"The representation of matter by a tensor was only a fill-in to make it possible to do something temporarily, a wooden nose in a snowman." "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."
Panta rei conditio sine qua non est
Regarding Quantum Mechanics (QM), the aim is to avoid the incomprehensible paradoxes and artifacts in it (watch the double slit experiment here), which originate from its textbook interpretation (Niels Borh's belief that quantum world can only be "seen" through classical "glasses"). We can indeed understand the quantum world (but not the current QM textbooks; cf. Richard Feynman), by changing the "glasses" through which we "see" and construe the quantum world: the universe modeled as a brain. Regarding the artifacts in QM, we may be in a situation similar to an Eskimo trying very hard to comprehend the notion of "trunk". In our case, we encounter an incomprehensible wave-particle complementarity, which could be just an artifact from our wrong thinking, like the "nose-arm complementarity" in the case of the Eskimo observing elephant's trunk. Surely 'the quantum system' doesn't live in any relativistic space, so one should expect all sorts of headaches and artifacts (e.g., "diese verdammte Quantenspringerei", Erwin Schrödinger) from imposing wrong "glasses" onto the quantum world 'out there'. (A typical example is Franco Selleri's quest for detecting de Broglie waves.) The prerequisites for the interpretation of QM suggested here originate from Schrödinger. Back in 1935, Erwin Schrödinger stressed the following: "The rejection of realism has logical consequences. In general, a variable has no definite value before I measure it; then measuring it does not mean ascertaining the value that it has." And in a letter to Einstein dated 18 November 1950 (quoted after J. Bub, p. 115), he 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.” We are obviously dealing with a new form of reality: a probabilistic assertion, and the Hilbert space itself, cannot accommodate the Kochen-Specker case in which "the something in question" is beyond an unequivocal "is or is not" state (cf. "an unequivocal true-false value" in Isham and Butterfield, p. 3; emphasis added):
Going back to Ernst Specker's tripod, if there are states of the tripod in which one of its legs has UNdecidable color, then not just this particular leg, but the whole tripod will be UNdecidable. It's a package. The phrase "an incomplete Kochen-Specker colouring" (Helena Granström, p. 2) has no meaning whatsoever; it is the result from imposing wrong "glasses" onto the quantum world. And if you subscribe to the modern quantum mysticism -- "the quantum state is not a physical object, it is a representation of our state of knowledge, or belief" (Itamar Pitowsky, p. 28) -- your brain will wind up in a schizophrenic state of, say, 68% "knowledge" of the quantum state, and 32% of "[what da heck is that uncolored KS sphere?]". No mental concepts, such as 'knowledge' or 'imagination', are admissible in the ontology of quantum reality. We must never mix apples with oranges (Res Extensa and Res Cogitans). Karl Svozil refers to this UNdecidable faculty of the quantum world as "ambiguity" (p. 4), and stressed: "This ambiguity gets worse as the number of particles increases." If you think about the quantum world with classical concepts, it will get from bad to worse, until you end up with the (old) cosmological "constant" problem (more on that from Alan Guth). As Erwin Schrödinger might have said in 1935, the same "variable" that has had no definite value before you measured it will continue to keep its UNdecidable nature after you "measure" it as well. And you can't fit it in any Hilbert space, of course (what is the dim(H) for 32% "uncolored" and 68% colored KS sphere?). Let's give it a name: potential reality. In the quantum realm, it (i) offers its context-dependent explications (a.k.a. "observables"), (ii) keeps the sameness (Genidentität, Kurt Lewin) of particles of the same type, which MTW regard as "a central mystery of physics" (p. 1215), and (iii) facilitates the ultimate quantum phenomenon: entanglement. It may be difficult to grasp, but is much simpler to the juggling with the possible implications from Bell's inequality and their loopholes (e.g., Ghim and Zhang). As to quantum gravity (notice the opinion of an expert here), the 'potential reality' is introduced to revive the physical objectivity of spacetime "points", by making the spacetime manifold itself an emergent phenomenon: "The requirement of general covariance takes away from space and time the last remnant of physical objectivity" (Albert Einstein, Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik 49 (1916) 769-822). The current formulation of GR can only determine "the mutual relations that exist between the gravitational field and the matter fields (i.e. the value the gravitational field takes where the matter field takes such and such value)", but not "the proper time between spacetime points" (Wiki; more from Butterfield and Isham), and the field equations "cannot even uniquely determine the topology of a manifold" (Alan Macdonald, Einstein's Hole Argument, p. 4). How can we fix these problems? By introducing two connections, geometric (local mode) and torsion (global mode of spacetime). The torsion connection is completely vanished (Hehl and Obukhov) in the local mode, hence its effect are considered "dark" (see Alex Murphy). Notice also that a hierarchy of 'potential reality' (never in plural), resembling the structure of cognitive concepts, is postulated (application here). In metaphysical terms, it supports the views of Aristotle and Spinoza: no "parts" of the infinite can exist, as the infinite Substance is indivisible. It's not like Russian dolls. In the case of a human brain (not mind or consciousness), the UNspeakable potential reality can be explicated with, for example, three (and many more) sayings, which produce "measurements" (if you prefer QM jargon) on it: 1. All are not hunters that blow the horn. None of these "measurements" can "collapse" the potential reality (Platonic idea) explicated with these sayings. And if our brain can work with 'potential reality', so can the universe modeled as a brain. Regarding the brain above your neck: its 'potential reality' is to its human self what EM radiation is to your subjective experience of 'color' -- no direct action of the human self on its brain is allowed in science. Hence it may be conceivable that the potential reality entwined with the human brain could be bridged to that of the quantum vacuum (BCCP). All you may need is an arrow of spacetime. (Notice, however, the 'two rules of success' here.) Forget about "energy conservation in GR". It's an oxymoron (details from Denisov and Logunov). What kind of "time" is implied in the non-linear dynamical cancellation of the two "fluxes" (Merced Montesinos), such that the ether would not "come back"? Can your wristwatch read it? The sole "explanation" of this ultimate puzzle of GR, offered by Chris Isham, was that, "after all, general relativity does seem to work well as a theory, and yet I can certainly read the time on my wrist watch!" But your wristwatch should not be able to read more than one instant from this (global) non-linear "time". Complex problems have simple, easy-to-understand wrong answers (Murphy's Law No. 15). We need quantum gravity, to uncover "the proper time [tau] along spacetime trajectories" (Carlo Rovelli; drawings here) and the genuine 'time variable' associated with the expansion of space due to DDE. Once we achieve this formidable task, we will (hopefully) find out what -- if anything -- might remain unchanged/conserved in this particular (global mode of) time. In the current 'GR without DDE', the dynamics is "entirely generated by constraints. The dynamical data do not explicitly include a time variable" (Karel Kuchar), and one can only hope that "the energy momentum tensor which is the source of gravity" might be conserved "due to the Bianchi identities" (E. Guendelman, p. 9). Such hopes are (i) utterly murky even in the textbook GR, because any observable of the gravitational field is "necessarily quasi-local" (Laszlo Szabados) and (ii) not applicable to the new dynamics of GR due to DDE. For example, Noether's Theorem holds only for flat spacetime, and the Bianchi identities are applicable only for 'GR without DDE'. At this point, I got an emotional response from Eduardo Guendelman, saying that the Bianchi identity is a mathematical theorem, so there is no ambiguity involved here. Well, I'm just a psychologist, so let me quote Matt Visser, p. 3: "... the Einstein equations of general relativity are local equations, relating some aspects (notice the poetry -- D.C.) of the spacetime curvature at a point to the presence of stress-energy at that point. Additionally, one also has local chronology protection, inherited from the fact (Sic! -- D.C.) that the spacetime is locally Minkowski (the Einstein Equivalence Principle), and so “in the small” (that's the sole application of those 'twice-contracted Bianchi identities', cf. George F R Ellis and Henk van Elst, Eq. 2 -- D.C.) general relativity respects all of the causality constraints of special relativity. Which is precisely the missing element needed to address the 'global properties of spacetime' in the presence of DDE. As R. Rakhi and K. Indulekha acknowledged (p. 5): "Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence (the same phrase was used by Sean Carroll -- D.C.), more of this energy-of-space would appear. (...) So the mystery continues." And so does the confusion about it -- click here. The intrinsic dynamics of the phenomenon of 'more space comes into existence' could only be detected in a reference frame from which this phenomenon is excluded, like 'not acting there'. But because DDE acts on the whole 3-D space en bloc, without any irregularities, there is no place in the universe in which we could install a clock and say -- look, this clock does read the (global mode of) time pertaining to the omnipresent phenomenon of 'more space comes into existence'. It is the theory of relativity itself, which cannot "detect" it. Which is why some people call it "dark". Although the mathematical meaning of the phrase "more space comes into existence" is not clear, I don't think Kurt Gödel would have called the ultimate source of spacetime points "dark". Once we move from physics to geometry, it's a whole new world there. Pity Mike Turner called it "dark"; that's so wrong! One cannot insert the "dark" energy of X into its consequence -- accelerated expansion of space. The source X does not belong, and cannot be fitted into the same 3-D space (Cauchy hypersurface) which is being created by X . You can do this only in GR textbooks that deal with 'GR without DDE'. Capiche? Notice also that Matt Visser (see above) considers the metaphysical assumption that the spacetime were "locally Minkowski (the Einstein Equivalence Principle)" to represent a fact. But we only have a mathematical fact that locally , "over" a point, one can indeed eliminate the gravitational "field" by hand (Hermann Weyl). But because nobody has so far explained the resulting quasi-local nature of the gravitational field's observables (see Laszlo Szabados above), nor the origin and the mechanism of inertial reaction "forces", I think we should be very cautious and open-minded in interpreting such mathematical facts and theorems, like the above-mentioned Bianchi identity. If you are looking for a genuine quantum-gravitational measuring device, your wristwatch (as well as the one of Kip Thorne) fits the bill, because it reads an already-linearized (see the explanation of 'already' below) time variable obtained from the "the proper time [tau] along spacetime trajectories" (Carlo Rovelli) and the (global mode of) time associated with the expansion of space due to DDE.
