Dear Fabien,

you're correct that in the essay as it is, the infinite number of states is an assumption. I made this somewhat more explicit in the Foundations of Physics article preceding this work, by introducing the notion of 'program world': physical states encode initial data, and programs take these as input, to spit out a measurement result. As there is a denumerably infinite quantity of programs, we get infinitely many possible measurements.

Classical physics essentially emerges from this using coarse-graining: that is, once you're unable to distinguish between certain states, and thus, have only extracted an amount of information about the system that's sufficiently below the finiteness bound, you won't notice any quantum effects. So yes, this is, I think, in some sense what you're saying: you lump all the real numbers in some interval together, and don't distinguish between elements of the resulting set.

Cheers

Jochen

Dear Harrison,

thank you for your comment. I'm happy to see that some of my ideas seem to resonate with you.

It's interesting you should mention contextuality---my earliest work in quantum mechanics was on that notion, and in a sense, you're right, you can think of a sort of 'contextual reference frame' in analogy to (perhaps generalization of) spatiotemporal reference frames. It wasn't primarily relativity theory I had in mind with the notion of relative realism, however, but merely the idea that we can attach the label 'real' to certain events only as relative to others---for instance, the electron's spin value being 'up' could be thought of as a claim about 'reality' only relatively to the measurement apparatus showing an 'up'-reading.

Your notions regarding---if I interpret you correctly---an inherent thermal 'noise' making the acquiring of perfect information about a system impossible remind me of Nelsonian stochastic mechanics. Is there a connection?

I will have a look at your essay---I hope I'll soon find the time to give it a good reading.

Cheers

Jochen

Dear Christi,

I'm happy that you found something you liked about my essay! Thanks for pointing me in the direction of your other papers---I'm always amazed, and a little bit humbled, at the depth and breadth of your ideas. I had, in fact, seen that paper before---one thing I'd been wanting to think about is how this relates to ideas by David Albert, who has proposed to explicitly 'pry apart' physical space and what he calls 'the space of physical determinables' to make sense of quantum weirdness. The latter seems clearly related to configuration space in some sense, so perhaps one could use your formalism to 'pull back' Albert's explanations into a familiar 3+1-arena, and see what they amount to.

But that's hardly even an idea for an idea, so far.

Anyway, you've given me quite the reading list, I'll try my best to eventually catch up, thanks!

Cheers

Jochen

Dear Noson,

thank you for your comment. I'm glad to get some endorsement from you---after all, some of the core ideas derive directly from your work. So I should really thank you!

Cheers

Jochen

Dear Vladimir,

I don't want to let this thread of conversation die, but I find myself more pressed for time than I had anticipated. So I'll have to try and be brief.

First of all, I think I agree with your general concern (oh, and thank you for reminding me of the Hegel quote, it's a hopeful thought in these present times). I have struck up a similar conversation with Fabien Pailluson over at his essay page, about how questions, once 'systematized' and transferred into the domain of mathematically expressed science, may lose some of their original meaning---in other words, how our desire for quantifiable answers may lead to the loss of the original question's substance. Perhaps it is also of interest to you.

I'll have to dash, but I promise to try and find the time to engage with your essay. Thanks again for your kind comments!

Cheers

Jochen

Dear Jochen,

Thank you for the reply and the interest in my mentioned papers. In the one with the representation of the wavefunction on space or spacetime, the representation, albeit complicated, is just like a classical field theory, with infinite-dimensional vector fields satisfying some global gauge symmetry. But once we put aside the differences in the complexity of the theory, as I said, we see it's just a classical field theory. This as long as no collapse takes place. I'm not sure if David Albert would find this at odds to his proposal to teach QM and explains how it differs from classical mechanics based on the fact that the wavefunction lives on the configuration space. Now we see that this was only a representation, and the things are as classical as it gets, including being local. The difference occurs if there is a collapse. Collapse, for taking place everywhere in space simultaneously, introduces nonlocality, and because of collapse, entanglement leads to Bell correlations. Now, one can say, "assuming that your representation is true". It is true, I mean a correct representation, and maybe there can be simpler or more natural ones. But both mine and the wavefunction on the configuration space are just representations. Mine, as opposed to the wavefunction one, (1) makes explicit locality and when exactly it's violated, and (2) is consistent with the idea of "ontology on space or spacetime". So there is no need to appeal to ontology on configuration space, not that this was a problem, but I submit that this is NOT the characteristic of quantum mechanics, since there is no difference here. The key difference is brought in by collapse.

