Hi Jens,

Thanks for reading, and for your great comments. It isn't that I am proposing a quantum mechanical framework of noncollapsing wave functions -- it's that I am trying to explain (like Joy) the appearance of quantum phenomena in a classical framework. Bell's framework is itself classical.

The symmetry of Schrodinger's wave equation is already there -- as a continuous wave function with solutions in both past and future (retarded and advanced). This is entirely unrelated to, and incompatible with, the probability function in quantum mechanics.

The only significant disagreement that Joy and I have had, is whether Bell's theorem proves anything at all. (That significance is blunted, however, by our larger agreement that the measurement domain of Joy's topological framework is complete and Bell's is not.)

I think that Bell's theorem does prove that no classical theory of continuous measurement functions can be derived from quantum rules -- which brings us to your research program. I don't have a problem with limiting the domain of quantum mechanical functions to an incomplete space of probabilistic measure, so long as one does not interpret the probability function as physical law. There are quite useful applications for quantum probability that should not -- and do not -- imply complete functions. That is, state preparation of the Schrodinger's cat experiment demands only one state, not a superposition -- the cat is always alive initially. There is no warrant to believe that observing its later state has causal efficacy, unless one were able to impose the symmetrical state of preparing a dead cat for the initial condition in expectation that the cat could be observed alive at some later time. By laws of thermodynamics and information conservation, this would require an infinite amount of time.

It follows that finite state calculations are always arbitrary and incomplete. This does not obviate correlation of quantum states in classically continuous measurement functions, as Joy Christian has shown.

Best,

Tom

Hello Tom - thanks for your detailed reply. Again, all I feel competent doing is to give you pointers. A specific example would be an excited three-quark state that decays into a ground state with production of a meson. If you understand that meson as a "cat / anti-cat" bound state, and assume time symmetry in quantum nature as you seem to propose, then I would expect the newly created meson to react with the three-quark state that ejected it. Not sure whether such a thing is possible with excited protons that would expell a pi meson when decaying back into the ground state ... something like that. It fall into the realm of what I understand as final-state interaction. Good luck! Jens

Right on, Jens! If you'll look a few posts above (18 Sept 1248 GMT), I posted an attachment of a draft paper I wrote in May proposing an EPR-Bell type experiment with fermionic condensate that depends on wave correlation rather than entanglement -- instead of particle ejection, we get singlet and triplet results and instead of particle-antiparticle annihilation and gamma radiation, we get angular momentum conservation.

I would be most interested if you would read and comment on the attachment. Thanks!

Tom

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  • Post #140

Hi Tom,

I think I've found the point of view for comparison with Joy's work, and it has a bearing on the construction of a 2D model.

View the hidden domain in Joy's work as having an enclosing S2 surface. The map of the rotation group space S3 to this S2 has 2 possible orientations for homotopy group PI3(S2)=Z2. The map of a S7 space associated with particle symmetries to S2 also has 2 orientations, PI7(S2)=Z2. When the hidden domain surface S2 only encloses empty space, the symmetry operations of rotation (S3) or particle symmetries (S7) are free to act everywhere to rotate +1 orientation into -1 orientation as they are reachable through S3 or S7. BUT when the hidden domain encloses holes in space (as in STUFT) or singularities where the symmetry operators do not apply, this is not possible and the hidden domain S2 surface will have an orientation (see my reply to Jonathan Sept 25 on my site for more).

The 2D equivalent is topological vortices, such as occur in both the theory and reality of superfluid helium. Using the right hand rule and defining orientation to be the vortex direction at the point between two vortices, the pair LR have orientation Down LR=D, and RL have orientation Up RL=U. As U=-D this notation gives LR=-RL, the same non-commutativity AB=-BA displayed by the quaternions S3 and octonions S7. New notation is needed because complex numbers are commutative. Now enclose a singlet vortex pair inside a circle S1 that defines the boundary of a hidden domain, such that the vortex orientation LR or RL is hidden. The same argument as for S3 and S7 also applies to this vortex scenario, and the S1 hidden domain boundary has either orientation U or D. So as in the S3 and S7 cases of Joy, in this S1 case the hidden variable is the orientation.

Do you think that such a vortex scenario could give a demonstrative model of the form you describe?

