Essay Abstract

Abstract: Is reality best described in digital or analog terms? In proper context, we are asking: what type of math is best for that purpose? However, I argue that our universe is genuinely non-deterministic, as conventional notions of quantum mechanics imply. Since mathematics is by nature deterministic, reality is not fully describable by any true mathematical model. The best answer to the original question is then, "neither - reality transcends mathematics." It is argued that some popular attempts to avoid the quantum measurement problem, such as the decoherence interpretation, are flawed. The logical case for DI is flawed by the circular argument at its core. More importantly: some experiments are described, which could falsify the DI. If successful, they would show that we can recover superpositions supposedly lost to decoherence. Hence our finding definitive experimental outcomes instead of superposed results is not due to the effects of decoherence. Those definite, exclusionary results show a genuinely indeterminate character of the universe.

Author Bio

I consider myself a "Renaissance man" because of the variety of studies and work I've been involved in. That includes some consulting at J-Lab using G4Beamline to model muon interactions, teaching at various levels, museum guide, etc. I am lucky that Internet search for "quantum measurement paradox" usually brings up blog posts of mine in top hits. I've published some in physics. The articles are about the relativistic dynamics of extended bodies, a sadly neglected topic. However, I am to be considered "an amateur"

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  • [deleted]

Hi dear Neil Bates,

Congratulations,it's a beautiful essay.

Your conclusion is interesting, a dodecahedre, I prefer the sphere of course but all is free of thinking.

Good luck.

Steve

    Hello Neil, I also agree that reality must transcend maths. Have you ever considered the mechanical model of a GRAVITON being represented by an Archimedes screw? This would certainly transcend Newton's famous equation, wouldn't it? Thanks for your essay.

    Kind regards,

    Alan

    • [deleted]

    Steve, the dodecahedron-bird was in a dream I had (for real) in IIRC the late 80s. It is just a poetic metaphor for the enigmatic nature of our universe, not a conceptual model of reality relating to its shape. It does have some relations to other ideas: I had the dream some years before reading about Penrose's "magic dodecahedron" of quantum mystery published in 94. That shape does lend itself to making Penrose's point about quantum entanglement. Note also, when the Platonic solids are used to represent elements:

    cube: earth

    tetrahedron: fire

    octahedron: air

    icosahedron: water

    and the dodecahedron is "quintessence" - the mystical fifth element of the heavens, and sometimes "the universe" as a whole. Since I knew that when I had the dream, I think it really did symbolize that whole issue of fruitlessly chasing after the ultimate nature of reality.

    Some physicists do refer to a special stuff or field they call quintessence. Wikipedia says: "In physics, quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe."

    However, my essential point is that the popular and spreading notion that decoherence explains why we don't see macroscopic superpositions, is false. I give logical arguments and propose experiments to test my challenge.

    • [deleted]

    If DI would be inconsistent with certain experiments, this would be an interesting finding. Anyways, i enjoyed your essay and the quantum mechanical depths you explore with rigorousity.

    I too outline an experiment to discriminate between a unitary deterministic evolution of the Schrödinger's wave function and the possibility that this wave function breaks down at some point. If you want, read it here and let me know what you think.

    Hi, Neil

    I agree that natural reality cannot fully be represented by mathematics (or any form of deductive system). I come to this conclusion by an entirely different route, which you might find interesting (my essay "topic/852"). No one has taken me to task (yet) for the core assertion: if nature is real, then it is non-deterministic; and if it is deterministic, then it is not real".

    Best wishes and thanks,

    Dan

    Neil,

    A wonderful essay. Not what I would consider "an amateur". Reading it, I assumed that your logic is valid [nothing stood out to contradict this assumption] and the logic is beautiful.

    In his Appendix A in "Dance of the Photons", Zeilinger has Prof Quantinger explain things in terms of sets of twins, with height, hair and eye colors as the 'properties' found by measurement. He then derives Bell's inequality from the data set and claims that violation of the inequality is grounds for abandoning local realism, and that we must then assume that these properties don't exist until measured, and moreover, that as soon as one twin is measured, the other, possibly 'infinitely' far away, immediately assumes the appropriate state.

    I find it easier to believe that one of the twins stopped at the barber shop and had his hair dyed.

    I show in my essay a plausible reason to suspect this. I'm unsure whether this may be what you are referring to when you state "we have to assume that something can and does generate statistics of some kind from wave amplitudes in the first place."

    So far, yours may be the only other essay to propose an experiment to test your idea.

