Ken,

I've been trying to put my finger on what strikes me as inconsistency in your desiderata. Perhaps you can help me understand where I'm missing the boat.

Desiderata: An LS formalism that does not admit an NS formalism but does admit a (3+1)D continuously mediated story between Source and sink that explains the measurement outcome.

My confusion: The way one obtains NS from LS is to demand the extremum condition of LS be satisfied instant by instant. This leads to the local as well as global conservation of some property or characteristic of the fields involved; in classical physics it's energy and in quantum physics it's probability. Thus, in order to avoid an NS characterization of your ultimate LS formalism, there can be nothing conserved instant by instant. But, if no field property or characteristic -- absolutely *nothing* -- is locally conserved, what *is* being mediated in a (3+1)D continuous fashion?

I can imagine a field filling spacetime between initial and final hypersurfaces (and therefore between the worldtubes of the equipment). This field has some 4D global property that satisfies an LS constraint, but this field does not possess any property or characteristic that satisfies any constraint instant by instant (for any foliation). Trying to mathematically model such a field strikes me as a perfectly reasonable thing to do (it's what we're doing graphically). But, the very field property that rules out the possibility for an NS formalism also rules out the possibility of a (3+1)D story. At least, that's the way it strikes me. Perhaps you can dispel my confusion :-)

    Dear Prof. Wharton,

    I very much enjoyed the essay and realize you are looking at this from primarily a mathematical perspective as it relates to the physics more so than from the philosophical bend. Never the less once the Lagrangian perspective is taken it's hard not to wonder about what it all means as opposed to simply what observable results it has mandated. That is while metaphorically you say the universe is not a computer, yet stop there as not to share with us how you actually would have it imagined.

    As for instance I recall reading one of the first criticisms of such a perspective written by one of Fermat's contemporaries, Claude Clerselier, in him saying "Fermat's principle can not be the cause, for otherwise we would be attributing knowledge to nature: and here, by nature, we understand only that order and lawfulness in the world, such as it is, which acts without foreknowledge, without choice, but by a necessary determination". So although the LSU is certainly not a computer it presents as universe mandated to follow a central rule where the nature of the outcome is predecided. 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. That's not that I think we might ever be able to have such a question answered simply I find it as one interesting to think about.

    "Our intuition, going back forever, is that to move, say, a rock, one has to touch that rock, or touch a stick that touches the rock, or give an order that travels via vibrations through the air to the ear of a man with a stick that can then push the rock-or some such sequence. This intuition, more generally, is that things can only directly affect other things that are right next to them. If A affects B without being right next to it, then the effect in question must be indirect-the effect in question must be something that gets transmitted by means of a chain of events in which each event brings about the next one directly, in a manner that smoothly spans the distance from A to B. . . . We term this intuition 'locality.'

    Quantum mechanics has upended many an intuition, but none deeper than this one. And this particular upending carries with it a threat, as yet unresolved, to special relativity-a foundation stone of our 21st-century physics."

    -Albert, D.Z. & Galchen, R., 2009. "A quantum threat to special relativity", Scientific American, 300, 32-39.

    Kind regards,

    Phil

      I don't know -- I'm quite suspicious of attempts to 'start with logic', as that's exactly how anthropocentric mistakes are most likely to sneak into the foundations in the first place. This goes doubly so for efforts built on information theory.

      Now, I am a big fan of Einstein's method of building theories from big-idea principles, but at the end of the day it's the comparison of the math with reality that is the only way to determine if those ideas were right in the first place.

      And I'm afraid I disagree with your sentiments concerning a derivation of SR from QM in an ordinary causal (NSU) framework. Your essay dismisses Bell's theorem far too cavalierly for my liking. If you really want to tackle Bell inequality violations in a spacetime framework, check out my essay references [6] and [12] to see how an LSU can do the trick.

      Gene,

      There certainly may be other anthropocentric biases built into physics, and it also is true that I only experience this one universe, so that might unfairly bias me against your ideas.

      That said, as a physicist, I want to explain the particular universe that I observe. Maybe it will turn out that the best explanation will require the use of other places and times outside "my universe", but I can't see myself seriously pursuing that possibility until I've ruled out some simpler options.

      Here's a quote I still kind of like from my entry to FQXi's very first contest:

      "Looking to quantum theory for answers about spacetime is like looking to a roadmap for answers about geology: it's a tool designed for something else entirely. In general, quantum theory tells us nothing about spacetime except what its formulators put into it in the first place."

      Best, Ken

      Hi Mark,

      Yes, you and Silberstein are further along than any other LSU-style approach that I know of, and it's great to see some new cosmological results coming out of it. For now I hope we can agree to disagree about the continuum/discrete issue, and keep finding points of contact, such as this essay. More to come...

      Rich,

      Thanks for the kind words -- although I think both you and Jackson may be misreading my main point to some extent. From what I can tell about your essay (and Jackson's, and McEachern's), you're still working in a conceptual framework aligned with the NSU. If there's some LSU approach buried in any of those essays, I must have missed it, but I'm certainly interested in any such efforts.

      Best, Ken

      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

      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

        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...?

          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?

            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