Subject: The Montevideo Interpretation of QM Date: Thu, 28 May 2009 13:58:31 +0300 From: Dimi Chakalov <dchakalov@gmail.com> To: Jorge Pullin <pullin@phys.lsu.edu> Cc: Rodolfo Gambini <rgambini@fisica.edu.uy> Hi Jorge, Q1: Does your interpretation of QM presuppose a *falsifiable derivation* of 'undecidable state'? Q1.1: For if the derivation is falsifiable, you can't have 'undecidable state', correct? Q1.2: If it isn't falsifiable, then your interpretation of QM is this: If I can't say anything decisive about the emergence of classical world, then I am *perhaps* using the Montevideo Interpretation of QM. Do you agree? Hope to read your answers in your updated arXiv:0905.4402 v2 [quant-ph] . Regards, Dimi
========================= Subject: Canonical quantization of general relativity
Dear Professor Pullin, Regarding your recent gr-qc/0209008 [Ref. 1]: would you agree that the crux of the problem with the canonical quantization of GR is the notion of a smooth, four-dimensional manifold [Ref. 2]? It leads to the infamous 'block universe' [Ref. 3] which is, I'm afraid, *not even wrong*. Please see http://members.aon.at/chakalov/Krasnikov.html http://members.aon.at/chakalov/Straumann.html http://members.aon.at/chakalov/Brandenberger.html http://members.aon.at/chakalov/Mavromatos.html#5 http://members.aon.at/chakalov/Lloyd.html#2 I will be happy to elaborate. Regards, Dimiter G. Chakalov
References [Ref. 1] Jorge Pullin. Canonical quantization
of general relativity: the last 18 years in a nutshell. Tue, 3 Sep 2002
16:15:39 GMT,
"General relativity only describes gravity, and therefore
a richer theory should come into play in order to have a unified picture
of all interactions, so general relativity indeed should be the limit of
a larger theory. But even if one ignores all other interactions, are we
completely sure that general relativity cannot be quantized? This appears
as an academic question. After all, if we know we need a larger theory,
why bother with determining if general relativity can be quantized?
"But isn't the fact that the theory is non-renormalizable
an indictment of this program? How could one quantize
such a theory?"
[Ref. 2] Robert Geroch. Partial Differential
Equations of Physics. Tue, 27 Feb 1996 14:24:05 -0600 (CST),
"We shall here discuss, in a general, systematic way,
the structure of the partial differential equations describing physical
systems. We take it as given that there is a fixed, four-dimensional manifold
M of "space-time events", on which all the action takes place.
"Fix, once and for all, a smooth, four-dimensional manifold
M [Footnote 1: We take M to be connected, paracompact,
and Hausdorff]. The points of M will be interpreted as the
events of space-time, and, thus, M itself will be interpreted
as the space-time manifold. We do not, as yet, have a metric, or any other
geometrical structure, on M ."
[Ref. 3] 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." ===== Subject: A fourth road to quantum gravity?
Dear Jorge, I hope my email of Wed, 04 Sep 2002 13:06:17 +0300 has been safely received. If not, you can read it at http://members.aon.at/chakalov/Pullin.html Regarding your review of Lee Smolin's "Three roads to quantum gravity" for Physics Today: have you noticed that there could be a fourth road to quantum gravity? The fourth route may come from BIOLOGY, not from individuals
who have been "remarkably insightful in their previous contributions in
physics" (Three Roads to Quantum Gravity, Lee Smolin (reviewed by Jorge
Pullin), Physics Today, 55(2), February 2002, p. 54),
Please see http://members.aon.at/chakalov/faq.html Since you've been working with Rodolfo Gambini since 1990, may I quote his remarkable paper "The Measurement Problem and the Reduction Postulate of Quantum Mechanics" [Ref. 4], in which he introduced non-positive definite density matrices. Only "these matrices are never obtained as the outcome of a macroscopic measurement" [Ref. 4], just like the UNspeakable at http://members.aon.at/chakalov/Vecchi.html and the empty waves that you call gravitational waves, http://members.aon.at/chakalov/Nature.html#note As I said before, I will be happy to elaborate. Best regards, Dimi
References [Ref. 4] Rodolfo Gambini, The Measurement
Problem and the Reduction Postulate of Quantum Mechanics,
"Here, I will show that there is a very natural modification
of the reduction postulate consistent with the rest of the quantum formalism
and with the experimental results that allows to solve the measurement
problem. In other words, the new reduction postulate is always consistent
with the Schrödinger evolution. Within this new approach events can
occur in any quantum mechanical system.
