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Posted-By: auto-faq 3.3 (Perl 5.004)
Archive-name: physics-faq/measurement-in-qm

 Measurement in quantum mechanics FAQ
 Maintained by Paul Budnik, [email protected], http://www.mtn-
 math.com


 This FAQ describes the measurement problem in QM and approaches to its
 solution. Please help make it more complete. See ``What is needed''
 for details.  Web version: http://www.mtnmath.com/faq/meas-qm.html

 1.  About this FAQ

 Last modified August 5, 1998 (section 7)

 The general sci.physics FAQ does a good job of dealing with technical
 questions in most areas of physics. However it has no material on
 interpretations of QM which are among the most frequently discussed
 topics in sci.physics. Hence there is a need for this supplemental
 FAQ.


 This document is probably out of date if you are reading it more than
 30 days after the date which appears in the header.


 This FAQ is on the web at: http://www.mtnmath.com/faq/meas-qm.html


 You can get it by e-mail or FTP from rtfm.mit.edu.


 By FTP, look for the file:


 /pub/usenet/news.answers/physics-faq/measurement-in-qm


 By e-mail send a message to [email protected] with a blank
 subject line and the words:


 send usenet/news.answers/physics-faq/measurement-in-qm


 The main sci.physics FAQ is in this same directory with file names
 part1 through part4 and can be retrieved in the same way.  You can put
 multiple send lines in a single e-mail request.


 This document, as a collection, is Copyright 1995 by Paul P. Budnik
 ([email protected]).  The individual articles are Copyright 1995 by the
 individual authors listed.  All rights are reserved.  Permission to
 use, copy and distribute this unmodified document by any means and for
 any purpose EXCEPT PROFIT PURPOSES is hereby granted, provided that
 both the above Copyright notice and this permission notice appear in
 all copies of the FAQ itself.  Reproducing this FAQ by any means,
 included, but not limited to, printing, copying existing prints,
 publishing by electronic or other means, implies full agreement to the
 above non-profit-use clause, unless upon explicit prior written
 permission of the authors.


 This FAQ is provided by the authors ``as is''. with all its faults.
 Any express or implied warranties, including, but not limited to, any
 implied warranties of merchantability, accuracy, or fitness for any
 particular purpose, are disclaimed.  If you use the information in
 this document, in any way, you do so at your own risk.
 2.  The measurement problem

 Paul Budnik [email protected]

 The formulation of QM describes the deterministic unitary evolution of
 a wave function. This wave function is never observed experimentally.
 The wave function allows us to compute the probability that certain
 macroscopic events will be observed. There are no events and no
 mechanism for creating events in the mathematical model. It is this
 dichotomy between the wave function model and observed macroscopic
 events that is the source of the interpretation issue in QM. In
 classical physics the mathematical model talks about the things we
 observe.  In QM the mathematical model by itself never produces
 observations.  We must interpret the wave function in order to relate
 it to experimental observations.

 It is important to understand that this is not simply a philosophical
 question or a rhetorical debate. In QM one often must model systems as
 the superposition of two or more possible outcomes. Superpositions can
 produce interference effects and thus are experimentally
 distinguishable from mixed states. How does a superposition of
 different possibilities resolve itself into some particular
 observation? This question (also known as the measurement problem)
 affects how we analyze some experiments such as tests of Bell's
 inequality and may raise the question of interpretations from a
 philosophical debate to an experimentally testable question. So far
 there is no evidence that it makes any difference. The wave function
 evolves in such a way that there are no observable effects from
 macroscopic superpositions. It is only superposition of different
 possibilities at the microscopic level that leads to experimentally
 detectable interference effects.

 Thus it would seem that there is no criterion for objective events and
 perhaps no need for such a criterion. However there is at least one
 small fly in the ointment. In analyzing a test of Bell's inequality
 one must make some determination as to when an observation was
 complete, i. e. could not be reversed. These experiments depend on the
 timing of macroscopic events. The natural assumption is to use
 classical thermodynamics to compute the probability that a macroscopic
 event can be reversed. This however implies that there is some
 objective process that produces the particular observation. Since no
 such objective process exists in current models this suggests that QM
 is an incomplete theory.  This might be thought of as the Einstein
 interpretation of QM, i. e., that there are objective physical
 processes that create observations and we do not yet understand these
 processes.  This is the view of the compiler of this document.