This is to me the ultimate puzzle in present-day GR. The sole "explanation" of Chris Isham was that, "after all, general relativity does seem to work well as a theory, and yet I can certainly read the time on my wrist watch!" I will desist to comment on C. Isham's observation, and will instead take the liberty of being (again) deadly boring, by explaining the difference between 'GR without DDE' vs 'GR with DDE'. First, a simple example from STR, with a trajectory of a Frisbee, on the fixed background of Minkowski spacetime: we can calculate the instantaneous state of the Frisbee at each point from the trajectory, and attach to this dimensionless point a well-defined vector. My teenage daughter couldn't understanding how it is possible to attach a vector to a "point", and I explained the puzzle by saying that the information from a finite interval from the history of this infinitesimal "point" is encapsulated in it -- we instruct this interval to shrink asymptotically toward zero -- so the vector is indeed well-defined. All this is possible under the premise of the fixed "grid" in STR. But once we move to 'GR without DDE', the "grid" is gone (Emilio Elizalde): at each and every "point" from the trajectory, the non-linear mutual determination of matter and space (John Wheeler) takes place. But in what time (see Chris Isham's wrist watch above)? There is no background grid or "ether" w.r.t.w. one can define the dynamics of 'GR without DDE'. Yet people don't ask such questions and prefer to just do calculations with the linearized approximation of 'GR without DDE'. As another expert explained to his undergraduates, "one begins by introducing the notion of a tangent vector to describe an infinitesimal displacement about a point p " (Bob Wald, p. 4). But again, in order to recover the true dynamics of 'GR without DDE', you need some "ether" or rather 'reference fluid' w.r.t.w. one can describe the fundamental phenomenon of transience (Abner Shimony): see the so-called Aristotelian Connection here. At this point, the 'GR with DDE' comes to rescue the Hamiltonian formulation of 'GR without DDE': we have a brand new, global degree of freedom of spacetime en bloc, hence can recover the transience of spacetime, as driven by the source of DDE, along the arrow of spacetime -- see above. To identify this same source in the quantum realm (called 'potential reality'), let's go back to the interpretation of QM here. In a nutshell, the so-called PR2 interpretation of QM offers a solution to the non-unitary "collapse" by replacing the alleged "U" and "R" processes with a new (at least to people like Ed Witten, Steven Weinberg and Gerardus 't Hooft) form of reality, known since Plato, called here 'potential reality'. Its quantum presentation is ubiquitous and has zero entropy; hence the familiar notion of time, which pertains to monotonic increase of entropy "in time", is not applicable to 'potential reality'. It may produce "shadows" in terms of 'quantum observables', yet these "shadows" cannot be traced back, to reveal any evidence of such events (or "quantum information") ever having emerged from 'potential reality'. It may act, yet not experience any backaction from its "shadows". Hence it is the ultimate "background" for QM and GR. It evolves along the arrow of spacetime (resembling the "memory" of the universe), by unfolding from 'the ideal monad without windows'. In the local mode of spacetime, every "point" is filled with an already explicated value of its 'potential reality', and as the latter evolves and becomes enriched, the "number" of its localized explications increases accordingly: more and more things come into existence in the universe. As John Wheeler put it, "Time is Nature's way to keep everything from happening all at once". Only with 'potential reality' there is no need nor place for any 'unitary dynamics' in the local mode of spacetime. This is the metaphysics of 'the universe modeled as a brain', viz. the interpretation of 'expansion of space' along the arrow of spacetime. From this perspective, if we follow the deflation time arrow in the local mode of spacetime, things will gradually fade away in a strictly non-unitary fashion, but will only approach asymptotically The Beginning, because it is logically impossible to reach It from/within the local mode of spacetime (cf. the paradox here). The solution is 'dual age cosmology'. The current situation with inflationary cosmology was presented by Alan H. Guth, the winner of the 2009 Isaac Newton medal, on 13 October 2009. He speculated that our galaxy could be an amplified "quantum fluctuation" (Part 2, 3:30 - 6:16),
... and then confessed his "Nightmare of Dark Energy" (Part 2, 11:36), on which the "eureka" of inflationary cosmology is grounded.
Let's go back to QM. Think of a trajectory of a Frisbee: at each "point" from the trajectory (the latter could be a perfect continuum of such "points"), the state of the Frisbee is a perfectly well defined fact, with a 'carpe diem' unit probability. I use this simple idea to introduce a new kind of cancellation mechanism, pertinent to 'potential reality', for removing the non-unitary "R" process (historical account from October 2002 here); hence the motto of this web site, since July 1997: Dead matter makes quantum jumps; the living-and-quantum matter is smarter. Notice that not only the "R" process is being removed (as did Hugh Everett III in his relative state interpretation of QM), but the alleged "U" process and Hilbert space as well. The established theoretical physics community, particularly Niels Bohr, ridiculed Everett's interpretation to the extent to which Hugh Everett left physics (and became millionaire). NB: Notice that if the PR2 interpretation of QM is correct, then all tentative solutions proposed for the measurement problem and the classical limit of QM, based on either probabilistic or "toposification" (Chris Isham), ‘neo-realist’ interpretation of QM (Cecilia Flori, p. 211), will necessarily be wrong. The next step is to elaborate on the continuum of such explicated quantum states (local mode of spacetime), which emerges from the back bone of the whole physical world (global mode). Here we enter quantum gravity, particularly the emergence of time and space from "something else" (Isham and Butterfield): check out the arrow of spacetime here, and think of 'the whole universe' as a huge brain which self-determines its consecutive quantum-gravitational states in line with the Bootstrap Principle of Geoffrey Chew. Also, the alleged quantum "fluctuations" are interpreted as flexibility of 'the quantum state' to offer potential states, one of which to be chosen (one by one) by 'everything else in the universe'. Hence the speculation about some "spacetime foam" and the insoluble problems from it (how do you tell apart spacelike from timelike at Planck scale?) are avoided from the outset. Possible practical implications are outlined here. "You do not know enough theoretical physics to help with any research in that area." To the best of my knowledge, nobody has so far offered some new cancellation mechanism as a joint solution to the measurement problem of QM and the cosmological "constant" problems. Such cancellation mechanism is built in the UNdecidable quantum state (quantum presentation of Platonic ideas) from the outset: instead of dealing with some |alive cat> & |dead cat> from the "U" process, we encounter an UNdecidable 'cat per se', so if we happen to observe an 'alive cat' as a fact, with unit probability, the 'dead cat' will happily live undisturbed in 'the UNdecidable quantum state'. No "collapse" nor dead cat doppelgänger à la Everett are needed.
To understand the origin of this whole mess, read the second sentence from the excerpt below (R.I.G. Hughes, The structure and interpretation of quantum mechanics, p. 77):
All these problems are resolved in the PR2 interpretation of QM from the outset. Moreover, the new cancellation mechanism is introduced to explain the ongoing, as-we-speak mechanism of 'the flatness problem' (asymptotically flat spacetime conjecture), producing an extremely precise balance between the two tug-of-war effects, CDM & DDE, of the geometry of spacetime at cosmological scales. Otherwise we have to inject up to 96% "dark stuff" (with all sorts of "ghosts") into the current theoretical physics, as calculated under the assumption that 'potential reality' doesn't exist. As Evalyn Gates put it (p. 196), the detection of DDE was "like finding an elephant on top of a table impeccably set with the finest china and silver (...). We stare in shock at the uninvited guest and demand to know where the elephant came from -- and how it got into (the) room." Regarding the arrow of spacetime: notice that the Frisbee-like sequence of explicated facts (local mode of spacetime) is inherently background-free, because the background (the reference fluid of GR and the UNdecidable quantum state) is 'not there', being placed ]between[ the "points" of the continuum of the local mode of spacetime. In other words, the "dark gaps" of the global mode are not like the real gaps between the tiles in R. Penrose's bathroom: regardless of how small tiles you choose, if you decrease the size of the tiles in a Fibonacci sequence, you will never ever reach the "gaps" from/within the local mode of spacetime (more on Fibonacci here). This proposal makes the local mode of spacetime a perfect 3-D continuum with dynamical topology of 'asymptotically flat spacetime'. The "dark" gaps of the postulated global mode of spacetime are completely sealed off by the arrow of spacetime -- the mechanism by which the "dark" gaps of the global mode are made nonexistent in the local mode is the same that makes the "speed" of light a fundamental constant (and also hides the mirror tachyonic world). This renders the Schlaefli conjecture (L. Schlaefli, Ann. di Mat. 5 (1873) 170), as well as all "branes" and other multidimensional superstitions in GR and string hypotheses (Lisa Randall; see also A. Vilenkin below) redundant, to say the least. In the context of GR, the global mode of spacetime is located "within" each and every point from spacelike hypersurfaces, as it "lives" exclusively on null hypersurfaces. (Unlike the geometry of spacelike hypersurfaces, the geometry of null hypersurfaces is not metric (D. C. Robinson), which leaves a challenging opportunity to introduce an additional, to the Christoffel connection, global torsion connection.) To be precise, the "duration" of the global mode, recorded with a physical clock (local mode), matches the "duration" of the atemporal "handshaking" transaction in Cramer's interpretation of QM: it has been already completed at each and every instant we "look" at it (see below). Hence in the local mode of spacetime, the dimensionless GW amplitude is zero, nonexistent, zilch. (Another case of reining a dimensionless amplitude, the mythical "quantum computing", is examined here.) Notice also that the hypothetical global mode of spacetime cannot be read by a physical clock (it will "stand still"). It is introduced to replace the "external time parameter" in H.-D. Zeh (p. 13) and the “auxiliary internal time” (cf. Macias and Quevedo, p. 8) by 'the reference fluid of GR'. The latter can "act" upon matter without being affected in turn by matter. In this unphysical "absolute" reference frame, an electromagnetic radiation field can indeed "stand still" (recall that EM radiation field cannot stand still with respect to any physical observer, Bahram Mashhoon, p. 14). The next metaphysical idea is straightforward: 'time' does not originate from 'change in space' but from 'change of space'. Only if you have the latter (global mode), you may introduce the former, as 'time read by a clock' (local mode). Why? Because one cannot insert the "dark" energy of X into its consequence: accelerated expansion of space. The dynamics of 'the change of space' is defined relative to the "omnipresent ether X " (global mode of spacetime). The latter is located "within" each and every point from the local mode of spacetime, and is wrapping the local mode by two (in fact, one) 'numerically finite but physically unattainable Aristotelian boundaries'. All we can physically observe is that the local mode of spacetime is being 'acting upon itself'. Such self-action will of course look "dark" to all local sub-systems (see Alex Murphy). Hence we can bridge QM and GR, and understand the origin of quantum and gravitational "waves": EPR-like correlations (global mode) will inevitably induce wave-like holomovement of physical stuff along the arrow of spacetime. Such wave-generation effects can be found in our brains and in many living organisms. Perhaps it determines the inertial reaction "forces" as well (don't bother to ask Criss Angel, he knows nothing about it). Recall what William Kingdon Clifford claimed in his paper ‘On the Space-Theory of Matter’, presented to the Cambridge Philosophical Society on February 21, 1870 (quoted after Domenico Giulini, p. 2):
Hence the space itself is endowed with dynamics, but then we need some ether w.r.t.w. such 'global dynamics of 3-D space' can be formulated. Then the only possibility -- trust me, there is no other option -- is to place the omnipresent ether, as 'the source of the "dark" energy', in the global mode of spacetime. Otherwise you will have to define the dynamics of space w.r.t. itself, and will look like Baron Munchausen. That's why we need an arrow of spacetime, in my opinion (but notice the opinion of Chris Isham above). NB: If this is the case chosen by Nature, then any approach to quantum gravity, based on the "splitting" of spacetime (Brett Bolen), will necessarily be wrong. Perhaps we may have to develop new mathematical theory of 'potential reality', such that the "state space" of Margenau's Onta (quantum presentation of Platonic ideas) would match the structure of cognitive concepts; notice that in the "cheating on 20 questions" the answer 'cloud' was explicated by a Baeysian learning rule (not the Born rule). For comparison, the categorification of Feynman diagrams requires "black boxes with many wires going in and many wires going out" (Baez and Lauda, p. 16), while in our case all wires are "instantaneously" (global mode of spacetime; see the Escher drawing below) keeping track of all virtual 'black boxes' as well (relational ontology), in order to dynamically adjust to the changing context of the game, until they jointly select the final, explicated 'black box': 'cloud' (see also the four dice here). NB: In the local mode of spacetime, the "duration" of the total negotiation with 'everything else in the universe' (relational ontology) is zero. Hence a wave pattern is being created, without any source of these "waves" being present in the local mode, and a new form of retarded causality (biocausality; see below) can be postulated -- a revitalization of Leibnitz' harmonia praestabilita, Jung's Synchronicity, and Einstein's Überkausalität. We definitely need mathematical theory of 'potential reality'. The task is highly non-trivial, but once we unravel the correct mathematical theory, the astonishing effectiveness of mathematics (Eugene Wigner) may drive us closer to the true quantum gravity of He Who Does Not Play Dice -- the world is not deterministic but flexible, and the 'chooser' of one possibility (one at a time) amongst infinitely many is 'the whole universe' in its state of ONE. All I've been getting so far is either dark silence or insults (some of them really harsh). Perhaps the situation will improve in 2010, after the sixth consecutive failure of LIGO Scientific Collaboration (LSC) to detect GWs with the so-called "enhanced LIGO". GW energy transfer is fundamentally non-linear phenomenon (Hermann Bondi), but is wiped out with the "linearized approximation" adopted by LSC. Also, GW energy is intrinsically quasi-local, in the sense that GWs do not propagate exclusively "in one direction only" (“when the waves are all moving in the same direction”, cf. P.A.M. Dirac, Ch. 33, p. 64), as they also have a holistic global component (atemporal "handshake"), which covers the whole 3-D space en bloc. Is it possible to detect some 'elementary shift' of the expanding metric -- the "intrinsic time interval associated to any timelike displacement", T. Jacobson, pp. 18-19 -- due to the omnipresent and perfectly smooth DDE? In what reference frame? Notice that you're dealing with some "fluid" that "has zero inertial mass! It can be accelerated with no cost, no effort" (B. Schutz, p. 255) and "provides an all-pervading energy density and negative pressure that are the same to all observers, at all places, and at all times in the history of any universe model, even the expanding ones." (p. 257) Similar rhetoric questions apply to the dynamics of the metric, producing inflationary gravitational waves on the 3-D "balloon" hypersurface. It's a bundle.
