Subject: Relativity of simultaneity Date: Fri, 7 Dec 2007 11:13:06 +0200 From: Dimi Chakalov <dchakalov@gmail.com> To: Vesko <vpetkov@alcor.concordia.ca> Maraba Vesko, May I take the stand of your students, and ask two questions regarding your latest arXiv:physics/0610046v2 [physics.gen-ph]. 1. Consider two observers in relative motion: observer A is at rest at a buss stop, and observer B moves w.r.t. A with constant speed of, say, 60 km/h. 2. At some instant denoted with t_1 by the two observers, they take an instantaneous snapshot of the Sun, such that the time readings of the clocks in their digital cameras stamp their images with some provisional reading denoted with t_1 by the two observers. 3. At a later moment t_2 (after app. 8 min), observers A and B will see the actual state of the Sun, which was existing as 'objective reality out there' at *their* t_1. Let's assign two three-dimensional cross-sections of the real four-dimensional world to the two observers, in relative motion, at t_2 . Q1: Will the two observers see different states of the Sun at
*their* t_2?Q2: If observer B moves with constant acceleration w.r.t. A , will the two observers see different states of the Sun at *their* t_2?Best regards, Dimi -----
"We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If for instance I say, 'that train arrived here at seven o'clock', I mean something like this: 'the pointing of the small hand of my watch to seven and the arrival of the train are simultaneous events'". Likewise, The fact that we cannot
experimentally verify such simultaneous
events does not imply that they cannot Same with the '
The underlying puzzle from Lucretius -- how do we get a finite region of space, with its "borders", from uncountably infinite, infinitesimal "points" -- is not even acknowledged. These are fundamental issues,
yet they seem so "obvious" that many physicists mention them
Can we unravel some
pre-geometric plenum which can replace "our thinking"? We certainly
shouldn't allow the human intuition or thinking to If such pre-geometric plenum
exists and has been tacitly introduced with the initial mathematical
assumptions, we should not expect to recover it again, from the
physical stuff we drop on the bare spacetime
manifold. Stated in philosophical terms, Let's try to be specific
regarding
Now, I hope one day Robert Geroch will agree to write a book on the
sentence above, as a sequel to his 1978 "General
Relativity from A to B", with the provisional title "General
Relativity from A to A + dt-and-ds", to explain the
The only "comprehensible", but
in fact highly misleading,
representation of spacetime is from Isaac Newton: an absolute 4-D
space, depicted with the whole white area in the picture above,
complemented with an absolute time, such that its elementary
"shift" Notice that Going back to present-day GR, there are two
interpretations of how the shift The first, and seemingly
"scientific", interpretation would be based on a typical
reductionistic, Marxist-Leninist approach to GR: the shift
"As a consequence of general
covariance, relativity becomes entirely constrained; the equations of
motion are a list of expressions which In summary, if we stick to this
Marxist-Leninist approach, we would dealing with just Which brings us to the second
option, inspired from brain dynamics:
the self-interacting human brain is not "frozen", and the brain can act
on itself, as we think The second option is very subtle
(cf. N. Dadhich): the present-day GR (recall Einstein's
opinion here) is build only on the
The so-called strong
hyperbolicity (J. David Brown, arXiv:0803.0334v1 [gr-qc])
can't resolve the inherent mathematical problems of ADM "dynamics", to
help reconcile GR with QM. Notice that the problem of
classical limit of quantum gravity does not originate from Quantum
Theory alone (which would be the case, had the present-day GR been
correctly formulated): it is It is impossible to "recover"
the genuine dynamics of GR by splitting the spacetime into two "parts",
and then "evolve" one "part" It is manifestly pointless to
"cure" the hyperbolicity of PDEs in ADM hypothesis (J. David Brown), just as it
would be pointless to "cure" Einstein filed equations by imposing
"second time derivatives" only (see below), or
make the metric of Kerr spacetime "geodesically
complete". There are many things in present-day GR that are
mathematically ill-defined, or "non tensorial" (cf. Hermann Weyl), or lead inevitably to
pathological behavior of matter fields which, just like the ultraviolet
catastrophe, has never happened (e.g., time-like naked
singularities, CTCs, and geodesic incompleteness; see Alan Rendall below), because with the current mathematical
apparatus all these "disasters" cannot be cured All these "disasters" are rooted
on the Marxist-Leninist presumption (see above)
that matter fields can The good news is that the
generic "ambiguities" that make ADM hypothesis mathematically
ill-defined are needed to preserve the inherent
For these reasons, there are no such things as quantum jumps or spacetime foam à la Wheeler's geometrodynamics. Also, the topology of spacetime and its "quantization" (cf. M. Albers, C. Kiefer, and M. Reginatto, arXiv:0802.1978v1 [gr-qc]) are solved from the outset, and two opposite and "dark" remnants from the global mode of spacetime (currently interpreted as 'cold dark matter' and 'dynamic dark energy from empty space') are expected to emerge in the local mode of spacetime. In today's GR, these tasks are
not feasible, because 'the physical stuff on the hypersurface' cannot So, once we work out the full
quantum gravity, we won't "recover" today's GR as some "low energy
limit", because the proper GR will be entirely different. Namely, the
main problem from the principle of general covariance -- "The requirement of general covariance takes away from space and time the last remnant of physical objectivity" (A.
