Do electrons think? (1949)

Sadly this seems to be an issue that is shrouded in a lot turf war within the physics community. As someone who is mostly interested in the history of it from my armchair, I think it's important to put out there:

The assertion that Bell's inequality shut down Bohemian Mechanics is absolutely false. This claim has been floating around since the the 60s. The biggest disagreement came from ... J.S. Bell himself. He was a proponent of Bohemian Mechanics and didn't agree that he had dismantled it.

==== The criticism ====

> Recently, however, physicists more commonly cite the Kochen-Specker Theorem and, more frequently, Bell’s inequality in support of the contention that a deterministic completion of quantum theory is impossible. We still find, a quarter of a century after the rediscovery of Bohmian mechanics in 1952, statements such as these:

> The proof he [von Neumann] published …, though it was made much more convincing later on by Kochen and Specker (1967), still uses assumptions which, in my opinion, can quite reasonably be questioned. … In my opinion, the most convincing argument against the theory of hidden variables was presented by J.S. Bell (1964). (Wigner [1976] 1983: 291)

==== Bell's Take ====

> There was, however, one physicist who wrote on this subject with even greater clarity and insight than Wigner himself: the very J. S. Bell whom Wigner praises for demonstrating the impossibility of a deterministic completion of quantum theory such as Bohmian mechanics. Here’s how Bell himself reacted to Bohm’s discovery:

> But in 1952 I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how parameters could indeed be introduced, into nonrelativistic wave mechanics, with the help of which the indeterministic description could be transformed into a deterministic one. More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the “observer”, could be eliminated. …

> But why then had Born not told me of this “pilot wave”? If only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing “impossibility” proofs, after 1952, and as recently as 1978? … Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice? (Bell 1982, reprinted in 1987c: 160)

> Wigner to the contrary notwithstanding, Bell did not establish the impossibility of a deterministic reformulation of quantum theory, nor did he ever claim to have done so. On the contrary, until his untimely death in 1990, Bell was the prime proponent, and for much of this period almost the sole proponent, of the very theory, Bohmian mechanics, that he supposedly demolished.

https://plato.stanford.edu/entries/qm-bohm/

> I never said anything about an alternative to wavefunctions

Unless you're denying that physical reality exists at all, to suggest that the wavefunction isn't physical reality is implicitly to suggest that something else is.

> He wasn't talking about a hidden variable theory, just about how to interpret the wavefunction, holding all theoretical elements constant: does it model our knowledge of physical states, or the physical states themselves.

If you're assuming there are "physical states themselves" that the wavefunction is merely our knowledge of, that's practically the definition of a hidden variable theory.

> The first one is simpler because we already know we are observing the physical states through an intermediary and that our knowledge is limited; the second one introduces a new capability to the universe.

Nonsense. Observation is an ordinary physical process that happens inside the universe; anything that "observing" can do must already be something the universe is capable of.

He's saying that just because the movements of particles are not predictable doesn't mean you all of a sudden get to claim "free will"-- the ability to somehow impose an arbitrary desire in the chain of causality between your sense experiences and your actions. In order for you to have "free will" in this classical sense, you'd have to control the "slit" the electrons "swerve" through. But you don't. They just act randomly. They're not the things that impose your will. Your will is still an illusion.

> what you mean by "experiments do not have results."

Let the experiment measure spin projection s_y of an atom previously prepared in spin state |s_x+>. It is known empirically that this experiment has two possible mutually exclusive results, +1/2 and -1/2, with probability of each being 1/2. Standard quantum theory accepts this and uses mathematics to predict those probabilities from data on the mutual arrangement of preparator and analyser of the spin.

Such predictions are difficult to be made in Everettian theory, because that theory describes both the particle with spin and those forming the measuring apparatus in the same way. When that is done, the physical process of measurement can be mathematically described by the Schroedinger equation, which may seem like a win, but it has a big downside: all it gives is a ray in the big Hilbert space of particle plus apparatus at later times; it is not clear what this calculation result is good for. It is not the prediction of real experiment's result; it is not even clear how to use it to calculate probabilities of those results. Certainly not by Born's rule - because what is the eigenfunction to be used in the Born formula? Such eigenfunction is, in standard theory, determined by the classical settings of the apparatus, such as orientation of the SG magnet. But there is no such thing in Everettian theory, there is just psi function.

It does not work as written. How is |O_up> defined in terms of the basis of the global Hilbert space? There is infinity of directions in space which we can choose as the defining axis of the ket |O_up>. You could calculate the inner product for any of them. Does that mean that the inner product is typically zero and to get a non-zero probability, one has to talk not about probability of possible results of measurement, but about probability on the space of possible measurement setups? If so, why bother with the concept of quantum measurement at all? Why not just say any configuration of the world from some measurable set has probability int |psi|^2 dq? That would be the other, non-projection Born rule (or interpretation of psi), which doesn't have the problem of preferred basis and does not need it to be chosen by the classical apparatus.