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...

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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

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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...

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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

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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...

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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,

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

Then, the metric for these 4D real Riemannian spaces in this Cartesian coordinate basis can be written where 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:



From here, we can solve the eigenvalue problem; and it turns out that the metric tensor always has three positive eigenvalues, along with

The four distinct geometries described by the metric are therefore as follows: (i) when 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 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

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 which indeed the above metric is a solution of, with 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.

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(CONTINUED FROM PREVIOUS POST)

As I said at the beginning of my previous post, I don’t expect you to take at face value the statement in my post from yesterday that I think there is a fundamental geometry with maximal symmetry. The post above explains what I think that should be and why, but I wanted to justify my reason for making the assumption as well, by explaining how I’d make use...

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(CONTINUED FROM PREVIOUS POST)

As I said at the beginning of my previous post, I don’t expect you to take at face value the statement in my post from yesterday that I think there is a fundamental geometry with maximal symmetry. The post above explains what I think that should be and why, but I wanted to justify my reason for making the assumption as well, by explaining how I’d make use of it.

The main point to begin with is in the point of conflict I have with the block universe view. I do think the evidence supports defining a particular foliation of space-time as the description everything that happens in a three-dimensional universe while it exists. In this regard, I’d admit a “spotlight” view of the universe as sweeping along this background geometry, with space-time mapped out in its wake, as a useful (5D) way of thinking about cosmic evolution; but I’d add that all that ever needs to be *real* is the 3D Universe, which exists or *endures* with this background geometry as an intrinsic, fundamental property.

As I said before, I don’t think this corresponds to a universe-as-a-computer description. While I think the dynamical expansion of space is predetermined according to the background geometry, I think local physics is up for grabs as long as it falls in line with the background structure—i.e. as long as it conforms to the basic metrical symmetry of that background. There is one caveat, however: the requirement of a particular foliation means a far more geometrical interpretation than is usually required, since the evolution of “now” in any frame has a global definition.

What this means, is that the usual interpretation of general covariance, as implying that the coordinates have no immediate metrical meaning, so “reality” in any frame can be thought of as the evolution of a synchronous hypersurface, would no longer be valid. For example, because of the way it relates to the Cartesian coordinate basis in the above derivation of the de Sitter geometry, the Lemaitre-Robertson representation of the de Sitter metric doesn’t appear to be very useful (cf. Figure 1 in my previous essay; by the way, the black hypersurfaces and red worldlines aren’t showing up when I look at the essay now on my computer, so I’ve attached the figures as individual PDFs below, in case you have the same problem). Also, it’s clear that in the statical coordinate system (cf. the other two figures I’ve attached) the description of the radial coordinate as being “timelike” beyond the horizon is wrong: the coordinate transformation (see, e.g., the Wikipedia article) is only valid out to the coordinate singularity at r^2=1/Lambda, beyond which one of the real Cartesian coordinates becomes imaginary. Therefore, it’s only by denying that the coordinates have any metrical significance, and by extension, neglecting the domain over which the transformation should actually be valid, that it’s possible to interpret this “radial” coordinate as being “spacelike out to a horizon, and timelike beyond that”. In the geometrical view, this r simply has no real meaning beyond the coordinate singularity.

So, to move on, I’d like a foliation of the geometry that really preserves the symmetry of the space that was derived from first principles. The natural choice, when de Sitter space is described as a 4D hyperboloid of one sheet in 5D Minkowski space, is to define this as the 3-sphere that shrinks to a finite radius and expands afterwards. One interesting property of this foliation is that the “universe” itself, as well as the four-dimensional background geometry, is parallelisable. Another interesting point is that the only worldlines of constant coordinate velocity through this 3-sphere that are actually geodesics are the ones with zero velocity. While all other particles in the “universe” that move through it at constant velocity are therefore in a sense “accelerated”, it also seems reasonable to describe them somehow as being “inertial” as well. In that sense, the torsion along these lines could be attributed to real space-time curvature (teleparallelism), and an “inertial” particle “moving” along one of these lines might be described as “massive”, whereas the geodesics that don’t “move” through space could be described as “massless”.

I apologise that this last point is quite conjectural, but it motivates a particular definition of a cosmological line-element that would be appropriate to use in the frame of these “massive” particles, from which a very intriguing result can be proven. The key point, after acknowledging that this “cosmic 3-sphere” is parallelisable, is to define a line-element that would work as a cosmological solution, from the perspective of these “massive” particles. Then, if we consider just the particles that are “moving” in the same direction along the 3-sphere, a (semi-crazy) possibility is to define the cosmic frame of rest as the bundle of null lines that point in that direction of motion, because the “massless” geodesics are moving relative to that bundle at the null velocity defined by the background geometry; i.e., we define the line-element that may be appropriate to use from this perspective, as where, for reasons of consistency, the *r*-coordinate is used here to represent *cosmic time*, and *t* represents the direction of motion of these “massive” particles along the parallelised 3-sphere.

Now, what’s intriguing about this is as follows: (i) the 3-sphere is isotropic and homogeneous, so it will appear isotropic from this frame as long as the observable bodies are all *relatively* motionless through it; (ii) the line-element, as a solution to the vacuum Einstein equation, is actually the cosmological form of the Schwarzschild-de Sitter solution, and, as I’ve proven in my dissertation (pages 170-177), in the cosmic rest-frame, r goes *exactly* like the flat LambdaCDM scale-factor; therefore, (iii) since r is also the coefficient of spatial expansion in this “universe”, according to the above line-element (which describes either spatial contraction to a singularity at r=0 or expansion from the singularity at r=0), the apparent rate of expansion in this apparently isotropic “universe” should be *exactly* as cosmological measurements have constrained the rate of expansion in our Universe to be; but (iv) the expansion rate is determined by the background geometry that’s justified from the point of view of symmetry (and leads to a result that would possibly explain *why* the space-time metric is Lorentzian), and is therefore in no way influenced by the material-content of the Universe, which could therefore conceivably be anything.

It’s also worth noting that the null lines aren’t orthogonal to the cosmic hypersurfaces, so they’re not synchronous in the cosmic rest-frame, which is the wrong assumption that’s always been made in cosmology that I argued against in my previous essay.

I guess that’s everything I have to say pretty much laid out on the table. I hope you could find it interesting, because I don’t mean to bombard you, and I certainly wouldn’t want to waste my time and yours if that’s all it would mean to you. In any case, I hope you see that my objection to the one point in your essay was not made without reason.

Sincere regards,

Daryl

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> 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?

Because every microscopic process is...

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> 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?

