Prof. Wharton.

I did not mean to be unkind; it is in my nature to be direct, and in that I may seem insensitive; sorry. I will try and chase up "Story of Your Life" and "The Hundred Light-Year Diary" at some point, but it has been a long time since I read science fiction.

Your answer to Torsten suggests you are interested in limiting the impossible infinity of possibilities "choice" brings to a block-universe. A fifth dimension tying future possibilities to past conditions is one way to imagine a suppression mechanism; something imagined many years ago; and while such imaginings are entertaining, I bugged out of that universe a long time ago. I suspect you realized that after reading my essay and some of my replies to relevant posts.

Cheers!

Zoran.

Dear Dr. Wharton,

I completely agree with you about the necessity to consider the universe all at once, and have made the same arguments myself. So, given that we both agree that there is some formal system which can describe the complete configuration of the universe, past present and future, my question to you is this: why are the axioms of that formal system true, as opposed to some other formal system?

An axiomatic system cannot, by definition, derive its own axioms. From an objective standpoint, one cannot claim that one axiomatic system is "more true" than other. All we can do is say that one axiomatic system describes our universe better or worse than another. But suppose we have found this system. Why is that system the one "true" system, and all other systems false?

If there is one axiomatic system that corresponds to objective reality, if that one axiomatic system is objectively true, there must be some way to break the symmetry between other axiomatic systems...some way to distinguish it, to show why this system is realized and others are not.

This question is unanswered by your essay, and I would argue that an honest look at this question leads to just one logical conclusion.

    • [deleted]

    Dear Prof. Wharton,

    Nice essay but I will not hide my disagreement that IT cannot come from BIT, a position you hold. The Quantum world has provided a safe haven for all sorts of pet theories and abstract contraptions to hide, so let me discuss and cross-examine you on the cosmic scale. So dear Prof. Wharton, kindly mount the witness box:

    1. Is the universe real? If so, is it an IT?

    2. If the universe is an IT as we its inhabitants would not be writing and reading essays if it were not, would it have a beginning?

    3. If it had a beginning, and that beginning was from "nothing", is nothing an IT?

    4. If nothing is not an IT but is rather "an immaterial thing", then has an IT not come from what does not have an underlying reality?!

    Whereas, you yourself have testified publicly that: "the only proper rebuttal is to demonstrate that there is some plausible underlying reality, after all" and the possibility of the contrary haven been demonstrated from exhibits 1 to 4 above,

    I now put it to you that, at least on the cosmic scale, "It from Bit" proponents can ... claim to have won the argument by default!!

    Cheers and all the best sir. You are discharged and acquitted since you were honest in your testimony. MORAL: IT can at the "very deep bottom" come from an immaterial source and explanation! - It from Bit, Wheeler, 1989

    Regards,

    Akinbo

    *You may wish to appeal this judgement after reading and criticizing my paper.

      I am an IT, I don't know why the system calls me Anonymous and turn me to a BIT despite being logged in.

      Akinbo

      Ken,

      I gave your essay a first reading last night. I am going to need to read it again. I have this curious sense that you are implicitly arguing for local hidden variables. Of course since you are working within a block universe idea maybe these are in fact nonlocal. I get this sense there is some subtle issue with what you wrote along these lines.

      I do get the sense that your argument is that block time is the proper view of spacetime from the perspective of the action principle. I would tend to concur with this. There is the question I think of how one treats Cauchy data for the initial and end points of a path integral. The role of dynamics is I think secondary. Dynamics just tells us what the system will look like along the parameterization or time variable of the path integral. Since we perceive spacetime according to a present moment that is carried along with time to the next moment we are sort of biased to see the world as dynamical. The action principle provides the Euler-Lagrange equation to permit us to convert the action principle into a dynamical principle.

      LC

        Dear Ken

        I am not competent enough to respond to the interesting points you raised about dynamics, it from bit and conceptions of Reality. Your arguments are expressed through the use of space-time. I have long ago concluded there is no time dimension and that observer-based physics (frames of reference, her past and future) should be replaced by one describing dynamics in an absolute universe.

        You mention the Born Rule and the double-slit experiment. May I direct you to Eric Reiter's unquantum website where he describes experiments that demolish the Born Rule. This agrees with my own 2005 Beautiful Universe Theory also found here where dynamics in a timeless Universe where propbability is emergent is suggested.