"When the outcome of the measurement is unknown, the state of the system after the measurement has taken place is given by [XXX] (8) and therefore the reduction process does not imply any abrupt change in the density operator. In other words the reduction of the state and the Schrödinger
evolution are now totally compatible.
"The density operator resulting from a macroscopic measurement
will have some negative eigenvalues with absolute values of the order of
the interference terms and therefore it could be called quasi-positive
definite. Due to the unitarity of the Schrödinger evolution it is
immediate to check that the quasi-positivity of the density operator resulting
from a macroscopic measurement is conserved by the evolution.
"The new postulate involves the use of non positive definite density matrices as intermediate steps in the calculation of probabilities for consistent histories. As we have stressed these matrices are never obtained as the outcome of a macroscopic measurement. In this approach the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories. "From a philosophical point of view one can adopt two
alternative realistic interpretations: 1) The state of the system changes
each time an event is produced. However a particular observer that does
not know what events have been produced is allowed to use the state obtained
by evolving the initial state with the Schrödinger equation. 2) If
one adopts the Many Worlds interpretation,
(...)."
========= Subject: gr-qc/0402062
Hi Jorge, Regarding the problem of time, in your recent gr-qc/0402062, you and your co-author wrote: "How is one to do quantum mechanics in such circumstances? The answer is: "relationally"." I'm a bit skeptical. See Daniel Terno, http://members.aon.at/chakalov/Terno.html#1 He mentioned the putative black hole evaporation, too. I can't see much future for LIGO either. What do you think? Best - Dimi ======== Subject: Trying to paint a
painting "relationally", without any canvas
Dear Jorge, Regarding my email of Mon, 16 Feb 2004 07:29:07 +0200, http://members.aon.at/chakalov/Pullin.html#Jorge : I'm reading your recent gr-qc/0402118 v1 of 25 February 2004 [Ref. 5], in which you and your co-authors addressed the problem of background-independent quantum theory of gravity "relationally": "We therefore see that the presence of constraints interfere with the idea of attempting the introduction of a relational time in quantum mechanics. One possibility to circumvent the problem is to get rid of the constraints." I am deeply puzzled by your ordering parameter, n . You wrote: "Without such an ordering parameter, one could not define
the conditional probabilities. The parameter n introduces
a notion of simultaneity in the construction (at a given spatial point).
In fact, several previous attempts to introduce relational times were problematic
due to the lack of such a parameter. For instance, this led Unruh [12]
to attempt to introduce in an ad-hoc manner a "mysterious time" in the
continuum theory to play such a role.
