On The Flow of Time by George F R Ellis

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The running of this competition gives a nice example of why the EBU model trumps the BU. In the latter case, what will happen at all times (future and past) is determined by the system dynamics plus initial conditions at any one time. In the case of this competition, the initial conditions set up the system dynamics, including the sztatement "The voting deadline has been extended to January 1, 2009." It is now January 3rd and it is still possible to vote (I just tested it, and cast a public vote successfuly). So what is actually hapening is not the same as what was determined as the stated system dynamics. It is precisely the reality of the existence such unpredictable system responses in the real world (none of us knows when the voting ands commenting will actually be closed down) that makes the EBU a preferable model to the BU.

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George, nice try but it is already predetermined in the BU where the prizes are going no matter how the voting is conducted. I have looked at all the permutations and in fact the BU model predicts that only existing FQXi members will be awarded prizes. LOL o_O.

Happy New Year and many thanks to George for responding in good spirits to so many questions here. I hope that in future contests more of the high profile entrants will find the time to follow his example because it adds a lot of value to the overall project.

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EBU model is preferred over BU and Ellis needs commendation for his exhaustive attention to the largest number of posts. All the very best to everyone. None should worry about the final results as one can only do one's job the best one can. The results should not be in the hands of the doer otherwise people may become workaholics, dangerous if one is not thoughtful enough!

[deleted]

The fact that the FQXI organizers changed their minds about the last voting date does not proof that this was not pre-determined. Also, in the MWI you would have many branches, so the BU is a collection of different histories.

I think that the EBU is pretty much ruled out by the many theoretical end experimental "no go" results against hidden variables in quantum mechanics. If the EBU picture as proposed in this essay were correct, then the outcome of some past event would be determined after a while, even if you were completely isolated from the rest of the universe. But then that implies the existence of hidden vraibles which point out which terms in the superposition that describes the starte of the rest of the universe are real and which are not before you perform any measurement.

Ellis has argued in this thread that you cannot completely isolate yourself from the rest of the universe. But the arguments presented by Ellis in his essay do not depend on any such arguments.

[deleted]

I cannot agree with George that his EBU hypothesis could be "a preferable model to the BU" (Jan. 2, 2009 @ 08:13 GMT).

The current BU hypothesis is adopted in basic GR textbooks. Consider, for example, Robert Geroch (General Relativity from A to B, University of Chicago Press, Chicago, 1978):

"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. [...] In particular, one does not think of particles as "moving through" space-time, or as "following along" their world-lines. Rather, particles are just "in" space-time, once and for all, and the world-line represents, all at once the complete life history of the particle."

LIGO Scientific Collaboration (LSC) have adopted this "block" view, and deeply believe that there is no difference between (i) observing the effects of GW radiation in the *past* (as calculated by Russell Hulse and Joseph Taylor in the case of the pulsar PSR 1913+16), and (ii) the detection of GWs "online", as they tweak the interference pattern at LIGO.

LSC have spend so far hundreds of millions of dollars and euro -- taxpayers' money -- yet all their "runs" have so far produced stunning failures. Yet they are determined to spend even more, perhaps billions, if the three satellites of LISA are indeed launched.

I think this is far more important than the flexibility of choosing the final date for voting. If George Ellis is right, then LSC might have been on a wrong track from the outset.

Perhaps it will be a good idea if George Ellis proves that EBU hypothesis could be "a preferable model to the BU" by calculating the localization of GW energy along the proper time of the wristwatch of LIGO's operator.

Good luck, George.

Dimi

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Hello George,

Above you write, "As long as any experiment whatever gives a future outcome that is not at present determined even in principle, the EBU description trumps the BU. And we have plenty of such experiments in quantum theory. The relativistic interpretation of the EPR experiments will have to adjust to this fact."

Yes! The block universe denies the inherent probabilistic nature of quantum mechanics, as well as the influence of the observer's free will in choosing how to measure a system; which basically denies free will.

Moving Dimensions Theory allows us to keep all of relativity while liberating us from the block universe, by noting that time is not a fourth dimension, but rather that it is an emergent phenomena that airses because the fourth dimension is expanding relative to the three spatial dimensions. The block universe is a human construct which is useful for calculations, but which is not *physically* real. The physical past no longer exists.

The amazing thing about MDT is that it provides a *physical* model for entropy, time and all its arrows and assymetries, quantum mechanics' nonlocality, entanglement, and probabilistic nature, while also providing a deeper principle and equation--dx4/dt=ic--from which relativity can be naturally deduced.