 For more information:

 Ed. J. Wheeler, W. Zurek, Quantum theory and measurement, Princeton
 University Press, 1983.

 J. S. Bell, Speakable and unspeakable in quantum mechanics, Cambridge
 University Press, 1987.

 R.I.G. Hughes, The Structure and Interpretation of Quantum Mechanics,
 Harvard University Press, 1989.

 3.  Schrodinger's cat

 Paul Budnik [email protected]


 In 1935 Schrodinger published an essay describing the conceptual
 problems in QM[1]. A brief paragraph in this essay described the cat
 paradox.
    One can even set up quite ridiculous cases. A cat is penned up
    in a steel chamber, along with the following diabolical device
    (which must be secured against direct interference by the cat):
    in a Geiger counter there is a tiny bit of radioactive
    substance, so small that perhaps in the course of one hour one
    of the atoms decays, but also, with equal probability, perhaps
    none; if it happens, the counter tube discharges and through a
    relay releases a hammer which shatters a small flask of
    hydrocyanic acid. If one has left this entire system to itself
    for an hour, one would say that the cat still lives if meanwhile
    no atom has decayed.  The first atomic decay would have poisoned
    it. The Psi function for the entire system would express this by
    having in it the living and the dead cat (pardon the expression)
    mixed or smeared out in equal parts.


    It is typical of these cases that an indeterminacy originally
    restricted to the atomic domain becomes transformed into
    macroscopic indeterminacy, which can then be resolved by direct
    observation. That prevents us from so naively accepting as valid
    a ``blurred model'' for representing reality. In itself it would
    not embody anything unclear or contradictory. There is a
    difference between a shaky or out-of-focus photograph and a
    snapshot of clouds and fog banks.

 We know that superposition of possible outcomes must exist
 simultaneously at a microscopic level because we can observe
 interference effects from these.  We know (at least most of us know)
 that the cat in the box is dead, alive or dying and not in a smeared
 out state between the alternatives. When and how does the model of
 many microscopic possibilities resolve itself into a particular
 macroscopic state? When and how does the fog bank of microscopic
 possibilities transform itself to the blurred picture we have of a
 definite macroscopic state.  That is the measurement problem and
 Schrodinger's cat is a simple and elegant explanations of that
 problem.

 References:

 [1] E. Schrodinger, ``Die gegenwartige Situation in der
 Quantenmechanik,'' Naturwissenschaftern. 23 : pp. 807-812; 823-823,
 844-849. (1935).  English translation: John D. Trimmer, Proceedings of
 the American Philosophical Society, 124, 323-38 (1980), Reprinted in
 Quantum Theory and Measurement, p 152 (1983).



 4.  The Copenhagen interpretation

 Paul Budnik [email protected]

 This is the oldest of the interpretations. It is based on Bohr's
 notion of `complementarity'. Bohr felt that the classical and quantum
 mechanical models were two complementary ways of dealing with physics
 both of which were necessary. Bohr felt that an experimental
 observation collapsed or ruptured (his term) the wave function to make
 its future evolution consistent with what we observe experimentally.
 Bohr understood that there was no precise way to define the exact
 point at which collapse occurred. Any attempt to do so would yield a
 different theory rather than an interpretation of the existing theory.
 Nonetheless he felt it was connected to conscious observation as this
 was the ultimate criterion by which we know a specific observation has
 occurred.

 References:

 N. Bohr, The quantum postulate and recent the recent development of
 atomic theory, Nature, 121, 580-89 (1928), Reprinted in Quantum Theory
 and Measurement, p 87, (1983).



 5.  Is QM a complete theory?

 Paul Budnik [email protected]

 Einstein did not believe that God plays dice and thought a more
 complete theory would predict the actual outcome of experiments.  He
 argued[1] that quantities that are conserved absolutely (such as
 momentum or energy) must correspond to some objective element of
 physical reality. Because QM does not model this he felt it must be
 incomplete.

 It is possible that events are the result of objective physical
 processes that we do not yet understand. These processes may determine
 the actual outcome of experiments and not just their probabilities.
 Certainly that is the natural assumption to make. Any one who does not
 understand QM and many who have only a superficial understanding
 naturally think that observations come about from some objective
 physical process even if they think we can only predict probabilities.

