• Questioning the Foundations Essay Contest (2012)

  • There May Be a False Assumption in the Minkowskian Geometry That Led to Block Time, Which Disagrees With Quantum Theory on Whether the Future Already Exists - A Short Look Through the Clues About Tim

Dear Jonathan,

I think your essay is right on target, and it rates very high in my opinion. Let me make a few remarks. First, let me say that I don't believe the manifold structure of spacetime persists to arbitrarily small scales, but this in of itself is hardly a radical position anymore.

1. I agree that one ought not to begin with mathematical models of time (or anything else!), but ought to begin with physical concepts, and then use whatever mathematics is necessary to get the job done. This may lead to mathematics that is "less convenient," but so be it! Choosing mathematically convenient but physically dubious models has caused too many problems in physics to even begin to list.

2. An excellent point you make: "Often more than one conceptual picture is described by similar mathematics." Likewise, there is often more than one choice of mathematical formalism to use in attempting to make a physical idea precise. Often the differences among these conceptual pictures or formalisms involve physical issues at the periphery of what is being considered when the theory is first developed. Only later are the distinctions recognized as important, and by this time it has often become "common knowledge" that a particular marriage of concept and formalism is the "only way to go."

3. You say "And then other physical laws, which also depend on there being a timeline (or rather, many), and behind them fundamental principles like cause and effect, which also depend on a timeline." Now, this is something I have thought about a great deal. Do cause and effect depend on a timeline, or does time depend on cause and effect? Or are they two ways of talking about the same thing?

4. You say, "Within the light cone, where events are in range of each other, there's a clearer sequence - one can say an event happens before another if it can influence it by getting a light signal there in time. This short range way of relating events has meaning, based on causality. But it doesn't mean there are long range time links across space, as in Minkowski spacetime." This, in my opinion, is the crucial point. The physical order is the causal order, and the "time-orders" given by choices of reference frame are not physical. They represent extra, noncanonical information added for mathematical convenience and should be given no weight when discussing issues of existence.

5. Continuing from 4, I believe another aspect of this false assumption is the "symmetry interpretation of covariance." Covariance in special relativity is, conceptually speaking, the statement that different inertial frames are "equally valid," and the usual way of making this precise is to invoke the symmetry group of Minkowski space (the Poincare group). I do not think this is the best interpretation, especially when one generalizes the discussion from special relativity to general relativity and then to the fundamental structure of "spacetime." I think a better interpretation is in terms of order theory. The causal order on Minkowski space is defined in terms of the light cones, and an event E is simply unrelated to events outside its light cone in terms of the causal order. Imposing a time order on Minkowski space refines the causal order by artificially relating E to most of the events outside its light cone (all those outside the same "spatial section.") Different frames of reference, then, are different refinements of the causal order. However, it is obvious that such a refinement carries no canonical physical meaning. The physical information is contained in the causal order, which does not imply a block universe.

6. These topics are a major focus of my essay, On the Foundational Assumptions of Modern Physics. Since you have evidently thought about these issues deeply, I would be grateful for any further thoughts you might have on the subject. I think that "spacetime" is essentially a way of talking about cause and effect, and that geometry is a very good approximation to this at currently observable scales.

Congratulations on an excellent contribution! Take care,

Ben Dribus

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    • Post #97

    Jonathan,

    You wrote (on Giovanni's page): "Pentcho, briefly, you and I have already discussed this question at length on my page, and I have shown you to be wrong, in a way that even you eventually didn't argue back about. The reason we call it "the spacetime interpretation" is because it's an interpretation. It's untested - unlike SR, which is extremely well confirmed by experiment. People often imply that spacetime is an unavoidable consequence of SR, but no-one will actually say that it is, because it isn't."

    Then you wrote (on my page): "Hello Pentcho, we can find out the answer to what we've been discussing. I thought I'd got it across, was trying to help to get to what's underneath the picture they imply, which sometimes can be false. Maybe you want to email John Baez, (baez@math.ucr.edu), or some other relativist, with the question 'is Minkowski spacetime an unavoidable consequence of SR, and the only possible interpretation?'. I'd be surprised if any relativist said yes to that. Anyway, please discuss it, if there's any further need to, on my page rather than on Giovanni's page. (Let me know what they say, if you email them.)"

    Here is a text where Minkowski spacetime is referred to as an useful diagram allowing one to get "an overall intuitive picture of a setup". Note that "if you want to produce exact numbers in a problem", special relativity is enough:

    David Morin: "Minkowski diagrams (sometimes called "spacetime" diagrams) are extremely useful in seeing how coordinates transform between different reference frames. If you want to produce exact numbers in a problem, you'll probably have to use one of the strategies we've encountered so far. But as far as getting an overall intuitive picture of a setup goes (if there is in fact any such thing as intuition in relativity), there is no better tool than a Minkowski diagram."

