of time along world lines, mentioned in my last posting. Perhaps
this is because all these equations are effective equations deriving
from a single deeper unified theory, and it is this common origin that
leads to the different times being consistent.
"How this could all arise from a
unified theory of quantum gravity and fundamental interactions is then what needs clarity."
I fully agree. As stated by Sergiu Klainerman: "A proper definition of
global solutions in GR requires a special discussion concerning the
proper time of timelike geodesics." And 'global solutions in GR' is
what we need to clarify most, before embarking to quantum gravity.
D. Chakalov
December 13, 2008
Last update: December 15, 2008
You wrote: "Time emerges from the separation into two different
subsystems: one subsystem (here: the gravitational part) defines the
time with respect to which the other subsystem (here: the
non-gravitational part) evolves."[footnote 2]
Footnote 2: "More precisely, some of the gravitational degrees of
freedom can also remain quantum, while some of the non-gravitational
variables can be macroscopic and enter the definition of time."
May I ask you to elaborate on the GR dictum -- 'matter tells spacetime
how to curve and spacetime tells matter where to go' -- in the
framework of your ideas, as clarified in footnote 2. Thank you very
much in advance.
As to the "problem of time", check out a simple Gedankenexperiment in
Wikipedia and its discussion here.
Regards,
Dimi
------
Dimi Chakalov wrote on Dec. 11,
2008 @ 14:01 GMT
Hi Claus,
I very much hope to hear from you. To explain my request posted on Dec.
3, 2008 @ 11:47 GMT, may I quote from your essay (p. 2): The
Schrödinger equation (1) is, with respect to t, deterministic and
time-reversal invariant. As was already emphasized by Wolfgang Pauli,
the presence of both t and i are crucial for the probability
interpretation of quantum mechanics, in particular for the conservation
of probability in time."
But if we accept your belief that time emerges only as some
“semiclassical time”, and is (p. 6) "only an approximate concept", how
would you address the Hilbert space problem? In your words: "What is
the appropriate inner product that encodes the probability
interpretation and that is conserved in time?" (C. Kiefer, arXiv:gr-qc/9906100v1, p. 15)
I wonder if you can solve the Hilbert space problem with some
“semiclassical time”, given your speculation that (Essay, p. 6): "...
the Hilbert-space structure, too, is an approximate structure and that
different mathematical structures are needed for full quantum gravity."
For if you can't solve the Hilbert space problem, your prerequisites
from the Schrödinger equation (p. 2) may not be relevant at all,
and you will have to start from scratch, by replacing the Hilbert-space
structure with ... well, something else (perhaps "different
mathematical structures", as you put it).
I believe Schrödinger provided a viable hint to this 'something
else' in November 1950; check out 'Quantum Mechanics
101'.
You wrote (Dec. 23, 2008 @ 17:05 GMT) that you "want to advocate a
novel perspective on the interpretation of the Wheeler-DeWitt equation
and its timeless nature: being very conservative and imposing only two
principles (universal validity of the Schr"odinger equation and the
semiclassical correctness of Einstein's theory)..."
The first principle you decided to employ, the alleged "universal
validity of the Schr"odinger equation", may be wrong, as I tried to
argue since I read Ch. 10, 'Quantum gravity and the interpretation of
quantum theory', in the first edition of your monograph "Quantum
Gravity" (May 2004).
Please check out my essay 'Quantum Mechanics 101';
the link was in my posting from Dec. 11, 2008 @ 14:01 GMT above.
You also wrote (Dec. 23, 2008 @ 17:05 GMT): "In the quantum theory, on
the other hand, spacetime has disappeared completely as a consequence
of the uncertainty relations, ..."
I believe it is safe to say that, while quantum theory has been
empirically established, there could be many *artifacts* from the
"filter" we impose on the quantum realm with the 'spacetime of facts'
of STR: please check out the KS Theorem in the essay on QM mentioned
above.
If you disagree, please explain your arguments.
If you agree, please notice that the Hilbert space problem (C. Kiefer,
Quantum geometrodynamics: whence, whither?", arXiv:0812.0295v1 [gr-qc])
may be solved along with the 'problem of time' en bloc , as it
should be done.
You claim that, in quantum gravity, "[mu]atter becomes both geometry
and matter" (p. 8), but because in GR "matter tells spacetime how to
curve and spacetime tells matter where to go", it is obvious that your
wristwatch cannot "read" the non-linear dynamics of negotiation between
the two sides in Einstein Equations (p. 1). Perhaps your (inanimate)
wristwatch will inevitably halt by trying to "read" such (global) time,
hence the illusion about some "problem of time".
Check out a Gedankenexperiment
from Wikipedia here.
You claim (p. 2) that "the main unanswered question in quantum theory
is, When does a measurement occur?", and stressed (Sec. 5) that "a
natural approach to understanding time in quantum theory is via its
classically conjugate variable, energy." All this reminded me of the
invisible cat, Macavity, which shows up only when no one is looking at
it, just like the
negative energy density in QFT (arXiv:gr-qc/9709047v2). Perhaps
Macavity is always unobservable or gauge-dependent,
and can be "located" only with a Gedankenexperiment from Wikipedia here.
I like your essay very much. The more I read it, the more I learn from
you. Thank you.
Best regards -- Dimi
------
Dimi Chakalov wrote on Dec. 11,
2008 @ 20:14 GMT
Adam:
Glad to learn that the ideas in your Essay are related to the
"invisible" (gauge-dependent?)
cat Macavity (arXiv:gr-qc/9709047v2).
Please check out the so-called Buridan donkey
paradox. Perhaps Macavity facilitates all "negotiations" between
the donkeys. As you conjectured in your Essay (p. 3), "perhaps time is
not merely a parameter, but another sort of thing, in quantum theory."
To the best of my knowledge, you are the first person to propose a new
sort of time-energy uncertainty relation (Sec.
5.3, p. 8). I hope you will be awarded 10xFirst Prize in this
contest.
May I try to answer the question in the title of your essay.
In your essay "Whither Time's Arrow?", you wrote: "Neither Newtonian
mechanics, special or general relativity, quantum mechanics, nor
quantum field theory picks a preferred direction in time, anymore than
these theories picks out a preferred direction in space."
The apparent "expansion" of space due to the so-called 'dark energy
from empty space' (L. Krauss, reference
available upon request) does not pick up any preferred direction in
space either, simply because this "direction" is omnipresent -- there
is no direction in which space does NOT expand. The latter is
ultimately needed as a reference direction w.r.t.w. we could discover
another, preferred direction of space expansion.
Notice that such task is banned in GR by default, because it would
require that GR determines the evolution of the lapse function and
shift vector, along the "arrow" of the spacetime foliation. But as the
lapse and the shift are gauge
functions, any conversion into some Dirac observables would
inevitably expose an *observable* absolute reference frame, and the
ether will come back.
