Monday, March 9, 2020

Trying to prove many-worlds from first principles

Mordecai Waegelly and Kelvin J. McQueenz write Reformulating Bell’s Theorem: The Search for a Truly Local Quantum Theory:
The apparent nonlocality of quantum theory has been a persistent concern. Einstein et. al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations.

We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds.
I accept those assumption. Local causality is axiomatic for all of science. Only Gerard 't Hooft and Dr. Bee believe in superdeterinism.

From this he claims to prove many worlds!! No, this is crazy. No set of assumptions can prove the existence of unobservable parallel worlds.

The root of his error is that he has a hidden assumption in favor of hidden variable theories. Such theories have been discarded for a century.

Gizmodo reports:
Scientists studying kea, New Zealand’s alpine parrot, revealed that the famously mischievous birds could understand probabilities, an impressive mental feat.

The pair of researchers put six birds through a series of trials to see how they made decisions when faced with uncertainty. When prompted to choose, the kea generally opted for scenarios where they were more likely to earn a reward. This work is further evidence of some birds’ general intelligence, according to the paper published in Nature Communications.
These parrots must be smarter than the many-worlds advocates.

The above paper admits:
On a branching model, it is difficult to make sense of the probabilistic predictions of quantum mechanics. Pre-measurement, Alice might assert "there is a 0.7 probability that I will see spin-up (rather than spin-down)". But given branching, it seems that Alice should assign probability 1 to there being an Alice descendant that sees spin-up. Pre-measurement Alice is not uncertain of anything; she knows she will branch into descendants that see contrary results in different worlds, and she knows that neither of her descendants is the "real" Alice -- they both have equal claim to being pre-measurement Alice. It is therefore unclear what the "probability 0.7" is a probability of. This aspect of the problem is often referred to as the incoherence problem.
This problem has no solution. If you believe in many-worlds, you have to abandon probabilities.

You might think that the probabilities could be interpreted as the possibility of a particular branching. That is, one possible parallel world has probability 0.7, and the another has 0.3. However the many-worlds advocates have never been able to make such a theory work.


  1. How do you feel about this: It's a little different from the usual, so I can imagine the unique Dark Buzz jumping either way.
    You can consider an exchange I had yesterday with Tim Maudlin here: I can imagine Dark Buzz having trenchant things to say about both sides of that.
    I'm very curious whether I can sustain an interesting dialogue with Dark Buzz, which I've now followed by RSS for several years. It would be interesting to me, for sure, so the question is whether it might be interesting to you.

  2. The Bell assumption that Maudlin calls "Bell-local" is what others call a classical theory of local hidden variables. I guess I agree with Maudlin that we need to understand Bell's theorem, not weaken it. But to me, understanding it means quantum mechanics is both local and non-classical.

  3. My thing, I guess, is to pursue multiple perspectives. Cherry-picking, for sure, I take license from Feynman, “The physicist needs a facility in looking at problems from several points of view.” So, yes, as I would put your final statement, QM/QFT is microcausal and noncommutative, but it is also natural to use the Poisson bracket to construct a noncommutative algebra of classical observables that is very close indeed to QM/QFT, as an alternative perspective. I find that understanding exactly how this extended CM is or is not the same as QM illuminates QM (as did Annals of Physics, I suppose.)
    Understanding Bell's theorem in the context of only QM is in a way relatively straightforward: microcausality and noncommutativity more-or-less cuts it. Understanding Bell's theorem in the context of both QM and CM needs something more, for which one starting point that has not yet been developed enough is, I suggest, a common Hilbert space formalism for both.

  4. Bell's theorem does not say anything about quantum mechanics. It only says something about classical mechanics theories.

  5. Dear Roger,

    You say: ``Local causality is axiomatic for all of science. ''

    I used to think so. But now I realize that QM (at least the non-relativistic Schrodinger's equation) has a part-global character.

    Each massive charged particle of e- or P+ always has the potential it sets up (for the other charged particles to ``feel'') anchored into its own *instantaneous* position. Simple statement, but apparently difficult to unpack for many philosophers of physics.

    In the non-rel. QM, the electrostatic potentials change instantaneously everywhere in the universe. So, there is a certain global character to it (aka instantaneous action at a distance, or IAD for short). So, it's a global theory, some one may say.

    However these same potentials also always remain anchored into the particle's current positions. So, no electrostatic potential field ever changes unless the particle positions change. Further, for e- and P+, the mass can be at least abstractly seen as being present ``at'' the potential-anchoring positions. So, there certainly is a local character to the potential fields.

    In the Schrodinger equation, there is nothing but V and \Psi which undergo changes.