        With best wishes

        Vladimir

        Dear Ken,

        I've been reading your article "The Universe is not a Computer" (arXiv:1211.7081).

        I share you concern for a lack of physical interpretation that tells us to use Lagrangian principle, unlike Fermat's principle, which has a clear justification for mathematical procedure (talking about light paths, etc.).

        What would you think of the following argument. Let's assume that any dynamic process, or system, can be used as a clock. Different states of system a labelled with some values of real variable, called time (t). We need as little change of state as possible between any two labels t_0 and t_1, to have a clock as precise as possible. Infinitesimal change of system state in quantum mechanics is Hamiltonian, which is units of energy. The mathematical variation method constructs entity with units of action (energy times time).

        This physical argument for introduction of Lagrangian principle fits nicely with quantum mechanics, which is discussed in http://www.fqxi.org/community/forum/topic/essay-download/1597/. Section five actually talks about principle of least action, while the other ones build a ground for it.

        In http://physics-essays.birukou.net/principle-of-least-action I describe uneasiness from a student's point of view about LQFT as it is taught at the moment.

        Let me know what you think. Do not hesitate to email directly.

        Mikalai

          Ken,

          If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

          Jim

          I respectfully disagree with Matthew's statement of falsehood of Feynman's point, quote, "that the double slit experiment contains the whole mystery of quantum theory". Article http://www.fqxi.org/community/forum/topic/1597 shows how results of double slit experiment lead to concept of interaction confinement, which expresses into unitary dynamic for a closed system, when seen from outside. The "seen from outside" is a relational nature of information as per Carlo's http://www.fqxi.org/community/forum/topic/1816.

          Also want to make a comment about "perfectly sensible local and noncontextual hidden variable theories". I found article that try to suggest tests of such theories. What about actual results? Aspect(&co)'s experiments, in relation to Bell's theorem, still say that nature is not run by hidden variables. Shouldn't we be sceptical here?

          Hello Ken,

          I only got part way through your essay before fatigue set in last night, but found the part I did read deep and engaging. Seeing your comments above, about seeking alternatives to the Block Time universe description, I wanted to mention the following.

          The possibility has been raised that the dimensionality of spacetime is not a constant, where CDT and Quantum Einstein gravity find that the cosmos was 2-d initially, and spacetime later unfolds to become 4-d. I discuss this somewhat in my essay from last year, but a paper of note just came out.

          "Dimensional reduction in the sky" arXiv:1305.3153 has as authors two of last year's essay contest entrants, Giovanni Amelino-Camelia and Michele Arzano, along with Giulia Gubitosi and Joao Magueijo. So how can there be block time, if the dimensionality of the cosmos evolves? Since spheres have maximal volume in 5-d, perhaps that is where things are ultimately headed. Care to comment?

          Regards,

          Jonathan

            I have to support Matthews points, and Daryl's. The so called 'no-go' theorems all have limited domains and rely on assumptions. I've now shown how the last one, Bell's theorem, can be overcome in my essay, the EPR paradox resolved as Bell and von Neumann anticipated using a real local mechanism but by 'unifying' QM and SR! The others then melt away as inapplicable.

            And Mikalai, the solution I present predicted an 'orbital symmetry' in the results for each detector if proper comparison of actual pairs was carried out. I assumed Aspect hadn't managed this, but to his credit it seems he had! Did you know he discarded over 99% of his data due to some unexplained "orbital asymmetry"? I only found this after researching the French version of his follow up paper. There was then no theory to explain it, now there is, and it derives a cosine curve at EACH detector, making QM uncertainty far more consistent, but also deriving the SR postulates. And as may imagined more emerges, including simplicity. Gordon Watsons essay provides the consistent mathematics.

            This would infer that Ken's assumptions were incorrect, though I still can't help feeling that Ken had a slightly devilish reason for drawing his provocative conclusions. I think I show that if we get dynamics right they overcome all assumptions about giving up reality and obeying imaginary stop signs. QM uncertainty emerges closely analogous to Kalusa's thesis, but I needed more space to develop that.

            I do beseech you to read mine very carefully and comment. "The Intelligent Bit"

            Ken, I need to read yours carefully again before commenting further, and also your considered comments on mine.