Here is a passage regarding the nature of time from page 350 of John A. Wheeler's 1998 GEONS, BLACK HOLES, AND QUANTUM FOAM:

"Theory suggests also that black holes of incredibly small size, at the scale of the so-called Planck length, are forming and dissolving all the time by the trillion, with the dimenions of every elementary particle. At that scale, with spacetime churned into quantum foam, space and time in fact lose their meaning. When we blend the two greatest theories of the twentieth century, quantum theory and general relativity, we have to conclude that time is a secondary concept, a derived concept. It has meaning only at a scale large compared with the Planck length and only well away from black holes, the Big Bang, or the Big Crunch. It is not a river that rolls inexorably forward. It is not a lake across which we glide. It is more to be compared with tempertature or with entropy, concepts that take their meaning only when large numbers of particles are involved. Time, we conclude, is of statistical origin, valid only when dimensions are large enough and when conditions are not too extreme." --page 350 of John A. Wheeler's 1998 GEONS, BLACK HOLES, AND QUANTUM FOAM

Moving Dimensions Theory, with its simple postulate of a fourth expanding dimension and equation: dx4/dt=ic agrees with this passage. Time is an emergent phenomenon, or, as Wheeler stipulates, "time is a secondary concept, a derived concept." Ergo time is not the fourth dimension, but it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. Now as this expansion distributes locality, it is also the source of quantum mechanics' probability and entropy's statistical nature as well as entanglement. It is why a photon, which travels by surfing the fourth expanding dimension, has an equal chance of being detected anywhere upon the surface of a spherically-symmetric wavefront which expands at the rate of c. It is why two initially-interacting photons remain both the same age and entangled.

So it is that the EPR Paradox is resolved as we are liberated from Einstein's/Godel's block universe. MDT provides a fundamental framework for all of QM and relativity, while also granting us free will and explaining entanglement, entropy, and length contraction with the exact same principle, from which time, and all its assymmetries, naturally emerges.

Einstein's Principle of Relativity, as well as his two postulates, derive from MDT's single postulate which is more concise and has the added benefits of providing for free will, liberating us from the block universe, weaving change into the fundamental fabric of spacetime, and providing a *physical* model for time and all its arrows and assymetries, entropy, and quantum nonlocality and entanglement.

MDT presents a new universal invariant--an elementary law from which Einstein's Principle of Relativity can be built by pure deduction. Begin with a universe with four dimensions x1, x2, x3, x4 where the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, dx4/dt=ic, and all of relativity naturally arises, as does quantum mechanics' nonlocality and entanglement, wave-particle duality, space-time duality, mass-energy duality, entropy, and time and all its arrows and assymmetries.

"Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to each other, how could it have been otherwise? How could we have been so stupid?"

--John A. Wheeler

Best,

Dr. E (The Real McCoy)

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That nothing happens in a spacetime or cosmology is due to the fact that time is a part of the field of gravity. This is what makes time, or at least coordinate time, something which is similar to vector potentials, in particular A_t, with internal gauge symmetries. These things do not exist in a physical sense. Of course gravity is an external symmetry. The gauge, or frame, dependent quantities in spacetime physics are something we "hang our boots on." This then a motivation for the idea of the block universe. Then quantum mechanics enters the picture and things become troublesome.

The question is whether there is a way to replace the classical block time universe with a quantum block time universe. General relativity does support the notion of there being a single spacetime which is fixed set of geodesics and curvatures. Quantum physics adulterates this view with there being events which correspond to the reduction of states in a measurement or decoherence. Within the Copenhagen interpretation these state reductions are purely random. As a result the block universe is not longer this one set of possible geodesics and curvatures fixed by a single set of mathematical diffeomorphisms. The block universe still remains in some sense from a GR perspective, but where geodesics are connected by points which are determined by wave function collapses that have no causal deterministic principles. Hence we have an uncertain block world. Assume one knows all the Cauchy data on some spatial surface of the world at a time t, where this assumes synchronous coordinates

ds^2 = -dt^2 g_{ij}dx^idx^j,

such as with FRW and deSitter spacetimes, so coordinate time can be identified with the proper time. This data is then insufficient to determine the state of this world at some later time due to state reductions and the inherent randomness induced by QM, measurement and randomness of decoherence. So as observers moving in the block world we are unable to construct the block from even a complete Cauchy data set we might have available.