Because every microscopic process is time-reversable. (read: time->CPT for precision.) You're talking about macroscopic arrows, which can be traced to low-entropy cosmological boundary conditions, not asymmetric laws. If you ask me what breaks the symmetry of the boundary conditions, I'll answer that we're now asking the same questions, and on some days I'll start speculating if perhaps they're not broken after all. (As for our knowledge about the past, consider what we would know about the future EM field if our eyes were actually atomic-recoil detectors, detecting their own emissions instead of absorptions.)

If there is a cosmic rest frame defined by distant events, then this view is somewhat nonlocal, right from the start. And it would seem to be rather convoluted to keep maintaining this rest frame near black holes. I'll note without comment that your "common sense" examples seem to be posed in the Earth's frame, not this cosmic rest frame.

I'm not sure the rest of your comments can be better addressed than via what I've already said, above and below. (You start getting into this "exists" business above, which we're coming into some agreement on below.)

Finally, I will caution you that I recently learned there is a term "time snob" as applied to A-theorists who believe that only *they* take time seriously, and who believe that B-theorists don't take time seriously. So don't be a time-snob. Or an existence-snob. :-)

Thanks again for all your careful thoughts on the subject, and I hope we will continue to agree to disagree, if only to encourage us both to be as precise and careful as possible.

All the best,

Ken

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Dear Ken,

Thank you so much for your posts. It means an awful lot knowing that you feel you've benefitted from this exchange, as I certainly have. Honestly, I really hope we can continue to agree to disagree, because for me it's all about getting things right, and being precise and careful at every step is such a huge part of that. In that regard, I don't know if it could be more beneficial...

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Dear Ken,

Thank you so much for your posts. It means an awful lot knowing that you feel you've benefitted from this exchange, as I certainly have. Honestly, I really hope we can continue to agree to disagree, because for me it's all about getting things right, and being precise and careful at every step is such a huge part of that. In that regard, I don't know if it could be more beneficial than to have an opponent who truly understands and can appreciate both sides of the argument for what they are.

I have some specific responses to what you wrote. Copying isn't working on my phone, so I'll only quote a few words.

>if there is a cosmic rest frame...

Is a whole 3d space that exists any more non-local than a 4d block that 'exists'? Also, Shelly Goldstein sure gave a persuasive argument last night in favour of Bohmian mechanics.

>And it would seem to be rather convoluted...

Do you have Hawking and Ellis handy? Can you flip to the section on spherically symmetric gravitational collapse? It refers to observers O and O', and there's an E-F diagram... Consider the implicit definition of time that's being used--I.e. the variable they use to refer to time's passage. You know I think there's an objective time variable for the whole universe. It's not the E-F advanced time parameter. In any case, I think we both agree that descriptions of actual temporal passage are inconsistent with einsteinian notions of the relativity of simultaneity, which is what they're implicitly assuming--I.e. they give a dynamical account of temporal passage while assuming a physical definition of simultaneity that's inconsistent with that.

Now look at the statical coordination of de sitter space in the images I posted above. The r coordinate becomes imaginary at the coordinate singularity. It's simply no good after that, for all t. I talked about this with Gordon Belot today, and he thought Felix Klein showed that this was the right way of interpreting the line element. I actually think the Schwarzschild 'event horizon' is also such a coordinate singularity. Remember, I think space-time is globally hyperbolic at a fundamental level.

Now, to get back to the E-F description. Do you have Kip Thorne's black holes and time warps? He recalls a conversation with Lipschitz, where he called Finkelstein's paper a revelation that lifted a fog (or something like that). It was what convinced Wheeler that black holes exist, etc.

Personally, I find all of this convoluted. I think you can only have my sense of existence or your sense of 'existence' and neither admits of the dynamical emergence of black holes in the universe. I think it's entirely inconsistent.

>I'll note without comment...

Ah, but I'm allowed to conduct my thought experiments assuming absolute simultaneity in the Earth's rest-frame due to the principle of relativity. The important thing in assuming a cosmic rest-frame is whether the empirical evidence supports that. Right?

>Finally, I will caution... (whole paragraph)

:) Can I say I feel justified to be just a little snobbish about these things, insofar as I personally think a non-existential definition of "exist" (and all other verbs) is a convoluted and misleading way of speaking, which has led to a mountain of confusion (by the way, a good chunk of my essay is devoted to discussing this)?

Again, thank you so much for discussing all of this. I can't tell you how much it means to have the opportunity to debate with you. It's been very clarifying. By the way, do you think Greene is really thinking non-existentially about the block? It seems to me in the quote I posted below, that he's really emphasizing the block's existence.

Best regards,

Daryl

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Hi Ian,

Thanks for some interesting comments! Yes, there are lots of things not addressed/explained in the essay (contextuality, etc.), so thanks for raising the issues.

I'm very curious about your impression that I'm denying contextuality; it makes me think you're reading quite deeply into this. On one level, my central example is explicitly contextual. In the double-slit...

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Hi Ian,

Thanks for some interesting comments! Yes, there are lots of things not addressed/explained in the essay (contextuality, etc.), so thanks for raising the issues.

I'm very curious about your impression that I'm denying contextuality; it makes me think you're reading quite deeply into this. On one level, my central example is explicitly contextual. In the double-slit experiment, there are entirely different (mutually exclusive!) pasts that correspond to different future measurements; if you choose to measure which slit it goes through, it really went through only one slit. But if you choose to measure the interference pattern, it really went through both slits. Depending on your definition of contextuality, that's most of the game right there. It certainly explicitly violates the assumptions of the Kochen-Specker (KS) theorem, without giving up on realism, via the so-called "retrocausal loophole". (People may not like retrocausality, but it's still a well-established way to violate the premises of the KS-theorem.)

That said, I'm intrigued by your impression, because in another sense I think my story *is* effectively noncontextual, in that one reality literally "pre-exists" before the measurement choice. I just had a very interesting meeting with Matt Leifer where he laid out a more general definition of contextuality that keeps the same basic spirit of the original but allows noncontextuality to be compatible with KS-contextuality in this sort of retrocausal framework. (I hope he writes it up soon!) So I think the story can in principle be KS-contextual but Leifer-noncontextual.

I *think* this is what you're getting at when you imply that I can't both have 1) an all-at-once story about reality, 2) an updating-story about our states of knowledge, and 3) contextuality. You obviously can have 2) in an all-at-once story, just as you can have a computer in a block universe, so 1) and 2) are fine together. I think here you're assuming that 1) and 3) are incompatible, but that's only true for something like Leifer-contextuality, not for KS-contextuality. So long as I have contextuality in the latter (which I explicitly do!), I don't need it in the former.