            Many thanks

            Peter

            Dear Peter and Matthew,

            Judging by IQit things, one needs a lot of, quote, "axioms". It is a complex thing. Alternative might be a simpler explanation, with potentially different fundamental concepts, then those in classical physics.

            To judge between the two, we need an experiment. In absence of experiment, Einstein's razor would have to be used :)

            I asked, if there are actual runs for effects due to presence of hidden variables. That shall help.

            More so, I think that we may find another suggestion for experiment in the following place. If classically-governed hidden variables is what nature does, then there is no theoretical restriction for tapping into quantum-channel key distribution (man in the middle attack), while QM without hidden variables implies that such tapping is impossible.

            Am I right? So, break quantum channel, make a ton of money, and, as a bonus, I will be the first to accept a more cumbersome explanation of reality, cause nature decides through phenomenology (experiment).

            Dear Daryl,

            (And Edwin, thanks for your nice comments, and for encouraging a more detailed exchange on this point.)

            Thanks for clarifying your views about how you don't necessarily subscribe to the universe-working-like-a-computer dynamical story, even if there is an objective "now". Usually these two views go together, and I can't say I've ever encountered anyone who wanted both objective simultaneity but not dynamics.

            That said, your prior essay did make it clear that you don't want a block universe, so you clearly don't like my all-at-once analysis either. I suspect that this puts you in the stochastic dynamics camp, but that doesn't solve the quantum no-go theorems. Stochastic dynamics is just ordinary dynamics with random inputs, with no essential difference when it comes to the problem of explaining entanglement, etc.

            But, to the heart of the matter: is it coherent to deny relativity of simultaneity?

            >And just because we're *able* to describe every thing in a coordinate system in which we're at rest, and dribble a basketball on a ship, doesn't mean that we should reject the obvious when we look out at the world.

            In other words, you're saying that in special relativity we *could* all pick a common reference frame to analyze everything , and that somehow it's more objective to do that. But just because there are situations where such an analysis might be (arguably) more natural, there are certainly situations where it's *far* from natural. I'm concerned you're cherry-picking the former examples in place of the latter.

            After all, in the frame of our galaxy (even leaving alone the CMB), we have no accurate clocks here on earth, apparent spheres are not truly spherical, etc. Should I be making these adjustments to my reality every time I design a laboratory experiment? Do the half-lives of radioactive atoms fundamentally change as I drive them around town?

            But what's convenient or "obvious" is not really the point. The point of relativity is that we happen to have beautiful symmetries that allow us to use the same laws in *any* inertial frame. Is this massive coincidence really not telling us anything about our universe?

            The key point at the start of Einstein's 1905 relativity paper is that we should be suspicious of "asymmetries which do not appear to be inherent in the phenomena". I am incredibly suspicious of such asymmetries, and this even extends to my suspicions about the time-asymmetries in standard accounts of quantum theory.

            >But as I understood your essay, I thought you were actually arguing that a real underlying geometry that we could update our subjective description of, as more information became available, is *not* precluded by quantum mechanics; e.g. "It is a subjective process, performed as some agent gains new information".

            Right; that's correct. But to make it work, given the no-go theorems , you need the so-called retrocausal loophole, which you get by analyzing the whole block at once. If you slice up the block into instants that are generated according to causal rules, you fall right back into the original premises of those theorems, and you can no longer describe events with an underlying reality.

            >I just hoped that because you've stated this point so well in that regard, you might be able to see that your own argument applies equally well in regard to relativity, which similarly derives its denial of an absolute reference frame from the Independence Fallacy -- i.e. it stems "from a motivation to describe a slice of a system independently from what lies outside."

            Interesting point! That's one way to view the relativity principle, I suppose, but not how I view it. In relativity it's not that one wants system A to be *independent* from system B, it's just that one wants to describe the interrelations of the systems from either A's perspective or B's perspective. (And the beauty is, you can do it with the same equations!) The independence is with respect to the frames of reference, not the systems. Perhaps you naturally equate a system with a frame of reference, which might blur this issue for you, but there are certainly some systems that present no natural frame of reference.

            One final point that may hearten you: there are quite a few physicists, especially in the quantum foundations realm, who take the idea of an objectively preferred reference frame very seriously. QM was basically developed in such a framework, so QM-style reasoning can convince people that there must be an objective frame of reference. The way around the no-go theorems in this story is to postulate faster-than-light influences in such a frame, as in the various "flash ontologies". So this is certainly a viable research program, and I wish you success with it.