    In the mainstream (textbook) QM, the \Psi field is completely determined by the potential fields. Hidden variables, therefore, must be seen as those variables that are in addition to these two. Schrodinger's equation successfully predicts all the known QM phenomena. (Even the non-relativistic one, within the regime of its applicability.)

    [In my new approach, there is a two-way interaction between \Psi and V, thereby introducing the nonlinearity necessary for solving the measurement problem, but without introducing a hidden variable.]

    In view of all these (and such) facts, QM cannot be completely characterized as being just local (as in collisions of balls in the Newtonian mechanics), or as just global (as in the Fourier theory, say of diffusion or waves).

    Philosophers first need to understand, absorb, and also hold in mind for all times, the above set of facts and observations. Unless and until they accomplish this part, they can't hope to make any consistent set of statements.

    To base arguments on an *implication* of the QM *axioms*, viz. Bell's *theorem* (and though enormously illuminating, it still is ``just'' a theorem), is not going to be very helpful in the absence of the understanding just stated.

    PS: I still don't know what to think of super-determinism. However, I cannot rule it out off-hand. Realize, super-determinism, even if valid, would pertain only to the *physical* aspects of the universe, not mental or spiritual. Free will would still exist---as a physically efficacious causal agent. It is not at all necessary to deny super-determinism just in order to save the free will. (Easy to see this point in the context of Newtonian mechanics. If you choose not to throw a ball, it doesn't trace the parabolic path.)

  6. Oh, BTW, another thing.

    The MWI (the Many-World Industries) would've made for a good joke ---if it weren't to be Government-sponsored.


  7. Many worlds isn't physics, just bad metaphysics dressed up in statistics. If you don't know how something works, inventing an infinite number of imaginary universes to hide your ignorance in isn't going to help you understand.

    When you are stuck in a hole, stop digging.

  8. Ajit, yes, if you can suddenly change V everywhere, then you can have instantaneous action-at-a-distance. Relativity and quantum field theory are designed to explain how a field can get from one place to another.

    There never has been any experiment showing action-at-a-distance.

    Superdeterminism is a scheme to deny free will. If you believe in free will, then you won't have much interest in superdeterminism.

  9. Roger, going back 2 days: "Bell's theorem does not say anything about quantum mechanics" directly, but it implies that QM does not satisfy all the assumptions that Bell makes. It's enough (most clearly seen in L.J. Landau, Phys. Lett. A 120 (1987) 54, that the observables of QM that are used in models that violate Bell inequalities do not commute. Including noncommutativity into CM is one way to make violation of Bell inequalities possible.
    [Noncommutativity and locality are intimately related because of microcausality, however: if operators do not commute, they must be associated with time-like separated regions of space-time.]

    Returning to today: Superdeterminism doesn't have to impinge on free will if it's understood to be about probabilities of actual events. Bell's arguments are all constructed from assumptions about probabilities. If a theory says that there's a half chance that I will choose cheese or ice cream after dinner, I still have that choice, it's just that in the past, it's been observed that I chose cheese half the time. Bell's idea of probability is extremely naive in its unstated assumption that probability "goes all the way down". I suggest that measure theory applied to random fields becomes mathematically delicate when there is a countably infinite or uncountable number of observables/beables, because one has to prove that either there is no implicit use whatsoever of the axiom of choice or that any use does not result in Banach-Tarski-type paradoxes. We can still use probability theory in careful formalisms, in particular if we follow rules similar to the Wightman axioms, however even operator-valued distributions are a little delicate.
    All that means that although we and a Deity might be able to predict approximate probabilities for what happens in future, a Deity's perfect choice of noisy discontinuous initial conditions doesn't necessarily allow them to predict the future error-free. I take the lesson from this to be that we should construct models top-down, starting from observed statistics of experimental raw data, extrapolating from those to predictions, then collecting more observed statistics of experimental raw data, and repeat, ..., instead of trying to create models bottom-up, starting from dimensionless points. We do have the tools to do this, both quantum fields and classical random fields (both of which can be understood to be just indexed sets of random variables with different relative relationships between them.) Our theories, however, as effective quantum or random field theories, do not predict anything perfectly.

    Thank you for your comments.

  10. Wikipedia says "Superdeterminists do not recognize the existence of genuine chances or possibilities anywhere in the cosmos."

    So I don't see any room for probability, free will, or anything like that. Everything is forced, from the beginning of the big bang.

  11. Roger writes, "But to me, understanding it means quantum mechanics is both local and non-classical."

    So you are saying that quantum mechanics has absolutely no nonlocal properties? How does a photon go through two slits at once?

  12. A photon does not go thru two slits at once. A light wave goes thru both slits. If you put a detector at the slits, then it will only detect a photon in one of the slits.