Einstein, If you're adamant in detecting GWs, you need to get grip
on the shift
Notice that people (perhaps some
Jehovah's Witnesses of ADM Formalism)
speculate about adjacent hypersurfaces, "separated" by 'the elementary
timelike displacement But they need to somehow "blur"
the deflation time that is hooked "asymptotically"
on The Beginning, to avoid the Cosmic Hen
Paradox, yet no real clock made from some physical stuff could
survive a roundtrip Gedankenexperiment to the "inflation stage": try to
deliver a clock at particular location (say, on your desktop in the University of Chicago) Instead, we should keep the
classical limit of quantum gravity If we interpret the shift To the best of my knowledge,
none of the Jehovah's Witnesses of ADM
Formalism has made an effort to explain to the general audience
'the proper time [tau]' (C. Rovelli) From our perspective, the
crucial question is this: where is the global holistic In the relativistic presentation, the global
"vertical" component of the shift is totally hidden to all relativistic
observers (local mode of spacetime), yet it "gets smuggled" into the
physical world through the "dark gaps" in the global mode of spacetime. Again, the ... while the
From: C. Kiefer
and B. Sandhöfer,
And notice, again, the new
cutoff from the Aristotelian First Cause, suggested to fix 'boundaries
of space' (in the vein of George F R Ellis’ 1984 notion of finite
infinity),
Apart from the so-called dynamic
dark energy of "empty space", there is no
trace left Thus, the issue of 'quasi-local energy conservation in
GR' can only be resolved "over" an extended domain of space in which
the "non-tensorial context", as fixed in
the global mode of spacetime, defines a pinpointed and
Regarding the latter, notice that in present-day GR they cannot be
solved in principle: it is logically
impossible for matter fields to produce
their "time", Apart from wishful thinking,
there is Apart from wishful thinking,
there is The proposed new degree of
freedom associated with every spacetime "point" (the bundle base
space), which may (hopefully) act as a perfectly smooth reference fluid, hence recover the
genuine dynamics of GR (cf. T. P. Shestakova, 0801.4854v1 [gr-qc]), has
been called 'global mode of spacetime'.
It produces holistic effects from 'the
universe as ONE', which look like some kind of cold dark "matter"
and dynamic dark energy of [you-name-it]
in the
Perhaps people just don't want
to talk like parapsychologists, which is why they deeply hope that such
effects might be produced by some "matter", even if 90 per cent from such baryonic matter is
missing. Imagine this: you visit your local butcher to buy sausages for
BBQ party, and he offers you some new special "dark" sausages that have
90 per cent less meat than the normal ones. The two kind of sausages
are placed on the same shelf, only one of them has ten times less meat.
