Hi Matt,

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

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

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

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

Cheers,

Ken

Dear Ken,

Have I got a cherry to pick with you ;)

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

All the best,

Daryl

Dear Ken,

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

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

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

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

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

concept, everything is well-ordered.

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

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

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

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

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

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

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

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

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

Hopefully I touched some of your points.

More later,

All the best

Torsten

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

Dimensional reduction in the sky

Your insights and opinions are of course welcome.

All the Best,

Jonathan

Dear Ken,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thanks for your time,

Daryl

Dear Ken,

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

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

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

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

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

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

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

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

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

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

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

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

(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 [math]ds^2=-A(r,t)dr^2+B(r,t)dt^2+r^2d\Omega^2,[/math] 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

Ken,

I very much enjoyed reading your thoughtful essay. The "Independence Fallacy" can also be examined in terms of quantum information theory (see my essay "A Complex Conjugate Bit and It"). Your all-at-once analysis is supported by Aharonov, Popescu and Tollaksen's time-symmetric formulation of quantum mechanics (Physics Today, November 2010).

You advocate a path integral in standard 4D spacetime approach, rather than "making almost everything interdependent in some strange [QM] configuration space". The problem is that while a static 4D block appears to remove subjectivity, as a God's eye view it is still based on forms created in the mind. The model is epistemic.

On the other hand, if a quantum configuration space is the ontic basis of being, our 4D spacetime collapses to a combinatorial group of symmetries with no unique solution. Perhaps dynamical time evolution is just the difference between the conditional entropy of the local observer (her ignorance) and reciprocal quantum entanglement entropy (the totality of all that is possible).

Best wishes,

Richard Shand

    Hi Stuart,

    Just because I'm advocating an all-at-once viewpoint doesn't mean I think there is a "formal system that can describe the complete configuration of the universe". In fact, my latest research is based on a framework that explicitly denies that one can deduce the exact configuration of any space-time region, even given the complete boundary conditions. (This is not to say there isn't one particular configuration, it's just that it's not knowable from only the external boundaries.)

    As for why the rules that govern our universe happen to be the way they are, that's a good question, but one that's tough to address until we have the correct rules at our disposal! At the end of the day I imagine it will look quite simple and possibly unique, but that day might not happen in our lifetimes...

    Best,

    Ken

    Hi Akinbo,

    I'm afraid you still probably won't like my (materialistic) answers to your questions... but here goes.

    1) Yes, Yes.

    2) Would it have a "beginning"? If you mean a temporal beginning, then I suppose so (although there are interesting cosmologies in which it would not; see Sean Gryb's excellent essay.) But I can tell by your later questions that you also mean a *causal* beginning, that determines the rest of the universe, and this I reject in my all-at-once viewpoint.

    3) If it did have a temporal beginning, associated with some cosmological boundary condition at the Big Bang, then while that boundary condition would certainly be an "IT", it would not need to result from anything else. Cosmological boundaries are like ultimate causes. There might be some rule that told us what that boundary might look like, but definitely not a causal rule in that it would have to evolve from something else. The all-at-once view helps with this perspective; if you're in a dynamical view, it may be hard to imagine a free-standing boundary constraint that doesn't evolve from anything else.

    4) see 3.

    Best,

    Ken

    Hi Lawrence,

    As for whether I'm arguing for local hidden variables depends on exactly what is meant by "local" (see Matt Leifer's comment above). But I certainly do think there's a nice all-at-once definition of locality, as in GR; in that case it's possible to have a "local" ontology and still have crazy features like closed-timelike curves. My hidden variables also have the feature that they are all associated with points on spacetime, and correlations between points can only be enforced by continuous pathways.

    I agree with your excellent point about how we're biased to see things as dynamical, but disagree there is necessarily a dynamical version of the all-at-once story I'm trying to tell. For example, the path integral only converges onto the Euler-Lagrange equations in the hbar->0 limit; is there a finite h-bar dynamical version? Well, arguably yes, if all you care about is probabilities, but I'm restricting the path integral further such that there is no dynamical version at all.

