On The Flow of Time by George F R Ellis

[deleted]

Dimi, I think it is healthy that we all have different ideas about what are the important issues are, and what are the best ways to treat time etc. It is fun and useful to discuss the relative merits of our preferred philsophical approaches, but the only way to determine who has the best idea is to see how far they take us towards a well formed theory and learn from the results.

Like many others I do not worry about the measurement problem when I try to think about quantum gravity because I dont think quantum gravity will solve it. I dont have a solid reason to believe that so I could be wrong, but I dont have time to try out every possibility. I am happy that there are others who think differently so that approach wont be neglected.

On the subject of gravitiational energy, a few years back I worked through a direct application of Noether's theroem to derive the covariant form for the energy conservation law in GR. I deposited the result in the arXiv at http://arxiv.org/abs/gr-qc/9701028. There is a lot that can be said about the nature of the solution but again I am not left with any particular issues that I think are of significance to quantu gravity. Perhaps someone else will be able to derve a useful clue from such considerations but that wont be me.

The best thing I can say is that you should also seek out those with the most similar ideas to yours because you will learn more from them than from people who are trying a different direction.

[deleted]

Phil, thank you for pointing out your arXiv:gr-qc/9701028v3, in which you wrote (p.9): "We are now in a position to consider the case of energy in a closed cosmology." Your manuscript appeared well before the advent of the "dynamical dark energy" (DDE), and I can't find any clues as to how one could include DDE in some 'closed cosmology'. Please advise.

I also appreciate your advice "you should also seek out those with the most similar ideas to yours because you will learn more from them than from people who are trying a different direction", and am I indeed following it, at my web site.

The reason for my postings here is this. Suppose you, George, Carlo, and all the rest on this Forum, myself included, were collecting different paper items, just as a hobby. If I was collecting paper napkins, while you and George were collecting bottle labels, then of course I cannot pursue you to switch to my hobby, nor the other way around.

I am definitely certain this is not the case, and I will patiently wait for the professional response from George Ellis, by January 1, 2009. I can't miss this unique opportunity, since his opinion is very important to me, and I am definitely certain that he does not treat theoretical physics as some hobby.

Dimi

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Dimi, Given an invariant lagrangian for the DDE you could apply Noether's theorem in the same way. The derived total energy for a closed cosmology would still be zero.

[deleted]

Phil, "an invariant lagrangian for the DDE" (Dec. 20, 2008 @ 19:21 GMT) presupposes some theory of quantum gravity, which would treat the energy density of the quantum vacuum -- the first choice for cosmological "constant" -- in the framework of such brand new quantum gravity. Perhaps it is a better idea to start with some far more modest task, such as George Ellis' finite infinity proposal from 1984, and see where we will end up. What do you think?

Dimi

[deleted]

Dear George,

Thanks for your comments. I see it as a step forward, so I appreciate that. Thanks. I see that it sort of comes with an out-clause, however, as you seem to now want to dismiss my arguments (and the contents of my essay) as philosophy.

As my essay deals with questions of the existence of time, instants, instantaneous magnitudes, space-time etc, a lot of it naturally is of a philosophical nature. However, I would also obviously contend that because it places the focus on things that are fundamental (motion, change etc), it is more foundational and scientifically based than essays that posit the existence of time. The work also does not come with a mathematical model to back it up. However, because the main point of it is to show that calculus (and analysis) [static] has its limits when applied to the physical universe [dynamic], trying to use calculus itself to demonstrate this would be impossible. As such, I do not think that this can really be used as a criticism of the work.

In relation to the instantaneous, it should also hopefully be clear that I'm not trying to negate that instantaneous values are extremely useful. The point is that they are non-physical, so one must be careful about what one infers about them. Zeno's paradoxes, the idea of time and space being quantized, change not being seen to be compatible with the bock universe, and even, it can be argued, the assumption of the existence of time, space, and space-time, are all the result of assuming that instants (and spatial points), and instantaneous magnitudes actually exist. As such, despite its lack of math, the work has direct relevance to a number of deeply fundamental problems and paradoxes in physics, while I think it could also play a part in the solution of some pretty stubborn problems/paradoxes in quantum mechanics and quantum gravity. Furthermore, because the work's possible validity is dependent on, and reducible to, the simple question of whether or not a body in relative motion has a determined relative position, I think it is quite clear-cut. Of course, it is still ignored by many, and although I realise this is just par for the course (changing ideas in physics isn't supposed to be easy), I do still find it frustrating sometimes.

