I thought I might add, because the statements I made above, about events that are really simultaneous not being perceived as synchronous in B's frame, may sound a bit mysterious,---that this is demonstrated in my essay by the fact that observers B and C' are totally causally disconnected, so what B describes as synchronous with the event illustrated by the red dot in Figure 2 is not the blue dot, where C' is "simultaneously in its own separate universe", but C (the yellow dot) at a *later* absolute time---i.e., when it gets to the blue dot as the universe (x-axis) evolves. C could emit a photon towards B at that (cosmic) time, which would travel through the one-dimensional "universe" evolving in absolute time, until it's observed by B; and B would infer that that event, which *really* occurred at a later cosmic time, was synchronous with the event that's illustrated by the red dot.

The thing is, that relativity theory doesn't tell us a priori the location of an observer along its worldline that coincides with the emission of a distant photon, nor the location of the emitter along its worldline that coincides with the later event when the photon is observed: all it describes is the space-time separation between any two events. We are left to infer the rest for ourselves, and the common practice is infer that such coincident (i.e., simultaneous) events in space-time occur at the same "time" in any frame---i.e., synchronously. This is what leads to Rietdijk-Putnam-type deductions that there has to be a block universe. But then those who want to deny this inference, often appeal to the fact that the theory can't really tell us a priori which sets of events were *actually* coincident---and claim, e.g., that the observer could really have been anywhere along its worldline in the region outside the light cone associated with the emission event, in the region known as "absolute elsewhere", thus denying the existence of an objective reality.

Many problems arise as a result of this inconsistency of thought, because when not backed into the corner of the block universe implication, everyone does commonly assume that synchronous events really are simultaneous in any frame, even in general relativistic solutions. And that's where the really new pieces of the puzzle come in when we do make the assumptions of absolute space and time that are consistent with the theory.

Dear Eugene

I apologize for not having seen your gracious and interesting post. If you find my diffraction paper interesting you might enjoy similar ones and things about my inventions etc. on My website . I did most of my researches in the days before the Internet - now that so much interesting material for study is available, I regret being less energetic than before (having joined the grandpa set) to make use of these opportunities. I've heard Joy's work being mentioned a lot here, and will study it. The algebraic geometry sounds very interesting, I will look at the reference you kindly provided.

Thanks and best wishes,

Vladimir

Hello all,

Thank you Daryl for your kind and interesting comments on my essay, also the same to Edwin. Daryl, I wasn't referring to your essay before, having only flipped through it until just now. I think it's very good, and unlike many of these essays, I agree with you about some things.

I don't see the linguistic thing you mention as a problem with block time, it might be a slightly different use of the word 'is', but to me the question of whether or not we have the language to describe it doesn't affect the question of whether block time is true or false.

I don't agree with a universal present moment - I think the concept of simultaneity at a large distance is always questionable. In Newtonian time it has some meaning, in Einstein's version it has less. I think it has even less than that - no meaning beyond the light cone. The reason is that in the universe we have different time rates locally. Relating them clearly doesn't work in different frames, as I mentioned in the essay. They're thought to be relatable in the same frame, but we can't easily check that.

Two clocks a million light years apart and not moving in relation to each other might keep the same time and run in sync. But that doesn't prove simultaneity. It just proves that two local time rates at a distance are in step with each other. To me relating the times of events with meaning is saying that an event is before another one if it can affect it by getting a light signal there in time to influence it. That means within the light cone, at short range.

This would explain why block time is wrong - what led to it depends on long-range simultaneity having enough active meaning to allow an event to be in the past to one observer but in the future to another. Without that, there's no block time, and a lot of the confusion about time goes away. Hope this makes sense...

best wishes, Jonathan

    Daryl and Jonathan,

    Thanks for those comments. I was tending to take the view that time is 'emergent' somewhat in the sense of Julian Barbour's essay in which one can simply 'factor out' time and retain only actions and distances as in his equation 5 (page 8) and his final equation. But that seems to reduce everything in the universe to 'local' action, and I have decided that that is just not sensible. In fact, I now consider it to essentially demand simultaneity. I have not put the time into this that either of you have, so I cannot defend this idea as well as either of you, but I'm pretty sure that Daryl's 'Cosmic time' or 'flow of time' is on the money. This semi-infinite universe cannot possible hang together as local actions and local distances with time defined only as a local way to keep score.