Hence many people at this Forum claim that we
should "forget" time, but somehow avoid the driving force of the
cosmological time arrow, and also the drastic contradiction between the
predictions of their theories and all astronomical evidence of the
cosmological time. As Thomas Thiemann acknowledged in astro-ph/0607380
v1:
"Why is it that the FRW equations describe the physical time evolution
which is actually observed for instance through red shift experiments,
of physical, that is observable, quantities such as the scale parameter?
"The puzzle here is that these observed quantities are mathematically
described by functions on the phase space which do not Poisson commute
with the constraints! Hence they are not gauge invariant and therefore
should not be observable in obvious contradiction to reality."
In short, to answer the question posed in the title of your essay, the
direction of time arrow is the one in which the amount of dynamic dark
energy (DDE) is increasing -- the more time elapses along the
cosmological time arrow, the more DDE we wind up with.
I tried to explain this paradoxical situation to my teenage daughter as
follows: Suppose you accelerate a car, but the fuel gauge shows that
you're actually gaining more fuel by accelerating the car. That's the
ultimate 'free lunch' provided by DDE, only physicists cannot explain
it.
A penny for your thoughts! It may be worth of billions, since we're
talking about the cleanest and truly unlimited energy source.
May I ask you to help me understand your main idea. You wrote:
" ... general relativity leads us to view spacetime geometry as part of
a dynamical system, as something that satisfies equations of motion and
evolves. But clearly the evolution here cannot be understood in a
temporal sense, unless we have at our disposal some external time
parameter in which to understand it."
...
"The observables so 'localized' are relational in the sense that they
are not defined on a background space but only relative to other
dynamical entities (matter fields, spatial volume, etc.). Observables
are not of the form A(x; t) (where x and t label an independent
manifold) but A(B) (where B is another observable and neither B nor A
is privileged in any sense)."
Footnote 5: "I restrict the discussion to classical systems in order to
make the presentation easier to follow. For the technically savvy, one
can transform to the quantum case, roughly, by thinking of the
functional relation or correlation A(B) as representing the expectation
values of A relative to the eigenvalues of B."
I am not "technically savvy" (cf. footnote 5), and
cannot grasp the line of thought in the three excerpts from your essay,
particularly the adverb "roughly" in footnote 5.
To be specific, the relational emergence of time poses a paradox, which
may be explained as follows.
Imagine a herd of Buridan donkeys, with two stacks of hey in front of
each donkey, such that the distance from any given donkey to its stacks
of hey is determined -- relationally -- by 'the rest of the donkeys in
the herd'.
Consider a donkey called A, and denote 'the rest of the donkeys in the
herd' with B, to match your idea in the second excerpt above.
We end up with totally halted/frozen set of (Buridan) donkeys, because
donkey A has to wait until the distance to its stacks of hey is
determined by B , but any donkey that belongs to the subset denoted
with B has to wait until the distance to its stacks of hey is
determined -- relationally -- by A.
And since none of the donkeys is "privileged in any sense" (cf. above),
the same halting occurs for all donkeys.
I restrict the discussion to classical donkeys in order to make the
presentation of the paradox easier to follow. Hope you can solve this
'classical Buridan donkey paradox', and show that the "relational
emergence of time" matches the time read by your wristwatch. Then
please proceed to the mystery outlined in your footnote 5 above.
Good luck.
Dimi Chakalov
------
Dimi Chakalov wrote on Dec. 10,
2008 @ 14:31 GMT
Dean:
RE your reply from Dec. 4, 2008 @ 02:16
GMT: to get the dynamics for 'the whole universe' -- the only
'truly isolated system' -- your first off task is to define some
reference object with respect to which you can talk about 'the whole
universe'. As you acknowledged, your procedure is 'local', hence you
are forced to "employ different internal times and patch them together
(using some suitable transformation rules)", which in turn makes your
"relational evolution" look like pulling yourself (and your horse) out
of the swamp by your own hair (Baron Munchausen).
The task is known since Aristotle -- recall The First Cause and Karel
Kuchar's Unmoved Mover ("The Problem of Time In Quantum
Geometrodynamics", in "The Arguments of Time", ed. by Jeremy
Butterfield, Oxford University Press, Oxford, 1999, p. 193).
I'm afraid you have completely missed the argument in the Buridan
donkey paradox.
D.C.
Three questions to the
technically savvy (cf. footnote 5 above)
readers:
Q1: If you allow all
donkeys to negotiate their 'relational evolution' in the global mode of time, as explained eloquently in Wikipedia, would you observe their collective
holomovement (like a shoal of fish swinging along a coral reef) and
their "quantum wave"?
Subject: The Hamiltonian formulation of General Relativity is
inherently flawed
Date: Tue, 2 Sep 2008 21:17:06 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Natalia Kiriushcheva <nkiriush@uwo.ca>
Cc: Angelo Loinger <angelo.loinger@mi.infn.it>,
Laszlo Szabados <lbszab@rmki.kfki.hu>,
Robert M Wald <rmwa@midway.uchicago.edu>
Dear Natalie,
I read with great interest your latest paper [Ref. 1].
Regarding the issue of (active) diffeomorphism invariance, and the task
for avoiding the restriction imposed by the "slicing" of spacetime (ibid.), perhaps you may wish to check out
----
[Ref. 1] Natalia Kiriushcheva et al., The Hamiltonian formulation of
General Relativity: myths and reality, arXiv:0809.0097v1 [gr-qc], http://arxiv.org/abs/0809.0097
p. 7: "The conclusion about the results of [19] and [26] should be that
the ADM decomposition is inessential and incorrect because it does not
lead to diffeomorphism invariance. This discrepancy between these two
recent results vindicates Hawking's old statement [27] "the split into
three spatial dimensions and one time dimension seems to be contrary to
the whole spirit of relativity", ... .
...
pp. 8-9: "In GR, an entire spatial slice can only be seen by an
observer in the infinite future [34] and an observer at any point on a
space-like surface does not have access to information about the rest
of the surface (this is reflected in the local nature of (3) in field
theories). It would be non-physical to build any formalism by basing it
on the development in time of data that can be available only in the infinite future and trying to fit GR into
a scheme of classical determinism
and nonrelativistic Quantum Mechanics with its
notion of a wave function defined on a space-like slice.
"The condition that a space-like surface remains space-like obviously
imposes restrictions on possible coordinate transformations, thereby
destroying four-dimensional symmetry, and, according to Hawking, "it
restricts the topology of space-time to be the product of the real line
with some three-dimensional manifold, whereas one would expect that
quantum gravity would allow all possible topologies of space-time
including those which are not product" [27].