            Best regards,

            Ken

            Thanks, Cristi ; yes, lots of common points! I had already noted your essay, and mean to comment on it, but it may be a week or so until I get a chance. More soon!

            Ken

            Hi Matt,

            Thanks for the insightful comments! I confess to perpetuating that particular fallacy (perhaps even on purpose to make my double-slit analysis seem more important than it really is). Although I did note that there are *other* ways to explain the double slit, and that the other ways don't naturally extend to the truly problematic cases.

            Your proposed research project is right on the mark; it's not so straightforward to define "locality" in a way that doesn't explicitly rule out retrocausality by definition (although I think GR has a good handle on it, at least in the sense that I would like to use the word). Noncontextuality might be even trickier.

            Although I'm making a big deal out of the distinction between all-at-once and dynamic stories, I don't see a project to define the difference as so important (certainly not as compared to the locality question). After all, either a given story gives QM and resolves the no-go-theorems or it doesn't. And given some definition of locality, it's either local or it isn't. The reason I'm drawing such a big distinction in these essays is mainly to draw attention to the *existence* of non-dynamic approaches. Not because non-dynamical approaches are *inherently* better, but simply because of their nice features and the fact that they're rarely considered seriously.

            As for generalizing Spekkens' definition of epistemic states, one issue is that while old-fashioned "states" live on instants, the natural ontology in an all-at-once account are histories that span durations. So you'll have cases that (if sliced up into 3D states) start out 'Spekkens-ontic' at the preparation but end up Spekkens-epistemic by the time they're measured. But since the latter is all that really matters (isn't it?) I'd put such cases squarely in the psi-epistemic camp. (Where I think any story along these lines would naturally end up.)

            Cheers,

            Ken

            Dear Ken,

            Have I got a cherry to pick with you ;)

            Seriously, though, thank you very much for your detailed and thoughtful response. I'm camping right now for my daughter's birthday, but you bring up a couple of points that I'd like a chance to discuss further when I get back to a computer, if that's okay?

            All the best,

            Daryl

            Dear Ken,

            thanks for you interest and sorry for the late answer. I'm on vacatrion with only limited internet access.

            My work is more in the direction of quantum gravity then GR. But I understood the arguments for a block universe.

            Pro block universe: The arguments are more in the direction of causality. If there is a unique path from the past to the

            future for every point then one calls this spacetime strongly causal. This concept forbids time loops etc. but it is to

            restrictive. In particular, if you have the Cauchy surface N then the spacetime has to be diffeomorphic to NxR. In this

            concept, everything is well-ordered.

            Contra block universe: In quantum mechanics and also in quantum gravity, you do have philosphically an open future: there are

            the possibility for more than one possible measured value. Now, if one assume that everything (including measured values of

            observables) is encoded into geometry than one needs a more complex geometry for the future, a tree.

            In my model, a tree appears naturally by the smoothness structure. As explained in the essay (hopefully), one has a complex

            quantum state given by wildly embedded submanifold. The resulotion of this wild embedded submanifold is given by a tree anf

            the branches of the tree representing the different measured values (the encoding of the probability is not clear to me now).

            From the GR point of view, I have a spacetime with naked singularities (the saddle points). In this singularities, some

            geodesics went in and some more went out (or you have the branching point of the tree). But this spacetime is now not a block

            universe (in the strong sense) andf it is not of the form NxR (but NxR with an exotic smoothness structure).

            Hopefully I touched some of your points.

            More later,

            All the best

            Torsten

            I wanted to add that Zeeya Merali and the FQXi folks have given this subject a Forum page, for discussion, which can be accessed at:

            Dimensional reduction in the sky

            Your insights and opinions are of course welcome.

            All the Best,

            Jonathan

            Dear Ken,

            Your response touched on a few points that I think deserve some more discussion, as I indicated before. The first thing I wanted to address was your reference to Einstein's point, 'that we should be suspicious of "asymmetries which do not appear to be inherent in the phenomena"', which you used to support an argument that the beautiful symmetries we do know of, which allow us to use the same laws in *any* inertial frame, should be telling us something about our universe. In this, you may be presuming that a presentist position would be inconsistent with there being something fundamental about the universe that would lead to the symmetries that appear to be inherent in the phenomena.

