Possible objection to hidden variables schema I know that local hidden variable theories have been ruled out by Bell inequalities experiments, but I have a more fundamental objection that I did not found discussed in the literature.
Let us consider one spin one-half particle and let's test it in a line of several stern-gerlach devices, testing various orientations of spin (say x,z,x,y,x,z,z,...).
In the hidden variable interpretation the particle should carry a very large number (potentially infinite) of labels, yielding the results of each following measure.
I found it completely innatural to assign to one particle an infinite string of possible future measurement results: It seems to me enough to rule out the hidden variable explanation. Am I wrong?
 A: You assume the spin projections have to be among those hidden variables. Bohmian mechanics is an explicit example showing that this is not necessary: with just the position of the particle as hidden variable, and then incorporating the coupling of the spin with the magnetic field in Schrödinger equation as usual, Bohmian mechanics perfectly predict successive Stern-Gerlach measurements, as explained in details in [1]. 
The gist of it, in very qualitative terms, is that starting from a wave function with a single fairly localised swell, it is split in two non-overlapping swell by the Stern-Gerlach, each corresponding to a different eigenvalue for the spin projection. The particle that surfed the initial state swell will then end up on one or the other final state swell, and the probabilities will be given by the modulus square of the wave function, as per the usual postulate of Bohmian mechanics [*]. A subsequent Stern-Gerlach would then proceed with one of the final swell of the first experiment as initial state, exactly as in traditional QM we start from the wave function collapsed by the first experiment, and the particle surfing it would again end on one of the two well-separated final state swells. Nowhere has spin been used as a hidden variable.
[1] Travis Norsen. The pilot-wave perspective on spin. American Journal of Physics, 82(4):337–348, 2014.
[*] Although, it is claimed that this postulate can actually be demonstrated from an quantum equivalent of Boltzmann H-theorem.