Michael

Hi Michael,

The plot thickens! Yes indeed, I think that " ... such a vortex scenario could give a demonstrative model of the form ..." and I wish even more strongly that you had been around last year when the fur was flying. There are a lot of things in my notebooks that I would have posted had I had indication that they could be understood, such as this entry 22 Aug 2011 that I framed as a lemma:

"Pair correlation (A|B) of nonrelativistic quantum events is independent of the continuous topology of S^7, in which correlated vector pairs of octonions correspond to bivectors in the spacetime of S^3, comprising an interval of simply connected information ranging all over S^3 and unitary to the initial condition."

That's inelegant,and I wouldn't have put it that way in public (just wanted to reveal my unfolding thinking process). I would have edited it to:

"All measured quantum correlations are independent of topology, such that continuous measurement functions in a simply connected space are unitary with the initial condition."

The proof of this lemma implies the theorem: "All physics is local." (Einstein)

Joy has been saying all along that the physical space is S^7, agreeing with your research that parallelization of simply connected S^0,S^1,S^3,S^7 is a space of complete measurement functions.

In a 2006 paper I proposed the measure space S^2 continuously projected between S^1 and S^3 with the result that non-commutative arithmetic functions exchange continuous curves for discrete points. (infinite quantization implies no quantization at all, which obviates collapse of the wave function.)

We're on the same beam -- commutativity of complex numbers implies the topological twist while preserving orientability of LH and RH elements as hidden variables.

Cool!

All best,

Tom

Dear Tom,

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

Dear Thomas,

Wow... The first perfect question surprised me. So simple but so deep. If the answer is no, then there is no way you could be asking it! And yes, there are many fundamental things that we cannot explain, at least not in the beginning.

I've never seen an approach like this to bell's theorem. Very interesting. You connected it to other notions I've never listened about. I also believe that measurement is connected to connected to some kind of information flow and that there is information flowing everywhere. I think this notion will be essential for future physics.

Nice work! All the best

Frederico

    Thanks, Frederico! You are very kind. Indeed, if physical reality is made of information alone, network connectedness and continuous flow are primary.

    Warm regards,

    Tom

    Dear Tom,

    A nicely written and very important essay. Well done on showing so clearly that we cannot think about physical reality without thinking, and hence the problems of life and consciousness are 'in the game' from the outset, and although our theories are radically incomplete without taking them into account, we can make immediate important progress if we do take them into account. A great score coming, and good luck in the finals!

    Best wishes,

    David

    That's true. I think this subject is more important than people usually think. I also believe the ideas in the community are not as clear and established as people think. For example, I think there is for now no theory that describes mathematically what is information flow. I mean, we know about it, but it is foundationally not finished, there I a lot of work to be done about it.

    Regards,

    Frederico

    Tom

    I appreciate your grasping even some of it. It's the tip of the iceberg, but I still made it far too dense, so most just glimpse parts of it then struggle to keep hold of it mentally. We think very differently, so your comprehension is very encouraging and rewarding.

    I have a paper on some important optical aspects due out soon in the Hadronic Journal. I'd be very pleased if you'd look over it and comment. The main paper itself is turning into a bit of a toombe, as each falsification I try fails and just reveals more connections and evaporates more paradoxes and anomalies. It needs the sternest test, so a single figure finish here may give it that exposure.

    I confirm I think yours also should be in the top 35 so will do what I can.

    Best of luck

    Peter

    Hi Tom,

    nice essay. I particularly like "physical measurement--which is based on local events whose causality is known, in measuring interactions bounded by arbitrarily chosen coordinate frames--has a constant relation to a metaphysical coordinate-free causality." However I disagree abut many worlds.

    Best wishes

    George

      Dear Tom,

      This is an interesting essay, and particularly timely from my perspective because gives me some new ideas about a subject I recently encountered. A few thoughts come to mind.

      1. The notion of "an infinite number of questions in an infinite length of time" (page 1 of your essay) also arises in pure mathematics in relation to Godel's incompleteness theorem (without the time factor, of course). The reason is that "proof" is taken to involve only a finite number of statements in terms of the axioms of the system (e.g. natural numbers), and one must be very lucky for this to suffice to prove a true general statement which may be true for different reasons for each of an infinite number of subsets of elements. One can always test the statement for particular choices of elements, or perhaps prove the statement for certain subsets, but in most cases one cannot decide the truth in a finite number of steps. This seems very analogous to the unbounded game of 20 questions.

      2. You have an interesting perspective on locality, and one I will have to think more deeply about. I like the Poincare disk analogy. For some time, I have wondered about the meaning of locality because of the assumptions it involves; ordinarily some sort of metric concept comes into play (in order to define "close" and "far away"). But quantum gravity considerations cast doubt on the notion that spacetime is a metric manifold. Perhaps locality should be defined in terms of interaction: if two systems directly interact, they are considered local. Entanglement makes this definition completely incompatible with the manifold assumption.