It's a bit similar to the "non-local" accusation I sometimes get; if you define locality as per Bell in a way that distinguishes the past and the future, my story is technically Bell-nonlocal, but if you define locality (as in GR) based on associating properties to points on the spacetime manifold, along with some topology that restricts action-at-a-distance, then my story becomes "local" again in some meaningful sense (though not, of course, BELL-local). See Matt's comment above for a promising set of research projects along these lines (generalizing locality and contextuality to deal with retrocausality in a meaningful way.)

Your time-symmetry questions will require another long subsequent post, but I will comment about the "frame" in which you're moving with light. This is actually the only frame *without* ordering, because in this frame every event has the same time-coordinate. Instead of a temporal order, everything literally happens at once. (The same is true for the spatial coordinate in the direction of lightspeed travel, with infinite Lorentz contraction.) So instead of a universe parameterized by four dimensions, that "frame" only is parameterized by 2 dimensions, with the other 2 dimensions squashed into the plane. In part because of this, it's not a true frame at all; you can't possibly unboost from such a "frame" back into a non-lightspeed frame and recover what you started with. And because of these problems I'm not sure it's a very good support of the point you're trying to make.

I'm not sure how you equate an order with an arrow. Spatial locations are certainly ordered, and yet have no inherent arrow. I'm just doing the same for time – isn't that how you thought of time when you worked on GR?

I'm in full agreement that the EM field goes through both slits when you measure interference! Are you in agreement that it only goes through one slit when you measure which-slit it went through? As for particles vs. fields, I can imagine fields that go through one slit and other fields that go through both slits. I can imagine particles that go through one slit but *not* particles that go through both slits. So if you think the photon is really going through both slits, why wouldn't you want a field ontology? (Assuming you want a realistic ontology in the first place, that is...)

More on time's arrow soon... Are there any other quantum effects that seem particularly problematic from my perspective? (For the quantum eraser story, you have to go back two essay contests to 'quantum theory without quantization'... But of course that has always seemed retrocausal, so that's sort of easy game.) I want to consider everything up front, before I get too deeply into this, to make sure there aren't any showstoppers that will stop me in my tracks further down the road.

In your response to Armin above, you asked "what was the point" of updating when you had it wrong the first time... I'll assume this is a bit tounge-in-cheek... But of course in *any* hidden-variable theory you have it wrong the first time, by definition; see my states of knowledge that describe the toy model in the essay. They're *explicitly* wrong, in that one *knows* that one doesn't know. Given such a situation, if you did gain new information (about the future setting, or outcome), of *course* you will update your knowledge. If not, "what was the point" in learning anything in the first place? :-)

Now, if you're problem is that I'm not giving an all-at-once account of *consciousness*, well... er... um...

That's not my field. ;-)

Thanks again!

Ken

PS; Daryl, I'm trying to find time to get to your mini-essay in the comments up above... hopefully next week.

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Dear Ken,

You wrote: "I *think* this is what you're getting at when you imply that I can't both have 1) an all-at-once story about reality, 2) an updating-story about our states of knowledge, and 3) contextuality. You obviously can have 2) in an all-at-once story, just as you can have a computer in a block universe, so 1) and 2) are fine together."

I have to strongly disagree with...

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Dear Ken,

You wrote: "I *think* this is what you're getting at when you imply that I can't both have 1) an all-at-once story about reality, 2) an updating-story about our states of knowledge, and 3) contextuality. You obviously can have 2) in an all-at-once story, just as you can have a computer in a block universe, so 1) and 2) are fine together."

I have to strongly disagree with this. In an all-at-once universe, where everything "pre-exists" and nothing "is", you really can't have an updating story about states of knowledge. I think Ian's right about that. The sequencing of your "updating story" still presupposes some sort of temporality. In an all-at-once universe, every instance of knowledge acquisition "pre-exists" as well, all at once. It's a set, not a sequence. You can try to define it as a sequence because of the "spatial" order, but the only way to get from one element to the next and "update" is in time. You can't have an updating sequence if the too-easily-smuggled-in fifth dimension that we know all about is *truly* singular--i.e. if the block doesn't exist, but really "pre-exists" *all-at-once*.

I know you know of the danger of conceiving of the block as an existing thing itself, because you've cautioned a couple of people about thinking that way in the comments here. I personally think it's the greatest and most common mis-conception that occurs when buying, hook, line, and sinker, into Einstein's relativity of simultaneity--which is why I spent so much of my (actual) essay discussing that. A block universe doesn't exist, whether one takes your view or mine on relativity and what constitutes an appropriate definition of "simultaneity".

The true all-at-once block universe can't in any way "update" because there's no temporality left in the description whatsoever--it's a purely mathematical model; a Lorentzian geometry that *isn't*. The alternative is that it's just a map of all the events that occur in reality--i.e. not a representation of reality itself, which is completely impossible to reconcile with reality, because something *is* updating.

The simplest alternative to the completely unrealistic model is to admit, as a first principle, absolute space, and therefore absolute motion and absolute simultaneity. This is completely consistent with the cosmologcal evidence anyway. For some reason, people get all hepped up about calling a cosmic rest-frame a "preferred" frame or a "privileged" frame. As my first post above indicates, this is complete nonsense and utterly ridiculous. The notion that the observers in such a frame are "privileged" supposes that all inertial observers should consider themselves as being "at rest"; that they can't stick out a measuring tape to use, that they conceive as "really moving" and use it to describe events. It's baffling that anyone ever bought the notion that the "man on the street" walking around considers himself to be at rest while the whole world just moves around him;--that two "men on the street" who walk towards each other will both think of themselves as being "at rest" while everything's moving around them, and that there's a day's difference in what they describe as happening "now" in Andromeda.

But that is *exactly* what the initial argument in your essay supposes.

Both men on the street are, however, thinking the same thing about what's at rest and what's moving around--and what they think is at rest is not a bunch of stuff in "space" that's orthogonal to their proper time axes; it's the Earth.

An absolute rest-frame is perfectly natural to understand, even if it's not the rest-frame of our everyday lives (the Earth) AND it's supported by the cosmological evidence--which is all that matters, because relativity theory tells us (i.e. due to the principle of relativity) that the physics has to work regardless of one's frame of reference and their associated preception/conception of "actual" motion; i.e., it tells us that we can do physics under the assumption that the Earth is "at rest".