    Best,

    Edwin Eugene Klingman

    I have read a conversation with Julian Barbour in which he says motion through time must be caused by some sort of psychological illusion. To me that approach fails in trying to interpret gravitational time dilation, and tends to need a second illusion, interacting with the first one, when interpreting motion time dilation. Two interacting illusions does not make for a good explanation.

    It is also denying the problem, and rather like marking the unexplored areas on a map with 'here be illusions' (just as the old map makers marked unexplored areas with 'here be dragons'). Barbour says time is 'nothing dressed up in clothes', like the emperor's new clothes. He's looking at it mathematically, but it's a conceptual problem - initially anyway.

    To me the thing that is like the emperor's new clothes is the fact that the illusion approach dismisses the laws of physics, and hence physics itself and much of our world, as an illusion. Some people have simply pretended not to see the problems with block time, because like the emperor's new clothes, it has been the standard view, to be accepted. Only recently have we been questioning it, because we need to if we are to get to quantum gravity.

    Best wishes, Jonathan

      Hi Jonathan and Edwin:

      The local reconciliation of temporal passage that's supposed to come from denying a metrical relation between events that exist outside one's past light cone is Howard Stein's thing. However, as Craig Callender pointed out in "Shedding Light on Time", by positing that "at least one event in the universe shares its present with another event's present", which he considers to be "the thinnest requirement one could put on becoming", "Stein's 'possibility' theorem [is transformed] into a 'no go' theorem for objective becoming in a Minkowski spacetime". Basically, what this means is that if we can say that *even just one event* exists at some metrical distance outside the light cone of another event---like, for instance, the emission of a photon by the Sun anytime in the past or future eight minutes---Stein's theorem tells us that the common way of describing what is "present" in relativity theory demands a block universe.

      I believe in the existence of Physical Reality, despite the fact that I can't know what simultaneity-relation describes the sapcelike surface that exists at any instant as I'm looking at my watch, because every experience I've ever had in my life tells me it's there. Therefore, although we can't scientifically prove or disprove its existence, I think a pure verificationist way of looking at things is the wrong approach. It doesn't lead to any clear understanding of things, but only allows some people the opportunity to wave their hands or shrug their shoulders.

      Therefore, given Stein's theorem, and the fact that I believe the Sun exists now---as in, I believe there's a well-defined spacelike metrical distance between the Sun and me now, which has a different length (and, e.g., isn't synchronous) in different coordinate frames---even though I won't see what it looks like now for another eight minutes---I completely agree with Roger Penrose's remark, when demonstrating his own version of the Rietdijk-Putnam argument in The Emperor's New Mind, where he notes that whether one uses observers' light cones or their simultaneous spaces makes no difference at all to the conclusions. ("Some relativity 'purists' might prefer to use the observers' light cones, rather than their simultaneous spaces. However, this makes no difference at all to the conclusions.")

      As to denying the relevance of coordinating distant spacelike events with a metric, that is not something that should be done lightly, and I think it just leads down a rabbit hole. All of science is based on the use of a metric---rather than a more general abstract topological space---to describe "distances" between two events, and there's a mountain of scientific evidence to support the fact that, regardless of which coordinate system is used, there is a Lorentzian metrical relation amongst all space-time events. This is the very reason why proper times are measured differently by observers in relative motion, and there is indeed a well-defined metrical relation between them according to relativity theory. Therefore, in relation to my above remarks, I think it's just wrong to argue that this metrical relation should somehow only crystallise when events enter one's past light cone, which is what I can only take your comments to mean.