So in what way can QM do this? Through the activity of wave function reductions Cauchy data is reduced, or the information it holds at one time is removed from the universe or unavailable at a later time. So the Markovian picture of moving in a block world no longer holds. If we consider this with gravity, this means that there is some physics which is able to adjust Cauchy data, which requires changing the appearance of masses (particles etc), in spacetime that is independent of gravity. Gravitation is a strange field, for it is not like electromagnetism where one can prepare a system in some specific way to communicate an EM wave from one region to another where those preparations can be independent of field data. I can set up an EM wave by introducing acoustical energy into a device or microphone, which is not strictly an EM field process, and use that data to establish an EM wave. To configure masses here and there in GR requires the application of energy which is itself a source of the field. Hence one can't encode new information onto the gravity field which is independent of the prior Cauchy data of the field. Yet, with state reductions it appears that QM in its random way might indeed do just that! The appearance of a particle "here" instead of "there" in a state reduction requires there to be some metric back reaction where the gravity field responds to this randomness. This is the basis for some of the strange physics with black hole radiation.

The block universe might be thought to remain in a pure form with the many worlds interpretation. However the block now includes a vast number of spacetimes which branch out with each wave function reduction. For the QED field the Compton wavelength of an electron is lambda = hbar/mc ~ 10^{-12} cm, and these branchings can occur for every QED process with a fermion on a time t = lambda/c ~ 10^{-22} sec. So for approximately 10^{80} leptons and baryons in the observable universe this could mean that on the synchronous time frame (Hubble frame) the universe branches out in an MWI sense 10^{100} times every second. Then given inflation and our observable universe is just 10^{50}th of the whole thing this indicates the whole universe branches in a huge number of paths every second ~ 10^{150}, and these branches continue and this has been going on since the big bang. I can't say whether this is correct or not, for quantum interpretations appear to be almost undecidable, but this is a lot to swallow.

Rovelli and others appear determined to banish time into dust. This is of course entirely possible. General relativity gives a meaning to proper time, where coordinate time is something determined by a gauge choice. A conformal time, or proper time can lock a choice of coordinate time with proper time, so called syncrhonous time. Yet all one has done is to make an appropriate gauge-like choice so that certain symmetries of the spacetime define a Killing time vector field. As such the notion of a global time is something which is observer dependent and not "real." We could just as well think of this the other way. A geodesic proper time is all that exists, and path integral deviations (quantum fluctuations etc) around that propertime define a local spatial coordinate frame. Then all such possible geodesics define local frames that patch together in a Cech cohomological sense to define a spatial surface. In this case what we call space is now the "fiction!" In that setting the phase imposed (again a gauge-like choice) on the wave functional over all such geodesics (or metric configurations) determines the spatial surface.

It is likely that time, which in a Euclideanized sense is t = hbar/kT is related to temperature. It is due to an averaging over many states or quantum transitions on a fine grained scale. Now, my thesis is that the universe exists at a quantum critical point, where just as with the onset of superconductivity a scale invariance is set in. This means that at the temperature T ---> infinity the physics remains the same, but somewhere below "infinity" what we call time is replaced with something else. That something else is are phase overlaps between unitariy inequivalent quantum groups as defined by nonassociative maps. For two quantum groups G and G' which are not unitarily equivalent, eg there exists no unitary map U:G ---> G', the elements of these groups g and g' are mapped to each other by an associator A:G ---> G', which is nonunitary, by Ag = g' and so a state transition within the group G can overlap with G' by g^{-1}Ag = g^{-1}g'. The associator map A also preserves quantum information! If time disappears something must take its place! These maps are what I think underlie what we call time, and frankly space as well.

In that setting the system of nonassociative maps on a fine grained scale are determined, a sort of block-map world view if you will, and where on a larger scale where time exists there is some ensemble of possible macroscopic outcomes from this. Given the transition g^{-1}Ag = g^{-1}g' it can be extended to define density matrices as

Tr(AO) = Tr ( |g^{-1}>AO and |g'> to define a standard density operator. Hence the trace gives Tr ( |g^{-1}>

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Lawrence: "However the block now includes a vast number of spacetimes which branch out with each wave function reduction."

Why not just a single eternal wavefunctional over the set of all possible space-times?