Then you added: "Since up to now we have made almost no assumptions about the nature of the "time" t chosen, it could happen that the same value of t occurs many times upon "evolution" in the parameter n . (...) We will discuss this in detail in a forthcoming paper." I wonder how you would define the ordering parameter n and the "evolution" of the "time" t , without resorting to the "mysterious time" of Bill Unruh. Looks like trying to paint a painting without any canvas whatsoever, http://members.aon.at/chakalov/Carlip.html#1 I think your task is insurmountable, for the following reasons. Please correct me if I'm wrong. The meaning of the expression "a physical object exists" is inevitably relational: we can infer the existence of an object iff there is a point in some state space, in which this object has a total probability of *one* of being at this point, and zero probability of being at any other point. This operational definition -- if you find such ontological probabilities acceptable -- inevitably fixes an instant of time in which a physical object exists "here", and does not exist "not-here". However, if you introduce two or more states of this same object, you will inevitably introduce a background time parameter: there will be two or more points in which the object in question will have a total probability of *one* of being at these points. Am I wrong? The way I see it, in background-independent quantum theory of gravity physical objects cannot, even in principle, enjoy the privilege of existence. If they exist, they will immediately introduce a background "time". Not surprisingly, all efforts to build 3+1-dynamics have failed, http://members.aon.at/chakalov/Carlip.html#Perez We cannot recover the 3+1-D world of tables and chairs from some incomprehensible mesh in which things cannot exist "here" with unit probability. My wild guess regarding your forthcoming paper is that you and your co-authors will have to address this problem. I suppose you have to divide the whole universe into two parts: a point called "here", and 'the rest of the universe'. You need the latter to ensure that the total probability of finding your object in 'the rest in the universe' is indeed zero in some instant of time, since in that same instant of time the total probability of finding your object at the place "here" is indeed one, and hence your object "exists". If so, you'll introduce a background time. Kill this background time, kill the very existence of your physical object. If possible, may I ask you to reply by March 19th, the deadline for abstract submission for GR17. If you can solve the problem, from your perspective, I wouldn't have to say anything, and won't attend the conference, http://members.aon.at/chakalov/Seevinck.html#note I believe you've noticed that my approach is entirely different, http://members.aon.at/chakalov/white_paper.html#NB http://members.aon.at/chakalov/Wagh.html#NB The puzzle is known since 1917, http://members.aon.at/chakalov/Thiemann.html#1 Specifically, no continued collapse can generate a black hole [Ref. 6], and this was just Einstein's opinion, http://members.aon.at/chakalov/Loinger.html The "mysterious time" of Bill Unruh strikes again, right? I believe Karel Kuchar [Ref. 7] has explained the task very clearly: we need to find a "natural time variable" for canonical GR, and to reconcile the standard quantum theory with STR. That's the task of my intended paper for GR17, since I dare to introduce a brand new reference object called Holon, which lives in a putative 'global mode of spacetime'. The math is almost absent, just like in Henri Poincaré's"The Relativity of Space" of 1897. I certainly prefer if you could crack the puzzle, and I don't have to attend GR17 in Dublin (I'm afraid many people will hate to see me there). I will appreciate your comments, as well as the opinion of your distinguished colleagues. Will keep it strictly private and confidential. If possible, please do reply by March 19th. Best regards, Dimi References [Ref. 5] Rodolfo Gambini, Rafael A. Porto and Jorge Pullin, A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence, gr-qc/0402118 v1 of 25 February 2004 "... the resulting evolution in the time is not exactly
unitary.
"Given the lack of an external time, one could try to
use a variable internal to the system under study as a clock. Such a variable
could not play the role of "t" in a Schrödinger equation,
since one expects it to be on a similar footing as the other variables
in the problem and therefore should be subject to quantum fluctuations.
There have been proposals in the past to build a quantum mechanics using
an internal variable as a clock. We will call these proposals "relational
time" (see the next subsection for clarifications on terminology).
"We therefore see that the presence of constraints interfere
with the idea of attempting the introduction of a relational time in quantum
mechanics. One possibility to circumvent the problem is to get rid of the
constraints.
"It should be emphasized the important role that the presence
of the parameter n plays in these formulas. Without such an
ordering parameter, one could not define the conditional probabilities.
The parameter n introduces a notion of simultaneity in the
construction (at a given spatial point). In fact, several previous attempts
to introduce relational times were problematic due to the lack of such
a parameter.
"Since up to now we have made almost no assumptions about
the nature of the "time" t chosen, it could happen that the
same value of t occurs many times upon "evolution" in the parameter
n . This eliminates the predictive power of the theory, at least
locally in time in the following sense: one could make a definite prediction
only upon completing the entire evolution of the system and determining
if the variable t takes a given value more than once. Only
then one could make sense of the probabilities and predict the probability
of a given observable taking a given value at "time t". We will discuss
this in detail in a forthcoming paper.
"Another aspect of the framework that requires further
analysis is the issue of the covariance of the predictions. As worked out
in this paper, the predictions are particular to a given choice of time.
This is unsatisfactory since one should expect the theory at least to exhibit
Lorentz invariance locally since it is derived from general relativity.
"Summarizing, the use of consistent discretizations of
general relativity free the theory from constraints and therefore one can
introduce a relational time as proposed by Page and Wootters avoiding the
main objections to such approach."