Daryl

P.S. Thanks for saying you'd respond to my "mini-essay" above. I'm sorry it had to be so long. By the way, the two posts I left the next day are off-topic, and only meant to justify the claim in the first paragraph of my response, becasue I don't think you'd trust the claim as truly justified (sort of in the way that Leibniz saw Clarke's claim of appreciating and agreeing with the principle of sufficient reason as actually not being the actual case). Similarly, what I'm saying in this post is that while you're claiming that your conception of "an all-at-once block universe that updates" is only four-dimensional, and even though you understand that it's too easy to start thinking of it five-dimensionally, I think you do still have a five-dimensional perspective. Maybe you can show me why I'm wrong. I'm ready to listen, and I don't mean this in any disrespectful or insulting way--I just personally think it's impossible to think of otherwise, because the true four-dimensional view really is impossible to reconcile with an updating reality.

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Hello again, Ian,

Okay -- time to tackle this paragraph from your original comment:

> Second, you (again, like many, but definitely not all people) also take 4-D spacetime to literally mean that time and space are equivalent. But if they are perfectly equivalent, why, then do they appear to be different? Specifically, why does time always have the opposite sign of space in any...

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Hello again, Ian,

Okay -- time to tackle this paragraph from your original comment:

> Second, you (again, like many, but definitely not all people) also take 4-D spacetime to literally mean that time and space are equivalent. But if they are perfectly equivalent, why, then do they appear to be different? Specifically, why does time always have the opposite sign of space in any realistic metric and isn't that alone evidence that they are, in fact, *not* the same?

Sure, but it's important to recognize that just because space and time are equivalent in some senses (they're both dimensions, and neither has a inherent direction) doesn't mean that they're equivalent in *all* senses. Yes, the signature of the metric is such that there is always a (highly-)local inertial frame with a time-like axis, but the whole point of GR is that one isn't forced to do physics in such frames. The mere fact that it's *possible* to do physics in other frames (using the same equations!) means that there must be essential features shared between space and time. And those features are topological: ordered, but without preferred direction. (Otherwise space would inherit a preferred direction in such non-inertial local frames, or *any* single global frame.)

>What mechanism produces time-asymmetry without producing an equivalent space-asymmetry?

Ah, now here you're getting into Eddington's idea that there might be some missing physics that we don't know to explain the evident time-asymmetry around us. And if you postulate such physics, sure, then you break CPT-symmetry with new physics. But it's widely understood that this isn't needed, and that the ultimate source of the apparent asymmetry is cosmological (widely, in the sense that it's accurately reported in many popular science books, from Carroll to Penrose to Greene).

To make a long story short, the asymmetry is in the boundary conditions, not the laws. We're closer to a low-entropy initial boundary than we are to any low-entropy final boundary. Therefore, here, there's an evident time-asymmetry. The spatial version of this would be a temperature gradient caused by asymmetric spatial boundary conditions. You don't need asymmetric physical law to get an asymmetry. (Yes, it's a mystery why the Big Bang was such low entropy, but that's an entirely different question.)

> (Recall that there are, in fact, two different senses of time-reversal symmetry.)

I think the relevant and useful sense here is the question: if you took a movie of events and time-reversed it, (or CPT-ed it), would it still describe a possible process?

>Where does the arrow of time come from (because if it doesn't exist, why haven't we reversed the aging process yet)?

Cosmological; see above.

>These are all questions that the 4-D spacetime literalists never seem to be able to satisfactorily answer (I've had this argument with someone at Fermi Lab once and he was unrelenting yet never could answer my points).

I don't know how much patience you have for wading through philosophical arguments on such topics, but you might try this:

http://philsci-archive.pitt.edu/4829/

One upshot is that it's perfectly possible (and easy!) to think in terms of the block universe without thinking that time or change are unreal. They are REAL features of the "4D-static" block. To think that only a dynamic perspective can treat time "properly" is to sell us 4D-blockers short. And if there's some seemingly-important feature of time that vanishes in the block view, it's crucially important to ask yourself why this isn't evidence that such a feature perhaps doesn't objectively exist.

All the best,

Ken

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Maybe consider this, from Einstein's autobiography:

“It is a wide-spread error that the theory of relativity is supposed to have, to a certain extent, first discovered, or at any rate, newly introduced, the four-dimensionality of the physical continuum. This, of course, is not the case. Classical mechanics, too, is based on the four-dimensional continuum of space and time. But in the...

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Maybe consider this, from Einstein's autobiography:

“It is a wide-spread error that the theory of relativity is supposed to have, to a certain extent, first discovered, or at any rate, newly introduced, the four-dimensionality of the physical continuum. This, of course, is not the case. Classical mechanics, too, is based on the four-dimensional continuum of space and time. But in the four-dimensional continuum of classical physics the subspaces with constant time value have an absolute reality, independent of the choice of the reference system. Because of this the four-dimensional continuum falls naturally into a three-dimensional and a one-dimensional (time), so that the four-dimensional point of view does not force itself upon one as *necessary*.”

So relativity forced the 4D point of view on us as necessary because space-time, according to relativity, is a 4D connected metric space, whereas in Newtonian theory it's a disjoint union of two metrics, E^3 and t. Because of this, the dimensionality of the physical continuum according to Newtonian theory wasn't obviously four. Relativity certainly clarified this. But in doing so, it seems for many, who have come to think of all four dimensions as real, to have introduced a fifth dimension, which is not represented at all in the mathematical model, but is nevertheless a part of the interpretation of the mathematical model in much the same way that the fourth dimension of Newtonian mechanics was always there even though some thought only of the three dimensions of space.

But Newtonian mechanics explicitly contains the fourth dimension (time) as a variable, and still people didn't always think of the dimensionality of the physical continuum as being four. So my question is this: is it really at all surprising, given that there's no justification for a fifth dimension which is anyway not formally accounted for anywhere in the theory, to think that people should have a difficult time understanding that their 5D conception of the block *actually is* 5D and not 4? Nevertheless, the "4D-static" conception of the block clearly is five-dimensional when you come to think of it.

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Hi Ian and Daryl,

Ian: Sorry about the heat; I hope it cools off soon! And I'm relieved to see that last point you made; It means we aren't far apart after all. Yes, your "arrows" on your spatial axes are just fine, for time and space both. We have to choose an ordering parameter, I suppose, and given this arbitrary choice it's true that one direction has a parameter that goes up and in...

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Hi Ian and Daryl,

Ian: Sorry about the heat; I hope it cools off soon! And I'm relieved to see that last point you made; It means we aren't far apart after all. Yes, your "arrows" on your spatial axes are just fine, for time and space both. We have to choose an ordering parameter, I suppose, and given this arbitrary choice it's true that one direction has a parameter that goes up and in the other direction the parameter goes down.

