The basic problem is the base assumption in EPR/Bell
formulation, not the results.
Bell’s
work regarding EPR (above article and…).
http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html
A single fixed experiment is setup along a single dimension,
with detectors oriented in a certain direction – pre-supposing quite innocently
the equivalence of any directions in space. While the dimensions of space, XYZ,
are equivalent by all measures, they are distinct.
Prepare three Bell
experiments – all with the same prepared but random (unmeasured) state source. But
each lined up along different XYZ directions. The detectors will use circular polarization (chirality) detection instead of
orthogonal axis detection to keep things simple.
Run trials and let the detectors pickup trials. We can go so
far as to say the detectors fill up a “hexrant” (pyramid) of space and capture
all trials going in that direction (though this grows more impossible as
spatial extent of the apparatus is increased). Some previous real-world experiments
have rotated a detector pair apparatus in time… that is not germane to this
argument.
We can agree that any of the trials go into their respective
hexrant pairs in opposite directions. They go into one of the three detector
pairs. The others go to other detectors pairs. The only way to get more than a
one third yield of trials to any given detector pair is to interfere in the
preparation of the states.
Bell’s
work and a deterministic hidden variable theory of quantum states can be
rationalized if two thirds of the prepared states are lost. They are “lost”
into the other hexrant pairs of space. The quantum statistics (where two thirds
of trials are lost) can be made to match a hidden variable theory where each
test pair member caries with it the information about its state.
The flaw of previous approaches to resolving the EPR paradox
were to assume that all directions were equally represented by an experiment in
one fixed axis (or even rotating in time but still paired along one axis) . The
other directions cannot be ignored.
Many experiments have tried to cover the loss argument by
capturing all created states – within the scope of the given axes (at a given
time) they are setup against. That is insufficient.
Concrete theories of hidden variables can be developed to
explain this apparatus which will completely agree with QM predictions. That is
better left to another longer discourse. Here is a simple model for the
specific Bell
experiments described though…
Assign each trial to each hexrant pair based on its QM
compatibility with that axial direction. The “preparedness” of the trials hidden
variables will be a mirror, inverse, or reflection of the quantum mechanical
result matrix (rotated appropriately in 3D).
Stepping back from the experiment above, one can also view
the result as being that quantum mechanics is not “allowing” non-QM results to
propagate along any selected axis. The results which do not agree must
necessarily be redistributed/rotated to the other axes, to give results according
to QM along each and every axes viewed individually (and at any point in time).
Directional symmetry and invariance are preserved.
One can invert this reasoning and say that each prepared trial
state outcome is correlated with a given direction within the framework of QM
states. Each pair of photons simply has no choice but to go off as QM would
send it, and it must go off along an axis compatible with QM. (albeit uniformly
in space/time in any statistical group/set).
Again directional symmetry and invariance are preserved.
Another way of looking at this is to agree that Bell’s theorem is
completely correct. The assumptions were correct about the x,y and z being
completely commutable in the equations, the trick is in seeing that they are
really continuously/actually being commuted trial by trial. That result is the
essence of quantum mechanics.
Other variants of the Bell/EPR experiments can be addressed in
similar ways in 3D space. (Bohm and Hardy).
The main point of the argument herein is that all states
(even/especially ones on orthogonal paths) must be tested for the experiment to
be valid against QM assumptions.
The good news is that this twist makes no difference to
quantum statistics whatsoever. The unconstrained nature and free propagation of the
prepared states was a given, the results are the same as predicted by QM, and
what we have stated in no way conflicts with the quantum mechanical
interpretation (Copenhagen, Born, etc.). The results do not even conflict with
the reasoning of Bell
and others. We have not rejected locality nor definiteness. What was missing is
the three dimensional nature of space, and that a trial cannot be in three
places at once.
Background:
Survey article in Scientific American gelled resolve to try
to get out this idea.
von Baeyer, Hans Christian (2013). "Can Quantum
Bayesianism Fix the Paradoxes of Quantum Mechanics?". Scientific American
2013 (June). page 46
http://www.scientificamerican.com/article.cfm?id=wave-function