    For more on this you might review my previous essay, the Universe is Not a Computer.

    Cheers,

    Ken

    Hi Mikalai,

    I enjoyed most of that last link you posted; excellent points!

    Where I think we differ is that I don't assign any particular foliation as fundamental; time and space are all blended together in an all-at-once viewpoint, so Hamiltonian formulations are not fundamental either (or indeed, even always possible). So the energy x time = action is a bit of a red herring in my book; this is no different from momentum x length = action, and any approach that doesn't treat both of these on the same footing is probably treating time as special in a way that I don't think is justified... at least not in an all-at-once perspective!

    Best,

    Ken

    Hi Jonathan,

    I have no real problems with (say) a 5D cosmology, so long as it's analyzed "all-at-once". I don't think it's even coherent to talk about the (time)-evolution of a 4D universe into a 5D universe, because the meta-time that this evolution is happening in is supposed to be part of both the 4D and 5D universe. Maybe this is what you mean by saying a block view is impossible, but I'd go so far as to say *any* view is impossible, unless you assign the meta-time as a sixth dimension (in which case I'd advocate for an all-at-once 6D view).

    Of course, there may be surfaces in an all-at-once 5D cosmology that are effectively the 4D universe that we experience, but that doesn't mean one can't take a 5D all-at-once view to describe this as well (which would include a 4D all-at-once view as a subset).

    Best,

    Ken

    Hi Richard,

    Thanks for the kind comments. Yes, there are some connections with quantum information theory, although I think the all-at-once view is more difficult to introduce there for a variety of reasons. And there are also connections with Aharonov's two-state formalism, but important differences as well. An all-at-once view of that proposal looks quite strange if you consider A) multiple particles, or B) how things compare on both sides of strong measurements.

    I'm not exactly sure what the problem is concerning the mind. While my view is effectively "psi-epistemic" as applied to the standard quantum story, I'm a firm realist about the universe actually being filled with one particular 4D field history. Sure, we humans came up with the idea of physical fields, but that doesn't mean that they can't comprise a realistic ontology.

    Best,

    Ken

    Dear Ken, what an excellent essay, I enjoyed reading it tremendously. Questions: is up is up or down is down? Is down is up and up is down? The Americans tell the Ausies correctly that you are the down-under people, whereas the Ausies retort correcyly we are the up-upper people and you the Americans are the down-under people. Both turn out to be correct from their respective frame of references as the center of their universe. Now back to this essay main point that time is a persistent illusion or is time a persistent real and our perception of no time is a persistent illusion of the illusion of time? Again both are literally correct from their respective frame of reference, however, KQID describes time is NOW in the block Multiverse every absolute digital time T≤ 10^-1000seconds as the Newtonian absolute time. Time is in a perfect symmetry that anything can go backward or forward at will. Every T, time-past-present-future collapse into the NOW and everything is rebooted, refreshed and renewed from Tn to Tn+1 to Tn+2 and so on. All the bugs are fixed and new version of the software Qbit is released Tn+x. No crash. This explains why computer like Multiverse does not crash. KQID: all things are one Qbit computed inside one singularity Qbit Multiverse. This is our block Multiverse all-at-once is a slice of all Minkowski events jump all-at-once according to Feynman's sum-over-histories to the next one and to the next one as you said like a movie running at ≥ 10^1000 frames/s, just like a movie of 120 minutes or two hours or 1/12th of day; hence we have Newtonian duration. This objective slice of our 3D Multiverse, not subjective slice as you pointed out is not possible. We do have as I called it KQID relativity ψτ(iLx,y,z, Lm) with its flexible c-timerod that gives length its length. When the c-timerod contracts its length contracts. At velocity at 0.6c, the time contracts KQID τ=(1-v^2/c^2)t=o.8t and the length = 0.8L. In short, KQID argues our Existence both absolute digital all-at-once: time disappears and relative Multiverse: time reemerges. This way KQID brings back our sanity, we can normally view the world as it is or as Ken Wharton and Leo KoGuan see the world from different lenses. As you wrote "the W's are now microhistories, span- ning 4D instead of 3D." Yes, KQID views micro histories are block all-at-once Multiverse moving along Lm Multiverse time line in the zeroth dimension as the 4thD that brings back time as we normally use time. Ken, your is an erudite essay encompasses everything. I read it at least three times and I need to read your article "The Universe is not a Computer" (arXiv:1211.7081). Excellent rating and please review and rate my essay Child of Qbit in time. Thanks, Leo KoGuan