    So thanks for a great essay, and I hope you get a chance to look at mine. Some of our ideas go quite well together. Good luck in the contest.

    Edwin Eugene Klingman

      • [deleted]

      I find this a very thorough discussion regarding the weaknesses of DI in it failing to resolve 'on its own' the measurement problem. However this is not exactly a new revelation, although admittedly an important one needing more exposure to be better understood and would argue particularly within the theoretical community itself. For instance many of the same points have been raised previously by Sheldon Goldstein and Detlef Dürr, proponents of the DeBoglie-Bohm pilot wave picture. The conclusion reached here with which they would concur is quantum mechanics taken as only requiring to be considered explainable as action(s) of the wave function alone as being inadequate, which Goldstein summarizes in his synopsis of Bohmian Mechanic to be found in the Stanford Encyclopaedia of Philosophy as follows:

      "It is widely believed by proponents of orthodox quantum theory that the measurement problem itself is somehow resolved by decoherence. It is not easy to understand this belief. In the first formulation of the measurement problem, nothing prevents us from including in the apparatus all sources of decoherence. But then there is no longer any room for decoherence to be in any way relevant to that argument. Be that as it may, one of the best descriptions of the mechanisms of decoherence, though not the word itself, was given by Bohm (Bohm 1952), who recognized its importance several decades before it became fashionable."

      However, in light of the fact that a completely consistent solution to the measurement problem has existed since Bohm's publishing of his interpretation in 1952, it is then not fair to say that it has not been resolved. Interestingly enough from Bohm's perspective its resolution is not to be found by considering the natural of the world as being digital or analog, to the exclusion of one or the other, yet rather the recognition that the acceptance of the physical reality of both as needed to account for the situation. As J.S. Bell reminded "Now in my opinion... ...The quantum phenomena do not exclude a uniform description of micro and macro worlds...system and apparatus. It is not essential to introduce a vague division of the world of this kind. This was indicated already by de Broglie in 1926, when he answered the conumdrum 'wave or particle'? by 'wave and particle'."

      So from this perspective, with the particle to account for the digital nature of the world and the wave as its analog counterpart, there's no need to resign one's self to believe that the attempt to ground reality in terms of physical space and time comprised of ponderable bodies is like "...something we seek and may never catch".

      "Some physicists, among them myself, cannot believe that we must abandon, actually and forever, the idea of direct representation of physical reality in time and space; or that we must accept the view that events in nature are analogous to a game of chance. It is open to every man to choose the direction of his striving: and also every man may draw from Lessing's fine saying, that the search for truth is more precious than its possession. "

      -Albert Einstein, "The Fundamentals of Theoretical Physics" in the journal [Science- May 24, 1940]

        • [deleted]

        First, to its enthusiasts in general: I regret not mentioning Bohmian mechanics in my article. Note restriction to 25,000 characters which made the piece shorter than I wanted. I had to ditch some extra discussion about other alternatives etc. I also needed a definite declarative point to grab attention. I also just don't think BM would work out. For example, I still don't see how a deterministic process could make nuclei decay in true random manner. Note that a remaining portion after many trimmings still has to show the same statistical behavior. I don't think any "mechanism" whatsoever can do that.

        Thanks Phil for the consideration and effort you put into essays and comments. Let me say in my defense, as elsewhere: I noted simply that we don't have any answer right now in the sense of knowing the answer, nor do we have a right to *assume* that there *must be* a reasonable answer to the QMP - not that in Nature there really can't be such an answer, and/or that we can never find it, and/or that BM cannot possibly be such an answer. I acknowledge that Bohmian mechanics is an option that avoids either the decoherence fallacy, or the inscrutability of collapse; however I am not otherwise impressed with it. Finally, regarding DI: It is wrong in any case to use fallacious methods and conceptualizations, to attempt to achieve the goal of understanding fundamental quantum reality - whatever is there to be attained. I hope that my experimental proposals will transcend just having to argue over these issues.

        • [deleted]

        Thanks, Edwin. I call myself an "amateur" because of my station in the operational and semantic scheme of things, it need not imply lack of ability (see for example Olympic athletes just for logical illustration.) Also, since there is a prize category for best amateur's essay, I should ID myself as eligible.

