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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 I consider the phrase 'at the same time' crucially important for http://www.God-does-not-play-dice.net/Minchin.html 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 http://www.God-does-not-play-dice.net/paper.doc 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, 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 Sure, but we need to find their joint dynamics. Please see my efforts at http://www.God-does-not-play-dice.net/Landsman.html#note_last I hope this whole poetry will be cast in math by November 2015. Best wishes, Dimi References [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]) --->--->--->---> in a precise form such that both fluxes cancel, and thus leading to a "More precisely, tµv = 0 tells us that the 'reaction' of the dynamical 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 [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 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 http://www.God-does-not-play-dice.net/Price.html#note I wonder if you or some of your colleagues would agree with my interpretation of 'conserved quantities' in the putative 'local mode of spacetime'. More at http://www.God-does-not-play-dice.net/Szabados.html#note Kindest regards, Dimi Chakalov
[Ref. 1] David B. Malament, Classical Relativity Theory, Version 2.4, 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.
============
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 any set (cf. below) of 'observables': the whole is more than the sum of its parts.
Consider a metaphorical example of 'real building displayed on a map'. In present-day GR, a genuine Dirac observable would require 'classical determinism' (cf. 'real building displayed on a map'), to define the set of all possible presentations of the real building by all possible maps in which the real building will remain unchanged/invariant. There are infinitely many possible maps under which the real building can be faithfully presented, but these maps are nothing but re-labeling (passive diffeomorphisms) of the "coordinates" of the real building 'out there'. These infinitely many possible maps are produced by re-labeling of the "coordinates" of the real building that would be fixed on some background and absolute spacetime. 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 observable either. 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. But there is no room for 'objective reality' in GR, because it will impose an aether in GR (cf. M. Montesinos). Isn't this simple? I believe even my teenage daughter was able to grasp the problem of present-day GR. Yet some people show thriving optimism for some "approximation scheme for Dirac observables" that can be extracted from "infinitely many gauge No way. Fuhgeddaboudit.
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]
"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 Charles G Torre, Physics 6210/Spring 2008/Lecture 32 =============
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 of three or more dimensions (cf. N. Brunner). Suppose the observable characteristics are presented with three possible colors:
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:
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 intrinsic blue 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'. What we observe in the local mode of spacetime are some fleeting "projections" (shadows on Plato's cave) from 'the quantum system out there' which exists as 'potential reality' (cf. Henry Margenau's Onta; more from Christian de Ronde) in the global mode of spacetime. 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 particular experimental context. But 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 computing unfeasible.) 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. 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 ? The sole answer is YAIN (both yes and no), 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
hoek (Dutch) 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. Well, if your brain can hold Platonic ideas, Mother Nature should do it as well. Now, try to 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.
The underling rule is this: the 'real universe' (local mode) is emerging
from an uncountably infinite set of 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 Hilbert space and Aristotelian logic, and the potential reality "outside" the Hilbert space, with the inevitable negative "probabilities" (R. W. Spekkens, arXiv:0710.5549v2 [quant-ph]). 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), we refer to the quantum becoming only. The full quantum reality resides in the quantum being, which is of course "outside" the Hilbert space. For additional arguments, check out the Gedankenexperiment aimed at deriving the classical limit of QM from STR. 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 philosophical terms, we follow the Bootstrap Principle of Geoffrey Chew (Science 161 (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.) Now, imagine this. C. G. Torre, Karel Kuchar, Chris Isham, Claus Kiefer, Jorge Pullin, John Stachel, Steven Weinberg, Lee Smolin, etc., were searching for HIV vaccine, say. One day they learn that some guy might be proposing a solution to their task, but the theory is posted on a web site only. Would they keep quiet and ignore it, for years? That's the difference between people who respect their field of research, and those who just play with their hobby.
D. Chakalov "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."
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. 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 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).
D.C.
Subject: Quantum
Mechanics 101 =============== 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 ===============
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, 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 stuff above, 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", 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.
D.C. [Ref. 2] Alexander Afriat and Ermenegildo Caccese, arXiv:0804.3146v2 [physics.hist-ph], 21 May 2008
p. 12: "Is the physical meaning of
[energy-momentum pseudotensor] t_ab compromised by its troubling
susceptibility to disappear, and reappear under acceleration?
"Everything suggests the
binary star PSR 1913+16 loses kinetic
energy as it spirals inwards. If the kinetic energy is not to disappear
without trace, it has to be converted, into radiation in this case. Since
its disappearance is only ruled out by the conservation law, the very
generation of gravitational waves must be subject to the doubts surrounding
conservation.
[Ref. 3] S.
Capozziello, M. Francaviglia, S. Mercadante, From Dark Energy and Dark
Matter to Dark Metric,
arXiv:0805.3642v1
[gr-qc] ===============
"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. 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 binding phenomenon: 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!
Subject: Re:
arXiv:0805.3178v1 [quant-ph] 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 (...). What entity chooses "the basis" (if any) or, in Mott's case, the "decohered history space" (if any)?
D.C.
================== Kindest regards, 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". To quote from Jonathan P. Dowling and Gerard J. Milburn, Quantum Technology: The Second Quantum Revolution, arXiv:quant-ph/0206091v1:
This "ambiguity" is from KS Theorem; see Fig. 1b online here. Last words from Karl Svozil, replacing "ambiguity" with "non-uniqueness":
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.
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.
==================
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. However, there can be no quasi-localized GW energy, nor Cauchy problems for the field equations, in an 'absolute map of objective reality'. 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:
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. In other words, there is no "empty space" nor "ether" in the local mode of spacetime. We have no choice but to start ab ovo. By the way, Faraday did not express himself in mathematical language either, yet many physicists acknowledged his ideas. Well, people change.
==================
================== 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 of the 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 of the 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 of the 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
==================
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
I'm afraid you do not understand Quantum
Theory in the first place. See
That's fishing in murky waters, to say the least. 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 |