In relation to change not being compatible with the BU, you say "Finally you emphasize your position thus: "as long as one recognizes that instants, instantaneous magnitudes, space-time points etc, do not exist [....]" This stance places you at loggerheadsa with virtually all other postings on this forum."

On this thread, certainly! As mentioned above, my conclusions are clearly a way off winning the day in a larger sense too. I certainly agree that I have no authority to impose my views on others. With our discussion, I was very happy to leave it 2 or 3 posts into our exchange. With someone such as yourself, however, I do sort of expect a certain level of fair play.

"You continue "I was talking about faith in the physical existence of things that are non-material, i.e. do not actually have any physical existence!" That sentence is a tautology because of the word "physical"."

Given that you believe that time physically exists, that was what I meant to show. In relation electromagnetism/the electromagnetic field, this obviously does have physical existence. In the case of space-time, however, and to quote Einstein again, it "does not claim existence on its own but only as a structural quality of the [gravitational] field."

Like time, if it is then assumed to actually have physical existence, all manner of paradox can be shown to result, while, if such assumptions are then used as building blocks in the construction of other theories, this also becomes very problematic. In relation to thoughts being immaterial but existing, because thoughts are simply the firing of neurons, they are not immaterial. The mental contents of thoughts (ideas, numbers etc) certainly are and also have existence, but only in a platonic, non-physical sense.

Finally, in relation to your saying that someone who believes in time is a realist, given that whether one believes that time exists or not, the past, present, future, instants etc, are still immaterial, making such a claim is analogous to claiming that someone is a realist because they believe in God.

Best wishes

Peter

PS: I just realised that the first sentence of my previous post didn't make sense. Hopefully its meaning was still sort of evident.

[deleted]

Dear George Ellis,

Thank you for the helpful and constructive discussion. Let me (i) clarify what puzzled you in my previous post, and (ii) summarize the arguments for and against the BU and the EBU and see whether you would agree. I believe such agreements are crucial for any advancement especially in fundamental physics.

1. I think you were puzzled because of our different views on the status of UB and EBU. I now understand from what you wrote in another answer:

"I am agnostic about whether both the BU and the EBU are epistemological or ontological in nature: the argument is about whioh description gives the more accurate view of reality, whatever one's position on the ontological issue regarding the nature of the BU and the EBU."

that we are approaching the debate UB vs EBU from different angles. In this situation nothing can be immediately done - simply we have to acknowledge this difference to avoid any misunderstanding. I explicitly try to understand whether the world *itself* is a BU or an EBU; so I ask an ontological question.

That is why I wrote that in terms of observations (not in terms of what *exists* when an experiment is performed) both BU and EBU can explain those experiments; here I had in mind the relativistic effects (an assumption, which I should have made explicit). But since the two views represent different worlds (the ontological viewpoint) there should be experiments that should rule out one of the views and gave the EPR experiment as an example.

2. Summary of arguments

2.1 Arguments for EBU (= arguments against BU):

2.1.1. "Our daily life experience is abundant evidence about the nature of reality." And you believe that evidence demonstrates that time objectively flows. Why I think this is not an argument against the BU is given at the end of the post.

2.1.2. The present knowledge about the nature of consciousness demonstrates, according to you, that if we feel the flow of time it should exist objectively. We disagree on this too. As it is controversial whether or not we know enough about the nature of our consciousness I think we should rely on physical experiments to determine whether the world is a BU or an EBU (you would say whether the BU or the EBU describes the world better). And then, if the BU wins, we should ask how to explain our feeling of time flow.

2.1.3. Irreversible processes and the quantum measurement problem. This is not an argument against the BU since the BU can accommodate such processes.

2.2. Arguments for BU:

2.2.1. The kinematical relativistic effects would be impossible if the macroscopic objects involved in these effects were not real (four-dimensional) worldtubes. As we both agree that in terms of observation the EBU is also in agreement with those effects. For you this is sufficient since physics discusses only outcomes of experiments, in your view (I think). But since the two views are drastically different - on the BU view the worldtube of a rod, for example, is entirely given, whereas on the EBU view the rod's worldtube is only partly given and grows - I think other experiments should be found to rule out one of the views.

