Hi Mark,

I'm not sure if by "story" you mean "explanation" or mere "description"... If the former, we're not on the same page: LSU explanations don't make much sense when viewed sequentially in 3+1D -- they require 4D "stories". But I'll assume you're merely using "story" to refer to my hoped-for-3+1D representation of what is happening between measurements.

As for whether giving up NS for LS means that *nothing* can be conserved instant-by-instant... That seems way too strong a conclusion. After all, there are aspects of Noether's theorems that provide conservation-type-rules (from the symmetries of the Lagrangian) even if the Euler-Lagrange equations are not strictly adhered to. There's a nice paper by Harvey Brown to this effect...

If you ask me about ontology, "what is being mediated", my best guess right now is the classical Lagrangian density itself, and the classical fields that comprise it. (Bearing in mind that those fields need not strictly adhere to the Euler-Lagrange equations, just as single-photon experiments obviously don't adhere to Maxwell's equations.)

On your last point, perhaps the problem is what you mean by "story" (see first paragraph above). Otherwise, I think we're on the same page. Also, note that LS approaches can give meaning to *new* instant-by-instant constraints, that don't make any sense in an NS framework -- such as enforcing a zero total Lagrangian density throughout spacetime (to pick a not-so-offhand example... :-).

Cheers, Ken

Phil,

Yes, lots of great philosophical questions at the heart of this stuff. Usually I just point people to Huw Price at this point, but I'll venture a few comments of my own.

Very nice quote about Fermat's principle, but if you'll look closely, the claim that "nature... acts without foreknowledge" is precisely the NSU assumption that the universe is just as limited as us humans.

When you get into words like "predecided", I'll direct you to my discussions concerning the block universe in response to Silberstein, above. The very word "predecided" refers to two different times (its subject and object), and therefore has no physics translation -- the philosophical concept of predecision doesn't make sense in the block universe of modern physics.

As for your excellent question: "The deeper question for me then is to ask how a universe underpinned by predecision can have physical outcomes present as being so seemingly lawless respective to their certainty." I certainly have a few thoughts. At one level, the hidden variables that I'm proposing (and that are necessary in any LSU) answers this to a large extent. Just because it's a block universe doesn't mean that we *know* the block; to the extent it's unknown, it appears probabilistic.

But I've only recently come to realize this isn't the whole story. You can't get all quantum phenomena simply by constraining deterministic fields at two times. And the path I'm going down right now -- departing from deterministic equations of motion, underconstraining the intermediate physics between the LSU constraints -- provides plenty of uncertainty all around. (Although one must also relax the Principle of Sufficient Reason to the point where our universe is just one of many possible solutions to the same ultimate constraints.)

As for that great quote you ended with, you may be surprised to see that we used that very quote to start Ref. [12]. We like the intuition of locality (as defined in that quote), and the LSU allows us to keep it, quantum phenomena notwithstanding.

Best, Ken

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  • Post #61

Hi Ken,

I really enjoyed your thought-provoking essay. I'm wondering how your idea fits in with Hawking and Hertog's top-down cosmology?

Thanks for a great read.

Cheers,

Amanda

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    • Post #62

    again reminding you about 946

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    • Post #63

    Ken, you never disappoint. Your surgeon's skill for dissecting critical assumptions not only exposes the real meaning behind them -- you underscore by example the truth of Jacob Bronowski's aphorism, "All science is the search for unity in hidden likenesses."

    The biased question -- "Doesn't Bell's Theorem prove that quantum correlations can't be caused by past hidden variables?" -- has indoctrinated a generation with the belief that the world is reduced to computation alone, that no local (read classical) theory is capable of continuous correlation of measurement values.

    I love your statement, "Now there's one last anthropocentric attitude that needs to go, the idea that the computations we perform are the same computations performed by the universe, the idea that the universe is as 'in the dark' about the future as we are ourselves."

    That is why I like Joy Christian's topological framework -- although not directly related to your Lagrangian schema, it does also " ... treat the universe as a global, four-dimensional boundary-value problem ..." in a continuum of correlated values, and in which Nature has a choice.

    I hope you get a chance to visit my essay ("The Perfect First Question") that incorporates Wheeler's information-theoretic philosophy into a framework of continuous measurement functions.

    Thanks for a great read -- and best wishes in the contest!

    Tom

      Sorry, must have been logged out. The above is mine.

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      • Post #65

      Dear Ken,

      Your passage

      "Is the universe ebectively a quantum computer?