            I've said before that I think there is strong empirical evidence to support the description of an ultimate cosmic reference frame, and therefore an objective "now". I've also said that I *don't* think space-time is just a superdeterministic solution to an initial value problem. I want to add that I *do* think there is an objective maximally symmetric background metric and that the order of objective temporal passage relates to a maximally symmetric foliation. This isn't something I can justify in a post here, so I'll only add that what I have in mind involves teleparallelism, as I think this background metric (de Sitter space) isn't *really* warped in the presence of mass, but rather the metric isn't conserved in local frames where there is torsion, and that's why space-time is described as being warped in such frames. Therefore, relatively speaking, it's a lot more like SR than GR, although we know that teleparallel gravity and GR are equivalent. The main difference with other approaches along these lines, is in the absolute foliation that I think needs to be assumed, which is the point I'm wanting to discuss with you, so what I'd like to do is press your point of criticism with this in mind.

            From your comment to Torsten above, I think your criticism might have been referring to the past-future asymmetry, but then I'd ask how it is that that *doesn't* appear to be inherent in the phenomena? I mean, if all the information we ever receive is *always* about events that occurred in the past, and that is about phenomena that never appear to be influenced by future events, then how does a past-future asymmetry *not* appear to be inherent in the phenomena? On the other hand, the background structure I'm referring to has the same t-symmetry that's usually found in most physical theories.

            But I also wonder if you're referring to the asymmetry in the description of a photon moving to the left *actually* getting further away from an inertial body than one that's moving to the right because the body is *actually* moving to the right--even though that body should, in its proper coordinate frame, describe a photon's velocity as being the same constant value in all directions of "space". Such a description is necessary if there's to be objective temporal passage and a constant speed of light, and although from one point of view (which you're arguing for) it may seem a bit contrived to argue for these "tilted" descriptions of reality rather than assuming simultaneously occurring events are synchronous in every inertial frame of reference, I'd argue that the alternative seems *far more* contrived.

            To begin that argument, I'd say first of all that the symmetry objection isn't really an objection against my view because I think the apparent symmetry in the phenomena *is* inherent in an objective background structure of space-time. And second of all, I think a *fair* assessment of what's contrived or not--of what we should be "suspicious of" or not--should openly admit concerns with both sides of the issue.

            I think many people have been so concerned with trying to accept the implication of a block universe, that they often forget what's so entirely *unacceptable* about it. In fact, I think many have found some way of coming to terms with the idea precisely *because* they've completely missed what is so entirely unacceptable about it. From what I read in your essay and your above reply to Torsten, and even by your argument that our knowledge of space-time symmetry should be taken to indicate something about what's inherent in the phenomena, I don't think you fall into the latter camp. By this, I mean that I don't think you have the wrong idea about an all-at-once block universe, as some people have, who think relativity should be taken to imply something like "all of space-time exists"; but by your argument that you think we should consider our knowledge--our empirically verified description of symmetries, etc.--as indicating something about reality, I think you *are* forgetting just how totally at-odds the all-at-once view is with *what we know*.

            I've been thinking a lot about the block universe idea, and particularly about what it can't be taken to mean, which a large part of my essay concentrated on; and I think the best way of getting some clearer idea without sneaking another dimension into the view, is to state its meaning in two ways: (i.) "nothing *exists*", where emphasis is placed on "exists" because the concept of anything existing implicitly assumes a dimension of temporal passage that, in this case, isn't the time-dimension of space-time, but would be another one, of the same form as the time-variable of classical mechanics; and (ii.) "everything doesn't exist", where everything refers to all of eternity, as reality all-at-once, which does not exist. Another way of stating this is that the block universe interpretation of relativity considers that the theory describes reality as all of eternity, but does not describe reality as *being* all of eternity.

            Nothing about this view is consistent with what we know of reality. So many people have worked to come to terms with it, only to end up with a view in which all of eternity is supposed to *exist*. They think of the apparent passage of time as an illusion that occurs "as our consciousnesses crawl upwards along the life lines of our bodies", etc. But we know that this sneaks in another dimension that's not there in the physical description; that the dimension that *would* describe existence, as it did in classical mechanics, is already used up in space-time. So nothing can exist. The four-dimensional world all-at-once 'is' temporally singular.

