Can quantum mechanics really be the same as underlying deterministic theory?

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Solution 1

I think at least some readers should have noted by now that many of these arguments, particularly the more pathetic ones, are questions of wording rather than physics. Once you made your model simple enough, you can map anything onto anything. Now this was my starting point: if a system is sufficiently trivial, you can do anything you like. Now how can we subsequently generalize some such very simple results into something more interesting?

This has been the ground rule of my approach. I am not interested at all in "no-go" theorems, I am interested in the question "what can one do instead?" I admit that I cannot solve the problems of the universe, I haven't found the Theory of Everything. Instead of pathetically announcing what you shouldn't do, I try to construct models, step by step.

I now think I have produced some models that are worth being discussed. They may perhaps not yet be big and complicated enough to describe our universe, but it may put our questions concerning the distinctions between quantum mechanics and classical theories in some new perspective. Clearly, if a system is too simple, this distinction disappears. But how far can one go? Remember that cellular automata can become tremendously complex, and quantum mechanical models also. How far can we go relating the two? This is how you should look at my papers. I happen to think that the question is very important, and one can go a lot further in relating quantum models to classical ones than some people want us to believe.

And is a calculation wrong if someone doesn't like the wording?

Solution 2

Current (experimental and theoretical) wisdom on deterministic approaches to quantum nondeterminism just say that any deterministc theory underlying quantum mechanics must be nonlocal. Research then goes on discussing the precise nature of this nonlocalness or ruling out certain versions.

On the other hand, there are those who construct nonlocal deterministic theories that somehow reduce to QM. A lot of work goes into Bohmian mechanics, which however has difficulties to recover realistic quantum field theory.

The paper by t'Hooft pursues a different approach, based on discreteness. However, his results are currently very limited, just reproducing the harmonic oscillator.

Solution 3

It is certainly possible that QM is based on a deterministic physical mechanism. The no-go theorems like Bell's theorem or the "Free will theorem" of Conway and Kochen are not effective against deterministic hidden variable theories because they require non-determinism as one of their assumptions. There are still many phisicist claiming that determinism has been disproven but they are commiting the logical fallacy . However, it is too early to say if 't Hooft is on the right track.

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Updated on August 15, 2020

Comments

  • user10733
    user10733 about 3 years

    I am perplexed by recent papers by 't Hooft giving an explicit construction for an underlying deterministic theory based on integers that is indistinguishable from quantum mechanics at experimentally accessible scales. Does it mean that it is deterministic complexity masquerading as quantum randomness?