Now, about collapse, the paper I attached to my previous comment can be taken as independent on the Phys Rev one I linked in the same comment. But to me they are related. The one about the post-determined block universe makes use of the fact that the ontology of the representation of the wavefunction is on space or rather spacetime. But it's not only this, it proposes an interpretation of QM where there is no collapse and the outcomes are still definite (so it's not MWI, it's just unitary single worlds). But earlier I stated that the key difference between QM and classical is isolated in the collapse. And in the other paper, that collapse is not necessary, it can happen unitarily. And in fact, if there would be discontinuous collapse, it would be undesirable, like breaking conservation laws, relativity of simultaneity, the evolution law, and is in tension with the Wigner-Bragmann derivation of the wavefunction for any spin and its dynamics for free particles, from the Poincaré symmetry. And locality. Now, most people think that all these are a small price to pay. For me, since I care about relativity too, it's a too big price.

OK, so back to isolating quantumness. How can I say that quantumness is not in unitary evolution, since it is equivalent to a classical one, but also say that the collapse may not exist? Isn't there a contradiction between these? Indeed, from the post-determined BU paper follows that the difference is not in the collapse either, at least in my interpretation without discontinuous collapse. The key difference, I think, is deeper, and need to be found, but I hint in that paper that it has to do with some topological constraints which can prevent most of the local solutions to extend globally, leaving to a zero-measure set of solutions which look as fine-tuned to go around Bell's theorem while still being local. Now, you may disagree with the post-determined BU, since I didn't prove that this is the case yet, but at least the paper with the representation on 3d space can only be refuted if some mistake is found in my proof. So at least for now the best way to isolate the quantumness is in the collapse, more precisely, the fact that it takes place globally on all of the degrees of freedom of the fields on 3d which I use to represent the wavefunction. And this can have the same effect on classical fields too, as we can see if we take as example my representation.

Thanks again for the comments,

Cheers,

Cristi

P.S. Even if I said earlier that from the representation of the wavefunction on 3d space follows that the quantumness is not due to the wavefunction being on the configuration space, but it's related to the apparent collapse, this is not in conflict to it being related to the quantization of the volume of the cells in the phase space. In fact, I think this is the point of convergence with what I said that I don't think it's in the collapse either, because I don't believe there is discontinuous, nonunitary collapse even for single worlds. If my program will succeed, I expect to be something topological that will result in full interactions being quantized, and here is where I think that the phase space quantization will result. But, as I said, I don't have a proof yet.

Dear Jochen,

you have written a wonderful essay and thought provoking.I got a question and proposition to make.....

The Godel's law can be written as.........Godel proved that any consistent mathematical theory (formalized as an axiomatic deductive system in which proofs could in principle be carried out mechanically by a computer) that contains enough arithmetic is incomplete (in that arithmetic sentences ' exist for which neither ' nor its negation can be proved)...................

I have few questions about it. This law is applicable to Quantum Mechanics, but will this law be applicable to COSMOLOGY.......?????.........

I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in that statement are applicable ok

I hope you will have CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory's Philosophy".....

Regarding proposition........

Why dont you make a new interpretation of quantum mechanics the 21st one, covering all aspects of it including intelligence, observations, experimental results, etc....I feel that with your knowledge you can definitely accomplish it

Best Wishes ....

=snp

    Dear Jochen

    Thank you very much for your answers, openness and focus on the big discussion. (brainstorm). Today there are many articles, books, conferences, but for some reason there are few brainstorming sessions. FQXi contests give this opportunity to all participants .

    Sincerely, Vladimir

    Dear Satyavarapu,

    thank you for your kind comment. I have to admit, I haven't thought about Gödel's theorem, or similar ideas, in a cosmological context explicitly---although I suppose, in some sense, the Gödelian phenomenon can be viewed as a consequence of embeddedness, i. e. of being a subject of the same theory used to describe some object system. That is, if there's no separation between observer and observed, the observer becomes subject to their own observation---and cosmology is really the ultimate framework of embeddedness. So, one might not be surprised to find some connection.

    That's not to say that these considerations will be of any import regarding theory building. There's sometimes an argument that Gödelian phenomena preclude a theory of everything---but I think that's misguided: think of something like a universe based on the Game of Life (in memoriam John Conway): you've got a perfectly simple theory of everything---just the update rules of the CA grid---but nevertheless, Gödelian considerations apply, as the system is capable of universal computation (and hence, 'contains enough arithmetic'). These manifest in general in the phenomenon of the question whether certain patterns ever arise being undecidable---so there will be unpredictable phenomena, but that doesn't mean that we can't discover the rules themselves.

    As for interpretation, well, in a sense every reconstruction leads to an interpretation, as well---but really, I think the market's kinda saturated.

    I will try whether I find something sensible to say about your essay. Best of luck in the contest!