2.2.2. The EPR-type experiments (e.g. the example I gave in my previous post). While I agree with you that we should study these effects more, one thing, I think, is clear - the future can affect the past (as in the example given in my previous post). You say these effects are apparent problems for relativity and therefore for both BU and EBU as well. In my view it is not a problem for the BU at all (the future exists there), whereas on the EBU it is a real problem - how can something that has not yet come into being can influence a past event? I have managed to see what Yakir Aharanov wrote on this in his book Quantum Paradoxes. You can also check and will see that the question above holds in full force.

Finally, I would like to just confirm the point on which we totally disagree and will not comment on it any more on this forum. I think the question of how our daily experience, where the feeling of time flow plays a major role, can be reconciled with the BU view is a secondary one and for this reason cannot be used as an argument against the BU. You disagree and say "Our daily life experience is abundant evidence about the nature of reality. If physicist chose to ignore all that evidence, then their theories are not adequately related to the real world. They are trapped in the "isolated laboratory" view of physics, a convenient fiction (no truly isolated laboratories exist either in space or time), instead of believing that physics should be able to describe the real world, as I do."

Then it turns out that Minkowski, Einstein ("It appears... more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence" and "the distinction between past, present, and future is only an illusion, however persistent"), Eddington (Events do not happen; they are just there, and we come across them), Weyl (The objective world simply is, it does not happen) and many other physicists, all ignored the evidence about the nature of reality provided by our daily life experience. Of course, what they wrote is not an argument since what someone says does not determine the nature of reality, but this also applies to all of us.

I definitely agree with you that "physics should be able to describe the real world" and what we have been discussing is precisely the question "What is the real world according to relativity?" So, the very question is what is the real world. I think we have to be very careful not to take for granted a given view of the world and then say the physics should be able to describe that specific picture of the world.

Vesselin Petkov

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Dear Vesselin,

With the quotes you mentioned, I think you are confusing the lack of differentiation between past, present, and future in relativity/times all being mapped out together (the central feature of the block universe resulting from the lack of absolute simultaneity), with the view that the block universe means that change and even our "sense" of the flow of time are illusions. I do not think that any of the quotes are referring to the latter. I'm happy to also find myself in a position where I can completely agree with George about something really significant and pertinent! (i.e. that such a view is completely incompatible with not only observation, but all reason too. Indeed, I think that so many people accept it is truly bizarre). In connection to this matter and the BU vs. EBU, if you have possibly been following my discussion with George, you will be aware by now that there is a third option (i.e. lack of absolute simultaneity/BU compatible with change).

Best wishes

Peter

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Dear Dimi Chakalov

In my view the key unsolved problem in classical General Relativity Theory (GRT) is not gravitational energy, it is the definition and nature of gravitational entropy, and the related issue of coarse graining in GR.

Issue 1: Gravitational entropy and gravitational attraction

Almost all the statements usually made about entropy and the second law of thermodynamics are false when the gravitational field is significant. In brief: the standard gedanken experiment in this regard starts by considering a container partitioned in two, the one half being filled with gas and the second half empty. The partition is removed so that the gas can now flow from the one side to the other; the standard statement is that the gas automatically ends in a maximum entropy state with the particles evenly distributed in both sides of the box. This is the opposite of what happens when gravity dominates: all the particles coagulate in one aggregate in one of the halves. The outcome is not what is stated in virtually all physics textbooks (for further discussion, see G Ellis: Am Journ Phys 63 (1995), 472; see also R Penrose, The Emperor's New Mind). Randomisation in phase space is countered by existence of attractors associated with the gravitational field, leading to the so-called "gravo-thermal catastrophe" (Lynden-Bell & Wood: Mon Not Roy Ast Soc 138, 495 (1968); see also Lynden-Bell, http://xxx.lanl.gov/abs/cond-mat/9812172).

How does this relate to the second law? Either the gravitational field itself has no entropy, and second law does not apply in the case of gravitational collapse; or gravitational field has entropy and the second law applies in that case too, but we don't know what the gravitational entropy is, as no good definition has been given yet. I emphasize here that of course we have a well developed theory of the gravitational entropy of the final state of gravitational collapse, that is, a black hole (see http://en.wikipedia.org/wiki/Black_hole_thermodynamics); but we don't have a good theory of gravitational entropy that applies to the developing gravitational structure in the early universe, or the collapsing stars in the later universe that lead to black holes. We have formulae for the entropy of the matter and radiation present, but not for the gravitational field itself.