      This essay argues "no" on both counts; we have erred by assuming the universe must operate as some corporeal image of our calculations "

      suggests some sort of attitude to mathematical details of so-called "quantum computer" and "the universe as approximation to quantum computer ".It is easy to know that quantum computer today is merely mathematical construction based on ideas of complex numbers algebra, where qubits, algorithms and Hilbert complex vector space are used to imagine such sort of software for future super computer (used by NATURE as well ). Some theorems of complex computational mathematics could be used in philosophy of the Universe as a whole, indeed.But,unfortunatelly, we cannot deduce any serious technical content from such poetical image as " Universe as Computer "(probably inspired by the art of the Enlightment) indeed. I suppose there is no real cognitive problem here...?

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        • Post #66

        You wrote:

        "Which past events cause

        the future boundary constraint? How do objects in

        the universe \know" what future boundary they're

        supposed to meet? Doesn't Bell's Theorem [13] prove

        that quantum correlations can't be....."

        All your statements based on light speed constant c

        Imagine please our universe this way

        Big Bang; Present; Big Crunch

        c=10^30; c=10^10; c=10^-10

        G=10^12; G=10^-8; G=10^-28

        h=10^-28; h=10^-28; h=10^-28

        alfa =10^-3; 1/ 137; 1

        e=0,1 ; e=e ; e=12

        What is your question to this picture?

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          • Post #68

          Thanks for the reply, Ken.

          I'm trying to understand your desiderata, so I'll go with "my hoped-for-3+1D representation of what is happening between measurements." :-)

          My questions are an attempt to understand what you mean by an LS approach that doesn't allow for an NS approach but nonetheless allows for a 3+1D representation. Specifically, I'm interested in how that might be mathematically instantiated.

          In order to avoid a time-evolved differential eqn (NS approach), the LS constraint cannot be satisfied instant by instant. Your response seems to agree with that, so no confusion there. Also, it seems to me, L cannot have any symmetries since they lead to conserved currents cast in conservation equations, i.e., NS formalism. Thus, L has no symmetries and satisfies a global constraint that cannot be satisfied instant-by-instant, yet this formalism allows for a 3+1D representation.

          Maybe it would be more productive to ignore my confusion and share your specific idea(s) for how this might work. I realize you don't have a finished product, so I don't expect anything precise. You allude to an idea at the end of your essay, so perhaps you could elaborate a bit on that.

          Hi Amanda,

          Glad you liked it, and thanks for the interesting question. Before your post, I had only read summaries of 'top down cosmology', and it originally struck me as making the time-reverse of the usual mistakes when it came to interpreting the wavefunction. But after your comment, I went back and read some of the original papers. I was pleasantly surprised to find that much of Hawking's original motivation mirrors my own complaints about the NSU -- especially the first 1.5 pages of Hawking's original http://arxiv.org/abs/astro-ph/0305562 . It's effectively a critique of the NSU, and concludes that the way forward is to look to the path integral (LSU).

          But that's where things go awry, because no one has ever come up with a realistic interpretation of the path integral -- even in laboratory experiments, let alone the whole universe. The '06 paper with Hertog simply assumes that once one has the "amplitude" (not probability!) of the universe the problem is solved, ignoring the fact that the quantum foundations community can't agree on what the amplitude/wavefunction means in the first place. So the motivation is great, but there's no LSU interpretation for Hawking to tap into -- because it hasn't yet been developed, probably for the reasons I outline in my essay.

          As it stands, though, top-down cosmology seems to hold that the *past* is a huge-dimensional configuration space (like I said, the time-reverse of the usual thinking), which is pretty confounding to someone like me, committed to the block universe. In fact, if you look closely, the argument goes like this: 1) We don't know the past, 2) We represent things we don't know in huge-dimensional configuration spaces, so 3) The past *is* a huge-dimensional configuration space. In other words, the time-reverse of the same anthropocentric (not anthropic) reasoning that I'm complaining about here.

          Still, thank you very much for drawing this connection; I'll definitely find it useful if I ever nail down this realistic re-interpretation of a (modified) path integral that I'm working on.

          Best,

          Ken

          Hi Tom,

          Thanks for the very nice comments! I'm way behind on reading essays, but I've added yours to the list... That's interesting about the connection you see with Joy Christian's work; I haven't yet put in enough effort to wrap my head around it, perhaps because I'm stuck in too much of a classical-spacetime mindset.

          Cheers!

          Ken

          Michael,

          Actually, I'm being much more heretical than you suggest. I'm not saying that we can't physically reproduce nature's computations, I'm saying that nature doesn't even *utilize* computations, at least not in the standard past-to-future sense of the word. I'm denying any map between reality and Hilbert space, as well as the premise that you're assuming when you say "used by NATURE as well". (I'm using nature=universe here, although I use only 'universe' in the essay.)

          Hope that makes it sound a bit more interesting... :-) And yes, I do propose an alternative path forward; I'm not just pointing out unresolvable problems.