Forget it. There is no need for "precise calibration" of a dead turkey. The insane efforts of LSC remind me of the old joke about a drunken man, who has lost his key somewhere in the dark, but is searching for it under the street lamp, simply because it is brighter there. Only LSC's "key" costs billions. Which is why I accused LSC members of aggressive professional negligence, and offered them to review my White Paper. They responded with dark silence, as usual.
To explain "already", let me quote from Thomas E. Phipps, Should Mach's Principle be taken seriously? Speculations in Science and Technology, 1(5) 499-508 (1978), p. 504: The crux of the idea of biocausality is well-known. Back in 1953, Wolfgang Pauli suggested that the concept of finality ("the end (telos), that for which a thing is done", Aristotle, Physics 194b33) should be considered as a complement to causality in deterministic and statistical laws. The stipulation here is that Aristotle's effective cause & final cause determinate jointly the next state of all material constituents of the universe relationally, in line with the bootstrap principle 'think globally, act locally' (global mode of spacetime; see the Escher drawing below), but in the local mode the resulting biocausality is retarded, along the arrow of spacetime.
From this perspective, detecting GW effects requires "online" access to the global mode of spacetime, in which the dynamical determination of spacelike and timelike directions (hence Lorentzian metric) is being produced -- one-at-a-time, along the arrow of spacetime. In simple words, this means that the proper GW detectors must be endowed with the self-acting faculty of the human brain, to match the "interaction of spacetime with itself" (C. Kiefer, p. 2; cf. also J. G. Pereira et al., arXiv:0909.4408v1 [gr-qc], p. 10, Eq. 7.2). As of today, nobody cares. Nobody. I can take it. I'm psychologist, and don't need quantum gravity to practice PHI. Why would a fish need a bicycle?
[click the image to enter the web site]
Hopefully, if we join our efforts and knowledge (included at the level of our collective unconsciousness, cf. Jungian Kollektives Unbewusstes), some day we may succeed. Meanwhile, please keep in mind the prediction of Robert Millikan, Nobel Prize in Physics (1923): "There is no likelihood man can ever tap the power of the atom." This web site is my feedback to all people, who are helping me, one way or another, with improving the theory. Feel free to download it (app. 11.8MB) from http://www.god-does-not-play-dice.net/PHI_info.zip By unzipping PHI_info.zip, a new folder, !Einstein_PHI , will be created on your hard drive. Find there START.html.lnk and open it (it is linked to this front page (index.html) in the website folder). If, for some reason, you believe we don't need new approach to quantum gravity, try to understand Sean Carroll's speculations (448 pages, January 2010): "... wavefunctions appear to collapse in one direction of time but not the other is not an explanation for the arrow of time, but in fact a consequence of it. The low-entropy early universe was in something close to a pure state, which enabled countless "branchings" as it evolved into the future." Yet he acknowledged: "we can't, once again, define a conserved total energy in any reasonable way." Consequently, the main speculation of S. Carroll about some "low-entropy early universe" is just as unclear as is its gravitational energy which would evolve "into the future". (Also, there may be a critical low geometric entropy state of the 'extremely early' universe, which may blur the timelike and spacelike directions themselves, and turn them into some primordial quantum dough from which nothing could possibly "decohere", ever.) As one of his senior colleagues summarized, "the magnitude of the entropy of the universe as a function of time is a very interesting problem for cosmology, but to suggest that a law of physics depends on it is sheer nonsense."
"... when treated in a multiverse framework, fundamental time is directionless and consequently physical laws inherit its time-reversal symmetry. Despite that reversal symmetry is broken for the local time by the bubble nucleation, the bubble still inherits laws of physics at birth from the multiverse, without modification. Thus the emergent time’s arrow in the bubble does not affect the time-reversal symmetry imprinted onto the physical laws that the bubble inherits from birth in the multiverse. (...) An emerging time in the multiverse does not appear plausible since the emergence adds information on the multiverse that wasn’t there prior (... but we face the same kind of emergent non-unitary phenomenon with DDE -- an evolving cosmological "constant" that springs from the quantum vacuum - D.C.)." ... and the obstinate belief of Andrei Linde ($164,179 FQXi Grant): Sure enough, Andrei Linde tried to answer the first off question of how many universes are in the "multiverse" (arXiv:0910.1589v2):
That's how 'potential reality' is being camouflaged in present-day GR, simply because if it were possible to detect the source of DDE as 'gauge invariant observable', the omnipresent and perfectly smooth ether (the source of DDE) will be exposed to direct physical observations, as 'spacetime acting upon itself'. Back in April 1986, Yakov Zel'dovich wrote in a letter the following (private communication): "Long time ago, there was a period of time during which there was still no time at all." Of course he was joking. Yet the 'global mode of time', pertaining to potential reality, cannot be read by any physical clock, because the poor inanimate clock will read it as 'stand still' or "no time at all", as Yakov Zel'dovich put it. Maybe The Beginning, which lives in "no time at all", is always with us (dual age cosmology).
In German, it reads: Der Geist bewegt die Materie. Physically, Der Geist may look like 'the ideal monad without windows'. However, no scientific predictions can be made about it, or else we will conflate religion with science. Thank God, this is impossible.
----------- Note: At the age of 57, my hair is getting lily-white, and I may claim that it is sufficiently white to enjoy surfing at porno in the web, yet still sufficiently black to attract real blond girls. Likewise, LSC members deeply believe that GW strain, which might hit LIGO some day, would be sufficiently weak to be modeled with the linearized approximation of GR, yet sufficiently strong to be detected with the so-called Advanced LIGO (cf. J. G. Pereira et al., arXiv:0909.4408v1). But LSC can't have their cake and eat it. As Hermann Weyl demonstrated in 1944 (Hermann Weyl, How Far Can One Get With a Linear Field Theory of Gravitation in Flat Space-Time? American Journal of Mathematics, Vol. 66, No. 4 (Oct., 1944), pp. 591-604), the linearized approximation of GR is "a shadow without power". Notice that LSC cannot describe smooth bi-directional transitions from strong GWs to very weak GWs, as they approach asymptotically their sudden death at the stage of "a shadow without power". Joshua Goldberg is manifestly silent on this crucial problem, and Kip Thorne didn't even mention Hermann Weyl's article in his lecture "Gravitational waves in flat spacetime". Instead, he tried to defend the so-called "invariance angle" of LIGO's arms with an article by Eugene Winger, which he has read as a student "around 1960". Just look at the L-shaped tunnels of LIGO: isn't this 'graviton parapsychology'? The persistent "evolution" of the beliefs of LSC members is really amazing. Back in 1981 (cf. Daniel Kennefick, p. 1), Kip Thorne had no difficulty in "finding a taker for a wager that gravitational waves would be detected by the end of the last century. The wager was made with the astronomer Jeremiah Ostriker, one of the better-known critics of the large detectors then being proposed. Thorne was one of the chief movers behind the largest of the new detector projects, the half-billion-dollar Laser Interferometer Gravitational Wave Observatory, or LIGO. He lost the bet, of course." Now LSC members are effectively saying 'just gives us a couple of billion dollars more, and we gonna make it'. Exactly how much more? The Advanced LIGO Cost Estimating Plan (M990310-05.pdf, updated 05.27.2003) is here, but is hidden to 'mass society' taxpayers. Notice that LSC have already prepared 'Plan B', in case they fail miserably again. In their latest "science white paper", submitted to the Astro2010 Decadal Survey (Bernard F. Schutz et al., arXiv:0903.0100v1 [gr-qc], p. 3), they wrote: Once the "Advanced LIGO" fails in 2015, they will celebrate the 100th anniversary of Einstein's GR with their "way to new physics", claiming that their total failure is actually of fundamental importance, like the negative result for the ether drift in the experiment of Michelson and Morley ... but with just a few billion dollars more for LISA and Einstein Telescope, everything will be just right.
D. Chakalov
Subject: STOP wasting taxpayers' money !
