From: danforth@riacs.edu (Douglas G. Danforth)
Subject: Re: Hidden variable theories, was: Uncertainty Princi
Organization: RIACS, NASA Ames Research Center
Date: Wed, 9 Sep 92 18:50:40 GMT


]From sci.physics Wed Sep  9 10:38:27 1992
]From: paul@mtnmath.UUCP (Paul Budnik)
]Date: 9 Sep 92 15:51:00 GMT
]Newsgroups: sci.physics
]Subject: Re: Hidden variable theories, was: Uncertainty Princi
]
]In article <1992Sep8.144555.455@cine88.cineca.it>, campo@sunthpi3.difi.unipi.it (Massimo Campostrini) writes:
]
]>   To be precise, any "hidden variables"-type theory consistent with
]> quantum mechanics must be nonlocal. Quantum electrodynamics and other
]> relativistic quantum field theories are local, according to any
]> reasonable definition of locality. (I agree that locality of
]> non-relativistic quantum mechanics is debatable.)
]
]The Schrodinger equation is local. Quantum mechanics plus the collapse
]postulate is a nonlocal theory that predicts nonlocal experimentally
]detectable effects.  Any theory of any form that is consistent with quantum
                                 ^^^^^^^^^^^
]mechanics must also be nonlocal. 


This assumes that Bell's theorem is a definitive and final answer.  For
inefficient detectors it is quite easy to construct a model which gives
the EXACT quantum mechanical two-particle correlations.  Bell's theorem
does not address this case of inefficient detectors. The detector counts (R)
used by Aspect and the correlation function he computes
	 
	 R++(a,b) + R--(a,b) - R+-(a,b) - R-+(a,b)
E(a,b) = -----------------------------------------
	 R++(a,b) + R--(a,b) + R+-(a,b) + R-+(a,b)

to estimate Bell's P(a,b) is conditionalized on the JOINT detection of both
particles. Joint detection can only be determined a posteriori (after the
fact) for inefficient systems. This implies (and is performed in practice by
coincidence counters) that the joint, global, data is filtered by the
experimental design.  The filtering introduces a form of nonlocality.

For perfect detectors, Bell's theorem still holds and the previous argument
can not be made.  Even for highly efficient detectors (in excess of 82.8%
see John Clauser's 1969 paper) the global filtering can not save locality.
Experiments have yet to reach this level of efficiency.

In summary, at this time, one can NOT make the claim that "Any theory of any
form that is consistent with quantum mechanics must also be nonlocal".


]> Again, instantaneous transmission of information happens in an
]> underlying hidden variables theory. In the quantum theory, since it
]> cannot be used to send a signal, this transmission of information is
]> absent by definition.
]
]This is false. The Shannon definition of information is that it allows one
]to select a limited number of alternatives from a wider range of
]possibilities. Encrypted data is information even though you cannot
]determine what the data is without a decryption key. In a test of Bell's
]inequality, we know from a local observation something about two things
]that happened at a distant site. These two things are the observation made
]at the distant site and the angle of a polarizer at a distant site. We do
]not know either of these, but we know something about the combination
]of the two of them. This is information and it is transmitted instantaneously
]if the instantaneous collapse postulate is true.

"If the instantaneous collapse postulate is true."  For polarizers aligned
with perfect detectors a measurement at A predicts with certainty the
measurment at B.  For inefficient detectors, a measurement at A does not
predict the outcome at B.  One must know whether a particle was detected
at B before one can assert the value of the measurement at B.  Knowledge
of the detection at B is not known at A.

]
]> Also only the hidden variables theory has to
]> give up causality; e.g. quantum electrodynamics strictly respects
]> causality.
]
]You are dead wrong again. In a test of Bell's inequality manipulating a
]local polarizer must instantaneously *affect* what happens at a remote
]location.

A local model of Aspect's experiment can be (has been) constructed where
manipulation of a local polarizer does nothing to a remote location.  The
local manipulation (at A) changes the states of detection at A. For
inefficient detectors there are 3 outcomes {-,0,+} where 0 is nondetection.
For a fixed hidden variable value, the outcome at A is affected by changing
the orientation at A.  However, the average response at A (averaged over
hidden variable values) is unaffected by such orientation changes.  Only
the joint correlation, carried by the hidden variables, is detectable.
(to be precise, it is possible to construct a model that has these
properties).

]          Thus either relativity, which is part of quantum electrodynamics
]is false, or causality is violated. See P. H. Eberhard, Il Nuvo Cimento 46 B,
]392, (1978) for a complete detailed analysis of this.

Again, to date, neither of these conclusions can be drawn.

]
]>    Since quantum mechanics, quantum electrodynamics etc. give
]> (unambiguous) predictions verified by experiments with an incredible
]> accuracy (e.g.: hydrogen atom and positronium energy levels, electron
]> and muon magnetic moment), according to Occam's Razor we must held
]> these theories true until experimental evidence suggests otherwise. 
]>    I find "methodologically wrong" to think that, since a few
]> predictions of an otherwise very successful theory have not (yet) been
]> tested, the theory should be considered wrong.
]
]But I do not think the parts of the theory that give these
]validated results are wrong. There is a trivial change one
]can make to quantum mechanics to produce a theory that has been validated
]to the same degree and that is completely local. One replaces the collapse
]postulate with the following alternative.
]
]   Quantum collapse is engendered by experimental conditions designed to
]   observe the classical parameters of a system. It is an objective event
]   that occurs for a variety of reasons that are not fully understood or
]   part of current theory. It has a local Lorentz invariant structure and
]   will thus occur spontaneously before the point that an experiment would
]   result in violating locality.
]
]The alternatives we face are a local incomplete theory or a nonlocal
]quasi-mystical (quantum collapse is caused by a conscious observer)
]complete theory.

Again, these are not yet the only altenatives.

]                 I see no reason to prefer the existing
]collapse postulate.

On this point, I whole heartedly agree.

]                    On two occasions I have challenged the readers
]of this newsgroup to come up with an *objective* reason for preferring the
]nonlocal theory and none has been forthcoming.
]
]Paul Budnik

Since we both seen to be working toward the same end, I offer no such reason.

-- Doug Danforth
Newsgroups: sci.physics