2: The arrow of time: gravitational entropy and cosmology

As a consequence of the above, a low entropy initial state is required in the very early universe in order for the arrow of time to exist in the late universe as we experience it, see Roger Penrose: The Emperor's New Mind and The Road to Reality for clear expositions. Penrose has formalised this in the Weyl curvature hypothesis: there is zero Weyl curvature in the limit at the initial singularity at the start of the universe (see http://en.wikipedia.org/wiki/Weyl_curvature_hypothesis and

http://www.nationmaster.com/encyclopedia/Weyl-curvature-hypothesis.)

Why this very special initial situation should have been the case is a separate issue from the claim that it must indeed have been so. The inflationary universe idea does not solve this problem, rather inflation depends for it success on this problem already being solved, as emphasized by Penrose. In any case this topic is absolutely on target as regards this forum: the existence of the arrow of time as know it needs to be explained somehow, and that explanation appears to depend on boundary conditions the very early universe: time as we experience it would not be the same otherwise. And that is a consequence of the nature of gravitational entropy, if it does indeed exist as an entity in its own right (that is, separate from the entropy of the matter taking part in the gravitational collapse).

3: Gravitational Entropy and gravitational energy

What is the relation of this to gravitational energy? One might think one could not discuss gravitational entropy with solving the issue of gravitational energy, but this is not so. One can approach gravitational entropy in various ways, for example through macro definitions and a phenomenological approach (following Lord Kelvin), micro definitions of entropy and a statistical mechanical approach (following Boltzmann), or through geometric definitions, associated with the gravitational field because of the geometric nature of GRT (following Penrose). To solve the whole problem properly, one really needs generic micro and macro definitions of entropy together with their relations to each other, which involves tackling the difficult issue of coarse graining in GRT (see Ellis and Buchert: http://za.arxiv.org/abs/gr-qc/0506106). And if one were to solve the issue in an asymptotically flat context, then yes one needs the Finite Infinity idea mentioned above in these postings to relate it properly to the cosmological context cosmology.

Only the phenomenological approach invokes the troubled issue of gravitational energy, where problems rise because of the equivalence principle and the requirement of general covariance. It is generally though that there is no tensorial definition of gravitational energy (see http://en.wikipedia.org/wiki/Gravitational_energy), but pseudotensor definitions exist (see http://en.wikipedia.org/wiki/Landau-Lifshitz_pseudotensor). These have not yet been used to give a satisfactory definition of gravitational entropy, as far as I am aware. There are also other approaches such as expressed in the paper by Philip Gibbs mentioned above; I think this also has not been related to gravitational entropy and the associated arrow of time

[deleted]

Dear Vesselin

I don't have time to give a detailed response to your last posting now, and indeed may not manage it before time is up as I depart for overseas tomorrow. However there is one paragraph in your reply I must comment on.

You state "I definitely agree with you that "physics should be able to describe the real world" and what we have been discussing is precisely the question "What is the real world according to relativity?" So, the very question is what is the real world. I think we have to be very careful not to take for granted a given view of the world and then say the physics should be able to describe that specific picture of the world." If you exclude from the real world the experiences of ordinary every day life, then you and I have completely incompatible philosophical views. It is that world of ordinary every day life that I wish to at least partially explain through my understanding of physics.

[deleted]

Dear George Ellis,

Your receny response post covered response to my query partly. i feel satisfied as i noticed a rationality in your response coupled with frankness and humility too. When one discuss 'established'concepts that like of space and time, one need not quickly jump to discard one or the other merely on the basis of an alternate concept explaining some phenomenon in Physics well. It is the totality of Physics that needs to be kept in mind. i agree when you indicate that an alternate approach can well appear to explain black holes behaviour than the present necessity to consider quantum nature of Gravity. If one looks at personal views of einstein and some other scientists of recognized authority, quantum mechanics may well be considered to provide explanations for the phenomena of atomic/nuclear and particle physics, the macro-level physics demand by the unique behavior of black holes may well find an alternate explanation from other than quantization of gravity. Garvity is the first interaction that the Universe has seen to emerge, followed by strong nuclear , e.m. and the weak nuclear. These all followed the demands of nature as the universe evolved. It is quite possible that gravity has some uniqueness we still need to identify that makes its union with a unified field difficult in the present day Physics.

[deleted]

George,

Four hours ago (Dec. 21, 2008 @ 12:55 GMT), you wrote: "It is that world of ordinary every day life that I wish to at least partially explain through my understanding of physics."