[Ref. 6] Petr Hajicek, Quantum theory of gravitational collapse (lecture notes on quantum conchology), March 2002, gr-qc/0204049 v1 "There is, in any case, a long way to any astrophysically
significant system and a lot of work is to be done
before we can claim some understanding of the collapse
problem."
[Ref. 7] K. Kuchar, Time and interpretations of quantum gravity, in: Proceedings of the 4th Canadian conference on general relativity and relativistic astrophysics, G. Kunstatter, D. Vincent, J. Williams (editors), World Scientific, Singapore (1992). Available online at http://www.phys.lsu.edu/faculty/pullin/kvk.pdf "The multiple choice problem is one of an embarrassment
of riches: out of many inequivalent options, one does not know which one
to select. The global problem of time is an embarrassment of poverty: one
really does not have any choice at all.
"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 time variable, while standard quantum
theory relies quite heavily on a preferred time.
"In my opinion, none of us has so far succeeded in proposing an interpretation of quantum gravity that would either solve or circumvent the problems of time". =========== Subject: Discretizing general relativity:
Eliminating the constraints?
Dear Jorge, You wrote in [Rodolfo Gambini et al., hep-th/0405183 v1] that "the major conceptual objections to using the relational approach to solving the problem of time are removed", and have recently produced two papers [Refs. 8 and 9], in which your and your co-authors claim that "the use of a relational time could yield a well defined theory". Just "details remain to be studied" [Ref. 9]. I wonder if your approach can be used for solving the Hilbert space problem, http://God-does-not-play-dice.net/Kuchar.html Also, a recent numerical study of gravitational singularities by David Garfinkle suggests that the Planck scale "will be reached in a finite number of bounces" [Ref. 10]. If "one chooses as clock a variable that is in a quantum regime" [Ref. 9], what will happen to the poor clock? I will appreciate the professional feedback from your colleagues as well. Regards, Dimi
References [Ref. 8] Rodolfo Gambini and Jorge Pullin, Canonical quantum gravity and consistent discretizations, gr-qc/0408025 v1 "Notice that all the problems are due to the presence
of the constraints. In our discrete theory, since there are no constraints,
there is no obstruction to constructing the relational picture. We have
discussed this in detail in [12]."
[Ref. 9] Rodolfo Gambini, Rafael A. Porto, and Jorge Pullin, Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance, gr-qc/0408050 v1 "The lack of constraints allows to tackle some of the
fundamental open problems of canonical quantum gravity. (...) The resulting
quantum theory approximates ordinary quantum mechanics well when the clock
variable chosen behaves in a semi-classical fashion with small quantum
fluctuations. If one chooses as clock a variable that is in a quantum regime,
the resulting theory is still valid but it will not resemble ordinary quantum
mechanics."
[Ref. 10] David Garfinkle, The nature of gravitational singularities, gr-qc/0408019 v1 ======= Subject: Re: Discretizing general
relativity: Eliminating the constraints?