"This restriction, imposed by the slicing of
space-time, must be lifted at the quantum level [35]; but, from our
point of view, avoiding it at the outset seems to be the most natural
cure for this problem."
==================
Subject: Quantizing Spacetime: Quantum Mechanics 101
Date: Wed, 29 Oct 2008 05:00:00 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: John <john.g.taylor@kcl.ac.uk>
Cc: Franklin Felber <felber@san.rr.com>,
Fran De Aquino <deaquino@uema.br>,
Alexander Kaganovich <alexk@bgumail.bgu.ac.il>,
Kazunari Shima <shima@sit.ac.jp>,
Motomu Tsuda <tsuda@sit.ac.jp>,
Chris.van-den-Broeck@astro.cf.ac.uk
Dear John,
I agree with you that in the quantum realm the spacetime cannot be an
affine manifold [Ref. 1], but for quite different
reasons,
Subject: Re: The Ashgate
Companion
Date: Wed, 29 Oct 2008 20:58:25 +0200
From: Dimi Chakalov <dchakalov@gmail.com>
To: Dean Rickles <drickles@ucalgary.ca>,
Dean Rickles <d.rickles@usyd.edu.au>
Cc: david.wallace@balliol.ox.ac.uk
Just never ever tell people you knew nothing about 'Quantum Mechanics
101'.
D.C.
-------------
Subject: Re: The Ashgate Companion
From: Dean Rickles <drickles@ucalgary.ca>
Date: Wed, 5 Dec 2007 00:52:12 +1100
Message-Id: <6D064C12-437E-455C-A3AF-6F0EB8DC93AA@ucalgary.ca>
To: Dimi Chakalov <dchakalov@gmail.com>
Cc: david.wallace@balliol.ox.ac.uk,
Dean Rickles <d.rickles@usyd.edu.au>
Dimi,
You won't receive the kind of polite response Chris Isham gave from me: instead, I
cordially invite you to get stuffed. Do some real work instead of
writing all of these stupid, rude emails - and go learn some physics if
you're genuinely interested in it!
[snip]
==================
Subject: Black holes?
From: Dimi Chakalov <dchakalov@gmail.com>
To: Demetrios Christodoulou <demetri@math.ethz.ch>
Cc: Shahar Hod
<shaharhod@gmail.com>, Jarmo
Makela <jarmo.makela@puv.fi>
Dear Dr. Christodoulou,
I searched all 594 pages of your arXiv:0805.3880 v1 for
"Loinger". Can't understand why you didn't even mention his articles
and monographs,
Perhaps you could explain your professional opinion on Prof. Loinger's
work in arXiv:0805.3880 v2, say.
Your two colleagues in the CC: list also ignored some basic facts about
those alleged "black holes".
Sincerely yours,
D. Chakalov
----
Note: Suppose naked
singularities (singular points that are not preceded by a
trapped region, and which are causally connected to infinity) occur "in
the gravitational collapse of a scalar field", as suggested by
Demetrios Christodoulou in arXiv:0805.3880 v1, by
working with "a spacetime manifold (M, g), with boundary, smooth
solution ofthe vacuum Einstein equations". How
come none of these vicious "naked singularities", the timeliked
ones included, have happened in the past 13.7 billion years?
I can't trust any 'smooth
spacetime manifold with boundary' obtained under
such drastically simplified case, because it may produce a hoax: some geodesically
complete spacetime tending to flatness at infinity along any
geodesic, thus "establishing the stability of Minkowski space" in the
framework of GR (Surveys in differential geometry: Essays on Einstein
Manifolds, 365-385, Surv. Diff. Geom. VI, Int. Press, Boston,
MA, 1999). If this were the case chosen by Nature, Demetrios
Christodoulou might be able to convert apples (GR) into oranges (STR),
along with "providing the basis for a rigorous theory of gravitational
radiation", but only after denouncing all rigorous proofs to the
opposite, from Angelo Loinger.
Unless you focus exclusively on
vacuum Einstein equations, there is no way to derive STR as some smooth
limit of GR -- read Anatol Logunov. The
very idea that Minkowski spacetime would provide "the basis for a
rigorous theory of gravitational
radiation" makes no sense, unless the reader of these lines can
demonstrate some smooth reversible transition between GR and STR. And
because the "gravitational radiation" makes no sense in the full
non-linear GR, the transition GR <--> STR (the alleged "basis for
a rigorous theory of gravitational
radiation") doesn't make sense either.
In the final chapter of arXiv:0805.3880
v1, Demetrios Christodoulou writes: "We are now ready to reach the
aim of this work, namely the analysis of the formation of trapped
surfaces", that is, a spacetime region where the future light cones
have cross-sectional areas decreasing with (or in the local mode of) time.
But if you employ the global mode of time,
you may never reach a trapped surface, ever.
Demetrios Christodoulou was
awarded 100,000
Swiss Francs, since he somehow managed to convince people that all naked
singularities, although inevitable, were somehow "unstable" and
therefore "physically irrelevant", contrary to Murphy's Law that has
been running in the past 13.7 billion years. If Demetrios Christodoulou
can embed the Dynamic Dark Energy (DDE) of [X] into his
"spacetime manifold (M, g), with boundary, smooth solution ofthe vacuum Einstein equations", and then
demonstrate that [X] does not, in any way, increase the chance
for any "naked singularity" whatsoever, I believe he will be nominated
for a Nobel Prize, and I will immediately delete this web site, of
course.
"And off course the
nature of the future “boundary” of the maximal development, when incompletess
holds, remains an open question", says Demetrios Christodoulou in arXiv:0805.3880
v1, p. 590. There are two typos in his last sentence, which is yet
another reason to correct arXiv:0805.3880 v1 and
produce a second (and maybe abridged) version, after studying carefully
the articles and monographs by Angelo Loinger.
Meanwhile, Demetrios
Christodoulou will have to suggest a rigorous solution to the Cauchy problems for the field equations and
other intricate problems of present-day
GR, ensuing from "a spacetime manifold (M, g), with boundary,
smooth solution ofthe vacuum Einstein
equations". In other words, he will first have to solve the real problems of GR, to address the objections
to those "black holes" and "gravitational waves" presented by Angelo Loinger. It may take some time to complete
arXiv:0805.3880 v2, even if Sergiu Klainerman
agrees to help him.
When will Demetrios
Christodoulou start working on arXiv:0805.3880 v2? When pigs fly, I'm
afraid.
D. Chakalov
May 27, 2008
Last update: May 31, 2008
==================
Subject: "The basic rules of the game are still to be uncovered", 1999
Bôcher Speech
Date: Tue, 27 May 2008 22:55:58 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Sergiu Klainerman <seri@math.princeton.edu>
Dear Dr. Klainerman,
I wonder if you'd be interested in exploring some old ideas summarized
at
Note: I recently asked Prof.