    In my view, if you want to prove that Minkowski spacetime is more than a useful diagram, you will have to find an example where Minkowski spacetime produces "exact numbers in a problem" that special relativity does not produce. I think there is no such example.

    Pentcho Valev

      Dear Jonathan,

      Your essay is well written, accessible, interesting and defends valuable fundamental points. I am sure it will do well! I was glad to see your defence of real change, and hence of things existing wholly in the present and causal powers being real factors in explanation-building. In our essay Julie and I argue that the concept of energy commits us to a view of material things as capable of changing, and link this to the ability to build scientific explanations. If this on the right track then the block universe model cannot be a realistic view, just as you so clearly argue.

      I greatly enjoyed reading your essay, and hope you will find ours interesting too. Good luck in the competition!

      Best regards,

      David

        Hello Pentcho,

        well maybe we agree, as I also think spacetime is sometimes nothing more than a useful system for diagrams of SR. But I thought the question was, is spacetime a necessary consequence of SR. I think almost no-one would say it's the only possible interpretation, and few would say it's a necessary consequence, though people do imply it sometimes. I suppose I was trying to show you where the whole edifice of relativity, as it is now, has a genuinely questionable area. Spacetime is one part of that set of ideas that hasn't been tested. But I know you have your own view of SR - anyway, you can check what I've said if you want, and ask people how spacetime detaches from SR. (Btw, I went to that cafe in Holland Park today, nice to think of Lee Smolin and João Magueijo sitting there talking.)

        Best wishes,

        Jonathan

        Jonathan,

        Let us replace special relativity with the deductive closure of Einstein's 1905 postulates:

        W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, Routledge, London, 1981, p. 199: "By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set."

        Now the difference between us can be clearly defined: I believe Einstein's light postulate is false, you will probably start looking for false "auxiliary" hypotheses. But we must agree on one thing: if spacetime is "flawed", some member of the set is false, and we should expose it.

        Pentcho Valev

        Dear Ben,

        It was very good to get your post, thank you. I agree with what you say, and found it heartening to get such a response. I'll read your essay.

        Your points 1 and 2 are very well put, and I agree with them - you set these things in a wider context. For instance "Choosing mathematically convenient but physically dubious models has caused too many problems in physics to even begin to list".

        I think the causal order can be what applies in your points 4 and 5, as you say, without being the most fundamental thing in your point 3. When we try to establish simultaneity across a distance (or an ordering of events across a distance), then to me the potential for a causal order can be used to trace the relationships between events. That may be simply a convenient system.

        It doesn't mean causality necessarily leads to the flow of time. You say: "Do cause and effect depend on a timeline, or does time depend on cause and effect? Or are they two ways of talking about the same thing?". I'd say a flow of time is required for cause and effect to happen. It looks that way because the time rate slows down and speeds up in certain situations. And the two ways in which this can happen seem rather different. I can't see how this kind of thing could happen to cause and effect on its own, though perhaps you see it as a dimensional thing with causality wrapped up in it. But to me an underlying flow of time is needed, as George Ellis has argued for in a recent arXiv paper. Without that I don't see how you can get causality going in the first place.

        Anyway, I'm looking forward to reading your essay, and thank you for your comments.

        Best wishes, Jonathan

        Hello Pentcho,

        I'm glad you agree that if spacetime is flawed, then there's a flaw somewhere in what led to it. That's what I've said in my essay. I've said Minkowski's assumptions about time may be wrong, and specifically about simultaneity across a distance. This is perfectly possible without SR being wrong, as anyone will tell you if you really ask.

        Let's just agree to disagree about SR itself, earlier on I did post the address of a page with links to many experiments confirming it. And if you think a flaw in spacetime has to mean a flaw in SR, then just ask any good relativist if SR could be right but spacetime wrong. And if he says that one is a consequence of the other, then give me his email address, and I'll have a word with him!

        Best wishes, Jonathan

        Jonathan,

        You wrote: "Minkowski's assumptions about time may be wrong, and specifically about simultaneity across a distance."

        Then you should formulate the false assumption in an explicit manner. But I don't think you will be able to find assumptions specific for Minkowski that are alien to special relativity.

        Pentcho Valev

          Dear David and Julie,

          Thank you very much. It's good to see more people questioning the block universe picture - after it was accepted unquestioningly for so long - and your ideas sound very good. I've argued that physics itself requires motion though time, and it looks like you've hit on a specific example of that arising, and can show it in a detailed way. I'm looking forward to reading your essay.

          Best wishes, Jonathan

          Hello Pentcho,

          I've said in my essay that the false assumption is that an event can be both

          past and future, in two different viewpoints.

          Best wishes, Jonathan

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          • Post #106

          Dear Jonathan,

          Thanks for the response, and I'll look forward to your remarks on my essay. I can already anticipate some of your potential criticism, but the criticism of the wise is far more valuable than the agreement of the ignorant!