[deleted]

I forgot that this email system does not like carrot signs, which cut off my message. So in replaceing them with () I soldier on:

Tr(AO) = Tr ( |g^{-1})AO(g| = Tr ( O |g^{-1})(g'| )

where for the observable O = 1 this defines the element Tr ( |g^{-1})(g'| ), or elements of a density matrix. The phase overlap of these elements is given by a generator delta E_grav = |E_g - E_g'|, which is the error induced by coarse graining over the states |g) and |g') to define a standard density operator. Hence the trace gives Tr ( |g^{-1})(g'| ) = exp(-dE_grav b) and defines an entropy delta S = delta E_grav/T.

Indeed time disappears, as potentially does space, but ultimately if these disappear they are replaced by something else. The physics for energy scaling from "infinity" to zero, the hot big bang to the cold final state for instance, is invarant. So on a fine grained scale time, temperature entropy and so forth are really manifestations of an underlying physics. This underlying physics simply has a renormalization group property which define what we call time, temperature and entropy.

Lawrence B. Crowell

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To restate my observation, time as an emergent effect is the series of macro states going from future potential to past circumstance. In this description, block time is a narrative structure with no physical reality, as the fundamental energy is recycled from one moment into the next, as the information defining each moment is transformed. "You can't have your cake and eat it too."

There is no God's eye view(Tegmark's bird's eye) of the series of events, because perspective is inherently subjective. If you sum all information together, it cancels out. The state of the absolute is everything and nothing. Anything between is subjective.

So rather then push "time" along this imaginary dimension into the probabilities of the future and require all events to happen, as with the multi-worlds model, or declare probabilities to be illusionary and demand the future to be deterministic, let it move past our point of physical existence and activity(temperature), from future possibility to past circumstance.

Accept that tomorrow becomes yesterday due to the earth's rotation, rather than trying to figure out this path from yesterday to tomorrow.

Even the quantum jumps(time) are interspersed with changes in scalar activity(temperature), so that this activity is the fundamental state and the jumps are emergent effect.

[deleted]

"There is no God's eye view(Tegmark's bird's eye) of the series of events, because perspective is inherently subjective. If you sum all information together, it cancels out. The state of the absolute is everything and nothing. Anything between is subjective."

For a simplistic description of this, consider that block time is essentially a basic narrative structure, like a film that exists and we only happen to be on one frame of it. The physical reality of the moment is the projector light and the movie only makes sense when the frames pass by this light. So while the light goes from past frames to future ones, the frames go from being in the future to being in the past. Now the physical reality is that past and future do not physically exist, as the same energy is being re-used for every moment. So it is like re-exposing the same frame to make the entire movie. Very quickly it would all just be white light, with no detail. It is only our individuality and the subjective perspectives created that separate all the frames out. We are like little mirrors of the present energy creating a parallel processor which summed together, like individual threads creating a larger rope, forms the larger serial of history that is the feedback loop of our awareness. In order for this loop to work though, we are constantly recycling the information of our past. While this better informs our understanding of the future, it also alters our knowledge in the process. Until we understand this cannibalization of the past, we really cannot understand the process of time.

[deleted]

On Jan. 3, 2009 @ 12:51 GMT, Lawrence B. Crowell wrote:

"General relativity gives a meaning to proper time, where coordinate time is something determined by a gauge choice. A conformal time, or proper time can lock a choice of coordinate time with proper time, so called syncrhonous time. Yet all one has done is to make an appropriate gauge-like choice so that certain symmetries of the spacetime define a Killing time vector field. As such the notion of a global time is something which is observer dependent and not "real." "

Larry: Do you believe all this can help George Ellis? As suggested previously (Jan. 2, 2009 @ 14:30 GMT):

"Perhaps it will be a good idea if George Ellis proves that EBU hypothesis could be "a preferable model to the BU" by calculating the localization of GW energy along the proper time of the wristwatch of LIGO's operator."

I am only trying to focus the discussion here, at George Ellis' thread, on this issue of paramount importance.

Perhaps you can help George with his EBU hypothesis, because in the framework of BU hypothesis the alleged localization of GW energy is still theoretically unclear. Besides, recall that LIGO Scientific Collaboration has failed to detect any GW effect whatsoever in five "runs" of LIGO, after spending hundreds of million dollars and euro -- all taxpayers' money.

D. Chakalov

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On Jan. 3, 2009 @ 12:51 GMT, Lawrence B. Crowell wrote:

"That nothing happens in a spacetime or cosmology is due to the fact that time is a part of the field of gravity. This is what makes time, or at least coordinate time, something which is similar to vector potentials, in particular A_t, with internal gauge symmetries. These things do not exist in a physical sense."