Then you ask your butcher about the stuff used to make these new
sausages, and he replies: 'I can't see it, it As to the second effect, 'dynamic dark energy of [X]', the situation is even more puzzling. The crux of the problem has been explained by Larry Kraus as follows (The energy of empty space that isn't zero. A Talk with Lawrence Krauss, July 6, 2006): "The energy of empty space had
to be precisely zero. (...) Symmetries produce two numbers that are
exactly equal and opposite because somewhere there's an underlying
mathematical symmetry of equations. So that you can understand how
symmetries could somehow cause an exact cancellation of the energy of
empty space. The reason why the global mode
of spacetime is And that is the essence of 'potential reality' residing in the
global mode of spacetime: the separation of the two modes of spacetime
is nothing but the "separation" of the potential future (global mode)
from the Hence we can 'have our cake and
eat it': on the one hand, we have On top of everything, we may have to explain both effects in 'one stroke', because the formation of galaxies seems to suggest that the two "dark" and tug-of-war effects of gravity work together. To see the imprint from the global mode of spacetime, left on the local mode, look at the Smooth Coordinate Presentation Problem, p. 5 and p. 16, from “Exotic Smoothness and Spacetime Models”, by Carl Henry Brans (9 May 2007). Perhaps if we consider the structure of spacetime outlined here, a perfectly smooth transition from Hyperfläche 1 to Hyperfläche 2 (see the picture above) may be possible, in which case the puzzle spotted by Carl Brans would be automatically resolved. Had the alleged 'smoothness' of
the manifold been But life is not that simple.
There exist just one kind of 'perfectly smooth transition', which is
fixed at the fundamental level of 'pure math' -- the connected Hausdorff topological space. This perfectly smooth transition is neither
"exotic" nor "ordinary". It is an exclusive feature of the In order to have "points" in the
Which does not mean that ' More on ' I tend to disagree, since up to 96 per cent
from the stuff in the universe comes from -- how shall we call it?
-- potential reality grounded on 'the ideal monad without
windows'.
The correct chart would be quite
different: 100 per cent -- There is no way to "see" the
input from the Holon in the global mode, because all physical
observations are inevitably, by the
laws of STR, directed to However, in the world of 'facts'
cast irreversibly at the 'absolute past' of the whole universe and
projected in the respective past light cones of the relativistic
observers, there should exist a tiny "remnant" from the driving force
of 'the universe as ONE', since
[lambda] isn't Speaking philosophically, the
guiding principle here is that If the reader has troubles with
understanding the holistic effects from 'the universe as ONE', which Going back to philosophy, the
putative structure of spacetime boils down to (i) unraveling the
so-called torsion (instead of adding
some Regarding the absence of torsion
in GR (cf. A. Trautman), perhaps we need
a new
spinor field. Consider Ted Newman's H-space. In the latest publication (Carlos Kozameh, Ezra T. Newman,
and Gilberto Silva-Ortigoza, Null infinity, H-space and equations of
motion, To quote from R. Sverdlov's arXiv:0802.1914v1
[gr-qc] (emphasis added): "In order to visualize the “spinning”
that goes on, one can replace infinitesimal points in spacetime by
small arrows. However, unlike the way it is normally done, these arrows
will not be aligned with a spin axis. Instead, these arrows will be,
themselves, spinning around This "other axis" is the global
mode of spacetime, which can be visualized only in some
non-relativistic presentation (cf. the vertical axis of the "dark water
spring" in the "GW lake" here). Once
we convert this picture to its proper relativistic presentation (again,
the recipe is explained here), the
"other axis" will be infinitesimal in the local mode of spacetime.
Namely, the "other axis" along which the very 3-D space " Obviously, any attempt at presenting the non-linear dynamics of GR with some linear (polynomial) time ('think globally, and then act locally, and then think again globally', ... etc.), leads to Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers. As stressed by Giulini &
Kiefer (gr-qc/0611141 v1, p. 16), there
should be infinitely many Wheeler-DeWitt equations, each for every
"space point", hence every "space point" is endowed with I wonder what Hermann Minkowski
would have said regarding such self-referential "dynamical description"
à la Baron Munchausen:
if we accept the view that 'spacetime' is Stated differently, the task is
to provide an answer to Mach's Question (cf. C. Schmid, gr-qc/0409026v1):
"What share has every mass in the determination of direction in the law
of inertia?" It seems that the whole universe must "know" about
everything "instantaneously", and this "knowledge" should be kept in
the global mode of spacetime: think globally, act locally. Locally,