      I've already noted elsewhere on this blog a very relevant observation that Tom Ray made in his essay: 'One recalls that prior to Descartes, all geometry was done with compass and straightedge---all "here" and no "there." Only with the development of analytical geometry were we able to identify relations between numerically distant points and a local coordinate system.' I don't understand why you would *want* to reject this. I agree that it seems to be hard to reconcile it with relativity without concluding that there has to be a block universe; but if you'd rather accept instead that it does work---and I'm certain that it does---I think you'd see that the interpretation of the emergence of relativistic space-time that I've described in my essay really works. The key assumption is that the metrical relation amongst events in space-time has to be Minkowskian, just as it is in the block universe theory.

      The linguistic thing is essential to forming a clear understanding of the problem, and how the theory works; and there are in fact important distinctions that need to be made between the meanings of *two* words in order to understand how special relativity can be reconciled with a flowing present. First and foremost is the copular verb: as Steven Savitt argues (see the top paper) it's really through a carelessness with the word "is" that McTaggart was able to show, even from a Newtonian perspective, that the past, present, and future are all equally real. According to presentism (which McTaggart tried to argue against), the past and the future do not "exist" in the same sense as the present, which is all that's supposed to be real. Instead, the past and future exist, according to the presentist viewpoint, *ideally*---i.e., brains, photons, computers, books, etc., existing in the present, carry, or form ideas about what was in the past or will be in the future. This is an extremely important distinction to make, because confusion does arise when one thinks of the real present as somehow flowing through the space-time continuum of events, with any particular event in the future existing as such until it eventually becomes present, then past---even if we're thinking of this sense of "existence" as something abstract---and it's only amidst such confusion that arguments like McTaggart's (or, e.g., those of Huw Price) prevail.

      But when one thinks of the present as enduring, with the ideal past emerging in its wake, as an unreal thing about which records exist in the present, and the ideal future as something that's anticipated in the present, there's no reason to think of McTaggart's argument as anything more than a misuse of semantics. As I noted before, it's also this way of thinking of all events throughout (space-)time as existing in some way that can be travelled to, that leads people to time travel paradoxes.

      This presentist thinking makes perfect sense from a Newtonian viewpoint. But relativity throws in another monkey wrench, because what is meant by "time" is---at least in one sense---not universal. Two events that occur at the same "time" according to one observer will happen at different "times" for another observer, and clocks will tick at different rates. For such reasons, it's difficult to see how it could be possible to reconcile a view that everything only exists "now" with relativity theory. The way to do this, I've argued, is to first make note of the distinction between space-time, as a four-dimensional *ideality*, and an enduring three-dimensional *reality*---a flowing Heraclitean present, with an absolute time defining an absolute simultaneity-relation, and associated sets of events that *truly* occur simultaneously, in a Newtonian sense. These events obvously then have to be said to occur at the same "time"; however, as described in different relativistic space-time coordinate systems, viz. those used by observers with non-zero absolute motion, the events that occur at the same "time", in the pre-defined sense of simultaneity, will not occur at constant values of the time-coordinate.

      Therefore, along with the distinction that I think needs to be made between the "existence" of "ideal" past and future and a "real" present, I think it's also very important to make a distinction between events described as "synchronous" in a given frame occurring at the same "time", and events that truly occur "simultaneously", at the same cosmic "time".

      Best,

      Daryl

      Jonathan:

      I typed up my previous comment before seeing this one, so I added it there. I agree with what you're saying here about people pretending not to see the problems associated with a block universe, and chalking things up to illusions. I think this happens because people don't want to change the basic way they think about the theory. The problem with that, I believe, is that the basic way people like to think about the theory---as dynamical---is demonstrably incompatible with what the physical theory has to say about the way they like to think about the theory.

      Daryl

      Hello Daryl,

      in reply to your last two posts, I agree with the latest one, that people don't want to change the way they take SR.

      They take SR with spacetime, and yet spacetime may be entirely wrong. It is impossible for anything to move through spacetime, almost by definition. Spacetime distances include imaginary numbers, which people accept in an 'emperor's new clothes' kind of way. But this may have no physical meaning. And, for instance, an event 4 minutes ago on Mars has zero separation in spacetime from right now where you are on Earth. All this may have no physical meaning. And because it leads to block time which requires illusions, spacetime is very questionable.