Subject: [Copy] Email sent to Living Reviews in Relativity
=========================
============================== Subject: Re: "yes, I do understand GR, but cannot discuss that now."
p. 2: "If you believe the recent observational data regarding the accelerating universe, then the SEC is violated on cosmological scales right now!" 1. Claus Kiefer speculated extensively about 'entropy' [Ref. 1], but we "do not have a rigorous definition of entropy for systems coupled to gravity" [Ref. 5; see also the discussion of Eq. 1 on p. 7 therein]. 2. We are also conditioned to believe that, since the Einstein field equations are "local", it would be impossible that "the global topology of the spatial section of an FLRW universe could have an effect on that universe's dynamics" [Ref. 6]. But Einstein field equations themselves are totally inadequate for addressing the main puzzle of non-unitary emergence of 'energy from empty space' -- see above. This opens an opportunity to seek 'the arrow of time' in global topology changes, to at least gather some hints as to how the Einstein field equations should be modified to tackle the source of "dynamic dark energy". 3. If we look at the "expanding" FRW universe above, the first puzzle we should notice is that the cosmological time, as read by our wristwatch, should not be observable: while FRW equations describe the physical time evolution, the "observed" quantities are "not gauge invariant and therefore should not be observable in obvious contradiction to reality", cf. T. Thiemann [Ref. 7]. 3.1. Thomas Thiemann has argued that a tentative solution may be offered with some of those "scalar fields" introduced ad hoc [Ref. 7], to bypass the direct approach to the "dark energy" from the quantum vacuum. Unfortunately, all those "scalar fields" are red herring, firstly because there is no symmetry mechanism preventing their strong coupling -- see Sec. 2.2 in [Ref. 8]. 3.2. Thomas Thiemann offered an 'either - or' dilemma [Ref. 7], but the answer to the puzzle may be 'both': the new physics that we're missing does affect QED, and of course the predictions for LHC. 4. Notice that the "dark" effects from 'potential reality' have to be camouflaged in GR as "gauge-dependent". This should be expected, as present-day GR cannot handle 'absolute structures' such as the source of 'energy from empty space'. Surely "absolute structures carry no observable content" [Ref. 9]. Perfect!
"Either the mathematical formalism, which has been tested experimentally so excellently in other gauge theories such as QED, is inappropriate or we are missing some new physics."
p. 4: "Transition functions relabel the points that constitute M, which for the time being we think of as recognizable entities, as mathematicians do. (For physicists these points are mere ‘potential events’ and do not have an obvious individuality beyond an actual, yet unknown, event that realizes this potentiality.)
===========================
Subject: Re: How to quantize spacetime without affecting relativity
Subject: Re: How to quantize spacetime without affecting relativity
Note: Watch Cecilia Flori's lecture "Topos formulation of Consistent Histories", 14.01.2009, http://pirsa.org/09010017. She handles the topos theory and the ice hockey stick with agility and unmatched precision.
Note: Excerpts from http://arxiv.org/help/endorsement : "The endorsement process is not peer review. You should know the person that you endorse or you should see the paper that the person intends to submit. We don't expect you to read the paper in detail, or verify that the work is correct, but you should check that the paper is appropriate for the subject area. You should not endorse the author if the author is unfamiliar with the basic facts of the field, or if the work is entirely disconnected with current work in the area." Stanley Deser refused to even consider endorsing my manuscript. I do hope some of his colleagues will agree. If you, my dear reader, have papers "that have been submitted between three months and five years ago" to [gr-qc] or [astro-ph] domains, and would agree to endorse the submission of my manuscript, please contact me by email as soon as possible, and I will send you my manuscript.
==========================
--------- Note: Forty years have passed since Roger Penrose suggested the so-called Cosmic Censorship Conjecture (CCC), and people continue to ground their efforts on it (cf. Jonathan Thornburg and Michael I. Cohen et al., p. 2) and offer bets and drawings of "quantum horizon geometry".
Which is why you need to address the global dynamics of spacetime: the increasing emergence of energy-of-empty-space due to DDE. Just one "closed timelike curve" (CTC) or "time-like naked singularity" in the past 13.7B years would have destroyed everything, and since there are no strict bans on such catastrophic events (they simply have never happened, just like the ultraviolet catastrophe), "prohibited" only by people's belief in the current "dynamics" of GR and CCC in particular, recall that those "famous" singularity theorems are from 1970s, when nobody was aware of the flux of DDE. Two examples: Geroch's theorem regarding CTCs (Robert Geroch, Topology in general relativity, J. Math. Phys. 8, 782-786 (1967)) and Tipler's theorem, which stipulates that, given the (obvious) possitiveness of the energy-momentum tensor, there can be no changes in the topology of spacetime, hence the causal structure of spacetime is secured (Frank J. Tipler, Singularities and causality violation, Ann. Phys. 108, 1-36 (1977)), are from the old days of GR without DDE. As Alan Rendall stated (p. 14), "The study of these matters is still in a state of flux." Which is why I requested endorsement of my manuscript. So far two physicists have replied (J. Thornburg and S. Deser), the rest (73) have not even confirmed the receipt of my email (sent between October 26th
===========================
---------- Note: Nothing from the text above is original. The legacy of Erwin Schrödinger and Henry Margenau is anything but some unpredictable "black swan". For comparison, if someone has been offering the guiding principles for HTTP protocol to the people at CERN, but they were refusing to develop it, the invention of the Web [Ref. 1] would have never happened. One can only hope that the upcoming sixth consecutive failure of LSC to detect GWs with the "Enhanced LIGO" will shake up the established theoretical physics community. If not, we will have to wait for the seventh consecutive failure of LSC in 2015, with their "Advanced LIGO". What a terrible waste of time. And money. Does anyone care?
==========================
Subject: Re: Tue 24 Nov 13:30pm - 14:30pm "What about the semiclassical approximation and the recovery of an appropriate external time parameter in some limit? (...) The discussion is also connected to the question: Where does the imaginary unit i in the (functional) Schrödinger equation come from? The full Wheeler-DeWitt equation is real, and one would thus also expect real solutions for [PSI]." "If the theory does not allow us, even in principle, to extend solutions arbitrarily far in one direction, it may be difficult to view this direction as a dimension of the world."
==========================
http://www.god-does-not-play-dice.net/#NB
=============================
In the textbook version of 'GR without DDE', the 'coordinate time' read by your wristwatch, and the very notion of 'energy conservation' during some interval from that 'coordinate time', cannot be rigorously defined. The tacit presumption is that 'space' itself does not "move" anywhere, simply because there is no "outer space" in which our 3-D space could "expand into". But only the second part from this tacit presumption is correct, since our 3-D space can indeed "move" or rather "emerge" (C. Isham, gr-qc/9310031, Option IV): the intrinsic dynamics of space -- here we enter 'GR with DDE' -- can only be defined with respect to a hypothetical global mode of spacetime, which is hidden ]between[ the "points" of the local mode of spacetime. The latter stands as a genuine perfect continuum (the "dark gaps" from the global mode are hidden by the so-called 'speed of light'), and has been studied in STR and in 'GR without DDE'. If we wish to think as proper relativists, this is the only choice we may have: see my email to Harvey R Brown above. Many people hate it and spit insults on me; other just keep quiet, but nobody has so far offered any viable alternative. But is there any alternative to 'the arrow of spacetime'? Back in 1772, on the occasion of the fall of meteorites, the French Academy of Sciences adopted a resolution categorically rejecting such ridiculous phenomena. The obvious reason had been that rocks cannot fall from the sky, simply because there are no rocks there. Likewise, when you look at the sky, you will never think that the space itself could possibly "move", in any way whatsoever. But once the "dark energy" from 'empty space' was confirmed, the intrinsic dynamics of 3-D space, hence 'GR with DDE', are unavoidable. Your good old wristwatch does read the dynamics of "dark energy" along the arrow of spacetime. E sarà mia colpa se così è? (Niccolò Machiavelli) D.C.
p. 7: "A New Scenario. The Principle of Gravitational Stability ought to be fully used in the very derivation of Space Time Uncertainty Relations, which would then depend also on the energy-momentum density of generic background quantum states; this leads to commutation relations between Spacetime coordinates depending in principle on the metric tensor, and hence, through the gravitational coupling, on the interacting fields themselves. Thus the commutation relations between Spacetime coordinates would appear as part of the equations of motions along with Einstein and matter field Equations.
===========================
Note 1: I really cannot understand why people believe that the source of "dark energy" should necessarily have positive energy density ("Treated as a fluid, this component has negative pressure (assuming positive energy density), ... " In the model presented here, these two self-imposed presumptions are dropped, and the source of "dark energy" is non-existent in the local mode of spacetime. None. Zero. Zilch. You can safely set it to zero, just as you usually treat the vacuum energy density in QFT. Yet the source of "dark energy" can take any value in the global mode, depending on the particular cosmological stage of the universe, because T (the energy momentum stress tensor of all matter and fields other than gravity, with positive energy density) can completely vanish/dissolve into the vacuum, and stay available there for any partial, full, or "over unity" recall, if needed. How? Because it is potential reality. Only people like George Ellis cannot grasp it. All we can physically observe is that 3-D space is acting upon itself. We cannot trace back this 'energy from empty space', which is why some people called it "dark". In the same vein, the human mind would be considered "dark", because all we can observe is that the brain is being acting 'upon itself', by thinking about the brain, with the brain. Gerard 't Hooft had a brilliant guess about the negative energy states, but his Ph.D. student Stefan Nobbenhuis ruined it, upon his guidance, by assuming that "there is no coupling other than gravitational (emphasis added - D.C.) between the normal matter fields and their ghost counterparts, otherwise the Minkowski vacuum would not be stable" (arXiv:gr-qc/0411093v3, p. 10). But the quantum vacuum can be stable without any gravitational coupling whatsoever, because gravity applies only to the explicated/physical form of reality, while the absolute value of energy stored in the vacuum is potential reality. The misleading adjective "dark" (Mike Turner) comes from treating the potential vacuum reality as 'physically real'. In the case of John Wheeler's 'cloud', only this last explicated physical reality will be subject to gravitational interactions, like the explicated Casimir energy. The 'cloud' has been explicated by an emerging context, while in the case of the "dark" energy from the quantum vacuum we encounter an emerging boundary: the energy here is not "boundary sensitive". It is 'the whole universe as ONE' (global mode of spacetime) that fixes the "boundary terms", so that we can only see a "cloud" with strictly positive mass. Surely the explicated "cloud" changes along the cosmological time arrow, but its "dark" driving force cannot be unraveled from the fleeting "cloud" (denoted with a in [Ref. 1]), just as we cannot unravel the UNdecidable Kochen-Specker quantum state from its colorizable projections. This is the legacy of Schrödinger and Margenau (see below), which I was hoping to explain on November 27, 2002. Notice that in GR you inevitably need to introduce some additional structure [Ref. 2] compensating for the absence of the global mode of spacetime. To understand the origin of these of additional structures, recall the prerequisites that necessitate 'time' regarded as 'change': we need two different and distinguishable states of a physical system, and some background w.r.t.w. the difference between the two states can be identified. In STR, the task looks quite easy: take two consecutive, instantaneous, point-like states of a Frisbee along its continuous trajectory, defined w.r.t. the fixed background of Minkowski space, and you're done. In 'GR without DDE', the background is the 3-D space itself, which is allowed to change its "curvature" only, following the bi-directional "talk" between matter and space: "Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve" (John Wheeler). But because of the Equivalence Principle adopted in GR, gravity must be able to vanish completely "inside" an infinitesimal "point", hence there is no localizable point-like gravitational energy density in such "point" and across its infinitesimally small neighborhood, to compute derivatives (Bjoern Schmekel). Hence the notion of 'time', conceived as 'change' from point-like state A to point-like state B (defined w.r.t. a background of 3-D space), becomes terribly complicated because of its dual, non-linear duties: "the metric is treated as a field which not only affects, but also is (at the same time - D.C.) affected by, the other fields" (John Baez). Notice the notion suggested by Viktor Denisov and Anatol Logunov: 'physicogeometric dualism'. Under these circumstances, people need to introduce some additional structures to define some "boundaries" of the whole spacetime; for example, some "fall-off conditions of the curvature in appropriate coordinate systems at infinity" [Ref. 2], because, in the case of the Einstein equations alone, "there are no physically motivated boundary conditions" (Alan Rendall). But notice that the background of 3-D space is still always there, in the sense that in 'GR without DDE' the space itself doesn't "move" (Robert Geroch). But once we endow the space itself with an additional degree of freedom, as in 'GR with DDE', it acquires new dynamics (arrow of spacetime), and those 'additional structures' that were introduced by hand [Ref. 2] should be derived from the "dark" ("no observable content", Domenico Giulini) global mode of spacetime. Don't try to bridge the two "mirror" worlds (introduced by symmetries or quasi-symmetries [Ref. 2]) with any physical stuff whatsoever. Don't try to explain the self-acting faculty of 3-D space with the physical, "colorizable projections" that can only show up with positive energy density. You will be baffled by the driving force of the cosmological time arrow [Ref. 1] and the cosmological "constant" problems forever (cf. Amedeo Balbi), or at least until you quietly retire. D.C.