Sergiu Klainerman for a copy from his paper "On Cosmic Censorship and
the Cauchy Problem", presented at the conference "BEYOND
EINSTEIN" (Mainz, 22-26 September, 2008). He first sent me by
mistake another paper, which is not yet completed (cf. my email from Wed, 12 Nov 2008 below), and then sent the
requested paper (cf. my email from Thu, 13 Nov
2008), which contained only the slides from his talk "On Cosmic
Censorship and the Cauchy Problem" at the conference in Mainz.
Notice below
my remark regarding elliptic differential equations, and follow the
links. I claim that 'strongly hyperbolic' Hamiltonian description of GR
is a myth, meaning that no physically realistic spacetime can be made
'globally hyperbolic' in the strict mathematical sense. The issue is
quite technical, and I was hoping that Sergiu Klainerman might be
interested. Since he didn't react to my email from Thu, 13 Nov 2008, I will try here to explain
the issue in a way comprehensible to my teenage daughter, stressing
that "the basic rules of the game are still to be uncovered", as Sergiu
Klainerman himself acknowledged in 1999.
Imagine a shoal of fish swinging along a coral reef, and try to design
the proper spacetime of their holomovement
(read a story from April 1984).
To obtain such holomovement, some "global web" of quasi-instantaneous correlations would be
required, such that all fish negotiate
their collective movement in the realm of 'potential reality' -- in
addition to, and "in the same time of", their communications by signals
sent with speed not exceeding the "speed" of light in vacuum (local
mode of time). Notice that we're talking 'relational ontology', as in
the Buridan donkey paradox.
There should exist an additional
input from 'the whole shoal', such that it does not make fish
trajectories "non-local" but quasi-local. This is the so-called
sufficient condition for fixing
the dynamics of bodies in GR. It works in the human
brain too (cf. Neurophysiology
101). The story goes back to Aristotle, which is why this additional connection was named after him.
Just ponder on the "appearance" of the affine structure and Christoffel
symbols (G. Nerlich and L. Szabados), and try to figure out what
agent or entity can develop an affine connection
and make the Hausdorff manifold connected,
as well as connect a bunch of "points" to form a 'set' (Georg Cantor).
It is not possible to derive The Aristotelian Connection from the
additional geometric structure you postulate on such connected
spacetime manifold afterwards, such as a metric (R.
Geroch). It is the primitive "binding" agent that acts as a
pre-geometric plenum and
defines the time-orientability and space-orientability
of the physical spacetime M (compared this
to the conformal recipe). It is 'the universe as ONE'.
Physically, it is located both "inside" the infinitesimal and
"outside" the cosmological horizon, thanks to which the spacetime is
"wrapped" by ... itself.
In other words, the "direction"
along which the self-wrapping of spacetime is produced is physically unobservable
(the balloon metaphor); otherwise the ether will be physically observable.
In short, no "black holes", no CTCs nor
Cauchy problems for Einstein field equations exist in Nature.
But if Sergiu Klainerman or any
other theoretical physicist can design some globally hyperbolic
spacetime with built-in time-orientability and "boundary conditions"
eliminating negative mass, which is also
free from such quasi-instantaneous correlations and "constraints" that naturally generate "waves", the suggestions above will be proven redundant,
hence wrong. Currently, there are no physically motivated boundary
conditions in the case of the Einstein equations, nor do we know how to
build a "mirror" for GWs (Alan
Rendall).
D. Chakalov
November 18, 2008
Last update: March 17, 2009
Subject: Re: "On Cosmic Censorship and the Cauchy Problem" (request for
paper)
Date: Thu, 13 Nov 2008 11:29:38 +0000
From: Dimi Chakalov <dchakalov@gmail.com>
To: Sergiu Klainerman <seri@math.princeton.edu>
Dear Sergiu,
> This is what I have meant to send you.
Seems to me that Slide 4, The Problem of Evolution, contains the same
unresolved problem mentioned in footnote 4 of your unfinished manuscript.
It is also very unclear to me how Bruhat-Geroch could cook up some
"unique, future, maximal, globally hyperbolic"
development by eliminating all traces from those cases which require elliptic
differential equations. I mean, the distribution of matter should
be governed by instantaneous correlations *as well*, wise men say :-)
Regards,
Dimi
-------
Subject: Re: "On Cosmic Censorship and the Cauchy Problem" (request for
paper)
Date: Wed, 12 Nov 2008 23:36:00 +0000
From: Dimi Chakalov <dchakalov@gmail.com>
To: Sergiu Klainerman <seri@math.princeton.edu>
Thank you very much, Dr. Klainerman.
It seems to me that your manuscript is not yet completed, and the most
important issue is placed in footnote 4, p. 4:
"A proper definition of global solutions in GR requires a special
discussion concerning the proper time of timelike geodesics."
I very much hope to read all about this 'special discussion'. If you
can solve the problem of the proper time
of timelike geodesics, I suppose you will suggest a brand new path
toward quantum gravity.
Please keep me posted.
Sincerely,
Dimi Chakalov
35 Sutherland St
London SW1V 4JU
==================
Subject: Graduate Students, Institute for Gravitation and the Cosmos,
Pen State
Date: Fri, 9 May 2008 16:34:50 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Martin Bojowald <bojowald@gravity.psu.edu>,
Victor Taveras <victor@phys.psu.edu>,
David Sloan <sloan@gravity.psu.edu>,
William Robbins <wrobbins@phys.psu.edu>,
Orcan Ogetbil <orcan@psu.edu>,
Stephen Movit <movit@astro.psu.edu>,
Adam Henderson <adh195@psu.edu>,
Chris George <george_c@math.psu.edu>,
Adrienne Criss <acriss@phys.psu.edu>,
Nick Conklin <nbc109@psu.edu>,
Tanja Bode <tbode@gravity.psu.edu>,
Eloisa Bentivegna <eub115@psu.edu>,
Nico Yunes <yunes@gravity.psu.edu>,
Shaun Wood <spw147@psu.edu>,
Edward Wilson-Ewing <euw122@psu.edu>,
Tyler Anderson <tba109@psu.edu>,
Jerzy Lewandowski <Jerzy.Lewandowski@fuw.edu.pl>,
Abhay Ashtekar <ashtekar@gravity.psu.edu>,
Roger Penrose <rouse@maths.ox.ac.uk>
Cc: Daniel Larson <djlarson@psu.edu>
Dear Dr. Bojowald,
It seems to me that you and your colleagues at the Institute for
Gravitation and the Cosmos are wasting your time with "loop quantum
gravity" and "gravitational astronomy", which might ruin the career of
many graduate students at Penn State,
and waste time, money, and computational resources (cf. the note below).