Then please do not ignore the first posting to your thread, and the rest of my comments and critical remarks.

I understand that you're leaving for overseas tomorrow. Wish you a nice journey, and hope to hear from you when you come back to your office. Please try, at least once, to reply professionally.

Dimi Chakalov

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Dear Vesselin Petkov

one further important point I will briefly raise regarding your last post: the EPR and Aharanov discussions are all based on the Schroedinger non-relatistic equation. There is therefore no reason whatever to expect their results to be compatible with Special Relativity ideas and effects, indeed it would be extremely odd if they were. The Dirac equation was developed precisely in order to extend the analysis of the Schroiedinger equation to be compatible with special relativity theory.

So please note that an EPR type argument only has a chance of becoming decisive in the present context of debate when it is based on the Dirac equation, not the Schroedinger equation. When you mix relativity based arguments with effects coming from the the Schroedinger equation, you are mixing incompatibles.

[deleted]

Dimi Chakalov

please explain carefully to me what was unprofessional about my posting of Dec. 21, 2008 @ 12:42 GMT.

[deleted]

With general relativity the Lagrangian for the motion of a particle is mc^2 int ds, where ds is the invarant interval. The action, would in general be Lds = pdq - Hdt, if we think of there being potentials and the like. This is a curious thing, for the action of GR motion including potentials, or mc^2 = k^2 - E^2 etc with DG equations, then we have an intertwiner between the proper time s and the coordinate time t. A Hamiltonian requires the imposition of a spatial surface (a part of a contact manifold) with a coordinate time. Yet in relativity this is a matter of a coordinate condition, similar to a gauge, and this defines a different notion of time entirely.

The Hilbert-Palatini action int d^4x(-g)^{-1/2}R has that determinant of the metric which will give an overall conformal term to the action for g_{ab} ---> Q^2g_{ab}. Hence the concept of energy conservation only holds at best according to tensor densities, and if certain symmetries can be applied to the system. The Ricci curvature scalar there is also

R = pi^{ij}dg_{ij} - NH - N^iH_i boundary terms,

and includes no apriori notion of time at all. Without the notion of time the concept of a Hamiltonian as the generator of time translations is lost. All this H does above is to define a soldering form between spatial surfaces.

For an Einstein space g_{ab} ~ R_{ab} (such as deSitter spacetime) and the Ricci scalar is then proportional to a proper time. So the H-P action reduces to a similar Lagrangian as for particle motion. So the action defines some proper time or inteval, which we regard as measurable in GR, but now for gravitational variables the Hamiltonian has no coordinate notion of time at all!

Ultimately we have an problem of two time variables, a proper interval which is tied to GR variables, and a coordinate time which is gives quantum wave dynamics, but is not physically relevant in GR.

To discuss cosmology and conformal coordinate consider the metric line element

ds^2 = -Q^2(dv^2 - dr^2 - r^2dOmega^2),

which is a set of conformally equivalent Minkowski spacetimes. Now let the conformal factor be time dependent so that

Q = dt/dv

then this line element is

ds^2 = -dt^2 Q^2(dr^2 r^2dOmega^2),

which is the deSitter spacetime. For Q = e^{Lt/3}, L = CC "Lambda," we then have that

dv = e^{-Lt/3} dt,

and so v is the conformal time v = -(3/L)e^{-Lt/3} on the deSitter cosmology. In this way one can define conformal Killing vectors K_t which will fix a conformal time on the spacetime, and mass-energy on the entire cosmology is "conserved" as a conformal quantity.

Now this is a conformal map between a spacetime foliated by three spheres and a flat Minkowski spacetime with flat spatial sheets. So there is a little matter of topology to consider here, for this will work "modulo" a point. So I really have to take a point out of the three sphere and connect their boundaries with infinity for the conformal map to hold everywhere, otherwise it holds almost everywhere. The conformal factor Q defines a spherical radius to the cosmology, which might be very large but is still finite. So the point which needs to be removed is bounded by a 2-sphere (think of 3-dim ball contracted to that point) which represents a homological cycle where there is a deviation between flat space and spherical space topology. This 2-sphere is the cosmological horizon, and if we look far enough back in time to the big bang we can look in to the "backside" of this horizon as the Planck area surface at the initial quantum fluctuation. This is the "umbilicus" which connects the universe to the initial quantum event (fluctuation) at the origin of the universe.