Note 2: Recently, J. M. Pons, D. Salisbury, and K. Sundermeyer (PSS) tried to solve the paradoxes of “frozen time” and “nothing happens” (arXiv:1001.2726v1 [gr-qc]), stressing the difference b/w the gauge generator and the Hamiltonian (p. 5): "These gauge transformations define equivalence classes within S, which we call gauge orbits. A gauge orbit represents a unique physical state (footnote 5), and its different points correspond to different coordinatizations. In another paper (arXiv:0902.0401v1 [gr-qc], p. 4), PSS illustrated their ideas with a "spatially homogeneous isotropic cosmological model", and acknowledged that "this model possesses the curious property that the only physical variable that changes in time is time itself!" (emphasis added - D.C.). Which makes this "time" unobservable, or rather 'observable only with respect to itself'. Pity PSS didn't ask Karel Kuchar to comment on their speculations, nor mentioned the new dynamics of 3-D space due to its "dark" energy acting on the whole spacetime en bloc. When will the Hamiltonian formulation of GR address this task? When pigs fly. D.C.
Example: Jim Hartle. Recently, a young theoretical physicist, Gareth Jones, defended his Ph.D. Thesis on "Searching for gravitational waves... ". He looked at Ch. 23 from Jim Hartle's textbook, "Gravity, an introduction to Einstein's General Relativity", to eventually understand the dimensionless GW amplitude (Eq. 1.64, p. 15) that would "cause a periodic strain (i.e., stretching and contraction) of the proper distance between points (Sic! - D.C.) in spacetime" (ibid., p. 182). But you can't hide the dimensionality of GW amplitude in 3-D space: check out SBG here. In order to prove LSC (at least 679 people) wrong, all you need is to drive the "background" in the linearized approximation of GR to its absurdity, as with the SBG argument. Not sure? Please explain the dimensionality of GW amplitude (h) in Kip's mantra:
If you look at Wiki, GW amplitude "is not the quantity which would be analogous to what is usually called the amplitude of an electromagnetic wave (...)." The alleged GW has frequency, wavelength, and speed -- all defined with proper dimensionality. Only the action of geometry on matter, embodied in the mantra above, is a dimensionless ghost that shows up only with ... "2.3×10-26" , say. How can Gareth Jones change his Ph.D. brain, to think as a physicist? Surely the entity that fixes a 'meter' cannot itself be defined with what it produces -- a 'meter'. Can he notice the intrinsic parapsychology of statements like "our best (lowest) upper limit on gravitational wave amplitude is 2.3×10-26" ? I think Jim Hartle
(along with Bernie Schutz) should be blamed for Gareth
Jones' professional career. It may be wasted by chasing ghosts with
real, taxpayers' money. D.C. Subject: Re: The
schizophrenic behavior of gravity (SBG) ============================
Ronnie, here's a story from Uncle Dimi. Suppose you're in a pitch dark room. You hold a torch in your hand, but want to "see" how the darkness itself looks like before you observe it with the torch. As you might have guessed, 'the darkness itself' stands for the 'UNdecidable quantum potential reality' that cannot be fitted into any Hilbert space whatsoever; more from Uncle John. Obviously, your task is not feasible. With your torch, you can only "see" the classical presentations of 'the dark room', which have been "filtered" through the classical spacetime at the scale of tables and chairs. So, what do you do? You use some QM textbook recipes for calculating probabilities for observing the dark room with your torch. NOT the dark room itself. And if you "look" with Hilbert space with dimensions 2, you may never notice any problems with your torch observations, as you can always infer what sorts of objects should have been in the dark room, before you turned on the torch and brought them into the classical spacetime of tables and chairs (recall the "quantum computing" mess). The real fun with QM starts when KS Theorem comes to play: your torch observations do not make sense. You cannot infer anymore what kinds of objects should have been in the dark room before you turned on the torch. (In the context of "quantum computing", quantum states both 'partly exist' as context-evoked latent observables and 'partly do not exist', being UNdecidable quantum state (never in plural) as well. It's an "eigentümlichen, klassisch nicht beschreibbaren" (W. Pauli), indivisible bundle of 'both ONE and many'. Capiche?) The essential ONE-"part" from the objects in the dark room will always remain unaccounted for. You can say NOTHING about it. It is UNspeakable. You just can't fit it into any Hilbert space on which you make your torch observations. It is the ultimate quantum reality 'out there', which I simply call 'potential reality'. You can say nothing about it, because any statement of yours refers exclusively to what you can "see" with your torch. This is my answer to your question "what it is exactly that the Kochen-Specker Theorem states", as you put it. Your mentor, Nicolaas Landsman, has tried some toposification of quantum theory, but notice that this is just another torch. Chris Isham also plays with that topos torch. Other people try another, 'non-commutative spacetime torch'. The math jungle is staggering. Don't go there, it's endless. How do I know? Because there is only one way to solve both the measurement problem of QM and the cosmological "constant" problem. Both problems, en bloc. Just recall the basic tenet of Copenhagen [Ref. 1], and compare it with the interpretation of QM discussed here and the arrow of spacetime: the instantaneous state of Die Bahn (trajectory) of all physical objects, at all length scales, is nothing but the local mode of spacetime, as it evolves from "point" A to "point" B, following the expansion of space due to the "dark" energy of the vacuum. Now you can make up your mind. Good luck with your Ph.D. Thesis.
=================================
===================== Subject: Re: PTI, by
Ruth Kastner We see only the end result from already-completed atemporal "handshaking" transactions, and of course we cannot trace it "back" to the global mode of spacetime -- all the negotiations between the offer-and-confirmation wave is one single event in the local mode of spacetime. In the local mode of spacetime, its "duration" is zero -- just like the proper time of a photon "between" its emission-and-absorption; see Kevin Brown. In the local mode of spacetime, all this "happens" over a "point". Which is why there is no "source" of the quantum-gravitational waves that is “waving”, as stressed by Anthony Zee. The second case of
fixing the physical constituents at this same "point"
concerns GR: we need to examine the "negotiations" of matter and
geometry, which also "take place" in
the global mode of spacetime:
"Space
acts on matter, telling it how to move.
In turn, matter reacts back on space, telling
it how to curve" (John Wheeler).
The local mode of spacetime is a perfect continuum, because the "dark gaps" from the global mode are completely sealed off by the so-called 'speed of light'. We also have a pocket of propensity-states (KS states; see below) to choose from, which cannot be fully derived from our past only -- this is the lesson from the Free Will Theorem. Sorry for repeating this all over again.
==================================== Note 2: A brief note on the Kochen-Specker Theorem. Carsten Held stated that the KS theorem, "by its mathematical nature, is not empirically testable", and since Ronnie Hermens seems to have some troubles with it, may I offer a brief, personal, and biased interpretation, ensuing from Ernst Specker's tripod. Imagine three quantum guys, Tom, Dick, and Harry, and think of the "spectral decomposition" of their quantum states as being presented by their hands, with the following specifications: upon observation at particular instant, they all have to simultaneously raise their hands (hermitian operators). Thus, each of them can, and have to, raise either his left hand (L), or right hand (R), or both (B). The famous KS Theorem says that the (spin 1) system {Tom_Dick_Harry} will exhibit the following "paradoxical" (from the viewpoint of classical physics) situation: if Tom and Dick happen to possess well-defined ("an unequivocal true-false value", cf. Isham and Butterfield above) quantum states of their hands (either L, or R, or B), then in that same instant Harry will not have any hands at all. For if the poor guy had 'hands' in that same instant, he would have the opportunity to choose one of his context-dependant quantum states -- either L, or R, or B. He will instead be shifted to the "uncolored" section from KS sphere. Next time you "measure" the system {Tom_Dick_Harry}, exactly the same thing can happen to Dick. Or to Tom. So, any time you observe some classical presentation of 'quantum state', be aware that nevertheless something essential is missing. It showed up in the case with Harry, yet it "covers" the whole system {Tom_Dick_Harry}, much like the "dark" energy from 'empty space'. Poetically speaking, the case with Harry was the "revenge" of the quantum Noumenon pertaining to {Tom_Dick_Harry} for our efforts to push it at the length scale of (unanimated) tables and chairs. Unlike the measuring devices examined in QM textbooks, the human brain can operate with its presentation of 'potential reality' elevated at the length scale of tables and chairs, as demonstrated with the example of three "measurements" (cf. the three sayings above). If our brains can operate with their UNspeakable potential reality, so can 'the universe as a brain'. Notice that if we constrain Tom, Dick, and Harry to raise only one hand (either L or R), people would entertain "quantum computing" and "topological quantum computation" (e.g., Michael H. Freedman), because the implications from KS Theorem will be obscured. But as the UNdecidable quantum state is still working in the quantum world, it cannot be harnessed with unanimated devices. I employ the notion of 'potential reality' to signify the UNdecidable KS quantum state -- the genuine 'quantum reality out there'. Can't fit it in any Hilbert space whatsoever. If you prefer, think of it as Reichenbach's Common Cause Principle. In summary, the Kochen-Specker Theorem demonstrates the UNdecidable KS quantum state. The latter is far more profound and important than the contextuality alone [Ref. 2] ("not all observables can be assigned definite values that are independent of the measuring context", cf. Ronnie Hermens). Namely, the conclusion that "only contextual values can be ascribed" [Ref. 2] does not shed light on the implications from the fact that contextuality is invariant to the particular place of the observables in the 3x3 array. As I wrote above, the same thing that happened to Harry can happen to Dick, or to Tom. Nothing -- not even some "contextuality" -- can save Harry (or Dick, or Tom) from the case in which he (or Dick, or Tom) must not possess any hands. If at some instant of measurement Harry must not have any classical hands whatsoever, yet at some other instant he -- the same Harry -- can and will obtain some contextual, well-defined, classical-able hands, then we are facing a phenomenon far more important than "contextual hands" alone. Namely, we can tell apart the contextualized classical-able hands, which can be filtered through the classical spacetime as 'classical hands', from those "intact" quantum states that can't. Which does not imply that the latter do not exist. In my view, only some quantum Noumenon can secure the ontological contextuality of quantum objects. The ontological contextuality may or may not provide 'the same Harry' with contextualized classical-able hands. It is also UNdecidable and Unspeakable, and of course 'not empirically testable'. Thus, if you observe the "hands" of some quantum object, be aware that you're only observing its contextualized classical shadows on Plato's cave, emanating from the ultimate quantum potential reality. NB: If the reader wishes to refute this interpretation of KS Theorem, please start with converting the "uncolored" section from KS sphere to some Hilbert space (your choice), to match the case in which Harry would obtain some contextual, well-defined, classical hands, at the expense of either Dick or Tom being shifted to the same "uncolored" section from KS sphere. What is the 'time parameter' pertaining to the dynamics of the reversible (KS sphere <--> Hilbert space) transitions, for all observables from {Tom_Dick_Harry}? Please don't hesitate! In a drastic contrast to the "collapse" and the Eigenvalue-Eigenstate Link from the old Copenhagen School [Ref. 1], the PR interpretation of QM employs the phenomenon of 'emergence' (e.g., Isham and Butterfield): in the case with {Tom_Dick_Harry}, one could only observe, at particular instant of time, the emergence of only one of its latent observables, say, {Tom, R}, just like the end result from the correlation and "negotiation" (global mode of spacetime) that led finally to John Wheeler's 'cloud'. This one final result (one-at-a-time) is 'physical reality' (local mode of spacetime), while the rest of Tom's latent states, plus Dick's latent states, plus Harry's UNdecidable KS state constitute the 'potential reality' of the system {Tom, Dick, and Harry}, which is in turn rooted on the quantum Noumenon -- "The ideal monad has no windows" (Döring and Isham). This is entirely different from any 'modal' or 'contextual hidden variable' theory. It goes without saying that a rigorous presentation of the ideas in the paragraph above is not available. These are just ideas presented with words. Back in 1935, Erwin Schrödinger also offered some very general ideas, presented with words: "The rejection of realism has logical consequences. 