        Aside from the experimental refutation of the claim of "mixture" output caused by decoherence, I do mean that something has to generate the statistical events from the wavefunction. It isn't just an intrinsic feature of the states, otherwise there would just be the superposition "photon hit in detector A" plus "... in detector B" forever. I wasn't addressing entanglement in the Bell sense of distant correlations, but the ordinary "entanglement" in DI of photon wave at detector A entangles with clicked state of detector A, etc.

        I will take a look at your essay, and withhold substantial comment until I'm sure I understand in depth. I think you (and other readers) would find other posts at my blog interesting too, find at Paradoxer.

        Dear Neil,

        I note that my reply to your comments on my 'Chip in the brain' essay are headed 'anonymous' - all is not well with my computer at present. The maths theorems I mentioned are available as an attachment to an earlier post to my essay. My email address, when I recover access to it, is michaeltdeans@gmail.com

        Best wishes, Michael T Deans

        Hi, Neil

        Thanks again for your great essay, and your appreciation of mine. In response to your statement (on my own thread), that "arguments can't decisively show what to think about determinism versus true indeterminism", I can offer some general, if somewhat dogmatic, arguments about causality. (This is posted on my thread as well).

        Following Hume, there is no causation in Nature. The appearance of it results from confusing cause with logical implication. This is a 'category mistake', like mixing mental with physical domains. The only truly deterministic systems are deductive systems, for the only 'necessity' is logical necessity. This is always a matter of definition rather than of fact, so that the "mistake" is confusing 'the found' and 'the made'.

        Similarly, randomness pertains only to mathematics, not to physical reality. Whether Nature is random is not a decidable question. The IDEA we have, of random physical processes--lacking, as you say, logically bound outcomes--simply reflects this confusion of the found with the made. We are never in a position to establish logical necessity (cause) in Nature (the found), and only sometimes in mathematics (the made). In other words, 'random' is a mathematical concept, not a physical one. Randomness in Nature, like causality, can only be a metaphysical assertion--that is, independent of decidable physical fact. (Historically, it was religious, since all cause was ultimately traceable to the First Cause.) If so, then experiment would be irrelevant.

        We cannot make meaningful ONTOLOGICAL assertions about events in Nature being either determined (caused) or undetermined (random). But we can make assertions about our own state of knowledge; we can say that something is 'undetermined' in the sense that for us it is undecided or unknown. This is not an assertion about Nature (the found) but about science (the made).

        The term 'determinism' is traditionally ambiguous. It can refer, on the one hand, to what can be determined epistemologically; on the other, it can refer to an ontologically real relationship of causal power existing between things or events. I believe there can be no determinism in this latter sense--and therefore no 'true indeterminism' either. The only determinism is logical implication (provability), and the only deterministic systems are deductive systems. The only indeterminism is logical undecidability.

        I do make statements in my essay to the effect that the apparent randomness of Nature supports its "immanent reality". I do not mean by that, however, to say that Nature is intrinsically random. It is rather the state of our own uncertainty (not Nature's) that requires us to regard Nature as bearing its own full reality--precisely because it cannot be fully accounted for in some deductive system. It is real because it is not a product of our definitions, because WE cannot determine what it is. This is separate from the question of whether it is 'determined' (causally) within itself, which is not a question we can answer. We imagine that it might be so determined, but what we are really thinking of is the logical determination within our own thought systems.

        Hope this is useful.

        Best wishes,

        Dan

        Hi Neil,

        I finally managed to find time to read your essay. Nice job! I have a few comments.

        - It seems to me that, at times, you are "mixing metaphors" a bit when it comes to the wave-particle duality issue, notably on p. 3. This is related to my next comment.

        - You talk about the confuser in relation to particle statistics. If you do this, you need to identify the type of statistics that is being produced by the beam, e.g. Poissonian, sub-Poissonian, or super-Poissonian, because it seems to me that it could make all the difference in the world which type of statistics is being sent into it.

        - I'm still not sure precisely if you are arguing *against* or *for* this interpretation of the wavefunction in terms of statistics. If you are, then you have to ignore the continuous wave interpretation entirely, at least that is my opinion. You have to pick one or the other. It makes no sense to mix interpretations (I am by no means saying you are the only one who does this, by the way - I think it is an inherent problem in how we interpret these things in general).