      Spacetime hasn't been tested, and like string theory, it can't be tested. Suppose it's entirely wrong - imagine sweeping it away. We'd be looking for missing pieces of the puzzle in a new landscape. Much of our present conjecture would be irrelevant.

      You talk about relating things in space, but the issue is, can we relate things in time? That's what we don't know - we know a lot more about space. We have reason to think we can't relate things in time as we have been doing, because look where it led - it led to block time, which doesn't work with the real world we observe. So time may be different. It may be meaningless to relate points in time at all. We don't know. All out attempts to relate points in time may have failed to work. But within the light cone, light signals give us an alternative method, meaningful, but perhaps just a crude approximation, perhaps also ultimately irrelevant to the way time really is.

      Best wishes, Jonathan

        • [deleted]

        Dear Edwin,

        You invited me to take part in your discussion. I have to apologize for not reading all contributions. Instead of referring to the weak points in Daryl's view, I just added to my essay a hopefully unmistakable explanation why SR is based on confusion between physical reality and what an observer measures.

        "Two events that occur at the same time according to one observer will happen at different times for another observer, ..."

        Do they really happen for observers or do they happen at the location where they happen?

        Let me tell a story that happened 50 years ago. In a rowing race over 2000 m in about 6 minutes, my crew was defeated by only as little as 0.02 seconds precisely measured with a Swiss Longines system. This was undeniably close to physical reality. Merely at start, we were a bit cheated because the acoustic signal reached us about 0.1 second later than the winning boat.

        Best,

        Eckard

        Dear Eckard,

        This perfectly demonstrates the point I've been making about problems that arise due to sloppiness with language. You wrote, "Do they really happen for observers or do they happen at the location where they happen?" Well said. The word "for" in the quotation you gave is meant in the sense of "according to" or "as determined by" or "in the proper coordinate system of", and therefore not in the sense of a gift. Events in space-time are locations or points on the four-dimensional map. What's meant in that quotation is simply that two events at the same value of the time-coordinate of one system will be at different values of the time-coordinate of another system.

        Since you've claimed that there are weak parts in my view, I'd very much appreciate those being pointed out so that I might have the opportunity to argue otherwise. I'd consider it a courtesy. I'll even briefly recap my position for that purpose.

        The past, present, and future don't all "exist" in the same sense: the past and future "are" purely ideal (ideel in German; i.e., not real anywhere but in *present* brains, computers, etc.) and the three-dimensional enduring present "is" real. Relativity adds another layer, complicating this picture further, because it comes to mean that together with the dual meaning of the copular verb "is" in relation to the dimension of time, there must also be a dual meaning of the word "time" if the theory should be reconciled with a Heraclitean flowing present. Thus, the common-sense impression of "time" that we have when we consider present "existence" in three-dimensional space---which is what we refer to when we say two events occur "simultaneously"---must be separated from the sense of "time" that's described by any space-time coordinate system. This is precisely because any claim that two events occur at the same "time" in the latter sense cannot be universal, since any change of coordinates describes one event as preceding the other; i.e., "synchronicity" is relative.

        This latter fact has commonly been taken to imply that relativity is inconsistent with presentism, because "synchronous" and "simultaneous" are thought to be synonymous; but I've shown in my essay the mathematical theory can be consistently reconciled with the above view of time, as long as we make the appropriate split between the meanings of the two words and define a global simultaneity-relation. Therefore, relativity does not require a block universe.

        Daryl

        Dear Jonathan:

        It *is* impossible for anything to move through spacetime by definition. I think the quotation by Geroch that I gave in my essay says that the best. Although the one by Weyl comes a close second. It's just that some people mis-construe that due to an inability to break away from the sense that things really change.

        If you're interested, I can prove to you that spacetime distances don't include imaginary numbers in de Sitter space. It's not a hard or long proof, and it's done from first principles. But it requires a positive cosmological constant.

