’t Hooft and predetermination
’t Hooft notes that at the Planck scale experimenters will not have much freedom
to choose settings on a measurement apparatus. Thus Bell’s position 2
gives license to search for a classical, local, deterministic theory behind the
quantum mechanical theory of the world at that level. So far so good.
However, presumably the quantum mechanical theory of the world at
the Planck scale is the foundation from which one can derive the quantum
mechanical theory of the world at levels closer to our everyday experience.
Thus, his classical, local and deterministic theory for physics at the Planck
scale is a classical, local and deterministic theory for physics at the level of
present day laboratory experiments testing Bell’s theorem. It seems to me
that there are now two positions to take. The first one is that there is, also
at our level, no free choice. The experimenter thinks he is freely choosing
setting label number 2 in Alice’s wing of the experimenter, but actually the
photons arriving simultaneously in the other wing of the experiment, or the
stuff of the measurement apparatus there, “know” this in advance and capitalize
on it in a very clever way: they produce deviations from the Bell inequality,
though not larger than Cirel’sons quantum bound of 2√2 (they are,
after all, bound by quantum mechanics). But we have no way of seeing that
our “random” coin tosses are not random at all, but are powerfully correlated
with forever hidden variables in measurement apparatus far away. I find it
inconceivable that there is such powerful coordination between such totally
different physical systems (the brain of the experimenter, the electrons in the
photodetector, the choice of a particular number as seed of a pseudo-random
number generator in a particular computer program) that Bell’s inequality
can be resoundingly violated in the quantum optics laboratory, but nature as
a whole appears “local”, and randomizers appear random.
Now “free choice” is a notion belonging to philosophy and I would
prefer not to argue about physics by invoking a physicist’s apparently free
choice. It is a fact that one can create in a laboratory something which looks
very like randomness. One can run totally automated Bell-type experiments
in which measurement settings are determined by results of a chain of separate
physical systems (quantum optics, mechanical coin tossing, computer
pseudo-random number generators). The point is that if we could carry out
a perfect and successful Bell-type experiment, then if local realism is true an
exquisite coordination persists throughout this complex of physical systems
delivering precisely the right measurement settings at the two locations to
violate Bell’s inequalities, while hidden from us in all other ways.
There is another position, position 5: the perfect Bell-type experiment
cannot be made. Precisely because there is a local realistic hidden layer
to the deepest layer of quantum mechanics, when we separate quantumentangled
physical systems far enough from one another in order to do separate
and randomly chosen measurements on each, the entanglement will
have decayed so far that the observed correlations have a classical explanation.
Loopholes are unavoidable and the singlet state is an illusion.