every spacetime "point" should be endowed with Well, just some gentle suggestions. As Chris Isham boldly declared, I "do not know enough theoretical physics to help with any research in that area". Everything stated here is a personal, "just another crank" opinion. Now let's see where we can "insert" the putative global mode of spacetime. Look in Bob Wald's textbook:
These "simultaneous events" are In Bob Wald's textbook (p. 4), this hypothetical fine-grained
structure of 'the infinitesimal' is
buried "in a Notice that, in the context of Abram Zelmanov’s ideas, the global mode of spacetime can be defined as "zero point of reference" (Rabounski & Borissova, arXiv:gr-qc/0304018v4): "The essence of Zelmanov’s
method is simple. As known, components of a tensor value are defined in
so-called ortho-frame, a system of orthogonal ideal (straight and
uniform) axes, which are tangential to real physical axes (curved and
non-uniform) at the zero point of reference (footnote 4). More on 'GR for pedestrians' We also read in textbooks that
GR is 'background independent', in the sense that Mother Nature creates
its case-specific spacetime as given by the respective solution of the
Einstein equations, once a distribution of masses is specified, prior
to which there should be a case-specific spacetime already laid out for
the distribution of masses: a But how does DDE 'exist',
really? And how did it manage to act on the whole universe One last note on the origin of inertia (physics/0610046 v2, p. 3): "Take as an example the open question of inertia. We do not know why a body resists its acceleration." Perhaps a modified Machian theory of gravity could provide the answer: you can't stir a coffee without disturbing a star. It may sound like poetry to some people, but I believe the issue is of paramount importance to everyone interested in the origin of what we call 'inertial mass'. The prerequisites from GR are outlined here. As to my Bulgarian friend, it is highly unlikely that he would tackle the 'relativity of simultaneity' in such non-relativistic, now-at-a-distance "reference frame". I wasn't even notified of the conference organized by Prof. Dr. Vesselin Petkov in June 2008. People change. As John Coleman noticed, "it is extremely difficult to induce penguins to drink warm water".
======================
The laws of STR are what makes
the energy of 3-D space (a
"curious energy that resides in empty space")
to look "dark", because STR is
designed from the outset to be blind to any phenomenon that (i)
operates in an absolute reference frame and (ii) acts on the whole 3-D
hypersurface This is the reasons why the
arrow of time, as driven by the so-called DDE, cannot show up in STR in
principle: there is no
Just a sample of such questions:
if you wish to observe the Notice that we cannot define the
Perhaps only Baron Munchausen can perform
such self-acting miracle, but LIGO
Scientific Collaboration haven't yet acknowledged his contribution
to "GW astronomy". Just click the image above. This seemingly sensible
statement from A.
Linde requires an absolute and perfect clock of the whole universe,
which would provide an absolute and perfect time, such that Namely, in the initial 10
Murphy's Law No. 15 reads: Complex problems have simple,
easy-to-understand wrong answers. In the case depicted with the
pictures above, we don't have a 'wrong answer' but a 'wrong
visualization' of a You can visualize the expansion of 3-D space (see also Ned Wright's balloon metaphor) and the "ripples" of its metric (see the GW "lake" here) only in some initially wrong, and highly misleading, non-relativistic presentations that display some "background" and "boundaries" for the spacetime, with respect to which 'things make sense', hence can be grasped and visualized by the human brain. Then you try to assure your students and the general audience that you can "remove" these non-relativistic visualizations with math. Only you can't. You need quantum gravity to explain things that pertain to 'the only truly isolated system' -- the whole universe as ONE -- so you better start telling your students the whole truth. As mentioned below,
there is no sunlight to blindfolded people, so it is 'gut zu wissen'
that with the current theory of relativity we are still I will report here any new developments (if any) on these questions right after the Third International Conference on the Nature and Ontology of Spacetime in June 2008. "Nobody has ever noticed a place except at a time, or a time except at a place", said Hermann Minkowski one hundred years ago. Specifically, he stressed that "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" (cf. Orfeu Bertolami, arXiv:0801.3994v1 [gr-qc], Sec. 1). Yet people are tempted to separate time from space, in the sense that "time" would refer to some object that changes its states by changing its position in "space", as labeled with some provisional coordinates. And even if this object is in relative rest, it is somehow intuitively obvious that its "clock" would continue to count its "time". Which seems to allude that the object somehow "moves in time", while the 3-D space is always dead frozen: there is no "empty 4-D space" waiting for the cosmological balloon to expand into. But if we use 'a kind of union'