Lawrence B. Crowell

[deleted]

Dear Peter,

I am not confusing anything. We have been talking about what the real world is (not about descriptions) - what you separated as two things is the same BU view. On this view, which follows from relativity of simultaneity and the other relativistic effects, the world is not separated into past, present, and future, which means that it is a forever given four-dimensional block with no motion in it (since the *macroscopic* physical objects there are a network of worldlines, or rather worldtubes).

What you wrote "that such a view is completely incompatible with not only observation, but all reason too" is plain wrong. The only explanation for such a claim could be the fact that you have been conveniently ignoring (let me stress it) the *irrefutable* arguments that the relativistic effects discussed here would be impossible if the macroscopic physical bodies were *not* worldtubes. On the BU view these worldtubes are entirely given, whereas on the EBU they are growing.

Now let me invite you to prove your claim by considering *experiments* (ultimately, the only thing that can confirm or refute a claim) not philosophical considerations:

1. See in Sec. 3 of my post of Dec. 17, 2008 @ 05:47 GMT the thought experiment version of the real experiment that confirmed length contraction. Try to explain whether the length contraction of a meter stick at rest in observer A's reference frame would be possible if the worldtube of the meter stick did not exist. More specifically, whether observer B (moving relative to A) would measure A's meter stick as a different three-dimensional meter stick whose different parts are green, red, blue, whereas A measures a red meter stick.

At this moment it appears that such experiments cannot rule out the EBU since both - BU and EBU - explain length contraction as a manifestation of the reality of the meter stick's worldtube. But since BU and EBU represent two drastically different worlds it is clear that other experiments should be considered in order to rule out one of the competing BU and EBU. Such an experiment, I think is the following.

2. The EPR-experiment described in my post of Dec. 20, 2008 @ 04:39 GMT (and the diagram there):

"Now, consider the following (I think serious) situation. Let events (P_B) and (Q_B) on the same diagram be the measurements of the two photon polarizations in an EPR experiment. And let (P_B) be the experiment that determines the outcome of (Q_B). So, on the EBU view, what is measured on (Q_B) has been determined by an event that has not yet come into being!? I hope, you now understand one of the reasons of why I have difficulty accepting the EBU view."

Can the future influence an experiment if the future does not exist? And it exists only in a BU. You can also test the "third option" you mentioned in view of the above experiments.

When you understand just these two arguments based on *experiments* specifically designed to test theoretical predictions of physical theories (not on observations directly taken from our daily experience) you should at least stop claiming "I think that so many people accept it [the BU} is truly bizarre". The very fact that so many people accept it should have made you seriously ask yourself "Why?"

Vesselin Petkov

[deleted]

George Ellis wrote (Dec. 21, 2008 @ 17:30 GMT):

"Dimi Chakalov

"please explain carefully to me what was unprofessional about my posting of Dec. 21, 2008 @ 12:42 GMT."

You ignored my critical remarks -- all of them.

You wrote (Dec. 21, 2008 @ 12:42 GMT): "In my view the key unsolved problem in classical General Relativity Theory (GRT) is not gravitational energy, it is the definition and nature of gravitational entropy, and the related issue of coarse graining in GR."

I respect your viewpoint, but please notice that you completely ignored all critical remarks in my posting from Dec. 16, 2008 @ 14:43 GMT.

You also wrote (ibid.): "These (pseudotensor definitions - D.C.) have not yet been used to give a satisfactory definition of gravitational entropy, as far as I am aware."

Perhaps because it isn't possible to explain one mess (pseudotensor definitions) with another one (gravitational entropy).

I am not aware of some precise definition of 'low geometric entropy', but if we trust the calculations by Penrose (cf. Singularities and Time-Asymmetry, in General Relativity: An Einstein Centenary Survey, ed. by S W Hawking and W Israel, Cambridge University Press, 1979), it seems to me that the initial gravitational entropy had to be *as low as possible*, which in turn means that we cannot begin by assuming a FRW form for the metric -- even approximately.

See Slide 3 from R. Penrose's talk "Before the Big Bang?" (7 November 2005) here.

Big mess. Which is why I asked you to get to the bottom of this 'gravitational energy' and its quasi-local -- in time? -- nature.