            This is why I indicated that in trying to come to terms with, and make use of the block universe theory, I do think you've come to neglect the significance of the issues that there are with it; i.e., because you're arguing that space-time symmetry should be telling us something fundamental about the world, about what "appears to be inherent in the phenomena", and yet you're using this to support a view that's inconsistent with anything existing. And there is nothing more blaringly obvious about reality than the fact that it exists. Things happen as it exists, and we describe those happenings by putting them in order of spatio-temporal occurrence. It *is* an error to then think of that description as something that exists; and I think it's just as wrong to think of reality as that description--as the mathematical model, sliced up as we choose to do because of its symmetry--but with nothing *existing*.

            So, I've told you how I think relativity theory can describe existence. I've taken standard arguments that have been given *against* existence--relativistic thought experiments that clearly show the relativity of time, as described from different perspectives--and I've explained how I think it's wrong to define the synchronous events that are described in arbitrary inertial frames as simultaneous.

            You asked, "Should I be making these adjustments to my reality every time I design a laboratory experiment? Do the half-lives of radioactive atoms fundamentally change as I drive them around town?" No. The principle of relativity, and therefore relativity theory, allows that we can describe everything from the perspective of an arbitrary frame of reference; in regard to the half-lives of radioactive atoms, I could hop into a spaceship right now and fly for the rest of my life at some relativistic velocity and when I die the Universe would be a heck of a lot older than it will be when I die if I just stay put; but this doesn't mean that there is no ultimate cosmic rest-frame--it just means that you can do physics without knowing what that frame is. But that doesn't mean that there *isn't* an objectively true geometry and actual objective temporal passage; actual existence.

            You wrote, "But just because there are situations where such an analysis might be (arguably) more natural, there are certainly situations where it's *far* from natural. I'm concerned you're cherry-picking the former examples in place of the latter". But I've taken standard thought experiments that have been used to show the relativity of simultaneity, and turned them around to show how simultaneity can be taken as an objective relation while synchronicity depends on motion with respect to the objective rest-frame. Recall the above example in which you and I are holed up in the cabin of a ship, which is roughly along the lines of what I wrote in my essay this year. If you were referring to this when you said my analysis might be arguably more natural, I think I should point out that this is *exactly* the type of thought experiment that's usually taken to indicate that the description of time and the synchronicity of events given from different points of view is relative. All I've done is to take the standard thought experiment a step further and explain the paradoxical implication regarding simultaneity from the perspective that something is *actually* in motion, with reference to its surroundings, despite the fact that there aren't any forces acting on it.

            Also in my original post above, I wrote that "On my essay page, I've also opened up a discussion involving a thought experiment from Brian Greene's Fabric of the Cosmos, which clearly demonstrates the relativity of synchronicity, and I've described how I think that should be correctly interpreted, and what I see as being wrong with the usual interpretation." This is a standard thought experiment that's stated clearly so that anyone with an interest in the physical world can understand it and be convinced of the relativity of simultaneity, and I've tried to explain how objective simultaneity works in that scenario.

            The point is that I'm hardly cherry-picking by considering the same illustrations that others have used to show that there is no objective simultaneity relation, and explaining what I think is the error in their reasoning.

            All the issues that have been contrived based on the theory of relativity stem from the simple fact that because everything can be described in isolation, without reference to an external world, people have wanted to conclude that there is no real external world. They've looked at the world through rose-tinted glasses in order to justify calling it red--i.e., they've denied objective reality, which is the one thing through which the whole theory can make sense, and through that denial they've concluded that we live in a paradoxical world, albeit with beautiful symmetries, that makes no sense.

            Consider the twins paradox, for example. The reason for all the fuss is that, according to relativity theory, since, by construction, both twins are always in inertial reference frames, one has to admit that either of them must be able to describe himself as always remaining at rest while his brother goes on a journey. But if we situate the twins in reality, there's just no way to reasonably argue against the fact that one twin in particular *actually* hops from one frame of reference to the other *and this completely resolves the paradox* (see, e.g., Schutz's Intro to GR book, at the end of the SR chapter).