of time and its 3-D space, the 'union' will be dead frozen as well: in
present-day GR, the 3-D space does "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." Then Cauchy problems for Einstein equations
and Closed Timelike Curves (CTCs) would be
inevitable, while time-orientability would be a rare, and
model-dependant, luxury of spacetime, if not a sheer wishful thinking. Most importantly, "what
general relativity does moves"
along a hypothetical 'universal time arrow' in such a way that "global
constraints" on the local mode
of spacetime are produced?Recall that we landed up with
"constraints" (cf. Karel Kuchar)
because of purely mathematical "reasons": some of the Einstein field
equations do Of course they will look like
"constraints": those 'second time derivatives' refer to the Perhaps only the human brain can "read" the non-linear time
of GR and QM. Your poor wristwatch can't -- it is locked "inside the train" -- so it will be
inevitably "frozen". For if you take a walk "outside the train", your time will be
comprised of Here comes an obvious question: but how can you rob 'the time inside the train' with an infinite "number" of points in the first place? But of course you can, and that's the beauty of the continuum hypothesis (cf. Kurt Gödel). If you stay 'inside the train' only, you won't feel "robbed" at all, but you will indeed notice some "dark" effects on your train -- see above. We may recover the More about this 'something else' on Sunday, 21 September 2008. The title of the talk is "The Arrow of Spacetime"; the venue is Munich. Space is Meanwhile, may I suggest to the
reader a quiz based on
Just a hint: Closed Timelike
Curves (CTCs) are unavoidable in present-day GR (cf. W. Bonnor), which means that In summary, if we treat the
spacetime as 'one entity', after Hermann Minkowski, we should not
disentangle the 3-D space from its time, nor should we use any non-relativistic pictures like those
above.
Regrettably, Prof. Karel Kuchar hasn't found time in the past two years to resolve this fundamental problem, although all this tallies to his filed of expertise. In my just-another-crank opinion, the only possible solution is the so-called scale relativity principle. I honestly claim that haven't
read any proposal similar to this principle. But given the opinion of
the leading British expect in quantum gravity, Prof. Chris Isham -- "You do not know enough theoretical physics to
help with any research in that area"
-- I consider it I am simply unaware of any similar efforts being posted on the Internet or published on paper. If the readers happen to know about similar 'scale relativity principle', please let me know. Thank you.
====================== Subject: Quantum Mechanics 101
======================
Subject: Seth
Major's students
--- Note: Naresh Dadhich didn't reply to my email from Mon, 24 May 2004 21:18:11 +0300. Mike Turner didn't reply to my email from Thu, 03 Jun 2004 02:47:26 +0300, and I never heard from Jorge Pullin, Bob Wald, and Rafael Sorkin, to name but a few. The only response from Steven Weinberg was that he doesn't have time to read my email. The incomplete list of physicists who ignored my proposals is here. At least four years have been
wasted. I was hoping that will be given a chance to talk at GR17 and EPS13, but my application for oral presentation was
denied. All I got so far is either dead silence, from physicists who
ignored my proposals, or insults ranging from relatively polite ( Under these circumstances, one
could hardly expect from me to be nice and polite to these ... well,
let's just call them 'people'. I am, and will remain totally frank
instead. If someone offers an idea which I consider very interesting
and fruitful ( À la guerre comme à la guerre.
Watch L. Smolin's ISSYP Keynote Session (Perimeter Institute, 01/08/2007 - 1:00 PM, duration 01:28:14) at http://pirsa.org/07080059/ He offered to the kids in the auditorium to "vote" on the two ideas about time, but failed to tell them that both Newton and Leibniz could be right: Newton's absolute time is the 'global time', while the relativistic notion of time is the 'local time'. More at the link from my email above. Here at this web page I only quoted from one of L. Smolin's book and tried to explain how he missed the fourth road to quantum gravity. He failed to mention my critical remarks sent since February 2002 (the last email recorded at this web site is from 15 September 2006), and has always ignored them. His only "argument", and also last email, was from Sun, 24 Feb 2002 17:30:25 +0000 (BST): "So don't refer me to web pages." I'm sure Lee Smolin can read web pages, but perhaps he "remembers" only those that suit him. Do you smell a rat? I do,
because kids have the right to know Were Karel
Kuchar and C. G. Torre invited
at Perimeter Institute, ever?