All I'm trying to say about the arrow of time is that we shouldn't say anything about it that we shouldn't say about the arrow of space *given known symmetries*. There are no accepted physical theories that allows a process to occur in the +x direction that could not also occur in the -x direction, and the same is true for +t and -t.

By an fundamental "arrow" of time I was talking about processes that are allowed in one direction but disallowed in the other, and if you generalize to CPT symmetry, there are no such accepted processes (depending on the status of objective collapse, which is the crazy exception that proves the rule is a good one!). So I think we can avoid my arrows and yet have your arrows, bringing us into more agreement. (The other type of arrow, that of evident T-asymmetries on the macroscopic scale, are due to T-asymmetric boundary conditions. But again we can have X-asymmetric boundary conditions that produce spatial arrows, so again time and space are still on the same footing in this regard.)

Daryl: Your argument seems to be that the 4D block view of Price or Greene is really a 5D view in disguise. Those are "fightin' words"! :-)

Suppose I have in my possession a DVD, that encodes (discrete) 2D video. The data on this DVD then can be expressed in a (discrete) 3D block, 2 spatial dimensions + 1 time dimension. The block is just as static as the DVD itself. Your argument seems to be that this 3D data is "really 4D", because in order to play it I need to introduce a new dimension. But this is evidently not true. The DVD does not encode a 4D structure. Playing it just projects it back to 2 space + 1 time.

I'm not sure exactly which logical error you're making that convinces you that the 4D block universe needs to be represented in 5D... Perhaps you're thinking of it from the perspective of some 3D structure in the 4D block? (Equivalent to thinking about the DVD from the perspective of a 2D character in the video.) If so, that's a mistake: you need to adopt Price's "view from no-when", outside the block in the same way that we're outside the DVD. Otherwise it's too easy to mix up objective and subjective notions (lots of sub-fallacies follow from this, but adopting the proper perspective solves them all with one fell swoop).

Another possibility is that you are simply too wedded to the growing-block view to think in any other way, and this clearly does require 5D. In that case every event in the universe needs 5 numbers to describe it; 3 to describe where it is, one (t) to describe when it is, and one more (t') to describe when one is discussing that event. (In most growing-block views, if t' is less than t, then the event is given some new property like "undetermined", but if t' is greater than t, then the event is given some different new property like "determined".) In order to keep track of these new types of properties, one needs 5D. Obviously, I don't think these new type of properties are an objective feature of reality, so I don't need a fifth dimension to keep track of them, and can describe everything in 4D. Of course, maybe they are real, in which case the block universe misses out on actual 5D physics. But you still can't argue that the block universe *is* 5D; it's explicitly 4D!

If you don't think you fall into either of the above fallacies, then maybe there's another conceptual framework that I need to be made aware of.

Best,

Ken

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Hi Ken,

What I meant when I was responding to Armin was not-so-much tongue-in-cheek (though I meant no offense) as it was trying to point out that the all-at-once paradigm doesn't make any sense to me when coupled with the concept of "updating." The former implies a singular while the latter implies a plural.

So here's the way I see it. What you could be saying is that we do an...

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Hi Ken,

What I meant when I was responding to Armin was not-so-much tongue-in-cheek (though I meant no offense) as it was trying to point out that the all-at-once paradigm doesn't make any sense to me when coupled with the concept of "updating." The former implies a singular while the latter implies a plural.

So here's the way I see it. What you could be saying is that we do an "all-at-once" analysis of the universe and then as we learn more information about it (both past and future) we continue to do so and thus "update" our information. In this way the underlying universe remains essentially "static" while our knowledge of the universe possesses an arrow of sorts (since we are gaining information about it). Now, I'm not particularly familiar with Matt's notion of contextuality and I'll have to do some digging into it, but from my own notion of contextuality there's a problem: the universe does *not* remain static. In other words, it is not always possible to deduce *past* states from future ones. It would seem that your argument does not address this issue.

Now, regarding the time-asymmetry issue, I disagree with Carroll, Penrose, et. al. Rather, I agree with Eddington who did not, necessarily, postulate new physics to explain this problem (he postulated new physics to address other issues). Eddington viewed the time-asymmetry question essentially entirely in terms of probabilities (actually, that's pretty much how he viewed everything). I really don't think it is that mysterious. The problem with the Carroll, Penrose, et. al. interpretation is that it assumes that the Standard Model is correct which in turn says that CPT-symmetry is inviolable. But there are notable problems with the Standard Model (it fails on a number of counts not the least of which is in relation to gravity). In addition, there is some evidence that CPT-symmetry is no inviolable. Recent studies of neutrinos suggest that it is possible that neutrinos and anti-neutrinos have slightly different masses. If so, this would be evidence of CPT-symmetry violation. All of this is to say that I think the cosmological case for the arrow of time is built upon some shaky ground (and I didn't even mention inflation). Heck, Sean Carroll himself addressed some of these issues at the last FQXi conference.

Now, to the c-frame issue. Obviously you are correct in saying the the c-frame itself is unattainable and, perhaps, unphysical in some regards (though clearly it is at least partly physical since light exists!). But the bigger point is that there *is* an objective ontology to relativistic frames. Otherwise, the Twin Paradox would really be a paradox. But it's not. The space-faring twin really is older --- they both agree on that when they meet again. Likewise, relativistic muons created in the upper atmosphere really do take longer to decay. And as two frames get closer and closer to c, they get more and more in agreement. That's the objectivity that I'm talking about that we all tend to ignore. If reality were completely subjective (relative), then the twins would each think the other was older.

This all goes back to that deep issue of time. While the laws of physics (mostly) seem to be time-symmetric, there's clearly a problem since we never see them run in reverse. If this is a purely cosmological problem, why is it that we never see, say, sub-atomic particles "un-decay?" Time is simply different. Relativity provides us with a convenient framework within which to treat time in a similar manner as space, but even *it* has a preferential arrow built into it --- allowing for complete time-symmetry in relativity produces logically absurd results. This is precisely because time is different in the metric --- it's sign is always opposite that of space. Incidentally, Lev Okun wrote an article about this very point a number of years ago but the cosmologists and many high-energy physicists still seem to cling to this notion that space and time are the same (and thus mass and energy also are the same), that the universe is really symmetric, that the Standard Model is correct, and that time-asymmetry is just an illusion perpetrated by cosmological expansion.

I hope that answers some of the points you have raised. If I missed responding to something, let me know.

Cheers,

Ian

P.S. It is thankfully much cooler today...