          Regarding the question of whether time or causality is "more fundamental," or if they are two different ways of talking about the same underlying structure, I note your emphasis on the permanent effect of time dilation as an important clue regarding the nature of time. The "pure causal" response to this might focus on the "objects" that are "aging," examining what an "object" really is in the context of a single fundamental structure (at the classical level). Something which I don't yet know your view on is whether "matter-energy" is something that "lives in spacetime" or if "spacetime" and "matter-energy" emerge together from some sort of microstructure, which is the case for many approaches to quantum gravity.

          In any case, perhaps we can discuss this more when you have had time to compare our ideas. Take care,

          Ben

          Jonathan,

          You wrote: "I've said in my essay that the false assumption is that an event can be both past and future, in two different viewpoints."

          This is part of some people's interpretation of spacetime, not a (physical) assumption from which (physical) conclusions can be deduced. If that is the problem, then there is no additional feature of spacetime that can be logically or experimentally falsified - spacetime is just as perfect and falsifiable as special relativity. The problem is with the interpreters, not with spacetime.

          Pentcho Valev

          Hello Pentcho,

          Well I partly agree on that. It is a physical assumption, but not a fundamental one, which is what I think you mean. As I've said in the essay, it's an assumption that is basic in the sense that many other assumptions stem from it.

          The more fundamental physical assumption underlying it (which I think is false) is one of Minkowski's, but not initially of Einstein's, though he took it onboard later. It's that simultaneity has meaning across distances beyond the light cone. I think you should see that I am not what you oppose - I am also critical of aspects of the existing use of relativity, as it stands at present. We disagree on what's wrong with it, and are in different places on the spectrum of views. But I think you should really argue with the people who are at the far end of the spectrum, who would defend that entire set of ideas.

          Best wishes, Jonathan

            Hi Jonathan -- Sorry I couldn't respond sooner. But I don't agree that the "block universe" view follows from Minkowski "unavoidably" or otherwise. Stein's argument has been picked up and elaborated many times since the '60s, most recently in the George Ellis paper you and he were discussing in the comments to his essay. You're right that the "block universe" does seem to be rigorously proved to many physicists, for reasons I discuss in my essay.

            I think you and George and I all agree (as you said in your 9/9 comment to George) that the problem with Rietdijk-Putnam "is in the assumption that simultaneity across a distance has meaning (beyond the light cone)." George quoted from his paper:

            "...the physical events that shape how things evolve are based on particle interactions, and take place along timelike or null world lines, not on spacelike surfaces, which are secondary. The concept of simultaneity is only physically meaningful for neighboring events; it has no physical impact for distant events, it is merely a theoretical construct we like to make in our minds. What we think is instantaneous makes no difference to our interaction with a vehicle on Mars. What is significant is firstly what happens over there, secondly what happens here on Earth, and, thirdly the signals between us. Simultaneity does not enter into it."

            But the three of us draw different conclusions from this. The point I try to make has to do with what you wrote above in responding to Daryl: "an event 4 minutes ago on Mars has zero separation in spacetime from right now where you are on Earth. All this may have no physical meaning. And because it leads to block time which requires illusions, spacetime is very questionable."

            I think the "zero separation" on any light-like interval most definitely does have physical significance. And it very clearly shows that Minkowski spacetime is very different not only geometrically but topologically from a 4-dimensional "block". The problem is that from the usual objective standpoint -- envisioning the universe as if "from outside" -- we can easily imagine the "block spacetime" but not the spacetime Minkowski describes.

            What I tried to say in my essay was that what Minkowski describes is exactly the spacetime any actual observer experiences, in the ongoing present moment.

            So I end up agreeing entirely with your rejection of the "block universe" at a fundamental level. But like George, I believe the problem is not with Minkowski but in the careless, unphysical way his equations are interpreted to correspond with our "common sense".

            Taking this common view "from outside", you think it's a problem that for some observers an event has already occurred, while for others it hasn't. But there's no contradiction between the worlds the observers actually see, in their respective present moments, only between the way each of them retrospectively reconstructs the set of supposedly "simultaneous", spacelike-separated events that took place at a certain past "point in time".

            My disagreement with George is that he still wants to imagine the past as a "block", which only perpetuates the misunderstanding about how space and time are physically connected in Minkowski's spacetime.

            I know my treatment of this in my essay was probably too abbreviated to be clear. If you get the chance, I'd appreciate it if you'd give me your comments on what parts of my Section 3 made sense to you and what didn't.

            Thanks - Conrad

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            • Post #110

            Jonathan

            I am also thinking about two levels of time.