Consider your latest Report
IGC-08/4-3, arXiv:0805.1192v1
[gr-qc], in which you wrote: "How quantum gravity regularizes
the big bang depends
crucially on properties of the quantum state."
I'm afraid you do not understand
Quantum Theory in the first place. See
If you and/or some your colleagues wishes to reply, please do it
professionally. It's about time.
Sincerely,
Dimi Chakalov
----
"Penn State is home to three of the 200 fastest computers in the world.
One of those – the Pleiades Cluster
– is owned by the Physics Departments Gravity Group and is dedicated to
the analysis of data from the Laser Interferometer Gravitational-Wave
Observatory (LIGO), whose goal is the detection of gravitational waves
and their use as a new tool of astronomical discovery."
Note: The tacit recipe for quantum gravity, which Martin Bojowald and
his boss Abby Ashtekar use, is this: take Quantum Mechanics and General
Relativity in their current formulation, with all their well-known
problems, blend them into some new theory (called "loop quantum gravity"), and hope that the
problems of QM may be solved from GR, and the problems of GR may be
solved from QM. Don't try to solve any of the initial problems of QM
and GR beforehand [Ref. 1]. Just hope and
pray that the "good parts" from QM and GR will cure all problems.
Imagine this: you have a car
(QM) which runs quite well on some roads, but fails miserably on some essential roads, and a helicopter (GR) that also
runs in some favorable weather conditions, but is totally useless in bad weather. Take the car and the helicopter, and
build a brand new vehicle, which will run better than the car and fly
better than the helicopter, and will also allow you to dive deep into
the ocean, as a perfect submarine.
That's the tacit recipe for
"loop quantum gravity". It also sweeps the garbage under the rug (e.g.,
"time-like singularities, however, do not generically arise", and
"generic singularities are then space-like or null", [Ref. 1, footnote 19]): just one naked timelike singularity in the past 13.7
billion years would be sufficient to destroy the whole universe. If Max
Plank was following the "reasoning" of Martin Bojowald, he would have
never discovered the quantum of action, since we all know that the
ultra-violet catastrophe, just like a naked
timelike singularity, has never happened.
But let's focus on a very simple
issue: does GR allow for any sensible formulation of the question of
the dimensionality of the world? Can you talk about 'dimensions' if you
cannot extend them into an arbitrarily large volume of 3-D
space?
"If the theory does not allow
us, even in principle, to extend solutions arbitrarily far
in one direction, it may be difficult to view this direction as a
dimension of the world", says M. Bojowald [Ref. 1].
It isn't "difficult". It is
impossible.
"One of the biggest mysteries is
that we live in a world in which it is possible to look around, and see
as far as we can" (L. Smolin, Three Roads to Quantum Gravity, p. 205).
If Martin Bojowald wishes to
speculate about the dimensionality of the world in the framework of GR,
he needs to fix the dynamics of GR in the
first place. Namely, he will first have to introduce 'boundary of
space' and 'global conservation laws' in GR (see the "causal diagram of
space-time region integrated over to derive global
conservation laws", Ref. 1, Fig. 8.1, p.
139).
Don't expect to get help from
QM, and subsequently from "loop quantum gravity". Get real.
D. Chakalov
July 31, 2008
[Ref. 1] Martin Bojowald, Canonical Relativity and the Dimensionality
of the World, arXiv:0807.4874v1
[gr-qc]. In: Relativity and the Dimensionality of the World,
Ed. by Vesselin Petkov (Springer, 2007,
ISBN: 1402063172),
Ch. 8, pp. 137-152.
"8.3.1 Singularities
p. 148: "Locally, solutions to Einstein’s field equations always exist
and determine the space-time metric as well as manifold. This played a
crucial role in our arguments given so far where we wanted to eliminate
backgrounds and consider dynamical space-time. These equations are,
however, non-linear and so global aspects are more difficult to
control. One consequence is that most solutions which we think are
relevant for what we observe are singular when extrapolated in general
relativity. They allow one to describe space-time only for a finite
amount of proper time for some, and in some cases all, observers after
which the classical theory breaks down [14]. This is usually
accompanied by a divergence of curvature, but in any case represents a finite
boundary to space-time.
p. 149: "If the theory does not allow us, even in principle, to
extend solutions arbitrarily far in one direction, it may be
difficult to view this direction as a dimension of the world. (...)
"This is not the case with
singularities. If we are interested in a four-dimensional
interpretation, then, we will have to deal with fundamental limitations
to the extension of four-dimensional objects, including space-time
itself.
---
Footnote 19: "There can also be boundaries to space arising from
singularities where space-time cannot be extended in spatial
directions. Such time-like singularities, however, do not generically
arise in relevant
cosmological or black hole solutions and thus can be ignored here.
(...) Generic singularities are then space-like or null."
---
==================
Subject: E sarà mia colpa se così è?
Date: Fri, 18 Apr 2008 05:36:49 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: ruffini@icra.it, maria.bernardini@icra.it, bianco@icra.it,
letizia.caito@icra.it, chardon@lapp.in2p3.fr, cherubini@icra.it,
dainotti@icra.it, fraschetti@icra.it, geralico@icra.it,
roberto.guida@icra.it, barbara.patricelli@icranet.org,
michael.rotondo@icra.it, jorge.rueda@icra.it, xue@icra.it
Cc: Angelo Loinger <angelo.loinger@mi.infn.it>
Dear colleagues,
I greatly admire your work on GRBs, but it seems to me that the
so-called black holes require a crucial object called event horizon, which is ill-defined in GR,
simply because cannot be defined within GR (I will be happy to provide
references). In other words, if something walks like a duck and quacks
like a duck, it may not necessarily be a duck ("black hole").
"GRBs are giving the first clear evidence for the extraction of energy
from black holes during the last phases of their formation process.
This new form of energy is unprecedented in the Universe, both for its
magnitude and its very high efficiency in transforming matter into
radiation, which reaches the 50% limit while the nuclear energy reaches
efficiency of 2-3% only. These sources, with their energy of 1054
ergs/pulse, dwarf the corresponding nuclear energy events with their
energy of ~ 1022 ergs/pulse."
----
Note: In the framework of the
theory proposed at this web site, the energy of GRBs could be identical
to the so-called "dark energy": please see the
Ansatz from 3 November 2002,
and consider the possibility that "negative energy densities" could
stay quietly in the 'potential future' (global mode
of spacetime) produced by the putative arrow of
spacetime.
All you may need is to model the
universe as a huge brain which "thinks" with its holistic ("dark") stuff, and also to
consider not two but three ontologically different forms of
reality, as explained here.
As to the references on the
so-called event horizon, check out the review articles by Jonathan Thornburg and Michael
Cohen et al. (emphasis and links added). Regarding the
"boundary of the region of the spacetime that is causally connected to
future null infinity", check out the proposed update of G.F.R Ellis'
1984 finite infinity proposal here.
