hi all. re: t'hooft's paper.
I have skimmed t'hoofts recent paper
considering a local hidden variable theory for
QM. I believe it is identical to a very simple
model Ive been developing for years but only
recently came up with a nice analogy.
consider a set of speakers and a microphone.
let the speakers vary sinusoidally.
describing this system mathematically gives rise
to a wave equation and a superposition of waves.
also, a hilbert space of parameters controlling the
speakers. (in t'hoofts paper, this is a set of
simple harmonic oscillators)
now imagine the microphone is actually a digitizer.
now consider the LSB, least significant bit.
that bit has a 50% chance of "firing" when a wave
passes thru the speaker. but no matter what you do to the
setup, you cannot increase this probability.
it appears to me the "firing LSB" is analogous
to the detection of a photon in quantum theory.
now, this is classical physics LHV (local hidden variable) theory
totally consistent with QM in a limited domain.
why? bells thm supposedly rules out such a construction.
the answer is very simple. the hidden variables
determine detection probabilities, and may
sometimes specify "no event". if you study
bells thm very carefully, you will find it cannot
rule out this possibility. (note, this is not
the same as the detector efficiency loophole noted
in the literature.)
Ive been promoting this theory on my mailing list:
(am always looking for a good mathematician or qm
theorist to collaborate with. would like to write
a paper on the subject but havent been able to
get the free time so far.)