        Zero distance between two points that are not identical is indeed a peculiar property of Lorentzian metrics. They're weird. But that doesn't mean we should deny the appropriateness of the Lorentzian metrical structure that's used to describe physical reality. That has been very successful, not even just locally, but also for describing cosmological data. Without the assumption of the RW metric to describe an emergent three-dimensional universe, how might you consistently relate all the cosmological observations?

        Best,

        Daryl

        It's true that spacetime has been very succesful in describing the universe. It has also made it possible to simplify many theories. But that may be exactly why we were reluctant to question it until we had to.

        The reason spacetime may be wrong, even though it works for describing many things, is that physics is full of equivalence. As I said in my essay, often more than one conceptual picture is described by similar mathematics. So we may eventually have to let go of spacetime, because conceptual flaws have been giving us a hard time, even though the mathematics seems to work. Spacetime is, after all, an interpretation of SR. And if an interpretation gives you conceptual problems, then you might need a different one.

        Best wishes, Jonathan

        Hi All:

        The discussion of Julian Barbour's conception of time brings up an issue that I think is important. His conception of time is very much like mine, in that he wants to remove the dimension of time from the description of what is real, and describe instead a succession of "nows". However, I believe he goes a step too far in this, by also denying duration and concentrating only on a physical description of what exists in the "now". This brings to mind an ancient fallacy about a footrace between Achilles and a tortoise, which is based on a similar denial of duration---viz., in principle. Since Zeno's purpose was to support the Eleatic thesis (block universe) by an argument that motion can't occur, it's his prior removal of duration from the picture that makes the "paradox" a fallacy.

        How did he accomplish this? Zeno described the footrace according to a sequence of configurations: the tortoise is halfway between Achilles and the finish line to begin with, but Achilles will have covered twice the distance as the tortoise at any subsequent "time"; thus, at one point the tortoise is three-quarters of the way to the finish line and Achilles is halfway there; when the tortoise is seven-eighths of the way there, Achilles is only three-quarters; etc. The tortoise is therefore "always" halfway between Achilles and the finish line. Therefore, Zeno concludes that motion does not occur.

        But motion can be defined as spatial displacement through an element of duration: as everything endures, bodies can move through space in time, with average displacement over time defined average velocity, etc.; therefore, by denying duration in principle Zeno has denied an essential ingredient of motion, and has therefore demonstrated no real paradox. Furthermore, by co-ordinating the axis of duration with space, it is simple to show that Achilles and the tortoise reach the finish line at the exact same time, and that if each keeps going at the same pace Achilles will indeed overtake, running on ahead always at twice the distance as the tortoise from the finish line.

        By using coordinate systems to describe space-time, relativity is just as capable of resolving Zeno's "paradox" as Newtonian mechanics. My question to anyone who would deny prior duration, and therefore the appropriateness of the metrical structure of all of space-time---whether emergent or a block---is this: how do you resolve Zeno's paradox? If the rearrangement of bodies in space essentially *causes* time, and there is no prior duration of space, how can one claim that anything moves at all?

        Daryl

          Daryl, All,

          I like your simple statement: "by denying duration in principle Zeno has denied an essential ingredient of motion".

          And the more I think about it, the more I am convinced that universal 'simultaneity' [but not 'synchonism'] must exist. Because, as you say, "If the rearrangement of bodies in space essentially *causes* time, and there is no prior duration of space, how can one claim that anything moves at all?" But any meaningful definition of "rearrangement of bodies in space" must almost certainly be 'local', otherwise we get into the synchronization problems that lead to all of the current confusion, and I cannot conceive of a universe that 'hangs together' though local behaviors, un-synchronized, across the vast reaches of the universe. Even in the absence of noise, this would seem to require perfect laws with perfect precision, operating perfectly, else things would drift into chaos in a way that we do not observe. Only a universal [Cosmic] time that effectively defines a universal 'Now' [presentism] can keep this whole thing going, in my opinion.