I think your last sentence points to a very tricky issue. The Higgs boson hypothesis, for example, is introduced by means of a gauge-breaking "mechanism". As explained by Holger Lyre, Does the Higgs Mechanism Exist? arXiv:0806.1359v1 [physics.gen-ph], pp. 2-3:

"... the status of the symmetries in question, gauge symmetries, is in fact a non-empirical or merely conventional one precisely in the sense that neither global nor local gauge transformations possess any real instantiations (i.e. realizations in the world). Rather their status is comparable to the status of coordinate transformations (the status of gauge symmetries will be addressed in detail in Sec. 3.1).

"How is it then possible to instantiate a mechanism, let alone a dynamics of mass generation, in the breaking of such a kind of symmetry?

...

"Indeed, how can any physical mechanism arise from the breaking of a merely conventional symmetry requirement? (Similarly, one would not think that any physics flows out of the breaking of coordinate invariance! -- Again this will be addressed in detail in Sec. 3.1.)"

But again, let's focus on George Ellis' EBU hypothesis, because if he is on the right track, it should be possible to calculate the alleged localization of GW energy "online", as it tweaks the interference pattern at LIGO.

As George Ellis explained (cf. my posting from Dec. 31, 2008 @ 14:32 GMT):

"This domain is coming into being at the present instant; and what is the present instant now will in another fraction DT of time be in the past."

Can you calculate the localization of GW energy "online", as it is "coming into being at the present instant", along the proper time of the wristwatch of LIGO's operator?

A penny for your thoughts! It may be worth of billions.

D. Chakalov

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Dimi,

The basic assumption with EBU is that the past is static. The problem is that it is not. For one thing, it is constantly being added to, as the present becomes past. If time and space are interchangeable, it should be remembered that the further we are away from something in space, the smaller it appears, just as the further away we are from something in time, the more the information about it is degraded. Dr. E makes the argument that time is an expanding fourth dimension, yet the consequence of that is the three dimensions of space which represent our understanding of the present, shrink, relative to this expanding dimension, as the present becomes the past. Even Einstein thought gravity, the coordinate system of spacetime, causes space to shrink, so he added the Cosmological Constant.

Time is inherently dynamic, so modeling it as static is asking for trouble. If the initial premise is flawed, all the complex logic in the world isn't going to make it right.

[deleted]

Dimi et al,

One reason why I found Hestenes article so interesting is that he points out a way around the following problem. We can write an action according to the invariant interval

dS = mc^2ds

which based on the proper time. Proper time is the time which is "real" in relativity theory. However, if a particle on that frame is counting a time there must be a mechanism for that clock. This would involve say a spring which holds two masses together, or some system of QM transitions. However, this involves a coordinate time, where the above action is dS = pdq - Hdt, where here the time "t" is the coordinate time. The zitterbewegung in the motion of an electron in its Compton radius looks like a way around this problem. As I think about his further, there are I think some very deep aspects to this problem.

This Higgs field may well be a phenomenology and spontaneous symmetry breaking an approximation. In technicolor theories of QCD the Higgs particle is a sort of condensate of T-quarks, and so in at least one sector the Higgs particle is a composition of QCD sources. The Landau-Ginsburg potential associated with the Higgs field has a fairly generic occurrence in many domains of physics. So we might expect that the Higgs particle is something which has a deeper basis.

Penrose's "The Road to Reality" makes for an interesting reading. It is intellectually engaging, but not extremely difficult so the large book can be read in a reasonable time frame. He talks about the 2-component spinor Weyl equation for the Dirac field (Fermions). There the two equations describe a "zig-zag" motion of the electron, which is related to the zitterbewegung. Penrose relates this to the occurrence of the Higgs field which gives a mass to the electron and other fermions. Hestenes illustrates how this can be described according to a gauge field, which suggests how the Higgs field is ultimately a composite of gauge fields or their sources.

The evolving block time world is certainly a way in which the concrete block of classical general relativity may have some substratum that is less "hard." If we think of that concrete it is made of molecules and atoms. These particles obey the rules of quantum theory, and on a larger scale have statistical mechanical properties. This is similar to Sakharov's perspective on how spacetime emerges from some "pre-geometric" construct. The purely quantum substratum of atoms and particles is analogous to quantum gravity and how space & time emerges. The statistical mechanical view relates to our current understanding of black hole radiation. So the block is hard, but it is not infintely hard. Hit it hard enough with some impulse and you get a response which an infintely hard "substance" would not return.