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Hi Ian,

Yes, I think we're just about on the same page; at least I think we agree where we disagree.

> What you could be saying is that we do an "all-at-once" analysis of the universe and then as we learn more information about it (both past and future) we continue to do so and thus "update" our information. In this way the underlying universe remains essentially "static" while...

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Hi Ian,

Yes, I think we're just about on the same page; at least I think we agree where we disagree.

> What you could be saying is that we do an "all-at-once" analysis of the universe and then as we learn more information about it (both past and future) we continue to do so and thus "update" our information. In this way the underlying universe remains essentially "static" while our knowledge of the universe possesses an arrow of sorts (since we are gaining information about it).

Yes! That's it precisely.

> Now, I'm not particularly familiar with Matt's notion of contextuality and I'll have to do some digging into it,

You'll have to email him directly... Nothing's written up yet, I don't think.

> but from my own notion of contextuality there's a problem: the universe does *not* remain static. In other words, it is not always possible to deduce *past* states from future ones. It would seem that your argument does not address this issue.

Alas, I guess I didn't write a good essay, because this was the #1 goal I was trying to accomplish, above all else.

I would hope though, that if I *was* able to successfully show that learning about a measurement setting would cause one to update the past in different ways for different settings (as I tried to do in my various examples), then one would have the *appearance* of contextuality, even if the past really was determined in some all-at-once sense.

> Now, regarding the time-asymmetry issue, I disagree with Carroll, Penrose, et. al. Rather, I agree with Eddington...

Yes, I knew your position of course... But it's important to state this outright when discussing time-symmetry; just because the asymmetries seem like common sense doesn't mean they're part of known physics. And while Eddington's challenge is possibly do-able, the difficulty is rather steep; not only does that viewpoint require that one show the current Carroll/Penrose/Greene/Price story is insufficient to explain observations, but it requires one to posit new physics that is (as far as I know) hypothetical and vague. So Eddington may have common sense on his side, but time-symmetry has pretty much all of modern theoretical physics on its side.

> If reality were completely subjective (relative), then the twins would each think the other was older.

But without acceleration, it *is* symmetrical; they *both* think the other is younger as they're moving apart. Until there is an acceleration and they come back to the same point (or at least to within a small-enough invariant spacetime interval), there is no objective fact of the matter as to which twin is really older.

> If this is a purely cosmological problem, why is it that we never see, say, sub-atomic particles "un-decay?"

The same logic as breaking-wineglasses applies here as well. Every process has its reverse. If there's one input and two outputs, the reverse simply requires a bit more coordination to bring two inputs together at the right place and time (as we can only control the inputs). Three-output decays, and reversing it gets quite tricky indeed. There's also the issue that decays which produce net energy require net input energy to occur in reverse; still do-able, but not nearly as likely (at least not without a low-entropy final boundary condition).

I guess I don't understand how the different sign in the metric implies some new *asymmetry* in your mind. Sure, space and time are a bit different, but... *that* different? One is symmetric and one is not? Surely such an asymmetry would show up in Mawxell's equations or Einstein's equation? What about my earlier argument that in different reference frames this would imply that *space* inherits the time-asymmetry?

Maybe we should move this to email, if you want... Let me know!

Ken

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Hi Ken and Ian,

Thanks for keeping this discussion going. And Ian, I'm glad to see that I wasn't mis-representing your point of view, and that we're in agreement.

First of all, I just want to ask you guys once more to look at the post I left above, on Jul. 10, 2013 @ 23:39 GMT. In relation to Ken's point about the arrow of time--i.e.

"All I'm trying to say about the arrow of...

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Hi Ken and Ian,

Thanks for keeping this discussion going. And Ian, I'm glad to see that I wasn't mis-representing your point of view, and that we're in agreement.

First of all, I just want to ask you guys once more to look at the post I left above, on Jul. 10, 2013 @ 23:39 GMT. In relation to Ken's point about the arrow of time--i.e.

"All I'm trying to say about the arrow of time is that we shouldn't say anything about it that we shouldn't say about the arrow of space *given known symmetries*. There are no accepted physical theories that allows a process to occur in the +x direction that could not also occur in the -x direction, and the same is true for +t and -t."

--that derivation presents a clear case in which he's completely, unmistakably right.

Now, in response to Ken's comments for me: thank you very much for posting them, and taking up the challenge in the spirit that it's intended--i.e., seriously, and in good faith. In that sense, "them were fightin' words" indeed. I'm not able to respond properly right now, because I'm just heading out to a metaphysics of time workshop in (breathtakingly beautiful) Lausanne, but I wanted to let you know that I have seen your post, and I'm really looking forward to keeping up the discussion.

Two things I will say: I'm very glad to see that we're in full agreement on the dimensionality of the growing block model--it's unmistakably 5D; and I agree that the DVD contains 3D data. On the latter point, my argument isn't that the data are "really 4D", any more than de Sitter space (see the post I mentioned) is "really 5D". I'll do a better job of explaining myself later, now that I have your argument to work with. Indeed, I do think the right conceptual framework has been missed in philosophy of time. Today, I'm going to look to either be shown that it hasn't, or to see which points in particular I need to address in order to clarify.

Best regards,

Daryl

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Hi Ken,

Please excuse me if I don't address points in the exchange you've had with Ian. I want to be as brief as possible in response to what you wrote to me. I do, however, need to provide some context for my criticism of your view.

My greater claim is that all accounts of any sense of temporal passage that I've read in my physicist's survey of the philosophy literature are...

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Hi Ken,

Please excuse me if I don't address points in the exchange you've had with Ian. I want to be as brief as possible in response to what you wrote to me. I do, however, need to provide some context for my criticism of your view.

My greater claim is that all accounts of any sense of temporal passage that I've read in my physicist's survey of the philosophy literature are abominations. They're no better (and maybe even worse because they're so explicitly wrong) than the physicist's foggy conception of temporal passage. All is a mess. And I think "subjective updating" falls right into this catagory. (Strong claim--and fightin' words indeed--so please allow me to explain. The upshot will be that you'll either see an error in a view that you support, that you weren't aware of before, or, by understanding my point, you'll be able to explain to me how subjective updating doesn't fall into this category).

More specifically, I claim that all accounts (that I've read or heard) of the presentist viewpoint, whether in favour or against it, make a very specific (and often explicit) error, which has confused the issue to the point that I do feel justified in calling these accounts "abominations". Because of this error, many--and then in light of relativity, many more--have committed what I'll call the Abortionist Fallacy (meant in the more general sense of "a failure to develop to completion or maturity") of arguing *from those erroneous descriptions* that presentism is false. In fact, the usual claim is that temporal passage is not as we commonly think of it--the most famous example being perhaps McTaggart's argument for the unreality of time.