            When the "paradox" was first contrived, the motions of celestial bodies were thought to be completely random, so there was reason to see some validity in the "paradox"; but even amidst this worldview, when constructing his cosmological model in 1917, Einstein noted that the velocities of the stars are all much less than c--which one wouldn't expect if one thought that random stellar motions should be uniformly distributed on the allowed interval--and used this to support a simplifying assumption that there is a cosmic frame of rest with respect to which the stars all have some small amount of proper motion.

            This brings me to cosmology, which everyone who argues for pure relativity seems to want to neglect. Since the ultimate point of debate has to do with the question, "is there, or is there not, a Universal frame of rest?", I simply can't understand how it could be considered justifiable to neglect the cosmological evidence. Since the point is that regardless of whether there is a cosmic rest-frame, relative to which everything in the Universe can be described as "*really* moving", Lorentz symmetry allows us to describe events from whatever frame of reference we'd like, that point can't be used as grounds to claim that there really is no cosmic rest-frame. That really is just like looking at the world through rose-tinted glasses in order to justify claiming that it's tinted red.

            Einstein argued that since the theory can be derived without assuming there is an absolute reference frame, the law of parsimony urges that we make no such assertion. All I'm arguing is that he pushed parsimony too far, without initially grasping the implication that this would have for existence, and how badly the theory would conflict with the apparent flow of time and consciousness--and that the assertion that there is no cosmic rest-frame is now perfectly well understood to be at-odds with the empirical evidence.

            So, I've gone on to show how the implications of relativity theory that seem at first to be paradoxical can in fact be interpreted in a way that makes sense intuitively, when the assumption of a cosmic rest-frame has been made. And I've argued that the cosmological evidence supports that assumption. For, even neglecting the CMB, it's obvious from galactic redshifts that there is a cosmic frame of rest. The galaxies all have some proper motion, but aside from those that are very close to us, their proper velocities are negligible compared with an isotropic redshift-distance relation. Assuming homogeneity of space (and a natural interpretation of the fact that the redshifts aren't, say, constant, but do increase with distance), we arrive at the conclusion that space is expanding in cosmic time, and we get a very good fit to the data when we do assume that the redshifts are entirely due to this cosmic expansion. But the evidence for a cosmic rest-frame doesn't end there: our interpretation of the detailed anisotropy signature in the CMB is based on the hypothesis that the effects of vacuum fluctuations in the early universe would have expanded along with space--and the model fits very well with the same parameters that have been constrained by other means. Furthermore, although proper motions of galaxies through space (including our own) are negligible in the redshift-distance relation, from the CMB dipole anisotropy we can actually infer precisely how quickly we're travelling through space; i.e. we can go a step beyond the inference from the redshift-distance relation, that there must be *some* cosmic rest-frame, and we can actually measure our own absolute motion--which is something that no one a hundred years ago thought we could ever possibly do.

            I'm sorry: I know this is a long post, and I know that my argument conflicts with the basic premiss of your essay; but I think, from your essay, that certain positions I've taken in this argument *are* consistent with your own views, so I'm hoping you'll be willing to fairly consider what I've written. As I said before, from a quantum mechanics point of view I admit that you may have an argument that the block universe is better; but since you based your premiss on relativity, I wanted to explain why I think the points you make in your argument are in conflict with the premiss, as those same points can be used to argue against it.

            I respectfully request that you consider my arguments somewhat more carefully, as they not only relate to your essay, but you've even indicated a greater interest in arguments against a block universe on this page. I assure you, as I've said here, that I've made no attempt at "cherry-picking", but have done my best to meet standard thinking about relativity that supports the block universe view head-on.

            Thanks for your time,

            Daryl

            Dear Ken,

            I can't reasonably expect you to accept, at face value, my claim that in my view maximal symmetry lies at the heart of everything. Or at least I can't reasonably expect you to accept that I'm justified in saying so, when you see my position on time as being opposed to that. So, I thought I should try to explain my reasoning in a post here. I hope you do find the analysis interesting, because it leads to what I think are a couple of very intriguing results.

            As I said my reasons lie along the lines of a teleparallel description of gravity that's based on a maximally symmetric background metric, interpreted geometrically, I'll begin by showing what I think that metric has to be. Afterwards, I'll explain how I think the teleparallel aspect of the picture should work.