Lawrence B. Crowell

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John:

Thanks a lot for your comment from Jan. 4, 2009 @ 14:41 GMT. I agree that the past cannot be static, as "it is constantly being added to, as the present becomes past", as you put it.

The same applies to the future in EBU hypothesis, as hinted in John Wheeler's statement: "Time is Nature's way to keep everything from happening all at once". Hence it seems to me that EBU hypothesis should somehow include 'things that we still don't know that we don't know'. If this is correct, George Ellis should allow some brand new things to *emerge* in his EBU, in blatant violation of the unitarity principle.

See how far we can go with philosophy? Let me please go back to the mundane affairs of GW astronomy, from my preceding posting from Jan. 4, 2009 @ 12:43 GMT.

Larry: I can't see anything in your latest posting from Jan. 4, 2009 @ 15:11 GMT that could be relevant to this ultimate test of George Ellis' EBU. Please laid out your professional opinion.

Best regards,

Dimi

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P.S. An example of John Wheeler's statement:

Mike Turner pointed out the accepted theoretical claim that elementary particles known as the W boson and the Z boson had no mass when the universe first exploded into being. Modern accelerator experiments have shown, however, that both are very massive today.

Hence one could argue that the W boson and the Z boson had existed "during" the inflationary stage as an Aristotelian potentia. As of today, perhaps the verification of EBU hypothesis (Jan. 4, 2009 @ 12:43 GMT) is also an Aristotelian potentia. I hope Larry will explain his professional opinion.

[deleted]

Dimi,

The question is whether there are some "philosophic" assumptions on which our "hard" physics rests.

Space is defined in terms of "dimensions,"but there is a less "hard" description of space called volume. Consider Lawrence's comment;

"This is similar to Sakharov's perspective on how spacetime emerges from some "pre-geometric" construct. The purely quantum substratum of atoms and particles is analogous to quantum gravity and how space & time emerges."

This 'pre-geometric" space is occupied by energy which is best defined by scalars, such as temperature and pressure. Because there is no geometric form, it could as well be infinitely "dimensional." It is only when we get specific form emerging that there are the reductionist three dimensions of space and one of time. Now physics considers these four dimensions as primary. Lawrence is right, we need to examine what is under that hard crust of static geometry.

[deleted]

When it comes to verifying the EBU, or any other concept of time, this probably will only come indirectly in how it is any such theory correlates well with observations of the distant universe and of elementary particle scattering events. Geometric constructions are not the "objects" we directly measure. In physics we are primarily interested in dynamical objects, eg particles which enter into some energy transition or change in momentum. Time as a geometric construct is something which "flaps in the breeze" to some extent.

The Higgs particle could well be a field effect similar to what happens with the onset of superconductivity, the Curie point and other phase transitions. In fact these are all given by the same Landau-Ginsburg potential. So some of these discussions on time, and in connection with the zitterbewegung motion of a fermion, it could well be that the gauge-like field associated with that is a dynamical process which underlies the Higgs mechanism.

The pregeometry here involves quaternions IMO. These are elements which in a Grassmann framed system describe noncommutative geometry. BTW, this may connect with the zitter-motion of the electron as well, but that is a long story. Quantum mechanics and quantum field theory involves commutators O(hbar), but on the order O(hbar^2) coordinates are noncommutative, such as [x, y] = A hbar^2 z, for A a particular constant. So for scales ~ A hbar^2 ~ L_p geometry dissolves, where one replaces geometry with algebra --- so to speak.

Lawrence B. Crowell

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Larry:

You wrote (Jan. 4, 2009 @ 21:00 GMT): "When it comes to verifying the EBU, or any other concept of time, this probably will only come indirectly in how it is any such theory correlates well with observations of the distant universe and of elementary particle scattering events."

In addition to such tentative possibilities, there is a perfectly justified, in my opinion, possibility to verify the EBU hypothesis: please see my postings from Jan. 4, 2009 @ 02:42 GMT and Jan. 4, 2009 @ 12:43 GMT.

If you wish to comment on these two postings, please go ahead. If you are reluctant to respond to my request, please say so, and I will pass this whole issue to other theoretical physicists (probably from U.S. National Science Foundation, since it supports the gamble undertaken by LIGO Scientific Collaboration).

Best regards,

Dimi

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