    Cheers

    Jochen

    Dear Christi,

    thanks for the fascinating discussion. One thing I'd like to understand---one can formulate classical mechanics on Hilbert space, as is done in the Koopmann-von Neumann representation. I wonder if one could apply your 3D-representation to the KvN-wave function; then, one could maybe more explicitly study how that differs from a quantum wave function, giving a hint of where the quantumness comes from.

    Personally, I think my biases are opposite to yours---I tend to think of space and time as ultimately derived entities, and I've got some sympathies with the recent developments regarding the duality between entanglement and spacetime-descriptions. This is an older idea than many realize, going back to (admittedly, somewhat heuristic) arguments of Carl Friedrich von Weizsäcker, and David Finkelstein with his 'spinorism'. But then, I come from a quantum background, so maybe that's to be expected.

    Lawrence Crowell, in his essay, has taken the notion of epistemic horizons into a context of topological obstructions, which he seeks to use to explain quantum mechanics/entanglement. If I'm honest, I'm afraid his stuff is a bit too advanced for me, but you might have a better chance---perhaps there's something that could be helpful to you in there.

    Regarding the question of collapse, I think to me, that's a (unavoidable) consequence of modeling---I make it more explicit in the Found. Phys. article, but the basic idea is that any function whatsoever can be written as a computable function augmented by an infinite reservoir of random bits---every set is Turing-reducible to a random set. So the best computable description of being faced with such a general world would look a lot like a compressible part with intermittent randomness---i. e. a lot like what we're seeing. But this has to be made more clear, I think.

    Anyhow, I'm very enthusiastic about your project---it's not completely aligned with my own predilections, but I think it's the sort of innovative and creative thinking we need in fundamental physics right now. Neither of us can realistically hope of getting it all right, but perhaps it's not too audacious to hope for planting a few seeds that, in time, might yield fruit.

    Cheers

    Jochen

    Dear Jochen,

    Indeed we can formulate classical mechanics on Hilbert space, as is done in the Koopmann-von Neumann representation. I think they can already be compared on the Hilbert space, as it was intended, but they also can in my representation. Maybe this will lead to some insights, nice idea!

    About the relation of QM and GR, I agree there may indeed be some duality involved. The way I imagine the duality is that ultimately there is a structure which looks like something like QFT in some representation, and something like a quantum GR (maybe of the sort I described in the paper I attached to my first comment) in another representation, so something like [QT]~[real QT]=[real GR]~[classical GR] :). I am not very much impressed when I see differences in approaches, because there are many ways to say the same thing. Maybe we'll see someday what's the real deal though. Until then, I hope there are enough biases to cover sufficient research directions to find it ;) Or, as you said it well, seeds.

    Cheers,

    Cristi

    Dear Jochen,

    I very much enjoyed your essay. I had decided not to comment on your essay because my opinion is that physicists project math structure on the world and then come to believe that physical reality has that structure. 'Qubits' are a fine approximation for spins on magnetic domains, but the Stern-Gerlach data on the famous post card shows anything but qubits. Only because Bell insisted on qubits (A,B = +1,-1) in his first equation did he arrive at his no-go theorem. If one uses 3D spin one obtains exactly the correct correlation, but this violates the projected structure. The spins of course have unit magnitude, but their 3D orientation determines their SG deflection that is the actual measurement. The measurements correlate perfectly. Of course, although Bell's reasoning was based on Stern-Gerlach, all of the experiments have been done with photons. I have not worked out a comparable solution, because I do not fully understand the "exotic quirks like orbital angular momentum". Regardless, I did not intend to come to your page simply to argue.

    But I just saw your comment on Xerxes Arsiwalla's essay expressing interest in his 'distributional processing' of subjective experience, and mentioning your 26 Mar 2020 publication in 'Mind and Machines'. Congratulations! Do you have a copy that is not behind a paywall?

    Anyway, in view of your expressed interest in a model or example of distributional processing, I wish to make you aware that, based on new info appearing 10 days ago, I have rewritten my essay to include such an example that you might find very interesting. I hope you will look at it and would welcome any comments (including argumentative!)

    Deciding on the nature of time and space

    Cheers,

    Edwin Eugene Klingman

      Dear Jochen,

      I approach from a, perhaps, more intuitive level.

      What got me interested in your essay was the idea that quantum mechanics and Godel's theorem might be shown to stem from one and the same first principle. Your rigorous conclusion is eventually my gut feeling hypothesis. And I'm longing for the most economical way to do justice.

      My question is what phenomenology or ontology in nature might model such first principle you speak of? Is it Planck's black-body cavity or some cosmic system of waves? Or is there some actual Hilbert Space to be found in nature?

      I ask this question because it seems to me that any self-referencing system (as must be Godel's set of all sets or Schrodinger's wave function) should basically model the observer as part of the same system it is aiming to observe/measure.

      In short, how would your Epistemic Horizons model the observer proper vis-a-vis its observable(s)?