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 second part from the last sentence was totally forgotten by the mainstream theoretical physics community, and only Henry Margenau paid attention to it. Yet even today very few QM textbooks mention KS Theorem, which is rooted on this forgotten (or rather ignored) consideration spelled out by Schrödinger in 1935. As to the first part, "a variable has no definite value before I measure it", perhaps the intact quantum world 'out there' exists as the UNdecidable quantum state. If this is the case chosen by Mother Nature, the mysterious transition from quantum to classical, which is essential to QM textbooks [Ref. 3], should be explained with the "back bone" of the quantum world -- potential reality. Notice that the quantum truth functional in QM textbooks (e.g., Ref. 4, p. 314) is not applicable to 'potential reality' due to the presence of the generic "intact" (not limited to KS Theorem) UNdecidable quantum state. For example, regarding the notion of spin ("klassisch nicht beschreibbaren Art von Zweideutigkeit", Wolfgang Pauli), Bob Griffiths rightly says (ibid., p. 196) that "there is no property (explicable at the length scale of tables and chairs - D.C.) corresponding to Sz = +1/2 AND Sx = +1/2 for a spin-half particle." Of course not. The whole point is that there must exist something that keeps the "sameness" (Genidentität, Kurt Lewin) of this spin-half particle, so that it can "pass through" it (the "intact" UNdecidable quantum state) and be able to switch between its allowed states, in line with the conservation law known from QM textbooks. Can we, with our Boolean logic, think of a quantum particle as possessing simultaneously perfectly well-defined position and momentum (ibid., p. 314)? Of course not. Does that mean that we can "impose bans" on such UNdecidable quantum state in the quantum world, just because we cannot think about it? Of course not. The "non-commutative" quantum state is simply not point-like. It may be perfectly well-defined as 'potential reality', yet not point-like. It has to be point-like only in classical mechanics, like the point-like states of a Frisbee along its classical trajectory. (The hypothetical abilities of the human brain to observe and act on the UNdecidable quantum vacuum state requires special considerations.) Let's not mix apples with oranges, because the 'time' in the quantum world (no time operators in QM) is not like the one at the classical world, and the "intact" UNdecidable quantum state simply cannot get there. With unanimated measuring devices, we can "measure" only one frozen point from the anti-relativistic "time parameter" in the Schrödinger equation, and by imposing such wrong, albeit inevitable, classical filter on the quantum world we may develop distorted and misleading impression about some "time parameter in the Schrödinger equation". The experimental fact that even by detecting electrons one-at-a-time they nevertheless build an interference pattern [Ref. 5] demonstrates their quasi-local nature, yet the probability for detecting individual electrons on the screen, as point-like events, is blind and deaf to their quasi-local nature: the interference pattern can only be produced if the individual electron was able to "sense" the two slits simultaneously, while the probability for its detection on the screen refers to registered events that are inevitably point-like facts. This should be the starting point for explaining "the central mystery of quantum mechanics" (Richard Feynman): the nature of the quasi-local UNdecidable quantum state. It is not a 'fact', and cannot be presented with any probabilities, as was the case with Harry above. If you teach Quantum Mechanics, start with the double-slit experiments and finish with the KS Theorem, which is grounded on the statement made by Erwin Schrödinger in November 1950: “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.” NB: There is nothing "probabilistic" or "stochastic" in the quasi-local UNdecidable quantum state that neither 'is' nor 'is not'. Can't fit it in any Hilbert space. There are three totally different cases in QM. With just one degree of freedom, we (not Mother Nature) calculate an observable with a single eigenvalue ("an eigenstate of k belonging to an eigenvalue k'," P.A.M. Dirac, p. 154); the second case is confined to 'contextual values' (we constrain Tom, Dick, and Harry to raise only one hand -- either L or R; see above); and the third case deals with the absence of any classical hands whatsoever, after KS Theorem and the Free Will Theorem. Quantum Mechanics is about this third case. Can't fit it in any Hilbert space. Tell your students about it, Prof. Doplicher. No kid should end up like A. Connes. Surely the quasi-local UNdecidable quantum state cannot be filtered through the spacetime of STR and the Boolean logic of propositions: the truth evaluator will be YAIN (both yes and no). Which is entirely different from the "toposification" of quantum theory suggested by Chris Isham -- neither true nor false, but "somewhere in between" [Ref. 6]. To quote Niels Bohr, "Mathematical clarity has in itself no virtue. A complete physical explanation should absolutely precede the mathematical formulation." And the physical explanation has been spelled out by Schrödinger and Margenau. Only the math is unknown. To move further (Machian quantum gravity), try to unravel the origin and mechanism of instantaneous inertial reaction "forces", starting solely from Albert Einstein's postulate that "the metrical character (curvature) of the four-dimensional spacetime continuum is determined at every point by the matter there, together with its state" (Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, 1917). No way. Something inherently quasi-local is again missing (try an experiment with your brain here), as hinted by KS Theorem and CK Free Will Theorem. In the case of GR, the torsional degrees of freedom are excluded from the outset. But I'll stop here, because, as many people complain, the story will (again) become deadly boring. I think Ronnie Hermens should ask his QM tutor (Nicolaas Landsman) lots of questions about KS Theorem. Perhaps he should also ask Chris Isham, after reading Ch. 9 from his famous textbook.
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Let me start with a quiz: Look at the two pictures below and tell the essential difference.
Yes, you got it right: the first picture is a negative image from the original. You may also say that, unlike Chuck Norris, those people at NASA, who offer a meta-observer view on the "expanding" 3-D space, use lots of math, but that doesn't really matter, because the essential similarity is that both images are jokes. Back in 1963, Roger Penrose offered a recipe for reaching infinity from any location in space, which was also a joke, although spiced with lots of math. To explain my not-so-humble opinion, I will ask Claudia Schiffer (who else?) to first read an interpretation of KS Theorem above, and then imagine herself in a global mode of space, such that she can monitor the dynamics of 3-D Flatlanders (instantaneous cross-section of the arrow of spacetime) and literally "see all six sides of an opaque box simultaneously, and in fact, what is inside the box at the same time." She will "see all points in 3-dimensional space simultaneously, including the inner structure of solid objects and things obscured from our three-dimensional viewpoint", as explained eloquently in Wiki. Her wristwatch, however, will be "frozen", because it cannot read simultaneously more than one instant from the "infinitely-fingered" global mode of time. To be precise: her wristwatch cannot read the "all time [tau]" which is "eternally present" (Karel Kuchar). This global mode of time emerges thanks to the additional spatial degrees of freedom (see the recipe for derivation of 'infinitesimal' below), which allow Claudia, along with John Bell's Aether, to qualify as 'the reference fluid in GR'. Claudia will also be able to understand Karel Kuchar, regarding a paradox called 'the problem of time', since she is its solution, dubbed "hidden unmoved mover" (Karel Kuchar didn't offer the math of his "hidden unmoved mover", regrettably). Now, Claudia is prepared to "look" at the (finite, in her absolute reference frame) cosmological time, and count to infinity (if she wishes to). Unlike Chuck, she can count to (actual) infinity by only one "point" from her (global mode of) time. Fine, but would she notice some "expansion" of 3-D metric, as she looks at the asymptotically flat 3-D space from both "inside" and "outside"? And how about the global dynamics of this 3-D space, as driven by its "dark energy"? Can she notice the emergence of "more space", as stated by her colleagues above (cf. R. Rakhi & K. Indulekha and S. Carroll)? Here's the problem of "more space". Some prelims from GR textbooks: unlike STR, the spacetime in GR textbooks is considered "dynamical", such that, to follow a well-know metaphor, the "actors" (matter) and the "stage" (spacetime) engage in a non-linear negotiation (Escher's hands): "Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve" (John Wheeler). But notice that, unlike GR textbooks, the non-linear negotiation between the two sides of Einstein equation is interpreted here as "taking place" in the global mode of spacetime endowed with additional spatial degrees of freedom, as "observed" by Claudia above. The difference resulting from Claudia's global mode can be explained by clarifying the notions of 'time' and 'tangent vectors' in GR textbooks. We all agree that 'time' is no longer a fixed background parameter, but the global mode of time, in which the non-linear negotiation of geometry of spacetime vs. matter "takes place", cannot be read by Claudia's (unanimated) wristwatch, employed in GR textbooks. This produces a plethora of "times" in GR textbooks, but "these definitions of time are in general unphysical, in that they provide no hint as to how their time might be measured or registered" (Butterfield and Isham). Here, all these "times" are literally embraced by Claudia, as she can "see" them simultaneously and en bloc, because her "all time [tau]" (global mode of time) is "eternally present" (Karel Kuchar). To elucidate the second major difference in treating the 'tangent vectors', recall that in GR textbooks you are invited to take the same meta-observer, bird's-eye view on the whole spacetime as in the NASA picture above: to explain the alleged "curvature" of spacetime, "it is easy to see it in a 2-dimensional surface, like a sphere. The sphere fits nicely in 3-dimensional flat Euclidean space, so we can visualize vectors on the sphere as 'tangent vectors'" (John Baez). Then you've been taught by Bob Wald "to work infinitesimally, using the idea that, on sufficiently small scales (this notion certainly needs clarification in the context of Thompson lamp - D.C.), a curved geometry looks very nearly flat (notice the poetry - D.C.). These departures from flatness can then be described via differential calculus. To do so, one begins by introducing the notion of a tangent vector to describe an infinitesimal displacement about a point p ." The major differences to the interpretation offered here are in the following. Regarding John Baez, the local mode of spacetime is not embedded in any "higher-dimensional flat spacetime", but in an infinite-dimensional purely geometric manifold (called here 'global mode of spacetime'). Hence 'the infinitesimal' (see below) is indeed equipped with 'tangent vectors', but they all "point" to Claudia's global mode of spacetime -- not to the local mode (this claim shouldn't be surprising, because a tangent vector of non-zero length can be fully confined into the space in GR textbooks only if the latter were Minkowskain flat, but then the vector won't be a tangent one). The new (to GR textbooks) "direction", resulting from the very "expansion" of space due to "dark" energy, is not the mythical foliation time orthogonal to the three Hamiltonian components that are somehow "tangential" to all hypersurfaces (cf. Kiefer and Sandhöfer below).