          Edwin Eugene Klingman

          Hello all,

          in your version of the paradox, they reach the finishing line at the same time. But in Zeno's version, Achilles runs much faster than twice the tortoise's speed, who has an arbitrary head start. When Achilles gets to where the tortoise was when Achilles started, it has moved on a little. When he gets to this further point, it has moved on a little further, and so on. The paradox is resolved because the tortoise knows a shortcut through the bushes.

          I don't see how you'd know if the universe was 'synchronised' in the Newtonian way you talk about. It might look the same anyway, with or without that.

          Best wishes, Jonathan

            PS. If there's a universal 'now', then why can't two observers moving differently get results that match up, when each tries to calculate what time it is 'now' for the other one? I've done the calculation, it comes out of SR, which has been confirmed by experiment, and which I think is absolutely right. I only question spacetime, not SR. It seems to me that to get your universal now, you have to deny SR itself.

              • [deleted]

              Dear Daryl, All,

              as I see it, the problem Zeno has is that he is trying to separate the idea of change in spatial separation from the ideas of time and energy. Concentrating just on change in distance. Which makes an unnaturally abstract process.I would like to argue that those three phenomena (change in spatial separation, passage of time and energy) are inseparable in nature, (considering a real change and not just parallax).

              In the explanatory framework I have been describing for some time now, passage of time at the foundational level (in the Object reality- like Bohm's pre-space) is the product of sequential change in arrangement of matter. The change (of relationship between the matter) is energy. Which means that change, which may be (indirectly) observed as a spatial change of position by an observer, is inseparable from passage of time and energy.

              So though, yes the distance can be halved and halved and halved, it will also be reducing the time taken and the energy involved. He is comparing smaller and smaller distances but also smaller and smaller times and smaller and smaller amounts of energy. He is not comparing the same situation each time, as he is not considering just one variable, distance and keeping the other parameters fixed (ie fixed time interval and/or fixed energy expenditure.) Which makes it an invalid experiment. If either energy or time interval between sample observations is kept constant the change in distance will not be continually halved.

              Edwin, perhaps now because as you wrote "And the more I think about it, the more I am convinced that universal 'simultaneity' [but not 'synchonism'] must exist" you may be able to appreciate how the explanatory framework I have been describing enables there to be that universal simultaneity as well as the observation of relativity, without contradiction.

              Hi Georgina,

              Actually, I've been seeing it that way for a while, and I think I told you that. But I've not been able to reconcile this with General Relativity, as that's not my area of expertise. So when Daryl published his essay, and I read his dissertation, I felt like he'd been doing the GR analysis I had not done -- and coming to the same conclusions.

              I do like your framework very much. And this essay contest is potentially working to get rid of a number of other troublesome assumptions. I am at the moment simply trying to keep up with the new entrants and separate essays into two stacks. I then intend to go back and re-read the essays in one stack at least one more time. Right now too many ideas are merging in my head and I am overwhelmed. I see very convincing arguments, but don't have time to check the math or check the references or even analyze the arguments properly. And even the comments on several threads are also a goldmine!

              Best,

              Edwin Eugene Klingman

              • [deleted]

              Edwin,

              I just thought that I should say how that paradox can also be addressed by the framework I am using.

              I have written a recent reply to J.C.N.Smith on my thread about why gravity can not be caused by curvature of space time. Even though I am using a framework that allows general relativity to be seen as valid.

              I agree there are very many good essay and comments.

              • [deleted]

              Dear Georgina:

              Thank you for joining back into the discussion. I do plan to carefully read through your essay (which I've only been able to glance through up to now), and eventually rate it. I hope you do mine as well.

              As to your above comment, I agree with it. I think that from what you've said you consider time and energy to be canonically conjugate variables, though, so I'm not sure I see the reason for bringing both into the discussion---unless that relates to your second comment about "why gravity can not be caused by curvature of space time[, even though you are] using a framework that allows general relativity to be seen as valid."