 There have been numerous attempts to develop such alternatives.  These
 are often referred to as `hidden variables' theories. Bell proved that
 such theories cannot deal with quantum entanglement without
 introducing explicitly nonlocal mechanisms[2].  Quantum entanglement
 refers to the way observations of two particles are correlated after
 the particles interact. It comes about because the conservation laws
 are exact but most observations are probabilistic.  Nonlocal
 operations in hidden variables theories might not seem such a drawback
 since QM itself must use explicit nonlocal mechanism to deal with
 entanglement. However in QM the non-locality is in a wave function
 which most do not consider to be a physical entity. This makes the
 non-locality less offensive or at least easier to rationalize away.

 It might seem that the tables have been turned on Einstein. The very
 argument he used in EPR to show QM must be incomplete requires that
 hidden variables models have explicit nonlocal operations. However it
 is experiments and not theoretical arguments that now must decide the
 issue. Although all experiments to date have produced results
 consistent with the predictions of QM, there is general agreement that
 the existing experiments are inconclusive[3]. There is no conclusive
 experimental confirmation of the nonlocal predictions of QM. If these
 experiments eventually confirm locality and not QM Einstein will be
 largely vindicated for exactly the reasons he gave in EPR. Final
 vindication will depend on the development of a more complete theory.

 Most physicists (including Bell before his untimely death) believe QM
 is correct in predicting locality is violated. Why do they have so
 much more faith in the strange formalism of QM than in basic
 principles like locality or the notion that observations are produced
 by objective processes? I think the reason may be that they are
 viewing these problems in the wrong conceptual framework. The term
 `hidden variables' suggests a theory of classical-like particles with
 additional hidden variables. However quantum entanglement and the
 behavior of multi-particle systems strongly suggests that whatever
 underlies quantum effects it is nothing like classical particles.  If
 that is so then any attempt to develop a more complete theory in this
 framework can only lead to frustration and failure.  The fault may not
 be in classical principles like locality or determinism. They failure
 may only be in the imagination of those who are convinced that no more
 complete theory is possible.

 One alternative to classical particles is to think of observations as
 focal points in state space of nonlinear transformations of the wave
 function. Attractors in Chaos theory provide one model of processes
 like this. Perhaps there is an objective physical wave function and QM
 only models the average or statistical behavior of this wave function.
 Perhaps the structure of this physical wave function determines the
 probability that the wave function will transform nonlinearly at a
 particular location. If this is so then probability in QM combines two
 very different kinds of probabilities. The first is the probability
 associated with our state of ignorance about the detailed behavior of
 the physical wave function. The second is the probability that the
 physical wave function will transform with a particular focal point.

 A model of this type might be able to explain existing experimental
 results and still never violate locality. I have advocated a class of
 models of this type based on using a discretized finite difference
 equation rather then a continuous differential equation to model the
 wave function[4]. The nonlinearity that must be introduced to
 discretize the difference equation is a source of chaotic like
 behavior.  In this model the enforcement of the conservation laws
 comes about through a process of converging to a stable state.
 Information that enforces these laws is stored holographic-like over a
 wide region.

 Most would agree that the best solution to the measurement problem
 would be a more complete theory. Where people part company is in their
 belief in whether such a thing is possible. All attempts to prove it
 impossible (starting with von Neumann[5]) have been shown to be
 flawed[6]. It is in part Bell's analysis of these proofs that led to
 his proof about locality in QM. Bell has transformed a significant
 part of this issue to one experimenters can address. If nature
 violates locality in the way QM predicts then a local deterministic
 theory of the kind Einstein was searching for is not possible. If QM
 is incorrect in making these predictions then a more accurate and more
 complete theory is a necessity. Such a theory is quite likely to
 account for events by an objective physical process.

 References: [1] A. Einstein, B. Podolsky and N. Rosen, Can quantum-
 mechanical descriptions of physical reality be considered complete?,
 Physical Review, 47, 777 (1935).  Reprinted in Quantum Theory and
 Measurement, p. 139, (1987).