But again, the main puzzle in your EBU idea are produced by your own statements, as quoted in my posting from Dec. 16, 2008 @ 14:43 GMT above. As you acknowledged (George Ellis, Dec. 4, 2008 @ 10:00 GMT):

"So a key element is how proper time relates to coordinate time as we move to the future, ... "

If you believe can resolve this 'key element', please test your solution with the problem of gravitational energy, from 1918.

Thank you for your (quasi-local?) time.

D.C.

[deleted]

Dear Prof George F R Ellis,

Increase in the inertial mass and the time dilation in the special theory of relativity are simple kinematic effects. These effects in the essay The Theory of Time, Space and Gravitation are a consequence of the gravitational action. Both physically and philosophically it is more suitable.

Yours faithfully

Robert Sadykov

[deleted]

Dear Colleagues,

I'm afraid we've been tearing apart George Ellis with our very diverse questions. I for one wish to apologize to George for my violent curiosity.

Perhaps we can put aside our questions, and focus on one issue, which I believe is the crux of his EBU proposal:

I look at my wristwatch, and record some linearized variable called 'coordinate time'. How does my wristwatch read it, given the premise that any finite interval from it belongs to the cosmological time?

[deleted]

Dear Vesselin,

Thanks for your comments.

"On this view, which follows from relativity of simultaneity and the other relativistic effects, the world is not separated into past, present, and future, which means that it is a forever given four-dimensional block with no motion in it (since the *macroscopic* physical objects there are a network of worldlines, or rather worldtubes)."

Again, if you had perhaps been following my discussion with George you will be aware that I do not think that the last 4 words of your sentence ending before the brackets need apply to the BU (I will get to worldtubes shortly). That is, if interpreted correctly, the BU is not incompatible with motion and change, and this can be seen to be a separate issue from the lack of absolute simultaneity. Moreover, I do not think that any of the quotes you provided refer to this issue (lack of change). They are all direct references to the lack of differentiation between past, present and future in relativity/all times being given and laid out. I'm pretty sure that there are no quotes by Einstein saying that motion and change are illusions. One will find a small handful of ones saying that space-time and time and space have no physical existence though.

"you should at least stop claiming "I think that so many people accept it [the BU} is truly bizarre". The very fact that so many people accept it should have made you seriously ask yourself "Why?""

Considering that I was referring to the standard interpretation of the BU (no motion, no change), but clearly accept lack of absolute simultaneity and the BU compatible with motion/change, I don't really appreciate your inserting the bracketed BU above.

In relation to worldtubes, I have by no means been "conveniently ignoring" your argument. Although I disagreed with it, I did not see it as representing a direct challenge to mine. In relation to worldtubes, though, although bodies can naturally be described as 3 dimensional (any massive body will be by default), and they can move (4-d, and because continuity, including the rotation of the hands of a clock, can be shown to simply be the result of the capability for motion in Nature, this dimension needn't be called time), worldtubes do not exist. Moving bodies do, and this is all that relativity requires. If your thought experiment holds, I think this is simply what it shows. That is, I think you are misappropriating the existence of 3-dimensional dynamic bodies with the existence of worldtubes.

Best wishes

Peter

[deleted]

Dear George Ellis,

Thank you for your quick comments and have a safe trip and all the best for the holidays and the coming 2009. I will also reduce my postings here since a very important deadline in January is fast approaching and I will have to do most of the work before the next semester, which starts here on 5th of January.

I will briefly comment only on this sentence: "If you exclude from the real world the experiences of ordinary every day life, then you and I have completely incompatible philosophical views."

In any case you will have the paper (on the debate BU vs EBU) based on my talk at the third spacetime conference in Montreal last June. I believe it will be published, which will make it available for criticism. Every winter semester I have been teaching a course on space and time and this year the present debate will be even more emphasized.

I do not think we "have completely incompatible philosophical views." You take for granted that "the experiences of ordinary every day life" can be explained and understood only in terms of an objective flow of time. As the stakes are at the highest possible level - our view of reality - I do not like to take anything for granted. All (even purely logical) options should be on the table.

We have nothing to lose if we do that, but we may have a lot to lose if we do not do it. Then rigorous analyses of all relevant or potentially relevant *experimental* facts confirming predictions of the modern physical theories should tell us what is the dimensionality of the world (at least according to relativity) and whether *macroscopic* bodies are completed or growing worldlines (or rather worldtubes since those bodies are spatially extended objects). That is why, in my postings here I have tried to concentrate only on experiments; in line with that I had in mind the real EPR *experiments*; so I have not mixed anything.

Vesselin Petkov

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