      More to say, but a student is pestering me. I enjoyed your essay, and wish you the best of luck in the contest! Take care,

      Ben Dribus

        Hi Geroge,

        Thanks! Yes, I know you disagree with the many worlds hypothesis. My view is that until we have a suitable alternative to collapse of the wave function, we need a place-holder for the middle value -- a coordinate-free system can never allow such a collapse because there is no particular point in the continuous range of measurement values into which it can collapse; i.e. the wave function is not probabilistic. So if Hawking ever actually said that the Everett hypothesis is "trivially true," I think that's what he meant. It's certainly what I mean.

        OTOH, Joy Christian's topological structure of S^7 physical space solves the problem. Physical measures default to the non-trivial topology of S^3, with no collapse of the wave function.

        All best,

        Tom

        Thanks, Ben ...

        Interesting that your teaching duties interrupted you. My own work responsibilities interrupted my reading of your essay this morning (I'm traveling on business). Actually, I was re-reading since I read and rated your essay with a high score days ago. Still organizing my comments.

        What is often called the "surprise version" of 20 questions (because the questioner is not aware until the end that there is no predetermined "right" answer) has the advantage of self-organizing its own constraints. Godel would say that those constraints were written in "The Book" even if one were incapable of calculating them. IOW, even given that not every infinite series has a finite answer, every answer requiring infinite time has a uniquely corresponding series of "questions." This stuff gets very abstract, and domain-dependent, as, e.g., Dedekind proves that there exists a pair of numbers in Dedekind cuts whose product is sqrt2, though one could never actually write those numbers.

        The bottom line is that we really know very little about the continuum. Neither in terms of the number continuum, nor of spacetime.

        What we *do* know, is that correspondence of boundary conditions to measurement values in any physical sense requires a bounded length of time. So a coordinate free measure of functions continuous from the initial condition is bounded in space and unbounded in time (and nevertheless consistent with the conventional general relativity interpretation of a universe bounded in time at the singularity and unbounded in space).

        "Perhaps locality should be defined in terms of interaction: if two systems directly interact, they are considered local." Right on brother; that's the way Einstein saw it, too. Further, though, it is of deep consideration that Einstein noted " ... if two ideal clocks are going at the same rate at any time and at any place (being then in immediate proximity to each other), they will always go at the same rate, no matter where and when they are again compared with each other at one place." In other words, the clocks do not lose their local rate of change; no matter how spacelike separated, they are always timelike correlated -- which gets into your metric question. I won't try to answer it, because it's already been answered by Joy Christian's topological framework. Indeed, Joy obviates quantum entanglement, and takes full advantage of a topological idea of distance that ordinary geometry cannot accommodate.

        Thanks for your thoughtful comments. I'll get around to commenting in your forum as soon as I can.

        All best,

        Tom

        If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

        Sergey Fedosin

        Sure, Peter, I'll be glad to take a look, with no guarantee that I will have the knowledge to evaluate it. Thanks for the kind comments.

        Tom

        I did not yet read all your essay, but I looked abstract and conclusion. There I find the first question, with which I agree: "Am I alive?"

        I gave you 10 points maybe in the last minute, possible.

        Please read my My essay

        Best regards Janko Kokosar

        Hello Tom,

        Assuming there will be no more casting about; it is my pleasure to congratulate you as a finalist. I enjoyed your essay greatly, though it took a couple of readings for some ideas to sink in. I think it is especially poignant; the overlooked point that being an observer is inherently centric. Whatever information is being received, it is coming from a distance toward the observer. That's all an observer sees, and never the receding wave.

        I made a similar point, once upon a time, though in a more philosophical setting or context. And I had to look through a lot of my old writings to find the references. Generally speaking; a point of view defines a frame of reference, and a sense of proximal and distal space. Toward and away are relative to the point of observation. And always it is that point at infinity which is bringing us information.

        So yes; I think you deserve to be in the finals. May the judges treat you kindly.

        All the Best,

        Jonathan

          Hi Jonathan,

          Thank you so much. You know that I also hold your research in high esteem, and it is the greatest reward for any of us to have like-minded friends "get it."

          I am happy to return the congratulations, and wish you the greatest success in the contest, with your journal, and in all other endeavors.

          All best,

          Tom