 [2] J. S. Bell, On the Einstein Podolosky Rosen Paradox, Physics, 1,
 195-200 (1964).  Reprinted in Quantum Theory and Measurement, p. 403,
 (1987).

 [3] P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Y. Chiao,
 Proposal for a loophole-free Bell inequality experiment, Physical
 Reviews A,  49, 3209 (1994).

 [4] P. Budnik, Developing a local deterministic theory to account for
 quantum mechanical effects, hep-th/9410153, (1995).

 [5] J. von Neumann, The Mathematical Foundations of Quantum Mechanics,
 Princeton University Press, N. J., (1955).

 [6] J. S. Bell, On the the problem of hidden variables in quantum
 mechanics, Reviews of Modern Physics, 38, 447-452, (1966).  Reprinted
 in Quantum Theory and Measurement, p. 397, (1987).

 6.  The shut up and calculate interpretation

 Paul Budnik [email protected]

 This is the most popular of interpretations. It recognizes that the
 important content of QM is the mathematical models and the ability to
 apply those models to real experiments. As long as we understand the
 models and their application we do not need an interpretation.

 Advocates of this position like to argue that the existing framework
 allows us to solve all real problems and that is all that is
 important.  Franson's analysis  of Aspect's experiment[1] shows this
 is not entirely true.  Because there is no objective criterion in QM
 for determining when a measurement is complete (and hence
 irreversible) there is no objective criterion for measuring the delays
 in a test of Bell's inequality.  If the demise of Schrodinger's cat
 may not be determined until someone looks in the box (see item 2) how
 are we to know when a measurement in tests of Bells inequality is
 irreversible and thus measure the critical timing in these
 experiments?

 References:

 [1] J. D. Franson, Bell's Theorem and delayed determinism, Physical
 Review D, 31,  2529-2532, (1985).


 7.  Bohm's theory

 Paul Budnik [email protected]

 Bohm's interpretation is an explicitly nonlocal mechanistic model.
 Just as Bohr saw the philosophical principle of complementarity as
 having broader implications than quantum mechanics Bohm saw a deep
 relationship between locality violation and the wholeness or unity of
 all that exists. Bohm was perhaps the first to truly understand the
 nonlocal nature of quantum mechanics. Bell acknowledged the importance
 of Bohm's work in helping develop Bell's ideas about locality in QM.

 References: D. Bohm, A suggested interpretation of quantum theory in
 terms of "hidden" variables I and II, Physical Review,85, 155-93
 (1952).  Reprinted in Quantum Theory and Measurement, p. 369, (1987).

 D. Bohm & B.J. Hiley, The Undivided Universe: an ontological
 interpretation of quantum theory (Routledge: London & New York, 1993).

 Recently there has been renewed interest in Bohmian mechanics.  D.
 D"urr, S. Goldstein, N Zanghi, Phys. Lett. A 172, 6 (1992) K. Berndl
 et al., Il Nuovo Cimento Vol. 110 B, N. 5-6 (1995).

 Peter Holland's book The Quantum Theory of Motion (Cambridge
 University Press 1993) contains many pictures of numerical simulations
 of Bohmian trajectories.

 There was a recent two part article in Physics Today based in part on
 Bohm's approach. The author, Sheldon Goldstein, has published a number
 of other papers on this and related subjects many of which are
 available at his web site, http://math.rutgers.edu/~oldstein.  S
 Goldstein, Quantum Theory Without Observers, Physics Today Part 1:
 March 1998, 42-46, Part 2: April 1998 38-42.

 8.  Lawrence R. [email protected] The Transactional Interpreta-
 tion of Quantum Mechanics

 The transactional interpretation of quantum mechanics (J.G. Cramer,
 Phys. Rev. D 22, 362 (1980) ) has received little attention over the
 one and one half decades since its conception. It is to be emphasized
 that, like the Many-Worlds and other interpretations, the
 transactional interpretation (TI) makes no new physical predictions;
 it merely reinterprets the physical content of the very same
 mathematical formalism as used in the ``standard'' textbooks, or by
 all other interpretations.
 The following summarizes the TI. Consider a two-body system (there are
 no additional complications arising in the many-body case); the
 quantum mechanical object located at space-time point (R_1,T_1) and
 another with which it will interact at (R_2,T_2). A quantum mechanical
 process governed by E=h\nu, conservation laws, etc., occurs between
 the two in the following way.