Notice also the notion of "when" in the second review article below.
To the best of my knowledge,
nobody has tried so far to implement John
Cramer's hand-shaking interpretation of QM to GR, by employing the third option regarding GWs, and Kevin
Brown's idea of "two more
"curled up" dimensions of angular orientation to represent the possible
directions in space": these two "curled up" dimensions may reside in
the "ether", and provide for the "dark" torsion in GR. The Angels
are in the details of the "boundary
points to all null-geodesics" (Jörg
Frauendiener) and the
geodesic hypothesis (Alan Rendall).
D. Chakalov
April 18, 2008
Last update: September 17, 2008
Michael I. Cohen et al., Revisiting Event Horizon Finders, arXiv:0809.2628v1
"There are two useful concepts
to describe the location of black holes in a spacetime, apparent
horizons (AH) and event horizons (EH). An EH is the true
surface of a black hole: it is defined as the boundary of the region of the
spacetime that is causally connected to future null infinity. Because
the definition of the EH involves global properties of the spacetime,
one must know the full future evolution of the spacetime before
the EH can be determined exactly. This difficulty has led researchers
to instead identify black holes with apparent horizons, (...).
...
"Since outgoing null geodesics diverge from the event horizon when
going forward in time, when going backward in time they will
converge onto the event horizon [11, 12]. All recent EH finders use
this observation, and follow null geodesics or
null surfaces backward in time [13, 11, 12, 14, 15, 16, 17, 18, 19,
6]."
"An interesting feature of this
interpretation is that, in addition to the usual 3+1 dimensions,
spacetime requires two more "curled up" dimensions of angular
orientation to represent the possible directions in space. The need to
treat these as dimensions in their own right arises from the
non-transitive topology of the pseudo-Riemannian manifold. Each
point [t,x,y,z] actually consists of a two-dimensional
orientation space, which can be parameterized (for any fixed frame) in
terms of ordinary angular coordinates q and f . Then
each point in the six-dimensional space with coordinates
[x,y,z,t,q,f ] is a terminus for a unique pair of spacetime rays,
one forward and one backward in time."
============
Subject: The Arrow of Spacetime
Date: Mon, 2 Jun 2008 04:27:30 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: Justin Khoury <jkhoury@perimeterinstitute.ca>
Cc: Laura
Mersini-Houghton <mersini@physics.unc.edu>, Andreas
Albrecht <albrecht@physics.ucdavis.edu>,
Paul Davies <deepthought@asu.edu>,
Brian Greene <greene@phys.columbia.edu>, Robert
M Wald <rmwa@midway.uchicago.edu>,
Roseanne Cheng <rmcheng@physics.unc.edu>,
editorial@nyas.org
Dear Dr. Khoury,
I regret that wasn't informed about your Conference on October 15th
last year,
If some day you decide again to gather people to discuss such issues,
please drop me a line. I suppose your colleagues would agree to discuss
ideas that are totally different, if not incompatible, with theirs.
Finally, let me take this opportunity to invite you and all your
colleagues to attend my talk (cf. the subject line)
in Munich on September 21, 2008,
Note: If we are to treat the
spacetime as 'one entity', after Hermann
Minkowski, a hypothetical 'arrow of time' can only make sense if an
'arrow of 3-D space' is introduced as well; hence the talk is about a
hypothetical arrow of spacetime.
If we reject the hypothesis
about some "curved block space-time" (G F R Ellis, gr-qc/0605049 v2, footnote 3), one option to consider is that
the cosmological time arrow may be driven by some hidden "dynamic dark energy" producing an arrow of spacetime. I plan to (i)
elaborate on the "boundaries" of such dynamical spacetime (basically,
this is G F R Ellis’ 1984 notion of finite
infinity, updated from Aristotle),
and (ii) introduce the so-called 'scale
relativity principle' aimed at clarifying the nature of 3-D space.
The prelims to Quantum Theory
& General Relativity are here and here.
The talk will be on Sunday, 21
September 2008, in Munich (the exact venue will be announced by August
31st), from 10 AM to 10:45 AM, after which a lively discussion is
anticipated.
Please confirm your
participation by August 30, 2008.
Thank you.
"The views of space and time which I wish to lay before you have sprung
from the soil of experimental physics, and therein lies their strength.
They are radical. Henceforth space by itself, and time by itself, are
doomed to fade away into mere shadows, and only a kind of union of the
two will preserve an independent reality."
(Raum und Zeit, in: Vorträge von der 80. Naturforcherversammlung
zu Köln, Physikalische Zeitschrift, 10, 104-111,
1908)
===================
Subject: Re: Young scholars from the New Vision 400 conference
Date: Wed, 4 Jun 2008 09:00:52 +0800
From: Yi Wang <wangyi@itp.ac.cn>
Sender: tririverwangyi@gmail.com
To: Dimi Chakalov <dchakalov@gmail.com>
Dear Dimi,
Thanks a lot for your information. The god-does-not-play-dice is really
a
good website.
You can find information of the New Vision 400 conference in this URL: http://www.nv400.org/
Best regards,
Yi Wang
2008/6/4 Dimi Chakalov <dchakalov@gmail.com>:
> Dear Dr. Wang,
>
> I wonder if you could email all young scholars from the New Vision
400
> conference this URL:
>
> http://www.god-does-not-play-dice.net/Szabados.html#talk
>
> It seems to me that adult
scholars aren't terribly interested in
> quantum gravity.
>
> Kind regards,
>
> Dimi Chakalov
>
Note: Yi Wang (Institute of Theoretical Physics, CAS, Beijing) has
written an exceptionally clear article for the young scholars
competition at the New
Vision 400 Conference [Ref. 1]. And because China
will become -- beyond any doubt -- the world leader in science and
technology by 2015, I strongly suggest to all readers of these lines to
register for the Conference (available from June 6, 2008),
and start learning Mandarin (it is
very tough, yes, but we have no choice).
Now, regarding the "eternal
inflation" [Ref. 1]: from the perspective of the
current theory of relativity, the alleged "inflation" is an
anti-relativistic, that is, acausal phenomenon (cf. Edward W. Kolb).
Its "dynamics" requires the hypothetical 'global
mode of time'. Each "event" from the latter consists of "infinitely
many" potential events, so if we "get
off the train", we will use only one event from the local
mode of time of the train, yet we'll have infinite "time" to "walk
outside the train". Every human brain
has access to the global mode of time, and every human brain uses a perfectly smooth and continual
local mode of time.