            Levels o Parmenides and level of Heraclites

            You can read my essay 1413

            Yuri

            Jonathen

            A handful of the missing jigsaw puzzle pieces emerge from applying the structures of logic (TFL and PDL) to the evolution of interactions over no zero time at a qauntum scale. I try to describe these in my essay, but as motion is difficult to visualise many haven't assimilated the complete ontology. I think you will. I hope you'll get to read it as I think it may be foundational.

            I look forward to your comments (and possibly your book). Do you like a bit of theatre?

            Best wishes

            Peter

            Hello Conrad,

            as I said when I replied before, I hadn't read your essay. But to me it's great - I've been amazed by the clarity of sections 1 and 2 reading them this morning. I love the way you write, it seems to me you think like I do, trying to get each idea across in a way that can be really assimilated as you go. And what you write seems important to me.

            Because these kind of questions have been looked at for some time in attempts to interpret quantum theory, I suspect that in themselves they won't provide a complete solution, but they could be an important part of it. And applying them to relativity as well is important.

            Just read 3-5. I understand that you had to abbreviate. I must say, to me people have been aware of these kinds of issues, and I generally trust the consensus over a century about both SR and QM. I think we can be mistaken about the interpretation of a theory, as with spacetime, but I don't think we're likely to have made an error in how it is worked through. I'm always suspicious of attempts to point out a direct error of that kind with SR. And the 'inside' and 'outside' viewpoints are clearly an issue in SR, because of the role of the observer. So when a large group of physicists decide that block time is a consequence of spacetime, and keep to this view for 50 years, and work with it even though it presents major difficulties, I believe them.

            Just to clarify my view, you say that I "think it's a problem that for some observers an event has already occurred, while for others it hasn't." I only think that's a problem because that's the single point that led to block time. And above all, it leads to what looks like the difference between past and future being one of perception only. The two observers can be passing each other in the street - that's the problem, and incidentally, I pointed out that the same problem also arises in George's EBU.

            In my essay I'm not specific about what removes that possibility (of an event being past and future in two different viewpoints), I just show the kind of thing that could remove it, and point out that even a slight difference to the rules about distant simultaneity could remove it (this strengthens other points that suggest block time is wrong). In my book I go into that question in more detail.

            I think your essay points out an important issue, which although it has been thought about before, may yet lead to breakthroughs. And I think you manage to write about it in a wide ranging general way that could make people think about it, and help with us getting there. As you can see, I'm keener on the general side of your essay than the specific, but to me it's a lot.

            Good luck and best wishes,

            Jonathan

            Hello Peter,

            thanks, I'll read it when I can.

            Best wishes, Jonathan

            Jonathan --

            It's very heartening to me to get such a positive response; thanks very much. The block time idea clearly needs to be overcome, and I look forward to seeing how you deal with it in your book. Your essay does a fine job of pointing out the difficulties of treating "now" as an illusion, a matter of perception. If such a basic aspect of all our experience is illusory, what are we supposed to trust, as a basis for empirical science?

            And I can hardly blame you for believing what's been an almost unquestioned consensus about the meaning of Minkowski spacetime. Nearly everyone has focused on the notion of spacetime as a 4-dimensional manifold, and dismissed as merely incidental the fact that it has a -+++ signature rather than ++++ or --++ or some other arbitrary combination. So people call it a "block universe" and rarely even mention that it happens to have a "hyperbolic" geometry... since that's just one more "count-intuitive" aspect of fundamental physics, or maybe even a technicality "without physical significance."

            There's a lot to be said about this, which I had to abbreviate in my essay down to the bald statement that Minkowski's geometry is nothing like that of a 4-d "block". But I suggest that Minkowski's spacetime is a web of intersecting light-cones in which there are no spacelike intervals between events. The so-called hyperplanes of simultaneity are figments of our rational imagination, due to our erroneously embedding Minkowski spacetime in a 4-d block. Not only do all the laws of physics ignore spacelike intervals; even mathematically we have to use imaginary numbers to represent them. So for me, the problem is one of seeing what Minkowski's mathematics is telling us, rather than rejecting or revising it.

            In your essay you wonder whether "there may be a rule we don't yet know about that prohibits relating 'now' moments across a distance..." I suggest this "rule" is already given by the light-cone structure of spacetime, and it's just our habit of thinking about the world "from outside" that makes this difficult to see. I don't mean to underestimate that difficulty, though. I'm still struggling to find good ways to illustrate the spacetime geometry we all experience "from inside."

            In any event, it will take some time before it seems natural for any of us to think about physics "in real time" -- and I'm very glad you're working on the problem.

            Many thanks -- Conrad

            Dear Jonathan - thank you for your explanations and your good wishes in your last message above that I have just seen.

            ----

            Hello. This is group message to you and the writers of some 80 contest essays that I have already read, rated and probably commented on.

            This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:

            Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.

            A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.

            An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.

            Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity

            Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.

            Thank you and good luck.

            Vladimir