              In that regard, I think we are in agreement. On Aug 15 at 18:53, I posted a reply to George Ellis on my topic which contained the following:

              "General relativity theory describes space-time as a field that is supposed to be warped in the presence of gravitational mass. In contrast, in order to reconcile relativity with true temporal passage, I've described space-time as the emergent map of events that occur in an enduring three-dimensional universe. As such, the space-time continuum of events is not conceived as a real substantive manifold that warps and moulds due to the presence of gravitational mass; and the need to describe the flow of time associated with a uniformly enduring homogeneous present [in cosmology; this statement's given within the context of George's comment], makes the basic concept of space that truly warps under the influence of gravity seem difficult to reconcile. For instance, in cosmology we take the description of perfect fluidity to be valid on the large scale, but if space-time is a substantive manifold that's truly warped under the influence of mass, so that the local passage of time is really influenced by localised mass, is it really very consistent to say that there should be a cosmic time that passes at the same rate in our Local Group as it does in the Coma cluster? Although the description of space-time that's given by Einstein's equations seems to coincide with the idea of a substantive manifold that truly dynamically warps under the influence of mass (although, in what dimension is the warping of space-time described as dynamically changing? Dropping the assumption of a global simultaneity-relation in space-time that coincides with a uniform flow of cosmic time, while retaining the concept of dynamical change, seems to lead to Zeno's paradox of infinite regression), if an absolute cosmic time is required in order to counter the implication [from the Rietdijk-Putnam argument] that we must only imagine ourselves as existing in a block universe, it seems that some more definite background metrical structure must be required to account for that.

              "And that's exactly what the RW metric provides in standard cosmology; therefore, although the local passage of time will be different in different gravitational fields and in different states of motion, the standard model still describes uniform global evolution. The same is true in the SdS cosmology I mentioned in my essay, given the description of r as the cosmic time coordinate. The difference, however, is that in FLRW cosmology the overall curvature of space and the evolution of the scale-factor are supposed to be determined by the large scale average energy content of the universe. Therefore, general relativistic dynamics are incorporated into the theory following the prior assumption of a cosmological background metric. Furthermore, this idea is supposed to be correct according to general relativity theory, so that, in taking the RW metric as background structure and passing it through Einstein's equations, we find that the overall empirical and theoretical consistency of the theory implies that the perfect fluidity of matter should be a good approximation to the large scale average; but it's really debatable whether the large scale distribution of matter really has approximated very well as a perfect fluid since structure formation, and it's anyway this aspect of the theory that really makes the horizon problem such a big problem [notwithstanding inflation].

              "Now, the idea that the evolution of our Universe might really need to be described through a well-defined background metric, through which space-time emerges as the map of events that occur in the Universe, seems better suited to a metric-affine theory, whereby the metric and local connection are independent quantities and gravitation is described in terms of torsion rather than curvature. If this were the case, then regardless of what the background metric would be (i.e., regardless of the [possible] triviality [of] its stress-energy tensor), space-time would be described locally through different solutions to the Einstein field equations [that could well contain non-vanishing stress-energy].

              "Therefore, if the SdS cosmological background could be used as such to describe the existence of galaxies on its fundamental worldlines, and if the distribution of galaxies would appear isotropic from every such perspective, it would be a legitimate cosmological background for a universe that *should* expand at all times, at a well-defined rate that would turn out to be modelled precisely by the flat LambdaCDM scale-factor, regardless of the actual curvature of space or its global energy content. Therefore, it would agree with empirical observations in our Universe, going a large way towards explaining why the Universe does expand, and would eliminate the flatness problem as well as the need for large amounts of dark matter and dark energy---and the horizon problem would no more be a problem than the requirement to account for that particular background metric. But then, it should be noted that this particular metric has the same form as the one that will describe the final state outside every bound cluster of galaxies in our Universe..."

              Neither George, nor anyone else, has offered anything in response to this. Since we agree that there can be both "universal simultaneity as well as the observation of relativity, without contradiction"---and I have demonstrated in my essay how this can work in the case of special relativity, with the mathematical theory emerging as the appropriate description of events that occur in an emergent universe with the required inertial and causal structures---I wonder if you (or anyone else) have any thoughts on this.

              Best regards,

              Daryl