    http://arxiv.org/abs/1204.4926

  • akhmeteli
    akhmeteli over 11 years
    Your first phrase may be too categorical. For instance, it is my understanding that there has been no loophole-free experimental evidence of nonlocality. On the other hand, nonlocality is an extraordinary claim, so it needs an extraordinary proof.
  • Ron Maimon
    Ron Maimon over 11 years
    -1: This is incorrect. The Bell theorem is effective against deterministic hidden variable theories which are local. The argument from superdeterminism is ridiculous, it is not science, it is conspiracy theory.
  • Ron Maimon
    Ron Maimon over 11 years
    t'Hooft doesn't "reproduce" anything--- he has a linear space which is a quantum state space, he just truncates the evolution to be deterministic on a special basis. The actual dynamics is still quantum, it isn't really an automaton--- you can't imagine that the states are classical underneath.
  • Mitchell Porter
    Mitchell Porter over 11 years
    't Hooft thinks there is an ontologically preferred basis and superpositions of those basis states are not real. The Bohmian treatment of measurement interactions shows that you can have a preferred basis and still describe other observables correctly - though the Bohmians also still have superpositions in their ontology, as states of the pilot wave (unless they take the "nomological" path, and treat the specific pilot wave of an individual system as a dynamical law rather than a physical state)...
  • Ron Maimon
    Ron Maimon over 11 years
    @MitchellPorter: I know what he says, but this is ridiculous--- you have to tell me how come a laboratory electron is described by a superposition. It doesn't help to say that there is a basis in which the Hamiltonian is a permutation. If we don't know which basis element out universe is in, we describe that with a probability distribution, not with amplitudes. Then there is no reason that the electron in the lab is described with amplitudes. It is just wrong.
  • Mitchell Porter
    Mitchell Porter over 11 years
    In Bohmian mechanics with a specific pilot wave, you can substitute the specific pilot wave into the equations of motion for the classical objects of the theory, and you end up with a pseudo-classical theory in which a classical equation of motion is augmented by a nonlocal potential. It must be possible to explain superposition in terms of this nonlocal potential, because the theory is still identical to Bohmian mechanics with a specific pilot wave, but no-one has ever taken this route and exhibited what such explanations look like...
  • Mitchell Porter
    Mitchell Porter over 11 years
    In the paper after this one, 't Hooft constructs his alleged mapping from a CA to a QFT. The CA is really simple but the mapping is a little nontrivial; at least, I haven't grasped the essence of it yet. It will be hard to say anything concrete about how or even whether 't Hooft can account for observed superpositions, until someone understands this further stage of his recent work.
  • user10733
    user10733 over 11 years
    "However, his results are currently very limited, just reproducing the harmonic oscillator" He does have two follow up papers showing equivalence of a bosonic filed theory in 1+1 dimensions and also a "superstring" like solution for undelying deteministic lattice (arxiv.org/abs/1207.3612 and arxiv.org/abs/1205.4107) However, the arguements there seem to me to be extension of the arguemnt for the first paper . I could not find any loophole in the mapping.. hence the question.. what precisely does the scheme violate?
  • user10733
    user10733 over 11 years
    I do agree that there arent many results especially anthing that would distinguish the model from others Thank you a lot for your comment . -- Ash
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @a25bedc5-3d09-41b8-82fb-ea6c353d75ae: (Please choose a better name for identification) - I haven't looked at the details as my impression about all these attempts is that they are dead ends; lots of technicalities, but in the ned nothing that adds understanding to what we know already. If quantum indeterminism is generated in Nature from an underlying discrete classical dynamics, I bet it is an elegant way, just like quantum mechanics is an elegant variation of classical mechnaics, not a messy one.
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @akhmeteli: Particle nonlocality is an ordinary experimental fact (already visible in interference experiments); it is only the precise form it takes in theory that is in doubt. So I don't agree that it needs extraordinary verification. The philosophical problems go away once one gives up the particle picture; then there is nothing counterintuitive left that would need extraordinary attention.
  • akhmeteli
    akhmeteli over 11 years
    @Arnold Neumaier: Is this "Particle nonlocality" a matter of your personal opinion or could you give a reference? Let me just note that quantum-like particle interference was demonstrated in a classical system: PRL 97, 154101 (2006) (e.g., hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf )
  • Ron Maimon
    Ron Maimon over 11 years
    @MitchellPorter: It took me a long time to understand it, because it is clearly wrong, and I tried to make a true map from CA to QM. What he is doing is what I described--- he takes a QM system and transforms it to a case where it turns into a permutation on a basis, and when he can do this (which is always) he declares he has gotten QM out of a classical automaton. The declaration is false, the method is producing an "t'Hooft quantum automaton" not a classical automaton since it includes superposition states a-priori.
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @akhmeteli: Geometric optics is the classical particle view of classical light, and has all the nonlocal features that appear in quantum mechanics, once you go beyond the realm of the validity of the approximation. This tells me (though it is not the mainstream point of view) that the root of quantum nonlocality is treating quantum objects as particles rather than as field excitations. In the context of relativistic quantum field theory, everything is local, showing that the weird aspects are nothing but a poor choice of intuitive visualization.
  • akhmeteli
    akhmeteli over 11 years
    @Arnold Neumaier: I cannot accept geometrical optics as an evidence of "Particle nonlocality" - you could mention the Coulomb law with equal "success" - yes, it is nonlocal, but it is just an approximation, which fails in experiments exactly where it predicts nonlocality. So we disagree on whether nonlocality is an extraordinary claim, and you gave no reference to support your point of view. Furthermore, I insist that there is no positive experimental evidence of nonlocality in quantum theory so far due to loopholes.
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @akhmeteli: All physics is just an approximation, which fails if you describe the situation in greater detail. And there is no positive experimental evidence for anything microscopic if one is as carefully looking for loopholes as in the literature on nonlocality.
  • quantropy
    quantropy over 11 years
    Locality=>Determinism (see J.S Bell in "Sixty-two years of uncertainty").
  • akhmeteli
    akhmeteli over 11 years
    @Arnold Neumaier: Sure:-) Then why are experimental papers on loophole elimination published in the best journals right now, if the loopholes are as insignificant as you describe? Why such a feverish race among the best experimentalists trying to close the loopholes? Zeilinger and coauthors wrote recently: "Violating Bell’s inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today." (PNAS November 16, 2010 vol. 107 no. 46 19708-19713). That is why I said that your summary may be too categorical:-)
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @quantropy: ''Locality=>Determinism'' only under some assumptions, which are not satisfied in quantum field theory.
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    @akhmeteli: One can never close all loopholes. Tha'ts in the nature of experimental work.
  • akhmeteli
    akhmeteli over 11 years
    @Arnold Neumaier: You give no references, and I am not sure this is a mainstream view - e.g., Zeilinger seems to disagree with it in this particular case (which, as I said, indicates that you were indeed too categorical describing experts' view of the experimental situation). It may well be though that you are right in this particular case, and the violations cannot be demonstrated with all loopholes closed, but that would mean that the loopholes are actually crucial, rather than insignificant, as you seem to argue.
  • Arnold Neumaier
    Arnold Neumaier over 11 years
    I never claimed that all my answers are mainstream. Nevertheless, they are usually correct (and I correct them when they prove erroneous). Truth doesn't depend on the number of nay-sayers.
  • Ron Maimon
    Ron Maimon about 11 years
    I agree that the models are interesting, and the program is important, but the main problem is that you have not shown that quantum mechanics in a beable basis is equivalent to classical statistics on a CA, and this might not be true (I think it isn't true without further restrictions). I will ask a direct question, as your interesting answers and comments have allowed one to sharpen one's thinking about this.
  • Curious George
    Curious George about 11 years
  • G. 't Hooft
    G. 't Hooft almost 8 years
    The new version v3 of my paper quant-ph/ 1405.1548 was sent to the ArXiv today, Dec 21, 2015. "The Cellular Automaton Interpretation of Quantum Mechanics”. My answer to the question posted here is: yes. Criticism is always welcome, even if it comes from amateurs, although I cannot guarantee response.