        Ian

          • [deleted]

          Ian, thanks for your thoughts. I'm not sure how to respond re mixing of wave particle metaphors. We already know that Nature expresses both traits. The DI interpretation tries to get "mixtures" out of wavefunctions via a sort of circular argument, as I noted. Remember, I am first trying to "get inside" their argument, then criticize it as being inconsistent. The whole point is, their argument is not really "coherent" (pun intended!) As for the statistics: the source is a "photon gun" that shoots one at a time, coherence time

          • [deleted]

          I already logged in and this rubbish shouldn't happen to me. I should not be shown as "anonymous" and where is the rest of my reply? I will try again:

          Ian, thanks for your thoughts. I'm not sure how to respond re mixing of wave particle metaphors. We already know that Nature expresses both traits. The DI interpretation tries to get "mixtures" out of wavefunctions via a sort of circular argument, as I noted. Remember, I am first trying to "get inside" their argument, then criticize it as being inconsistent. The whole point is, their argument is not really "coherent" (pun intended!) As for the statistics: the source is a "photon gun" that shoots one at a time, coherence time

          • [deleted]

          Hi Dear Neil, sorry for my late answer, I have some difficulties now to answer to all posts on the net.I thank you for this explaination, spiritual, it's a beautiful philosophycal extrapolation.

          Good luck in this contest.

          Regards

          Steve

          • [deleted]

          Neil,

          Great essay. I did read your discussion on this blog too about not getting into Bohm's theory. In my essay I propose a test to see if an electron in flight in a double slit experiment is in fact a wave or remains a particle and rides the pilot wave. If Bohm is correct, the electron could start anywhere on the wave front as it goes through one of the slits - including a spot that is destined for destructive interference. Since the electron wont disappear, it would have to jump to a different location to make it to the detector on the other side. This behavior may produce a different expected distribution of electrons than the distribution produced by a pure wave phenomenon.

          Keep up the good work.

          Chris

            Chris, thanks for your comment. I will study your full essay when I have more time. I do have a first impression of your electron proposal as presented here: It reminds me of the Afshar experiment (easy to look up), which is a modified double-slit experiment. It sets up a way to show that wave interference occurred (fine wires in way of the dark fringes, so they don't intercept many photons) even though we can later use directional sighting to apparently see from which slit a photon came. I think this means that the detector collapses one of the directional waves, and simply makes "an appearance" of having come exclusively from one slit, rather than a retrodiction showing "which way the photon came" all along. Hence we really can have apparent which-way information, and still show the interference, as Afshar claims is being done (even though I'm not aware of him using my framing of the issue.)

            Note: in haste, writing about the density matrix, I referred to if being an example of fallacious thinking. In and of itself, it is not and is useful in practice. However, the DM is sometimes employed in a fallacious way to argue why or how we don't see macroscopic superpositions. This happens when the presenter fails to appreciate the circular argument constituted by the squared modulus rule being already introduced into the mathematical structure, but itself without explanation or justification of when in the course of time, the modulus ("amplitude" in common usage) reduces to statistical results.

            Here again I attempt to resubmit my full (but edited) reply to Member Ian Durham, that got truncated (maybe from use of double less than symbol) and other issues. It includes my attempts at LateX, which did not work there. I'm just leaving that as is, I can't take time to labor over perfecting my handle on this LateX interpreter.

            >

            Ian, thanks for your thoughts. I'm not sure how to respond re mixing of wave particle metaphors. We already know that Nature expresses both traits. The DI interpretation tries to get "mixtures" out of wavefunctions via a sort of circular argument, as I noted. Remember, I am first trying to "get inside" their argument, then criticize it as being inconsistent. The whole point is, their argument is not really "coherent" (pun intended!)

            As for the statistics: the source is a "photon gun" that shoots one at a time, coherence time much less than shot interval (hence presumably "Fock states.") They do not interact with each other, this is not about bunching/anti-bunching etc. Maybe best said, I expect the type of photons to be used here, that usually are to make such points. Hence the statistics of detector hits should be from the amplitudes squared, basically binomial (for each channel individually, since of course the other channel must be "no" if the first is "yes") (like coin tosses (generalized chance per head or tail of course) with definite clear tries) and not Poisson types.

            I am definitely arguing against the DI in terms of statistics, but more than that (the falsely framed argument, but also that the experiment would show continued full superpositions coming out of BS2 after the decoherence, not "a mixture.") We know what statistics to expect for various phase differences, it's as given by the formula I = A^{2} B^{2} 2AB cos $\theta$, where I is "intensity" equivalent to hit frequency. (I saw the above examples, but I'm putting up old fashioned LateX commands in protest, or what am I missing?) But the key point is the claim about how "amplitudes" turn into any kind of "statistics" at all ...

            BTW, I sure would like to be a FQXi member ...