 1) The ``emitter'' (E) at (R_1,T_1) emits a retarded ``offer wave''
 (OW) \\Psi.  This wave (or state vector) is an actual physical wave
 and not (as in the Copenhagen interpretation) just a ``probability''
 wave.

 2) The ``absorber'' (A) at (R_2,T_2) receives the OW and is stimulated
 to emit an advanced ``echo'' or ``confirmation wave'' (CW)
 proportional to \\Psi at R_2 backward in time; the proportionality
 factor is \\Psi* (R_2,T_2).

 3) The advanced wave which arrives at 'E' is \\Psi \\Psi* and is
 presumed to be the probability, P, that the transaction is complete
 (ie., that an interaction has taken place).

 4) The exchange of OW's and CW's continues until a net exchange of
 energy and other conserved quantities occurs dictated by the quantum
 boundary conditions of the system, at which point the ``transaction''
 is complete. In effect, a standing wave in space-time is set up
 between 'E' and 'A', consistent with conservation of energy and
 momentum (and angular momentum). The formation of this superposition
 of advanced and retarded waves is the equivalent to the Copenhagen
 ``collapse of the state vector''. An observer perceives only the
 completed transaction, however, which he would interpret as a single,
 retarded wave (photon, for example) traveling from 'E' to 'A'.

 Q1. When does the ``collapse'' occur?

 A1. This is no longer a meaningful question. The quantum measurement
 process happens ``when'' the transaction (OW sent - CW received -
 standing wave formed with probability \\Psi \\Psi*) is finished - and
 this happens over a space-time interval; thus, one cannot point to a
 time of collapse, only to an interval of collapse (consistent with
 relativity).

 Q2. Wait a moment. What you are describing is time reversal invariant.
 But for a massive particle you have to use the Schrodinger equation
 and if \\Psi is a solution (OW), then \\Psi* is not a solution. What
 gives?

 A2. Remember that the CW must be time-reversed, and in general must be
 relativistically invariant; ie., a solution of the Dirac equation.
 Now (eg., see Bjorken and Drell, Relativistic QM), the nonrelativistic
 limit of that is not just the Schrodinger equation, but two
 Schrodinger equations: the time forward equation satisfied by \\Psi,
 and the time reversed Schrodinger equation (which has i --> -i) for
 which \\Psi* is the correct solution. Thus, \\Psi* is the correct CW
 for \\Psi as the OW.

 Q3. What about other objects in other places?

 A3. The whole process is three dimensional (space). The retarded OW is
 sent in all spatial directions. Other objects receiving the OW are
 sending back their own CW advanced waves to 'E' also. Suppose the
 receivers are labeled 1 and 2, with corresponding energy changes E_1
 and E_2. Then the state vector of the system could be written as a
 superposition of waves in the standard fashion. In particular, two
 possible transactions could form: exchange of energy E_1 with
 probability P_1=\\Psi_1 \\Psi_1*, or E_2 with probability P_2=\\Psi_2
 \\Psi_2*. Here, the conjugated waves are the advanced waves evaluated
 at the position of R_1 or R_2 respectively according to rule 3 above.

 Q4. Involving as it does an entire space-time interval, isn't this a
 nonlocal ``theory''?

 A4. Yes, indeed; it was explicitly designed that way. As you know from
 Bell's theorem, no ``theory'' can agree with quantum mechanics unless
 it is nonlocal in character. In effect, the TI is a hidden variables
 theory as it postulates a real waves traveling in space-time.

 Q5. What happens to OW's that are not ``absorbed'' ?

 A5. Inasmuch as they do not stimulate a responsive CW, they just
 continue to travel onward until they do. This does not present any
 problems since in that case no energy or momentum or any other
 physical observable is transferred.

 Q6. How about all of the standard measurement thought experiments like
 the EPR, Schrodinger's cat, Wigner's friend, and Renninger's negative-
 result experiment?

 A6. The interpretational difficulties with the latter three are due to
 the necessity of deciding when the Copenhagen state reduction occurs.
 As we saw above, in the TI there is no specific time when the
 transaction is complete. The EPR is a completeness argument requiring
 objective reality.  The TI supplies this as well; the OW and CW are
 real waves, not waves of probability.

