From: danforth@riacs.edu (Douglas G. Danforth)
Subject: Re: Night Thoughts on Bell's Inequality
Organization: RIACS, NASA Ames Research Center
Date: Fri, 9 Oct 92 20:05:50 GMT


]Night Thoughts on Bell's Inequality
]-----------------------------------
]

First of all Robert, I'd like to thank you for a very clear and
thoughtful presentation.  Nicely done!

And now to some comments ...

]The hidden variable model, by contrast, is much cleaner.  Of course
]each photon knows which way the other will jump - they were in contact,
]and plotted the whole thing together.  Each photon is carrying state
]away from the point of contact, enough state to ensure they remain
]correlated, like synchronized swimmers heading for opposite ends of
]the pool.
]
]Alas, no; and at last we come to Bell's inequality.  How clever must
]these photons be, how much state must they contain, to reproduce the
]perfect correlation we observe?

I can tell you exactly: 
    Equal to the number of degrees of freedom in a 2-dimensional patch.
    A table lookup with 2 bounded real parameters.

]                                 Let us make the most generous assumption:
]each photon may contain an algorithm of arbitrary complexity working on
]an arbitrary amount of state.  The photon is a universal Turing machine.

Too much.

]
]Nevertheless, one can set up an experimental arrangement where no
]algorithm, no prior state, is enough to maintain the corelations.     

Ah, well, you have fallen into the trap of assuming Bell's inequality
is the final word.

]                                                                   The
]best algorithm can maintain only partial correlation,

False.

]                                                      and any worse
]one will maintain even less correlation - hence the inequality.

The inequality is derived under the assumption that A^2=1 and B^2=1.
It assumes that the outcome of a measurement can only be spin up or
spin down.  This is false.  There is also, nondetection.
The "synchronized swimmer" can also drown!

As soon as you allow this possibility then Bell's inequality can not
be derived.  In fact one can construct an objective local model that
has the property of producing +1, -1, or 0 over a surface (2 hidden
real parameters) that will give you exactly the QM correlations.

]                                                                 But
]the correlations are indeed maintained.

Yes, and this does not rule out hidden variables.

]
]This refutes not just current hidden variable theories, but all possible
]hidden variable theories that work on the assumption of correlation
]maintained by prior collusion.

Not true.  It rules out hidden variable theories that rely on complete
detection.

]                                That is, all "local" hidden variable
                                          ^^^
]theories.

Again, not true.

]           Since the theories cannot be patched, their adherents are
                               ^^^^^^^^^^^^^^^^^
]busy looking for loopholes in the experiments.  Good luck, folks.

Well, I'm coming from a very different position and that is that any
field theoretic model of quantum phenomena MUST include the condition
of observable and nonobservable.  The reality is the field out of
which particles and other fields are composed.  One can not, would not,
expect to be able to experience this field under all circumstances since
that which experiences the field is constructed from the field (us).
"Particles" become an ill defined facet of the field, being simple
quasi-stable states that are sometimes localized and sometimes dispersed.

I would expect that nondetection is the rule rather than the exception
for all experiements.  For me it is not a loophole.

But then nature doesn't have to follow my whims.  If experiments with
photons can obtain a joint detector efficiency greater than 77.8%
(the probabilty of detecting a particle at B given that one is detected
at A) then the model I have in mind is ruled out.

]
]The principle of locality was enunciated thus by Einstein:
]
]        "But on one point we should, in my opinion, absolutely
]         hold fast: the real factual situation of system S1 is
]         independent of what is done with system S2, which is
]         spatially separated from the former."
]
]And it is this principle that we must abandon, in *any* theory that
                                                    ^^^
]is able to explain what we observe.

Sorry,  this is just not true.

]
]So, any hidden variable theory that saves the phenomena must be a
]nonlocal hidden variable theory,

Again, not true.

]                                 in which the two photons share state,
]and a state change produced by Castor's interaction is visible to
]Pollux, at the other end of the labyrinth.  In other words, correlation
]between hidden variables is maintained across spacelike intervals.

Nope, the correlations are formed from a mixture of local interaction
and the experimenter biasing the joint data by throwing out those data
where only a single photon is detected.

]
]And that, I think, explodes the whole thing.

Not at all.  This stuff is really subtle.  From 1935 to 1964 is 29 years.
From 1964 to 1992 is 28 years.  Just about right for a new interpretation
don't you think?

]Hidden variable theories predict nothing new, explain nothing new,
                          ^^^^^^^^^^^^^^^^^^^  ^^^^^^^^^^^^^^^^^^^
			  true, to date.       well, explain what is.

]and cannot even save the common-sense notion of locality that seems
]to be the issue generating all the emotion.

False.

]                                             I submit, then, that
]hidden variables should be relegated to the same scientific Valhalla
]as epicycles and phlogiston: they fought well, and are now history.
]
]Robert Firth

Good try, but a little premature.

Thanks for the post.

Douglas Danforth