          Best,

          Ken

          Yuri,

          You picked out the one group of sentences that I was setting up as straw men, as bad arguments that I don't agree with, to complain about.

          I'm happy with a constant speed of light, but that's completely beside the point of my essay.

          Ken

          No, I'm not; I agree with Huw Price on this issue.

          Dear Ken,

          very nice essay. I completely agree with you about your claim: teh universe is not a (quantum) computer. Determinism has influenced physics sine a long time. But non-local phenomena arise (like EPR), so we have to go deeper and find models to include te indeterminism. Hidden variables are no real path but non-computability is a way. What I mean are real non-algorithmic real numbers. By definition there is no algorithm (or law) to calculate them but they exists. So, if our future is non-computable then we keep up the concept of the free will etc. But as a consequence we need the contiuum (probably you do not like this point). One reason, why I keep up the concept of a smooth manifold.

          If you like, have a look into my essay.

          Best

          Torsten

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            • Post #75

            Dear Prof. Wharton,

            Thanks for your reply as it clarifies for me what an LSU presents for you as being within a broader context. As to your last remark that it requires one to "relax the Principle of Sufficient Reason to the point where our universe is just one of many possible solutions to the same ultimate constraints" leaves me somewhat confused. That is are we talking about LSUs being differentiated only by their initial primal conditions, as to what initially has them being composed of, or rather what order initially emerges from what otherwise would be the same primal conditions. In this respect I like the thoughts of Leibnitz that when such is considered there needs to be found a difference between what is certain and what is necessary. From this I've always taken him to mean one needs to look at the differences between what might exist and what is able to be realized as existing, as only the latter can be found to be a reality.

            Once again I thank you for your excellent essay, as I do think the LSU conceptualization is something worthwhile to have explored respective of the pursuit of answers regarding the hows of the physical world. I also find such a conceptualization may perhaps form a bases from which the whys of it for those who are so inclined wondered about may be addressed as well.

            "We have said that the concept of an individual substance [Leibniz also uses the term haecceity ] includes once for all everything which can ever happen to it and that in considering this concept one will be able to see everything which can truly be said concerning the individual, just as we are able to see in the nature of a circle all the properties which can be derived from it. But does it not seem that in this way the difference between contingent and necessary truths will be destroyed, that there will be no place for human liberty, and that an absolute fatality will rule as well over all our actions as over all the rest of the events of the world? To this I reply that a distinction must be made between that which is certain and that which is necessary."

            -Gottfried Wilhelm Leibniz, "Discourse on Metaphysics" (1686)

            Kind Regards,

            Phil

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            • Post #76

            What is your evaluation Gerard 't Hooft article?

            Discreteness and Determinism in Superstrings ?

            arXiv:1207.3612 (replaced) [pdf, ps, other]

            >In order to avoid a time-evolved differential eqn (NS approach), the LS constraint cannot be satisfied instant by instant.

            Ah, here's the point of confusion. In any given instance, between any two particular measurements, I see nothing wrong with the intermediate fields obeying *some* continuous constraint. After all, I expect the fields to be smooth/continuous themselves.

            Here's an example (not actually what I'm going for, but useful for this discussion): Suppose a photon/EM-field in a double-slit experiment is a continuous field, with LS rules constrained by both the past preparation and the future measurement. This 4D story can be represented as a 3+1D description, but different future measurements could easily have different past behavior. So in 3+1D the field might obey differential equation A if future boundary/measurement A' is imposed (corresponding to an interference measurement), but would instead obey differential equation B if future boundary/measurement B' is imposed (corresponding to a which-slit measurement). So there's no master differential equation and NS fails as an "explanation". And yet, both A and B might conserve the same quantities, so one still gets the behavior that you're worried that LS rules out. Does that sound reasonable?

            Right now my research is taking me more towards something that roughly maps to stochastic quantum mechanics (esp. Larry Schulman's ideas, if you're familiar with his non-classical 'kicks'), where 'conserved' quantities are only conserved on average, in some statistical limit. But I see nothing fundamentally wrong with the approach in the previous paragraph, as an example of how LS might not map to an NS story.

            Ken,

            You say,

            "How would the founders of quantum theory have met these challenges if they thought the universe ran according to the mathematics of the Lagrangian

            Schema { not as a computer, but rather as a global four-dimensional problem that was solved \all at once"?"

            How about modeling with a quantum computer? Computers are only means to build a complex scenario that mimics a hypothetical situation. You're not saying that some aspect of the universe runs like a computer. With our understanding of gravity's properties, it is a mystery that only empirical evidence seems to address, as I explore in my essay.

            Liked your essay. A great deal of substance here.

            Jim