From the perspective of the 'time read by a physical clock', however,
the global mode of time will inevitably look frozen, like the proper time of
a photon. Not because the global mode
of time pertaining to 'the universe as ONE'
doesn't evolve, but because the poor inanimate clock cannot "read" all
infinite potential events that are embedded "within" each and every
complex potential event from the global mode of time. Your inanimate
clock can read only the time parameter of, say, a Frisbee on a
background Minkowski space, but not the proper time [tau] in the
background-free GR (cf. C. Rovelli).
So, how is this model of 'the
universe as a brain' related to
"inflation"? In one sentence: the alleged "inflation" is an artifact
from the current, and incomplete, GR,
because with the present-day GR it looks like 'one non-relativistic
event from the cosmological time, as read by some physical clock', and
subsequently people think of it as something that has happened across
the entire universe, right "after" The Beginning, with "duration" just 10-30 sec, as
measured with their clock "inside the
train". But with the additional degree of freedom called 'global mode of time', this
seemingly "10-30 sec" would be infinite for all
local observers "inside the train",
because their watch will read this "last" portion of deflation time as
'getting asymptotically close to The Beginning', without actually
reaching it -- ever.Thus, once created with
such Aristotelian "boundaries",
the universe becomes truly eternal for all observers in the local mode
of time, since they are "wrapped" by the holistic state of 'the universe as ONE' (global mode of
time), which is also known as the Aristotelian First Cause. Curiously, in such model
you have indeed "eternal inflation" in the local mode of time, as well
as a dual age of the universe:
finite in the global mode (currently some 13.7 billion years "after"
The Beginning), and infinite/indecisive in the local (teleological) mode of time, as read
by your wristwatch "inside the train".
And because 'the universe as ONE' is simultaneously
"outside" the boundaries of the local mode of spacetime and
"inside" it -- in the "dark gap"
between everytwo successive events from the
local mode -- no observer in the local mode can actually "reach" the
Beginning-and-End (also known as [John 1:1]).
Otherwise you will be baffled
with the question from L. Mersini-Houghton, "what selected such
extremely unlikely initial conditions for the birth of our universe?" (arXiv:0809.3623v1,
p. 2), and with the metaphysics of some "conformal boundary where the
space-time conformal geometry extends smoothly to a region prior
to it" (Roger
Penrose).
I suppose the young scholars attending the New Vision 400 Conference
would have many questions to ask -- please don't hesitate! As usual,
there are no definite answers. Read, for example, Eric Linder (11
February 2008), Dark
energy, Scholarpedia, 3(2):4900, and ponder on the
following question: how the two tug-of-war effects of gravity, CDM and dark energy of [you name it], shape
the galaxy formation and evolution? The current stipulation is that
"the dark energy hardly affects galaxy formation and evolution at all,
since galaxies form in the matter dominated era" (Ben Moore,
email communication, 4 June 2008). But we may accept such opinion only
if we know the "dynamics" of the evolution of that "dark energy of [you name it]", then solve the Coincidence
Problem, and finally prove that the two "dark" effects of gravity do not
have common origin, to make sure that DDE does not play some
hidden role in the galaxy formation and evolution. Better keep our mind
open and wait for the BOSS.
As to the adult scholars, if you encounter the familiar
statement endorsed by Chris Isham --
"the background Newtonian time
appears explicitly in the time-dependent Schroedinger equation" --
don't buy it. I'm afraid this widely advertised opinion is 'not even
wrong': see the implications from KS Theorem above,
and readJan Hilgevoord's
article from here.
Chris
Isham may have different opinion, but he still hasn't provided any
evidence whatsoever.
D. Chakalov, a.k.a. "just another crank"
June 4, 2008
Last update: June 5, 2008
P.S. Perhaps because nobody
knows how to deal with the cosmological "constant" interpreted as
vacuum energy (cf. Richard Feynman), many
people are ignoring this fundamental task, and suggest a whole zoo of ad
hoc postulated "scalar fields" (cf. T. Padmanabhan) and other exotic
stuff, which reminds me of an old joke I heard from my daughter:
Q: What is green, lives
underground, has one eye, and eats stones?
A: The One-Eyed Green Underground Stone Eating Monster!
Now, replace the question line
with this one, after Daniel
Eisenstein:
Q: What would be like tossing a
ball in the air, waiting for it to fall, and instead seeing it
accelerate upwards and disappear from sight?
I certainly cannot answer it,
since it would seem that the ball has acquired some kind of self-acting faculty, and has also gained
access to some pool of "negative
mass" that looks like the "dark
energy" from the undisturbed
quantum vacuum (when nothing is "looking at it" with Casimir effect,
say), so the quantum-vacuum "dark stuff" may qualify as 'quantity zero'
(George F R Ellis), such that it
can be actualized only through some innocent "closed system";
for example, a ball that we would toss in the air, waiting for it to
fall, and instead seeing it accelerate upwards and disappear from sight
due to that sneaky quantum-gravitational "dark stuff" inside it, ....
Well, this doesn't make much
sense as a theory for propellantless propulsion,
so let's wait for the BOSS
instead. Meanwhile, keep in mind the two main unresolved issues in GR.
First, any energy contribution to the physical world, which
comes from 'pure geometry' -- the grin of the cat without the cat, as
noticed by Alice -- will
inevitably look "dark", in the sense that there is no way to trace back
its origin [Ref. 2]. My interpretation is that
such holistic, "contextual" effects
cannot be represented with any tensor
in principle: it would be like
"tossing a ball in the air, waiting for it to fall, and instead seeing
it accelerate upwards and disappear from sight", as explained
eloquently by Daniel
Eisenstein. Put it differently, proper energy conservation laws in
GR are prohibited from the outset (e.g., consider the inevitable
"unphysical" stuff in Wald & Zoupas, gr-qc/9911095), so if we
wish to understand GR, we need quantum
gravity.
Secondly, there is no way to
make GR "parametrized theory" (cf.
C. G. Torre above), because the genuine
non-linear "time parameter" in GR cannot be read by any
physical clock (cf. C. Rovelli): all
instants from this non-linear "time" are the nexus of an already-completed
negotiation between the two parts from the Einstein filed equations. As
Laszlo Szabados stressed above (emphasis added),
"this is a consequence of a much deeper fact, namely that the metric
has a double role: it is a field variable and defines the geometry at
the same time." And also John Baez:
"the metric is treated as a field which not only affects, but also is (at
the same time - D.C.) affected by, the other fields".
It should be agonizingly clear
to all young researchers from the New Vision 400 Conference that their
wristwatch will display such non-linear time as "frozen": it is logically
impossible for an unanimated physical system, evolving along a linear
(polynomial) time, to literally create its time,
and at the same time evolve in that same time. Only the
human brain could "read" such
non-linear and quasi-localglobal
mode of time; in present-day theoretical physics, it has produced
the notions of Heraclitian time (p. 13) and the so-called auxiliary
internal time (pp. 8-9), in Macias & Quevedo, arXiv:gr-qc/0610057v1.