            So, we begin by hypothesising that there is this maximally symmetric geometry that lies at the heart of it all, and the first question is, "What is it?" I think it should be real, so my first instinct is to coordinate a number of real lines. But since space-time has Lorentzian signature, Euclidean space seems like a bad background geometry to use for this purpose, and imposing Lorentzian signature on a "real" metric space by simple definition seems contrived. A more natural definition of a real metric space with maximal symmetry and zero curvature is that it is Euclidean space (and this is anyway the usual definition), and according to *that* definition, Minkowski space is naturally derived through a Wick rotation of one coordinate. From this point of view, Minkowski space isn't real.

            Instead, we can consider spherically symmetric spaces with the induced metric, [math]ds^2=\sum_{\mu=0}^{4}dx_{\mu}^2,[/math] [math]\sum_{\mu=0}^{4}x_{\mu}^2 =\alpha^2.[/math]

            By demanding only that the four dimensions of the maximally symmetric space itself are real, it's easy (and interesting) to see that this metric actually represents four distinct real 4D spaces, by arbitrarily solving the bottom equation for one coordinate and allowing that it can be real or imaginary; i.e., by writing [math]x_0=\pm\sqrt{\alpha^2-\sum_{i=1}^{4}x_{i}^2 }.[/math]

            Then, the metric for these 4D real Riemannian spaces in this Cartesian coordinate basis can be written [math]ds^2=d\mathbf{x}^2\frac{(\mathbf{x}\cdot{d}\mathbf{x})^2}{\alpha^2-\mathbf{x}^2},[/math] where [math]\mathbf{x}=(x_1,x_2,x_3,x_4)[/math] is a real vector, and alpha is now the spherically symmetric space's *intrinsic* "radius of curvature". From this line-element it's straightforward to write down the components of the metric tensor in this basis:

            [math]g_{ij}=\frac{1}{\alpha^2-\mathbf{x}^2}\cdot[\alpha^2-(\mathbf{x}^2-{x_i}^2)],~\mathrm{if}~i=j,[/math] [math]g_{ij}=\frac{1}{\alpha^2-\mathbf{x}^2}\cdot{x_i}{x_j},~\mathrm{if}~i\neq{j}.[/math]

            From here, we can solve the eigenvalue problem; and it turns out that the metric tensor always has three positive eigenvalues, along with [math]\lambda=\frac{\alpha^2}{\alpha^2-\mathbf{x}^2}.[/math]

            The four distinct geometries described by the metric are therefore as follows: (i) when [math]\alpha^2\geq\mathbf{x}^2(\geq0)[/math] and alpha^2 is positive (this is the one case where x_0 is actually real), the space is a closed 4-sphere with positive-definite metric tensor; (ii) when [math]\alpha^2\leq\mathbf{x}^2[/math] and alpha is a non-zero real constant, lambda is negative so the *real* metric is Lorentzian; (iii) when alpha=0, lambda=0 so the metric is degenerate and the metric describes a lightlike hypersurface of 5D Minkowski space; and finally, (iv) when alpha is purely imaginary (and non-zero), the metric is positive-definite for all [math]\mathbf{x}\in\mathbb{R}^4.[/math]

            In terms of the original embedding, these four geometries are: (i) a closed 4-sphere in 5D Euclidean space; (ii) a hyperboloid of one sheet in 5D Minkowski space; (iii) a light cone in 5D Minkowski space; and (iv) a hyperboloid of two sheets in 5D Minkowski space.

            The point of the derivation is that, beginning from the requirement of maximal symmetry and the usual definition of "real space", and maintaining the real basis in an embedded space, it can be shown that the only *real* space with maximal symmetry *and* Lorentzian signature is case (ii), which is de Sitter space. From the point of view of wanting to describe the apparent symmetries of nature, and particularly the Lorentzian symmetry of space-time, as fundamental properties of reality, this result seems significant--especially when it's noted that the cosmological evidence supports a pure cosmological constant which could be essentially geometrical. Then, the vacuum Einstein equation would be [math]R_{ab}=\Lambda{g_{ab}},[/math] which indeed the above metric is a solution of, with [math]\Lambda\equiv\frac{1}{\alpha^2},[/math] although the metric wasn't derived with reference to general relativity; e.g., I allowed for general metrical signature, but instead maintained that the space had to be real. But as I said, only in case (ii) is the metric really relativistic, because that's the only case in which this real space has Lorentzian signature.

            I hope you don't mind if I try to explain briefly how I'd make use of this result. I'll do that in another post.