On Wed, 18 Aug 2004 14:27:27 -0500, Jorge Pullin wrote:
> > I wonder if your approach can be used for solving
the Hilbert
Jorge, I'm afraid "considerably simpler" won't work. I think the problem is generic to all relational approaches, yours included. You and all relationists take for granted that a quantum
system, A , is real/exists (i) only in *relation* to another object, not-A
, that it is
Hence your picture is completely frozen, and you cannot determine UNIQUE values of two or more SUCCESSIVE states of A and not-A . Also, please recall that in gr-qc/0402118, you and your colleagues were unable to make the evolution in such relational time *exactly unitary*, http://God-does-not-play-dice.net/Pullin.html#5 I think this is a very serious constraint, which you cannot
eliminate/bypass, since it comes from the very definition of 'relational
If you believe that I'm wrong, please try to solve the Hilbert space problem. Martin Bojowald, for example, has encountered "infinitely many surplus solutions" in gr-qc/0402053, http://God-does-not-play-dice.net/Kuchar.html#Martin Can you shrink these (or yours) "infinitely many surplus solutions" into a trajectory, and make the evolution *exactly unitary*? I'm not aware of any successful effort, even by employing some 'sum-over-whatever' idea, resembling Feynman path integral approach. > > Also, a recent numerical study of gravitational singularities
by
If a quantum beast rests on the Planck scale, it will probably bear little resemblance to anything we can possibly imagine. Can you shield the poor quantum clock at the Planck scale from quantum fluctuations so that "nothing has to happen to it per-se"? Again, please try solving the Hilbert space problem, as
'the proof of
Should you decide to write me back with some concrete ideas, please be assured that I will keep them strictly private and confidential. Regards, Dimi P.S. In my email of Thu, 27 May 2004 21:05:36 +0300, Subject: Re: Info, I wrote: "Regrettably, I was shifted into the evening poster session, and have no idea how to squeeze everything on a tiny little poster, http://God-does-not-play-dice.net/about.html#poster "I think it's not fair. If you agree, can you talk to Thomas Thiemann or Brien Nolan?" You did not reply, and I assume that you consider it fair that I was buried into a poster session at GR17, http://God-does-not-play-dice.net/GR17.html#last D. ============= Subject: The fiducial inaccessible
background time n
Hi Jorge, Regarding my email from August 19th last year, http://www.God-does-not-play-dice.net/Pullin.html#August_19 I would like to comment on your recent gr-qc/0501027 v1 [Ref. 11], in which you and your co-authors elaborated on what you called 'fiducial inaccessible background time n '. (My whole web site is about this special "time", only I call it 'global mode of spacetime'.) You say that this fiducial background time n is "an inaccessible variable, we could only measure it if we had a perfectly classical clock" [Ref. 11]. Please correct me if I'm wrong. The first problem with this 'perfectly classical clock' is that "such a time is truly an abstraction in the sense that no physical clock can provide a precise measure of it [UW89]: there is always a small probability that a real clock will sometimes run backwards with respect to Newtonian time", as stressed by Chris Isham, http://www.God-does-not-play-dice.net/white_paper.html#NB The second problem is that it is impossible to have a clock that would work perfectly, regardless of what its state is. In the example provided by John Baez on 11 March 2000, http://math.ucr.edu/home/baez/uncertainty.html we might have a perfect clock only we set d/dt = 1 for the instantaneous state we're interested in. But then this 'perfectly classical clock' will freeze. To sum up, I believe we have encountered a genuine *paradox of time*: if we adopt the textbook lore that "time is precisely no more and no less than that which is measured by physical clocks", http://math.ucr.edu/home/baez/week1.html then we should not observe any change in the world around us. The fact that we observe change in the world around us *indicates* that this change does not, and cannot be produces from/by some 'perfectly classical clock'. What, then? Here comes my interpretation of your 'fiducial inaccessible background time n ' [Ref. 11]. It's not at all fiducial, and can easily be accessed. All you need is a brain, http://www.God-does-not-play-dice.net/Azbel.html#self This is a genuine Perennial and is 'eternally present', but is not some mythical beast, as Karel Kuchar suggested, and you don't need to be a virgin to understand it either [Ref. 12]. If I'm on the right track, I'm afraid you can never resurrect the Page-Wootters proposal, and the objections put forward by Karel Kuchar still hold, only in a bit different context; please see the *dynamics* of relational reality at http://www.God-does-not-play-dice.net/Miller.html#transience Again, please correct me if I'm wrong. I extend this request to all colleagues of yours. My personal opinion is that the change we observe around us (we call it 'time') comes from the asymmetry of 3-D space, but that's a different thread that involves Bill Unruh's 'mysterious time' upgraded to the global mode of spacetime. Regards, Dimi
References [Ref. 11] Rodolfo Gambini, Rafael Porto,
Jorge Pullin, Fundamental decoherence in quantum gravity, gr-qc/0501027
v1,
"As a consequence, one can complete the Page-Wootters
quantization of the discrete theories and introduce a relational time [4].