Notice that if you prefer to
treat the human brain as some unanimated zombie
or IGUS (cf. Jim Hartle), you will have to consider
the human mind and consciousness as some unphysical ghosts that can act
directly on the brain and the physical world (creating,
for example, the "illusion" of time, cf. Hermann
Weyl). On the positive side, perhaps you'll never get insults from the established
theoretical physics community, and may even join the famous LIGO Scientific Collaboration.
On the negative side, I'm afraid you will be ready to retire.
Check out, again, the prelims to
Quantum Theory & General Relativity here
and here, the story about the Higgs boson here, and make your (free will?)
choice. More on 21.09.2008.
"One of the key problems in
quantum gravity is the non-renormalizable nature of gravity. In order
to have a renormalizable or finite theory for gravity, one need to
suppress the quantum fluctuations in the high energy
regime. On the other hand, the slow roll eternal inflation needs large
quantum fluctuations. So it is likely for quantum theory effects to
kill slow roll eternal inflation. One explicit example of this general
argument is shown in Subsection D of this section.
"It is well known that it is very difficult to construct a measure for
eternal inflation. Two classes of measures are considered in the
literature, namely, the global [6, 7] and local [8, 9, 10] measures.
However, regardless of technical difficulties such as divergences or
gauge dependence, both the global and local measures suffer problems of
the nature of quantum gravity."
[Ref. 2] Yurij
Baryshev (June 25, 2008), Energy-momentum of the
gravitational field: crucial point for gravitation physics and
cosmology, Problems of Practical Cosmology, June 23-27, 2008, St. Petersburg,
Russia, pp. 1-3.
“Schrodinger
(E. Schrödinger (1918), Phyz. Zeitschr. 19, 4) showed
that the mathematical object tiksuggested
by Einstein in his final general relativity for describing the
energy-momentum of the gravity field may be made vanish by a
coordinate transformation for the Schwarzschild solution if that
solution is transformed to Cartesian coordinates. Bauer (H.
Bauer (1918), Phyz. Zeitschr. 19, 163)
pointed out that Einstein's energy-momentum object, when calculated for
a flat space-time but in a curvilinear system of coordinates, leads to
a nonzero result. In other words, tikcan
be zero when it should not be, and can
be nonzero when it should.
…
“How can one detect, localize, hence extract energy from a
non-localizable field by means of an antenna, like in gravitational
wave detectors? If there is no local energy density of the field,
then there is no energy in a finite volume,
too.”
================
Subject: "The quasiclassical realms of this quantum universe", arXiv:0806.3776v1 [quant-ph]
Date: Wed, 25 Jun 2008 05:13:46 +0300
From: Dimi Chakalov <dchakalov@gmail.com>
To: IGUS Jim
<hartle@physics.ucsb.edu>
Hi Jim:
Back in January 1997, I sent you my critical comments regarding your gr-qc/9701022.
I haven't yet received your professional reply, so I will only suggest
you to check out my essay 'Quantum Mechanics 101' at
In your terminology, it is about the dynamics of the reversible
transition [non-settleable bets] <--> [settleable bets] , after
your arXiv:0801.0688v2
[quant-ph].
If you wish to speculate professionally on "the quasiclassical realms
of this quantum universe", perhaps you should read your papers a bit
more carefully.
Take care,
Dimi
----
Note: The physically
observable part of the quantum system -- the three
colored legs above -- can indeed form "an
exhaustive set of exclusive alternatives" (cf. arXiv:0801.0688v2 [quant-ph])
that belong to one instant from the local mode of time , t ,
as read by your wristwatch. And because the so-called "decoherence"
doesn't work -- try to resolve the task above
-- we need to answer the question of how the quantum system
exists as physically UNobservable dough of potentialities (global mode of time), firstly, and secondly -- how
the "classical world" emerged in the first instants of the cosmological
time, as read by your wristwatch.
So, because no reference to an
external "measurement" agency can be made in quantum cosmology, and the
alleged "decoherence" can't solve the measurement (macro-objectification)
problem nor the Hilbert space problem, I decided to write an essay on 'Quantum
Mechanics 101'.
Perhaps J. B. Hartle will never read these lines, although, as he and M. Gell-Mann stressed, "quantum mechanics is
best and most fundamentally understood in the framework of quantum
cosmology" (ref. [2] in arXiv:gr-qc/0502016).
Notice the task of formulating "a quantum mechanical measurement of some part
of the geometry of some region", from Louis Crane below. In the context
of Donald Salisbury's proposal (cf. arXiv:gr-qc/0105097v1),
some brand new "symmetry group" should be made "projectable" onto the
phase space (cotangent bundle), and the first off challenge of finding
such new "symmetry group" is that diffeomorphism-induced
transformations are not
the sole requirement to achieve "projectability": we need to
incorporate Karel Kuchar's multifingered time (called here global mode of time) which may have the unique
faculty of advancing along directions perpendicular to the constant
time hypersurfaces (recall that we have infinitely many Wheeler-DeWitt
equations -- one equation per space point, cf. Giulini & Kiefer, gr-qc/0611141v1,
p. 16), and hence acquire (hopefully) the origin of some
future-directed timelike vector in classical GR, instead of just
introducing it by hand (e.g., see the initial assumptions in Wald & Zoupas, gr-qc/9911095, from
February 7, 2008). Obviously,
neither Kuchar's multifingered time nor the so-called "explicit (but
unmeasureable) time" (W. G.
Unruh) or 'the Heraclitian
time' of Unruh & Wald can show up as 'observables
in GR'. This is a fundamental issue in GR.
Our poor (inanimate) wristwatch could "read" such
multifingered time only as "frozen"
(eternity blind, John G. Bennett), which in
turn tallies to the idea that the "dynamics" (if any) of GR can only be
generated by constraints, as with the Hamiltonian
formulation of GR.
Notice also that there is no
need to "recover" QM and GR in a "classical limit" (cf. Louis Crane
below), because we have a rock solid "back bone" of the whole
quantum-gravitational realm in the form of 'local mode of spacetime',
at all length scales.
Louis Crane
has of course quite a different opinion, and he has recently been
awarded $135,247 to sort out some "New Approach to Quantum Gravity,
with Possible Applications to the Origin & Future of Life". Well, I
never heard from Louis Crane, but I do hope he isn't some unanimated zombie
or IGUS, and wish him best of luck with his project.
I only regret that Gustaf
Strömberg (cf. below) is not here,
because back in 1961 he wasn't aware of all the "dark stuff" in present-day GR. Surely the
'eternity domain' must be described as non-metrical (ibid.): see the sufficient condition for
the elementary displacement in GR.
D.C.
June 25, 2008
Last update: June 27, 2008
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