Subject: Re: If time is
discrete, ..., if time is continuous, ... Note: Surely the Nobel Prize laureate and member of Perimeter Institute’s Scientific Advisory Committee (SAC) is a very busy person, so let me lay out the crux of the matter in just a few sentences. Consider the so-called dualistic
conception of time (cf. Joy Christian):
"a classical clock is supposed to register the time But in background-free theories
such as GR, the dynamical evolution must be parameterizable If you ignore the ideas know
since Plato and use a linear time only, perhaps
only Baron Munchausen could
perform such self-acting miracle.
But if you model the universe as a I have a feeling that will never be invited to talk at Perimeter Institute and get a glimpse at its "open atmosphere where anybody can criticize anybody, honestly and directly". Or at least not until L. Smolin retires or G. 't Hooft writes his landmark paper "201 wrong theories for the cosmological constant", whichever comes first.
============================== Subject: Particles do have spacetime feelers
Dear Vesko and Nasko, I can't believe that time flies so damn fast.
I vividly remember our I just read a beautiful paper by Harvey R. Brown and Oliver Pooley [Ref. 1], which I believe will appear in the forthcoming volume "The Ontology of Spacetime". Vesko: Please send me your editorial article
and any other paper you http://members.aon.at/chakalov/Wagh.html#QM I think the issue is very subtle; please see
Eq. 1 and Footnote 5 in More on these "complications" at http://members.aon.at/chakalov/Mashkevich.html See also some jokes at http://members.aon.at/chakalov/Azbel.html#note_2 http://members.aon.at/chakalov/Kiefer.html#note Just like in the good old days! Not that they were good, but at least I was young. Nasko: Please call me anytime that is convenient for you. I do owe you a lot, and will never forget what I learned from you: particles do have spacetime feelers, http://members.aon.at/chakalov/Bell.html Vesko: If you come to Sofia some day, please call me, perhaps we all could try to make another mini-seminar, over a glass of gin tonic or five:-) And please send my love to Svetla. Best wishes, Dimi Reference [Ref. 1] Harvey R Brown and Oliver Pooley (16 March, 2004), Minkowski space-time: a glorious non-entity, physics/0403088. pp. 2-3: "We have seen that for Einstein the inertial property of matter [footnote 3] requires explanation in terms of the action of a real entity on the particles. It is the space-time connection that plays this role: the affine geodesics form ruts or grooves in space-time that guide the free particles along their way. The intuition was well expressed by Nerlich in 1976: ...without the affine structure there is
nothing to determine how the "In GR, on the other hand, this view is at
best redundant, at worst T^µ v;µ = 0 (1) "This result is about as close as anything is in GR to the statement of a conservation principle, and it came to be recognised as the basis of a proof, or proofs, that the world-lines of a suitably modelled force-free test particles are geodesics. [footnote 4] The fact that these proofs vary considerably in detail need not detain us. "The first salient point is that the geodesic principle for free particles is no longer a postulate but a theorem. GR is the first in the long line of dynamical theories, starting with the Aristotelian system and based on that profound distinction between natural and forced motions of bodies, that *explains* inertial motion. The second point is that the derivations of the geodesic principle in GR also demonstrate its limited validity. In particular, it is not enough that the test particle be force-free. It has long been recognised that spinning bodies for which tidal gravitational forces act on its elementary pieces deviate from geodesic behaviour. [footnote 5] "What this fact should clarify, if indeed clarification is needed, is that it is not simply *in the nature* of force-free bodies to move in a fashion consistent with the geodesic principle. It is not an essential property of localised bodies that they run along the ruts of space-time determined by the affine connection, when no other dynamical influences are at play. In Newtonian mechanics and SR, the conspiracy of inertia is a postulate, and its putative explanation by way of the affine connection is a postulate added to a postulate. "And it is here that Einstein and Nerlich part company with Leibniz, and even Newton. For both Leibniz *and Newton*, absolute space-time structure is not the sort of thing that acts at all. If this is correct, and we believe it is, then neither Newtonian mechanics nor SR represent, *pace* Einstein, a violation of the action-reaction principle, because the space-time structures in both cases are neither acting nor being acted upon. Indeed we go further and agree with Leibniz that they are not real entities in their own right at all." -- "Footnote 4: See, for example, Misner et al. (1973, §20.6, 471-80). "Footnote 5: See Misner et
al. (1973, 480; ex. 40.8, 1120-1; and §40.9, 1126-31). These
authors refer briefly on p. 480 to the complications that
quantum physics is likely to
introduce to the question of geodesic behaviour. (...)" |