"An immediate consequence of having a "quantum clock" variable in quantum mechanics is that the evolution is not unitary [5, 6]. Both the clock and the system under study evolve unitarily and under the usual rules of quantum mechanics in terms of a fiducial background time n (we use the letter n to emphasize that we are working in a discrete formulation, though this is not central to the points discussed in this paper). "This time is an inaccessible variable, we could only measure it if we had a perfectly classical clock. What we can measure are the dynamical variables of the problem, in particular t , the variable that describes the clock. This variable is represented by a quantum operator and it will have an expectation value and a dispersion. Upon evolution, the dispersion will increase. "One can show that if one prepares the clock initially
in a state in which t is highly peaked around a given
value of the fiducial time n, the quantities under study (let
us call them O) will evolve according to an approximate Heisenberg equation,
but there will be corrective terms that imply that pure states evolve into
mixed states.
"Summarizing, we have shown that unitarity in quantum
mechanics only holds when describing the theory in terms of a perfect idealized
clocks. If one uses realistic clocks loss of unitarity is introduced. We
have estimated a minimum level of loss of unitarity based on constructing
the most accurate clocks possible. The loss of unitarity
is universal, affecting all physical phenomena."
[Ref. 12] Karel V. Kuchar, Canonical quantum gravity, gr-qc/9304012 v1, 8 April 1993. "The third alternative is to say that because perennials
are constants of motion, it does not matter when they are observed. (...)
This does not make me too happy either. If all time [tau] is eternally
present, all time is irredeemable."
"Perennials in canonical gravity may have the same ontological
status as unicorns -- a priori , these are possible animals, but a posteriori,
they are not roaming on the Earth. According to bestiaries, the unicorn
is a beast of fabulous swiftness, strength, and beauty, but, alas, it can
be captured only by a virgin [38]. Corrupt as we are, we better stop hunting
mythical beasts."
============ Subject:
The consistent discretization approach to classical and quantum general
relativity
Hi Jorge: Regarding your consistent
discretization approach to classical and
http://www.God-does-not-play-dice.net/gw.pdf Each student "in the shoal" will proceed to its unique classroom in just one “quantum jump”, from t_0 to t_1 , but this “quantum jump” is a PERFECTLY continuous transition. All you need is an 'ideal point', http://www.God-does-not-play-dice.net/Stachel.html#point I bet Max Plank would have loved the idea, but not the guys in Potsdam. All the best, Dimi ============ Subject: Typo
in gr-qc/0603090 v1?
Hi Jorge, I didn't know about Wigner's paper of 1957, ref. [11]. Thank you. In gr-qc/0603090 v1, you and your colleagues wrote "quantum mechanics involves and idealization". Could this be a typo? RE your fundamental decoherence (p. 5), you wrote: "So we conclude that any physical system that we study in the lab will suffer loss of quantum coherence at least at the rate given by the formula above. This is a fundamental inescapable limit. A pure state inevitably will become a mixed state due to the impossibility of having a perfect classical clock in nature." It seems to me that you're suggesting some sort of one-directional and irreversible "flow" of quantum systems towards the world of tables and chairs, while I believe this "flow" should be smooth, reversible, and bi-directional, http://www.god-does-not-play-dice.net/Brody.html The limit ¯h --> 0 is singular (the recipe for "classical limit"), so it won't work. As to the long-standing issue of
time in GR, please see
RE the measurement problem, see
RE "quantum computing", see
What do you think? Regards, Dimi Note: I haven't heard from Jorge Pullin so far, and will make some very brief comments on his latest paper: Rodolfo Gambini and Jorge Pullin, Relational physics with real rods and clocks and the measurement problem of quantum mechanics, July 6th 2006, quant-ph/0608243 v1. Regarding "a perfect classical clock to measure times" (cf. Wigner's paper above), click here.
Rodolfo Gambini and Jorge Pullin: "Another point to be emphasized is that our
approach has been quite naive in the sense that we have kept the discussion
entirely in terms of non-relativistic quantum mechanics with a unique time
across space." Well, if you're interested in my opinion (Jorge Pullin obviously isn't), but don't have problems with your neocortex (cf. Petr Hajicek below), click here.
Petr Hajicek, p. 13: "We can say:
What really exists are only the local presences. The past as well as the future
are nothing but products of neocortex." =================
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