Before I get to my main point, which is very simple, please let me explain what I mean by "Abortionist Fallacy". Consider the following (which I claim to be true): The purpose, or grand aim, of thought experiments, should be to make perfect sense of things that are not intuitively obvious to begin with (cf. Galileo's boat experiment). If this statement is true, then due to his prior definition of simultaneity, Einstein committed the Abortionist Fallacy when conducting his special relativistic thought experiments, from which he inferred the relativity of simultaneity, and therefore simply aborted the sensible notion of objective passage (cf. my first post above).

So, now: what's the one thing that's wrong with all attempts to describe temporal passage? It's simply the all-too-common idea that events (the things that happen, occur, take place, etc., which make up space-time) *exist*.

The error occurs whenever verbs are used to describe events. This is because all verbs--and particularly the copular verb 'is', 'will be', 'was', etc.--smuggle a sense of temporal passage into the mix because every last one of them has existential meaning. People are already dead wrong when they say, for instance, "look at this worldline, with a few points (t_1, t_2, t_3, etc.) labelled on it. The fact of the matter, in the presentist view, is that *at* t_1, only t_1 exists; at t_2, only t_2 exists, and t_1 no longer exists. The reductionist, or minimalist viewpoint--and what follows from McTaggart's argument--is that all t exists; i.e. the object represented by the worldline has temporal parts; etc."

I'm claiming that "exists" in the first and second sentence, as well as "has" in the second sentence, are completely wrong words to use, which totally confuse the meaning.

People might refer to events at certain times as being "real" or "Real", in a sweeping spotlight sort of way (the past is "real" in some sense, because I can talk about it, etc.). But the thing that actually matters isn't the big "R"/little "r" distinction. The thing that actually matters is the use of "being", which carries existential meaning.

The reason is simple: in a Newtonian conception of reality (my previous essay shows that relativity presents no real problem either, as long as "simultaneous" isn't mis-defined a la Einstein), how many dimensions are there in the physical description of "this chair exists here?" Since the chair's a 3D object, I hope your answer is "4D" (otherwise we've got an even bigger issue; cf. quote from Einstein's autobiography, above). Similarly, when we say "t_1 exists" or "all t exists" or "an object has temporal parts", or "an observer's subjective knowledge updates", we smuggle in a further dimension.

Just as "the existence of a 3D block" requires a fourth dimension in the physical description (even if the block doesn't change, still "while changing it exists"--Heraclitus), or the "existence" of an event needs 1D in order for the event to be described as something that exists, so the idea of events in 4D space-time as "existing" requires a 5D description. In essence, when we say (or think) "Jan 10, 1982, 1:26:32 exists", we think of the 3D world on Jan 10, 1982, at 1:26:32, as *existing* (i.e., when we say "is", "was", etc., we impose another dimension in the conception of that *instant*). The dimension in which events are described to "exist" is a hyper-time dimension, above and beyond the time-dimension describing the 3D universe's existence.

No one in their right mind has every supported this view outright (except maybe science fiction writers and growing block supporters like Ellis--although there's an argument that he's therefore perhaps *not* in his right mind), yet what I'm claiming is that when people assume a "third person"-view of eternity, a "view from no-when", a "God's eye-view", there is an overwhelming tendency to think that "God", the "third person", *exists*. Then the confusion sets in. Greene very explicitly describes the frozen block as something that exists, for example, patently assuming this hyper-time-dimension.

Now, how does this ubiquitous error factor into our debate? Basically, when you think that something subjectively updates their knowledge of the block, I'm saying you can't but assume such a hyper-time dimension. If everything really is singularly on par, you simply can't get this updating of knowledge within the block, any more than a fish can swim a distance through water, or electricity can flow through a wire, in an *instant*. In the sense of this hyper-time, the entire block has to be instantaneous, and therefore perceptions of it can't crawl along it and update.

When you describe reality as all of eternity, all four dimensions of the physical description of events that occur in reality, *at-once*, assuming a "God's eye view" of all the events that occur, you simply can't turn around and claim that your "God" exists *without adding the metaphysical structure associated with that*.

Parsimony is supposed to favour the block universe view of reality, which doesn't assume the extra structure of "3D space that exists"--i.e. a foliation--but what I'm saying is that "blockers" really don't have the more parsimoneous theory anyway. In fact, the view that all of space-time exists (Greene's view, etc.) assumes the same amount of structure in the sense that it assumes that something (of any dimension) *exists*; but because the thing it assumes exists actually has one higher dimension, it actually assumes *way more* structure. That's argument 1 against the "Humean minimalist" view--i.e., it's not actually minimalist at all.

Argument 2 is that the structure in the "anti-reductionist" view that "minimalists" want to do away with--viz. the foliation of space-time--is actually supported by cosmology anyway, so it's really a non-issue in the first place, if you take empirical evidence to be the supreme arbiter.

That's pretty much my argument in a nutshell. I don't think I'm committing any of the errors that you mention, but simply saying that I don't think you can get what you want to get without committing them yourself. I'm ready to listen, though, if you think you can get out of argument 1. Then, even still, I think I win by argument 2, since empirical evidence is supposed to trump all. In order to argue against me there, you'll have to overturn a whole area of physics--but still, I am willing (eager, in fact) to listen.

Best,

Daryl

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Dear Ken,

This is miles better!

First of all, I'm glad that you don't think acceleration resolves the twins paradox. But I do wonder why you would use 'acceleration' rather than saying something like 'the boosted twin', especially since acceleration has been wrongly thought by many to resolve the paradox.

But now to important stuff. I was talking with someone yesterday about...

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Dear Ken,

This is miles better!

First of all, I'm glad that you don't think acceleration resolves the twins paradox. But I do wonder why you would use 'acceleration' rather than saying something like 'the boosted twin', especially since acceleration has been wrongly thought by many to resolve the paradox.

But now to important stuff. I was talking with someone yesterday about my concerns with using verbs to describe space-time points, events, all of space-time, etc. What I learned was that a B-theorist uses the word "exist" non-existentially. Personally, I consider it nonsense to use language that doesn't actually apply to things by redefining words in such a convoluted way. Moreover, I think it leads to a lot of confusion, especially because it's so hard to not fall into the trap of thinking of these non-existential things that 'exist' as *existing*. (As an example, when you read what you wrote, don't you find it hard to not think of a *static* block? I think it's really hard to think of the block as a temporally singular, non-existential thing. I honestly can't make sense of "a thing that doesn't exist." Then I also have a tough time not thinking of existence *and* motion along the block when you write "updating is performed by a 3D agent over time"). And finally, I think if what's being proposed is so nonsensical that it can't even be properly described because the language comes to mean something else entirely, that's a pretty good indicator that it really is just nonsense.

