Jaynes is misunderstanding the class of hidden-variable theories Bell’s theorem rules out: the point is that the hidden variables λ would determine the outcome of measurements, i.e. P(A|aλ) is 0 for certain values of λ and 1 for all other values, and likewise for P(B|bλ), in which case P(A|abλ) must equal P(A|aλ), P(B|Aabλ) must equal P(B|bλ), and eq. 14 does equal eq. 15. (I had noticed this mistake several years ago, but I didn’t know whom to tell about.)
Good catch! Jaynes does not seem to restrict the local hidden variables models to just the deterministic ones, but allows probabilistic ones, as well. This seems to defeat the purpose of introducing hidden variables to begin with. Or maybe I misunderstand what he means.
My recollection is that Jaynes deals with this point. He discusses in particular time varying lambda (or I’d say maybe space-time varying lambda). As a general proposition, I don’t know how you could ever rule out a hidden variable theory with time variation faster than your current ability to measure.
He has another paper, where he speculates about the future of quantum theory, and talks about phase versus carrier frequencies, and suggests that phase may be real and could determine the outcome of events.
The obvious way to get “random” detection probability deterministically would be the time varying dependency on the interaction of photon polarization, phase of the wavefront, and detector direction.
If you’d like to discuss this in more detail, I’d keep this thread alive for a while, as it’s an issue I’d like to clear up for myself.
(I’ll look up the paper when I have more time. EDIT—paper put in first post.)
Jaynes is misunderstanding the class of hidden-variable theories Bell’s theorem rules out: the point is that the hidden variables λ would determine the outcome of measurements, i.e. P(A|aλ) is 0 for certain values of λ and 1 for all other values, and likewise for P(B|bλ), in which case P(A|abλ) must equal P(A|aλ), P(B|Aabλ) must equal P(B|bλ), and eq. 14 does equal eq. 15. (I had noticed this mistake several years ago, but I didn’t know whom to tell about.)
Good catch! Jaynes does not seem to restrict the local hidden variables models to just the deterministic ones, but allows probabilistic ones, as well. This seems to defeat the purpose of introducing hidden variables to begin with. Or maybe I misunderstand what he means.
My recollection is that Jaynes deals with this point. He discusses in particular time varying lambda (or I’d say maybe space-time varying lambda). As a general proposition, I don’t know how you could ever rule out a hidden variable theory with time variation faster than your current ability to measure.
He has another paper, where he speculates about the future of quantum theory, and talks about phase versus carrier frequencies, and suggests that phase may be real and could determine the outcome of events.
The obvious way to get “random” detection probability deterministically would be the time varying dependency on the interaction of photon polarization, phase of the wavefront, and detector direction.
If you’d like to discuss this in more detail, I’d keep this thread alive for a while, as it’s an issue I’d like to clear up for myself.
(I’ll look up the paper when I have more time. EDIT—paper put in first post.)