      Dear Ken,

      I found your essay very well-argued and I was especially impressed how you tailored your conclusion to the theme of the contest, i.e. that"Instead of winning the argument by default, then, It from Bit proponents now need to argue that it's better to give up reality."

      I have two questions:

      1. How is your framework different from Bell's "Superdeterminism"?

      It seems that if one wanted to express Superdeterminism in terms of 4-dimensional space-time one would arrive essentially at your way of looking at things. If that is true, then you are of course correct that your framework overcomes most of the objections to deterministic explanations for quantum phenomena. Is that what you are driving towards? In some of your previous works, I remember you mentioning that one should perhaps not be so quick to give up retrocausality, and if your present work is meant to be along the same lines, it seems to me that there really is no retrocausality in it because there is only one effect (The coming into existence of spacetime "as a whole"), whereas retrocausality requires at least two effects in a causal relation.

      2. Can one really sensibly attribute a definite path to photons?

      Of course one can use an affine parameter to substitute for the proper time in those contexts where one needs to give an expression for the time evolution of the photon as it "moves" in space, but as I understand it, the parameter is completely arbitrary. It seems to me that fixing the path of a photon removes the arbitrariness of the affine parameter and thereby transforms it into something as "real" as proper time itself. But if the parameter has a reality of its own, then it must also define relationships to the analogous affine parameters associated with all other objects. In effect, it seems to me that fixing the path of a photon then introduces a whole new parallel layer of a web of relations analogous to the web of relations between the worldlines of objects but now in terms of the integrals of the affine parameters (let me call these 'affine parameter worldlines' for lack of a better term).

      Although one might look at it as metaphysical baggage, I don't think this is necessarily a bad thing because it may permit your framework to be experimentally tested. One would have to be able to deduce how the attribution of a fixed path to a photon or a set of photon(s) in some situation fixes the 'affine parameter worldlines' and see whether one can set up an experiment where one might encounter effects beyond those predicted by quantum mechanics based on the requirement that 1) these be consistent with one another and 2) they be consistent with the 'affine worldline parameters' of other objects, such as the emitters and absorbers.

      I'm not sure how I would go about this mathematically, but otherwise the prospects for testing your framework experimentally do not seem very good. And, as you know, this a pretty much indispensable before your work can be accepted widely as a physical, as opposed to metaphysical, framework.

      In any event, I enjoyed reading your work and wish you all the best,

      Armin

        Hello,

        If I may be allowed to inject myself into this discussion: I think that without further specifications, the 'meta-time' in 5D cannot be part of the 4D universe because when transformed to a frame in which it is a proper time, it is constituted of one more quantity than spacetime proper times (i.e. 4+1 vs. 3+1).

        In order for it to play any role in 4D there needs to exist a map which defines the relation between events in 4D and 5D. In Euclidean space, this is obviously not a problem because such a map is nothing other than an embedding, by which one may view 4D as a surface in 5D. I don't know whether such a map exists or can even be defined for the Lorentzian metric.

        If someone knows the answer to this, I would greatly appreciate it as it plays a crucial role in the framework that I am working on.

        All the best,

        Armin

        Dear Ken,

        It occurred to me that the experimental approach that I suggested to you might more likely work better the other way around from the way I described above, namely, that the real affine parameter and the web of affine parameter worldlines may introduce additional constraints not present in standard QM which forecloses certain results (or configurations of results) in your framework that are allowed under standard QM. Of course, to be sure, one needs to do the math, but I hope that you nonetheless found my suggestion useful.

        Armin