So what's my point: I do understand what you've written here, insofar as every time you say "I'm" you're really speaking non-existentially about what you "are". I'm actually pretty okay with the description until the last paragraph, because I don't think you're being too cavalier with your use of non-existential verbs until that point. But in the last paragraph, I think you're getting a bit carried away when you use three in a row ("updating is performed") in a way that tends to give the impression that you're not only talking of the block as something that 'exists' but doesn't really exist, but also of a sequence of updates that move up the world line.

Alternatively, you could say (with the use of single quotation marks to indicate non-existential use of verbs) "The whole 4D block 'exists'. My world-line 'exists' in it. At each point along my world-line, I 'have' some knowledge of the entire 4D block; i.e., as I may 'know' something about past, present, and future events at each point of my world-line. At 'later' times, my knowledge of the block is more complete than at 'earlier' times." (I know "earlier" and "later" are adjectives, but I think it's good to still use the single quotes there). Maybe you could sum that up by saying, "one's incomplete knowledge of the 4D block 'is' a monotonically increasing function of one's worldline, where at each point along the worldline, that incomplete knowledge 'is' 4D".

I think we're now on the same wavelength about what you want to describe, and I think the description of 'subjective updating', if stated carefully in this way, making sure to note the non-existential meaning of 'exist', etc., is about the best you can do. But then I simply have to wonder why you want it to be that way anyway. One reason, from our discussion above, might be that you don't like quantum non-locality. But I have a tough time seeing how a fear of existence in a world in which magic happens, can lead one to want to 'live' in a world where one doesn't actually *live* at all; where one doesn't actually *exist*. I think it's better to try to sort out our problems than just give in to unrealistic implications--and I honestly think a realistic version of quantum theory, or really quantum gravity, will come about after we've taken the more immediately necessary step of properly interpreting and understanding relativity.

I guess that brings the discussion back to the one we were having above. Would it be at all possible to take that up again now? I think I've shown an ability to really understand this position that I think needs to be rejected, being very open to thoughtful consideration of its meaning and implications. I think you'll find if you do read what I wrote there, that I've given the same thoughtful consideration in coming to my own position on the matter.

One more thing I wanted to say before I quit, in relation to the point you made early on about symmetry, is this: last night at the summer school on physics and philosophy of time that I'm attending, Stephan Hartmann gave a talk about the No-Alternatives Argument, which basically runs as, "Physicists have identified certain constraints, C, and have a set of data, D, that they want to use to construct a quantum gravity. To date, only string theory seems to meet all of C and D. Given the amount of effort that's been put into the construction of an alternative, we can be optimistic to some extent that there reall are no alternatives." The "some extent" is evaluated using Bayesian analysis.

My objection to this entire line of reasoning comes in at the very beginning. It's true that having identified C, the usual goal is to try to construct a theory that adds C explicitly into the framework. But we know of cases in history, where ideas have been rejected for a long time just because they were naively thought to be at-odds with some constraint or other that people thought necessary to hold onto. For instance, given a butterfly's ability to easily flutter about, or even the fact that the Earth retains its atmosphere, people felt quite strongly for a long time that the Earth has to be fixed at the centre of the solar system, and this constraint was violently held onto (e.g., Bruno). But then Galileo showed (with a simple thought experiment that didn't even need to be conducted) that butterflies can flutter around just as well in the cabin of a ship, as they can when it's back at harbour, and it was realised that this constraint wasn't necessary to the realisation of the data, and the Solar System could, for all that constraint had mattered, be heliocentric. In light of what I've written about symmetry above, I would like you to consider that perhaps the standard symmetry constraint of modern physics maybe is being made too explicitly, for all the observed symmetries that must be reconciled.

Cheers,

Daryl

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Hi Daryl,

I'm glad we're coming to some agreement... And yes, it's not exactly fair to deny the use of the verb "to be" to B-theorists by insisting on an A-theory definition! (There's a "Be-theorist" joke in there somewhere...) I'll encourage you go re-read some of that piece by Price with this fact in mind.

> As an example, when you read what you wrote, don't you find it hard...

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Hi Daryl,

I'm glad we're coming to some agreement... And yes, it's not exactly fair to deny the use of the verb "to be" to B-theorists by insisting on an A-theory definition! (There's a "Be-theorist" joke in there somewhere...) I'll encourage you go re-read some of that piece by Price with this fact in mind.

> As an example, when you read what you wrote, don't you find it hard to not think of a *static* block? I think it's really hard to think of the block as a temporally singular, non-existential thing. I honestly can't make sense of "a thing that doesn't exist." Then I also have a tough time not thinking of existence *and* motion along the block when you write "updating is performed by a 3D agent over time"

I *try* to think of a static block, because my innate-but-wrong time intuitions are too strong to fight any other way (you'll best be able to fight your "motion" intuitions in exactly this manner). The DVD example is useful, but perhaps not going to help you. Maybe the idea of a 4D block in the mind of a 3D person may help, although this 4D block isn't real in the same way that the actual universe is. What it really comes down to is that you don't *need* to think of the block as temporally singular; after all, it's not, any more than a full description of the universe written on a blackboard is spatially singular. (One needs different language to talk about the representation vs. the actual; perhaps where we're getting into all of our linguistic problems.)

> But then I simply have to wonder why you want it to be that way anyway.

What I "want" has nothing to do with it. That's what relativity tells us. Sure, I can go down your road of denying certain features of relativity, but "why do you want it to be that way anyway?" :-)

Your last point about starting from bad premises is right on target with me -- after all, that was the topic of last year's contest, and I effectively wrote about this very issue. But this point is *only* salient if most people are indeed making the wrong assumption. So when I look around at quantum physics and see that 99.9% percent of theories are assuming a dynamical framework, and 0.01% are analyzing histories 'all at once', I don't see myself on the side of a widespread but wrong assumption. Physicists implicitly break time-symmetry in their ontology all the time, often without even realizing it. I happen to think it's the common-sense, A-theory side of things that's the impediment to progress, precisely because it's far too easy to fall into that style of reasoning without thinking it through carefully.

Okay, I'm running out of time (ha) before I'm off to a conference, but I'll head back up to that first comment on simultaneity and see if I can say anything useful.

Best,

Ken

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