The new "direction" from the "dark" energy is non-existent in ADM presentation, since it pertains to the 'absolute time' of the 'absolute structures'. Small wonder Karel Kuchar couldn't dig it out from present-day GR: you have a plethora of unphysical "times" from the foliation recipe, and no reference fluid (global mode of spacetime), which makes you 'eternity blind' (John G. Bennett). The crucial "direction" of the so-called "expansion" of space due to the "dark" energy from empty space (Lawrence Krauss) requires a brand new dynamics of GR. In GR textbooks, the flexibility of space is limited to its "curvature" only, and, if you manage to compute a linearized snapshot from Einstein's filed equation, you inevitably end up with a frozen "block" spacetime: "There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes" (Robert Geroch). Then the new dynamics of spacetime, due to the "dark" energy, can only spring from something "outside" (the local mode of) spacetime. That is, from "outside" both sides in the Einstein equation -- the global mode of spacetime. It literally creates both "more space" (cf. R. Rakhi & K. Indulekha and S. Carroll above) and "more matter". The proper dynamics of 'GR with DDE' cannot be unitary. Enter the puzzle of "points": the perpetually re-created world of facts (local mode of spacetime) and its ultimate source 'the ideal monad without windows' (Döring and Isham) contain uncountably infinite points ('the set of all sets', maybe). The cardinality of such "set" (if any) is not even aleph-0. Once created by The Beginning, the local mode of spacetime is wrapped by its special "boundaries" (see SRP below), such that the 3-D space of the local mode is de facto infinite (dual age cosmology). The "number" of points inside a sphere with a given radius will not increase if we double the radius, nor will this "number" decrease if we flatten the sphere to 2-D surface, as demonstrated by Kurt Gödel in 1947. NB: These so-called points are a special non-Archimedean entity. It was Lucretius who pointed out the unknown mechanism by which these "points" build up any finite domain of space. The task of revealing some pre-geometric plenum which "connects" these non-Archimedean "points" was missed by Felix Hausdorff and Roger Penrose, to name but a few. But again, what sort of "dark stuff" could Claudia see? Maybe she can only notice the emergence of "more space" from the quantum-gravitational "monad without windows" in terms of the increase of the "memory" of 'the universe modeled as a brain' along the arrow of spacetime. But because Claudia is placed simultaneously at the two "boundaries" of 3-D space (see below), at two 'ideal endpoints' of Beginning-and-End, which wrap up the whole 3-D space -- from the infinitesimal "point" to the expanding cosmological horizon -- she won't see any real expansion whatsoever. Just the universe getting more "knowledgeable", in terms of "memory" increase. On the other hand, the 3-D Flatlanders (local mode of spacetime) will only notice that the two 'ideal endpoints' or "edges" of the local mode of spacetime (denoted with S and L, see below) have acquired some 'numerically finite but physically unattainable values' (one of which is the Planck scale), and will recall the old idea that the universe looks like an unbroken ring with no circumference, for the circumference is nowhere, and the "center" is everywhere. Why? Because they cannot see Claudia's "infinitely-fingered" global mode of time. But they will also notice some puzzling "projection" from the dark energy, cast on the 3-D space, just as they can notice, and indeed measure, the "projection" of space curvature, cast on the 3-D space (see Larry Krauss, p. 12). While we don't know the nature of gravity, we are accustomed from GR textbooks to treat it as 'curvature of spacetime', although it shows up more like 'deviation of something from something else that might be "flat" but you can't tell, because you have only one "flat" point'. The "projection" from "dark" energy, cast on 3-D space, is just as weird and misleading as the 'curvature of space', yet it bothers people much more than the puzzling nature of gravity (the latter has to disappear on "points", so you have only one "flat" point as a reference object for "curvature"). People from NASA may ask, what kind of stuff is "expanding", creating the illusion (see also the misleading picture below) about galaxies "running away" from each other, in line with the Hubble Law? Wrong question. In the local mode of spacetime, nothing could possibly "expand" or be "curved". The actual illusion is that something is "expanding" (or "curved"). It is the illusion from NASA's meta-observer view. NB: All such illusions, the absolute structure of space included, should be eliminated by proper relativistic presentations, such that the sole invariant object in space will be an infinitesimal "point". Its 3-D projection or "shadow" does look like a "point", but upon a closer view by Claudia it unveils its infinite-dimensional nature. The picture below (as well as the one from NASA above) can only be seen by some meta-observer (Claudia), who can also see the whole universe, and of course count to infinity (like Chuck Norris). The 3-D Flatlanders can't.
Such kind of illusionary "expansion" (much like the "curvature" of space) may be caused by some 3-D "projection" from something, maybe some process or mechanism, which takes place in the global mode of spacetime. How about the old idea of the mutual penetration of the Large and the Small? Perhaps Einstein would only look at my efforts and say ... well, he was a very polite person. But because he also was, on some occasions, driven solely by his personal taste and instinct, rather than sound physical principles [Note 1], let me try to follow his style. On 21 September 2008, I suggested a scale relativity principle (SRP) aimed at explaining the nature of space (don't confuse it with Laurent Nottale's scale relativity). If we are to think as proper relativists, I believe we should abandon the absolute structure of 3-D space in today's GR [Note 2], and work out new symmetry presentations of The Large and The Small. I also admit that SRP is direct prediction of my theory, hence if it turns out to wrong, so will be my whole project, started in January 1972. I believe physical objects can be considered "large" bzw. "small" only with respect to the macroscopic length scale of tables and chairs. If a volume of space changes its size toward 'the Large/Small', the metric of space in 'the Large/Small' will be altered accordingly, in such way that the "size" of objects in that sphere or volume will remain unchanged in the volume-determined reference frames of 'the Large/Small', yet will continue to look 'Large/Small' in the initial macroscopic scale frame of classical mechanics. The idea of SRP involves (i) an omnipresent observer (Claudia) endowed with 'the eternally present all time [tau]' (Karel Kuchar), (ii) space inversion producing CPT-invariant presentations of 'volume of space', and (iii) macroscopic observer located at the length scale of classical mechanics, from which the postulated mutual penetration of the Large and the Small starts to unfold. We have three possible views on 'the length of objects' in 3-D space. First, the viewpoint of a macroscopic observer who can simultaneously see (i) 'the Large' as an expanding volume of space, and herself being located inside such expanding sphere, and (ii) 'the Small' as contracting volume of space, and herself being located outside such contracting sphere. Consider a table with length two meters, located inside a sphere with diameter two meters, along with the macroscopic observer inside this sphere. If the table is stretching toward the size of a galaxy, it will look like 'getting larger' to the first observer, but its intrinsic length will always remain "two meters" to a co-moving observer in its scale-dependent reference frame evolving toward 'the Large'. The co-moving observer will never, in no circumstances, register any change of the length of the table, as her metric also expands with the same rate as the expanding table toward 'the Large'. Likewise for the journey toward 'the Small': take the first observer and the two-meter sphere at macro-scale, perform space inversion, and now the CPT mirror image (like turning a rubber glove inside-out) of the macro-observer will find out that she is now located outside a contracting sphere, as the table is now running toward the Planck scale, yet a co-moving observer will again see "her" table as keeping its intrinsic length of 'two meters' in her scale-dependent reference frame toward 'the Small'. This is the 'second view'. And the third view is that of a fixed meta-observer like Claudia (global mode of spacetime), who will see a table stretched to the size of a galaxy, a table at the initial macroscopic length scale, and a table squeezed to the size of an atom, all of which possessing 'the same
UNdecided (KS-like) length'. But the center of the sphere is not a bona fide mathematical point -- it is an 'infinitesimal', such that one can treat it as 'the smallest possible rubber glove' and perform CPT space inversion, by replacing (not 'reversing', as in Wu-Ki Tung's textbook, Ch. 11) all "points" inside 'the infinitesimal rubber glove' with all points outside it, that is, with all points of Claudia. Notice that we cannot use quantitative notions like 'more' and 'less' regarding any "number" of points -- neither those of Claudia nor those inside 'the smallest possible rubber glove'. Were the 'infinitesimal' an abstract mathematical point, the operation 'space inversion/replacement' would be impossible, and then there would be two opposite and privileged views on 'the Small' and 'the Large', and the latter would be 'absolute qualities of space', just like in GR textbooks. Thus, an operational definition of 'infinitesimal volume of 3-D space' is that which permits space inversion at (i) the minimal, hence infinitesimal, volume of space (S) and (ii) an arbitrarily large (inverse-proportional to S) volume of space (L). Now Claudia can simultaneously "see" the very same center of the sphere (infinitesimal volume of 3-D space, S) in a space turned "inside out" as well; one could perhaps say that Claudia is "residing" at two superposed inverted states of 3-D space, as she is able to see both S from L and L from S -- simultaneously. Claudia is not restricted (as we are) to choose one of the 'views'. She is placed at S = L, and is wrapping the whole (seemingly "expanding", according to the first macroscopic observer above) 3-D space en bloc. On the other hand, we will see that '3-D space' has just been created, such that we are now endowed with two distinguishable views on two "copies" from Claudia: one that pictures Claudia hidden 'inside the ever-shrinking infinitesimal' (the view toward 'the Small'), and the opposite, time-invariant view that pictures Claudia hidden 'outside the ever-expanding cosmological horizon' (toward 'the Large'). It doesn't matter whether this shrinking or expanding is (or is not) "accelerated": either way, the "number" of points is a non-Archimedean notion that cannot be subject to quantitative evaluations like 'more' vs. 