Wednesday, September 14, 2022

Superdeterminism does not Save Locality

A new paper argues:
This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death of the scientific methodology.
This paper is really misguided. First, superdeterminism is not an interpretation of quantum mechanics. As you can see, it is not listed as such on the Wikipedia page. The premise of superdeterminism is that QM is wrong. It only appears correct in some cases, because we cannot properly test it.

Second, superdeterminism does not save locality. QM is local, while superdeterminism requies nonlocal conspiracies.

Bell’s theorem is almost universally considered as conclusively showing that nature is fundamentally non-local. ...

If so, Bell’s argument shows once and for all that no local hidden variables are possible and that nature is fundamentally non-local. Or so the vast majority believes.

Superdeterminism offers an alternative approach to this. In a nutshell, superdeterminism amounts to an attempt to save locality despite Bell’s experiment.

No, competent physicists do not believe that. Bell's argument shows that a classical hteory of local hidden variables cannot explain the predictions of QM. That leaves two obvious possibilites. Nature could be nonlocal classical, or local quantum.

Local quantum is what everybody believes, and what the textbooks say. You only get nonlocality if you insist on pre-1925 classical mechanics.

To justify the superdeterminism conspiracies, it invokes time travel arguments.

As it is well known in the time travel literature, time travel cannot result in changes in the past (see, among others, Lewis 1976 and Arntzenius and Maudlin 2002). Suppose a time traveler travels back in time and tries to kill his younger self. We know the time traveler will not succeed, or else contradictions will ensue. For if the time traveler kills his younger self (and we bar resurrection), he will not grow up to later jump back in time and kill his younger self. Even if time travel were possible, autoinfanticide by exploiting time travel is not.4 Time travelers who attempt to kill their younger selves will fail. Why do they fail? The standard answer in the literature is that they would fail for ordinary reasons: a sudden change of heart, the bullet will surprisingly miss the target, a bird would just pass through and stop the bullet, failure of nerves, or (famously) the time traveler would slip on a banana peel. In an interesting twist, Horwich (1987, ch. 7) discusses a thought experiment devised to cast some doubts on this idea. What would happen, so goes the thought experiment, if a future Time Travel Institute for Autoinfanticide were to send back in time thousands of time travelers attempting to kill their younger selves. Despite (we can imagine) their training, their loaded weapons, their strong motivations, and the easy unprotected targets, they would all fail---for autoinfanticide is impossible. A big series of coincidences must be guaranteed to happen to stop their attempts.
So if a big series of coincidences can stop you from kill yourself when you travel back in time, then then could also make QM appear to be true when it is really false.

No experiment can tell you what is going on, because the superdeterminist rejects it.

The third argument against superdeterminism that is voiced by authors as Shimony et al. (1976), Maudlin (2019), Baas and Le Bihan (2021), and Chen (2021), boils down to the idea that the enterprise of doing science would not be possible in a superdeterministic world. Maudlin (cited by Chen 2021) phrases it this way (2019):
“If we fail to make this sort of statistical independence assumption, empirical science can no longer be done at all. For example, the observed strong robust correlation between mice being exposed to cigarette smoke and developing cancer in controlled experiments means nothing if the mice who are already predisposed to get cancer somehow always end up in the experimental rather than control group. But we would regard that hypothesis as crazy.”
Again, the idea is that experimental science is only possible if our choices of testing conditions are independent of the physical properties that determine experimental outcomes – an assumption violated by superdeterminism.
That is all correct. But this paper goes on to advocate superdeterminism, because it is supposed to be a way of saving locality from Bell's argument.


  1. Dear Roger,

    > "Local quantum is what everybody believes, and what the textbooks say. You only get nonlocality if you insist on pre-1925 classical mechanics."

    Well, see:

    States in QM are nonlocal. In the non-relativistic QM, evolution of states too is nonlocal --- the Hamiltonian operator used in the Schroedinger equation is nonlocal. However, in the relativistic QM (RQM), while states remain nonlocal, the Hamiltonian is local in the same sense in which the propagation of changes in the fields is a local process in the EM theory.

    As to the pre-QM theories, as I noted in my paper, the Fourier theory is nonlocal, and so is Newtonian gravity. However, interactions between particles of Newtonian mechanics are local, and so are the propagation of changes in the EM fields. There is no single, overarching, "classical" ontology to speak of. If you insist on using the word "classical" as if there were a single ontology to it all, you run into errors.

    In general, when it comes to RQM, the notion of locality has to be taken in a more technical / advanced sense --- it refers to measurement events, not to states. Further, though neither commenter at the above URL (Dr. Motl included) touched upon it, one must remember that states remain normalized even in RQM; the evolution has to be unitary; and this constraint has implications for the sense in which we can take the word "locality" in RQM. The notion of locality used in RQM (including in QFT) is not quite the same simple notion as that with which we can describe the interactions (the forces of the direct contact) in the Newtonian mechanics of particles.

    Hope this helps.


  2. Ajit,

    Roger is correct here to state that QM is local. The "nonlocality" of quantum states that you mention is simply that they contain correlations. One could similarly call classical probability distributions "nonlocal" when they are non-separable due to the presence of correlations.