      Chidi Idika (forum topic: 3531)

        nice work very well done.can finiteness be borne out of infinity through anthropic bias ?kindly read/rate my essay https://fqxi.org/community/forum/topic/3525.all the best to you

          Dear Chidi,

          thanks for reading my essay, and taking the time to comment! I think your intuition is spot on, if I understand you correctly. The possibility of self-reference in quantum mechanics comes about due to the universality of the theory---due to the fact that it applies to every system. That's why singling out a specific sort of system as an 'observer', which itself isn't subject to quantum rules (something like Wigner's 'consciousness causes collapse'-interpretation) is one way out of trouble---which is, however, difficult to square with our current understanding of the physical world.

          In my model, the self-reference enters in a sort of oblique way. For one, you can write the state of a system by means of the outcomes of certain measurements---that's just like giving a list of properties of the system, like describing an electron as 'charge -1, spin +1/2, mass 511 keV', and so on. So in general, a state can be viewed as a list of measurement outcomes.

          A measurement, on the other hand, can be defined by the set of all states for which it yields a particular outcome---in my setting, we only have dichotomic measurements (+/-1 valued), so you can simply just give a list of states for which it has the value +1, say.

          So now, you can see where the circle closes: a state can be written in terms of measurements; each of these measurements can be written in terms of states; these states can again be written in terms of measurements; and so on. So, you can have a stat depending on a measurement depending on that very state---so that's where the self-reference comes in.

          In a larger sense, I view the general Gödelian phenomena as a mismatch between the world 'out there' and a model of the world. The model, after all, is a feature of the world in any non-dualistic theory---it's something that's concretely there, some particular brain-state, or neuron-firing pattern, or what have you. So we have a model of the world, that's itself part of the world---you can view this like a detailed map of an island laid out on the ground; if it's sufficiently detailed, it will contain a copy of itself at that point where it's placed on the ground, which will itself have a copy within it, and so on.

          In this sense, any model including a model of the modeling agent will be subject to phenomena of incompleteness in some sense---or else, succumb to circular inconsistency. I make this point somewhat more in detail in last year's entry, and in a slightly different way in my recent article in Minds and Machines.

          I will take a look at your essay, perhaps I'll find something interesting to say.

          Cheers

          Jochen

          Dear Michael,

          thanks for reading my essay, and taking the time to comment! I'll have a look at yours, and see whether I can find something interesting to say about it.

          Cheers

          Jochen

          Dear Edwin,

          I'm glad you found something to like about my essay! There is, I think, a subtle point about how 'laws of nature' formulated by physicists track 'the real world'---or perhaps, don't. We're certainly never faced, in the real world, with the sort of idealized systems that feature in our models---no frictionless surfaces, no spherical cows, and yes, no qubits (Nancy Cartwright talks about 'how the laws of physics lie'). On the other hand, experimental data has been predicted to stunning levels of accuracy using these idealized systems, so it's hard to escape the conclusion that the models do get something right (as it's sometimes put, the success of science would otherwise amount to the miraculous).

          But one can prove 'unsharp' versions of Bell's theorem, where one does not make any assumptions about the nature of the system upfront---where, indeed, nothing needs to be assumed other than that there exists a well-defined joint probability distribution for all experimentally accessible quantities. Likewise, one can take loss of systems, or mismeasurements, into account.

          Thanks, also, for your interest in my paper in Minds and Machines. You can access the full text here. If you have any questions or comments, I would be happy to discuss them!

          I will now go and see what your essay can teach me about distributional systems.

          Cheers

          Jochen

          Dear Jochen,

          Thank you for reading my essay and commenting. I've responded there.

          My point about Bell's theorem, based on sharp or 'unsharp' versions, is that treating spin as classical yields the actual Stern_Gerlach data distribution seen on the postcard, and also reproduces the desired correlation. Imposing a qubit structure, while statistically appropriate for spins in magnetic domains, destroys locality. I find that too heavy a price to pay, and my opinion seem compatible with the many essays that question whether there is any necessary connection between our projected formal structures and the underlying reality ("whatever that might mean"). As Dascal quoted Curiel:

          "just because the mathematical apparatus of a theory appears to admit particular mathematical manipulations does not eo ipso mean that those manipulations admit of physically significant interpretation."

          While Bell reasoned based on Stern-Gerlach, all of the experiments are based on photons. I am trying to grasp the OAM aspects of photons that have been reported for years and am unable to challenge the photon based experiments in the same way that I challenge SG experiments.

          I almost decided to burden you with a longer rational supporting the above argument, but, unable to use graphics and equations here, I'll spare you.

          Thanks again, and good luck in this contest.

          Warmest regards,

          Edwin Eugene Klingman