'less'. What matters is that the good old 3-D space has just been re-created, like a Phoenix Universe, along the arrow of spacetime. The mechanism is the same as in The Beginning, but without the initial "inflationary stage" -- just an elementary step of the arrow of spacetime and an elementary increment of the memory of 'the universe as a brain', which leads to "more points" being emerged in its memory, available to choose from in the next elementary step: the universe only gets smarter, richer in terms of physical content, and more flexible, just like an evolving brain. If some day [John 1:1] decides to halt the arrow of spacetime, the UNdecidable nature of 'the infinitesimal' will be nullified, the Thompson's lamp paradox will suddenly become solvable, the number of "points" will become denumerable (e.g., there will be roughly 1099 "atoms of volume" in every cubic centimeter of space, as claimed by L. Smolin, p. 61), and the 3-D space will cease to exist. From our viewpoint, such development is logically impossible (the vacuum cleaner paradox). Unless such "halt" happens, we cannot see the two "copies" or 3-D shadows of Claudia -- the 'infinitesimal volume of 3-D space' and its space-inverted image "outside" the cosmological horizon. We can only observe the local mode of spacetime: an (de facto) infinite and asymptotically flat 3-D space equipped with two physically-unattainable "sliding" boundaries (L and S) toward The Large and The Small. The 3-D projection from the arrow of spacetime -- one-at-a-time -- can only be noticed by the emergence of "more space", and post factum only, due to the so-called 'speed of light' (see above). Meanwhile, Claudia keeps the two inverted views simultaneously. But from the viewpoint of her wristwatch (see above), her global mode of time now runs simultaneously in opposite directions -- in all possible directions in 3-D space -- which will make her (and ours) unanimated wristwatch dead frozen, like the proper time of a photon "between" emission-and-absorption; see Kevin Brown. (This is the exact meaning of 'Your Global Time is ZERO', which was posted on this web site on March 14, 2004, to commemorate Albert Einstein's 125th birthday; see the implications for an atemporal "handshaking" medium above.) Such symmetry over 'space inversion' and the two "superposed" inverted views of Claudia (needed for derivation of three views on 'the length of objects' in 3-D space; see above) reveal the sole invariant object in 3-D space -- the infinitesimal volume of 3-D space, called "point" [Note 3]. The latter will be a 'temporal point' to Claudia, because of her additional spatial degrees of freedom that enable her to "see" the global mode of spacetime along the "vertical" arrow of spacetime. But if looked upon with her (and ours) wristwatch, the same "point" will be stripped from its infinite spatial degrees of freedom, and will be frozen [Note 3]: the global time of your dead wristwatch is ZERO. Subsequently, the "cross-section" of the arrow of spacetime (see above) displays an instantaneous snapshot of infinitely many "frozen points" -- the local mode of spacetime -- which build up a perfectly legitimate already-correlated universe. The famous Bahn is not in the cross-section. It emerges only by driving the frozen flat cross-section, equipped with Claudia's absolute 'now-at-a-distance' (transcendental tachyon), along the "vertical skewer" of the arrow of spacetime -- one-at-a-time only, as a re-created Phoenix Universe. It is certainly very difficult to think of one infinite-dimensional object (infinitely many radii of Claudia's sphere) as 'infinitesimal point' that builds up 3-D space. This 'infinitesimal point' is really a tough character. Perhaps the last thing one can possibly imagine about a 'point in 3-D space' is that it could be an infinitesimal projection and 3-D shadow from Claudia being placed at S = L . After this shaky exercise with the sole invariant object in space, called "point", we need to explain the two 'scale factors' (for the lack of better terms), which create 3-D space: S (from Small) and L (from Large). S refers to 'the infinitesimal point', and L to 'the maximal yet finite volume of an ever-expanding 3-D space'. We postulate: LS = 1 . This is the recipe for a natural "boundary" (cf. G F R Ellis' Finite Infinity) imposed on L due to the "extension" of the infinitesimal "point" S . If we think of The Beginning as the case in which L equals exactly S (L = S = 1), we can understand the "inflationary stage" in which a tiny little difference between L and S is being introduced by [John 1:1], after which the two scale factors will run (but only Claudia can tell the proper duration of this "run") in opposite directions, to produce 3-D space tightly filled -- perfect continuum -- with infinitesimals S and bounded by an "expanding diameter" L . Now Claudia will be placed in the global mode of spacetime -- both inside S and outside L . She will be able to "see" the whole (infinitely-connected, by Claudia) local mode of spacetime en bloc, and her global mode of time will be just like that of our brains: an atemporal and infinite-dimensional "handshaking" medium by which each and every infinitesimal S is simultaneously correlated -- the 'absolute now' of Claudia -- with 'the rest of the universe', as depicted in the Escher drawing below. And since their EPR-like correlation is "spanned over" an infinitesimal "point", in the local mode we will see the blueprint from quantum waves and relic inflationary waves, yet their source will be inevitably "dark". (In order to detect quantum waves "online", one would have to perform a perfect non-demolition measurement avoiding any point-like collapse, by screening the quasi-local wave over extended 3-D domains.) Notice that Escher's hands can be moved only by an arrow of spacetime, not with the kinematics of L and S alone.
In summary, there are no "genuine" nor "absolute" dimensions of physical bodies, according to the scale relativity principle. The spatial relations of 3-D space -- inside/outside and left/right -- should occur from four-segment "lily" spacetime diagram of the global mode of spacetime (notice the fav icon of this web site). Once such four-segment spacetime diagram is properly constructed (we also have to explain rotation symmetry), perhaps we could calculate the cancellation of 'all but one' potential states of quantum-gravitational systems, and recover the correlated states that build up the local mode of spacetime, valid for one frozen snapshot from Die Bahn only. The frozen snapshot from the "film reel" (the arrow of spacetime) will show an already-correlated set of point-like values of all physical variables, in line with the Bootstrap Principle 'think globally, act locally'. The atemporal (with regard to our unanimated wristwatches) correlation "takes place" in Claudia's global mode of spacetime. She is residing in (L = S), and her two "superposed copies", toward L and toward S, contain uncountably infinite "number" of classical-able states from which one correlated and re-created physical universe is being explicated as 'local mode of spacetime': one-at-a-time, along the arrow of spacetime. Notice, however, that the direction of the arrow of spacetime "points" only to the global mode which is totally hidden in the local mode: the "dark gaps" in the latter are completely sealed off by 'the speed of light', rendering the local mode a perfect continuum. Thus, our wristwatches [Note 3] are perfect example for quantum-gravitational measuring devices, as they can in fact read one 'dynamical instant' from Claudia's absolute time since The Beginning, but because we can "look at" this dynamical instant only with a physical "torch", we inevitably see a dead frozen snapshot (local mode of spacetime), as explained eloquently by Robert Geroch. Everything said here pertains only to the kinematics of spacetime; to obtain its dynamics (the arrow of spacetime) we need to include the Aristotelian First Cause "by hand", because nothing in this purely kinematical structure can or should point directly to God. In modern parlance, SRP is expected to "suffer" from Gödel's incompleteness theorem, but because of the fundamental nature of SRP, the additional elements in it, which belong to some 'meta theory', will be from 'outside science'. More in my next talk, probably in November 2015. Perhaps the "projection" of the dynamical metric in 'the Large' onto the macroscopic scale produces the illusion of "expanding universe", as only seen by the first observer (cf. above): the cosmological horizon is 'ever expanding' along the arrow of spacetime, while the Planck scale is fixed. Perhaps the asymmetry stems from the fact that the "size" of 'the infinitesimal' is fixed (bounded from below), while the 'maximal volume of space for gravity' (L) increases with the age of the universe, like an expanding horizon bounded by L : Panta rei conditio sine qua non est. By the way, have you seen an UFO with your very eyes? If these guys can switch off the inertial reaction "forces", perhaps they can fly effortlessly, much like we move our thoughts. And if they can modulate the metric of space, perhaps they can make their pathway in the whole Milky Way just "two meters". From their perspective, they will indeed fly 'two meters', while the space will be "running towards them". Perhaps in such altered-metric space they fly literally 'from point to point', and with a very low speed of, say, just 2 m/s, as recorded by their wristwatch. I wish I knew what is 'space' [Note 4]. There is so much latent energy packed in the quantum vacuum. Perhaps all we may need is access to the global mode of spacetime. This surely sounds unclear and farfetched, but recall Christopher Columbus: If we don't leave for India, how can we discover America?®
"I have again perpetrated something relating to the theory of gravitation that might endanger me of being committed to a madhouse." (Ich habe wieder etwas verbrochen in der Gravitationstheorie, was mich ein wenig in Gefahr bringt, in ein Tollhaus interniert zu werden; English translation by N. Straumann).
"The right side (the matter part) is a formal condensation of all things whose comprehension in the sense of a field theory is still problematic. Not for a moment, of course, did I doubt that this formulation was merely a makeshift in order to give the general principle of relativity a preliminary closed expression. For it was essentially not anything more than a theory of the gravitational field, which was somewhat artificially isolated from a total field of as yet unknown structure."
--------- The criticism is fully justified: reading my web site is anything but fun. I am considering writing a book, but it will be intended to kids age 15+, and will have to be complemented by a DVD with video lectures, to explain the crux of the idea about 'the universe modeled as a brain'. Why kids? Because the future belongs to them (I will soon hit 58, Deo volente). My work on quantum gravity concerns very few people, all of whom have this utterly negative attitude of 'the worst of criticism is neglect'. Just a few examples: the last time I heard from Claus Kiefer was in 2003, only to tell me that he can't open the CD ROM I sent him by surface mail, because all computers at the University of Cologne run on Unix. The last time I heard from Karel Kuchar was on 8 Jan 2003, and from John Baez on 14 Jan 2002. The case with Chris Isham was even worse. And look what happened with my talk in 2008. Thinking about the future, I can imagine only two developments regarding SRP. One possible case will be that it is just crap and delusion, so obviously wrong that none of the renowned experts made the slightest effort to show my stupid dilettante errors. Will see. Planck's Law of Thermal Radiation was met with very nasty attitude by the established scientific community [Note 5], as it literally blew away their comfortable world. If SRP turns out to be correct, it will cause far more "damage" to many established scholars studying canonical quantum gravity and "gravitational wave astronomy" (at least 679; see also [Note 6]). But could SRP be correct, really? Well, as I mentioned previously, the two rules for success are: And nobody is curios anyway. (For those who are: I believe SRP embedded in an arrow of spacetime offer the only possible solution to the mind-brain problem -- the mind has to be both detached from matter, to preserve its ontologically different nature, and linked to it, in order to communicate with its brain via the bi-directional "talk" depicted in the Escher drawing above.) Therefore, there is no need to use paper -- everything I need to say is, and always will be posted at this web site, available to anyone interested. If some day it turns out that SRP in 'the arrow of spacetime' had hit the right track toward quantum gravity, I suppose people will be interested to explore it (see the download link above). Besides, we don't live in 18th century: "When this lowly chap informed the Lucasian Professor of Mathematics that he had formulated the inverse square law of gravitation years before the publication of Principia, Newton is said to have flown into a rage. The two had already sparred over their optical theories, and when Newton took over as president of the Royal Society in 1703 (the year of Hooke’s death), he began erasing all traces of Hooke. Famously, he tossed the only contemporary portrait of Hooke onto a fire."
"An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning: another instance of the fact that the future lies with youth."
p. 1: "Equivalence
principle implies no local definition possible in any
situation: must attempt "regional" definition in regions at least as
large as a wave-length. Comment: I highly recommend B. Schutz' video lecture and manuscript to all Jehovah's Witnesses of Gravitational Astronomy. Compare it to B. Schutz' article "Gravitational Radiation", gr-qc/0003069 v1. More here. D.C.
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"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the Pursuit of Happiness."
Why should we deny their unalienable Rights of Life, Liberty, and the Pursuit of Happiness? "The hottest places in Hell are reserved for those who in times of great moral crises maintain their neutrality."
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Check out the communist censorship of Paul Ginsparg's "moderators" 