 Q7. I am curious about more technical details. Can you give a further
 reference?

 A7. If you understand the theory of ``advanced'' and ``retarded''
 waves (out of electromagnetism and optics), many of the details of TI
 calculations can be found in: Reviews of Modern Physics, Vol. 58, July
 1986, pp. 647-687 available on the WWW as:
 http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html

 9.  Complex probabilities

 References; Saul Youssef Quantum Mechanics as Complex Probability
 Theory, hep-th 9307019.  S. Youssef, Mod.Phys.Lett.A 28(1994)2571.

 10.  Quantum logic

 References: R.I.G. Hughes, The Structure and Interpretation of Quantum
 Mechanics, pp. 178-217, Harvard University Press, 1989.

 11.  Consistent histories

 References: R. B. Griffiths, Consistent Histories and the
 Interpretation of Quantum Mechanics, Journal of statistical Physics.,
 36(12):219-272(1984)

 M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics
 of Information, edited by W. Zurek, Santa Fe Institute Studies in the
 Sciences of Complexity Vol. VIII, Addison-Wesley, Reading, 1990. Also
 in Proceedings of the $3$rd International Symposion on the Foundations
 of Quantum Mechanics in the Light of New Technology, edited by S.
 Kobayashi, H. Ezawa, Y. Murayama and S. Nomura, Physical Society of
 Japan, Tokyo, 1990

 R. B. Griffiths, Phys. Rev. Lett. 70, 2201 (1993)

 R. Omn\`es, Rev. Mod. Phys. 64, 339 (1992)


 In this approach serious problems arise. This is best pointed out in:
 B. d'Espagnat, J. Stat. Phys. 56, 747 (1989)

 F. Dowker und A. Kent, On the Consistent Histories Approach to Quantum
 Mechanics, University of Cambridge Preprint DAMTP/94-48, Isaac Newton
 Institute for Mathematical Sciences Preprint NI 94006, August 1994.


 12.  Spontaneous reduction models

 Reference:

 G. C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D 34, 470 (1986).

 13.  What is needed?

 All comments suggested and contributions are welcome. We currently
 have nothing but references on Complex Probabilities, Quantum Logic,
 Consistent Histories and Spontaneous Reduction Models. The entries on
 the following topics are minimal and should be replaced by complete
 articles.


 +  Copenhagen interpretation

 +  Relative State (Everett)

 +  Shut up and calculate

 +  Bohm's theory

 Alternative views on any of the topics and suggestions for additional
 topics are welcome.

 14.  Is this a real FAQ?

 Paul Budnik [email protected]

 A FAQ is generally understood to be a reasonably objective set of
 answers to frequently asked questions in a news group. In cases where
 an issue is controversial the FAQ should include all credible opinions
 and/or the consensus view of the news group.

 Establishing factual accuracy is not easy. No consensus is possible on
 interpretations of QM because many aspects of interpretations involve
 metaphysical questions. My intention is that this be an objective
 accurate FAQ that allows for the expression of all credible relevant
 opinions.  I did not call it a FAQ until I had significant feedback
 from the `sci.physics' group. I have responded to all criticism and
 have made some corrections. Nonetheless there have been a couple of
 complaints about this not being a real FAQ and there is one issue that
 has not been resolved.

 If anyone thinks there are technical errors in the FAQ please say what
 you think the errors are. I will either fix the problem or try to
 reach on a consensus with the help of the `sci.physics' group about
 what is factually accurate.  I do not feel this FAQ should be limited
 to noncontroversial issues.  A FAQ on measurement in quantum mechanics
 should highlight and underscore the conceptual issues and problems in
 the theory.

 The one area that has been discussed and not resolved is the status of
 locality in Everett's interpretation. Here is what I believe the facts
 are.


 Eberhard proved that any theory that reproduces the predictions of QM
 is nonlocal[1]. This proof assumes contrafactual definiteness (CFD) or
 that one could have done a different experiment and have gotten a
 definite result. This assumption is widely used in statistical
 arguments.  Here is what Eberhard means by nonlocal:


    Let us consider two measuring apparata located in two different
    places A and B. There is a knob a on apparatus A and a knob b on
    apparatus B.  Since A and B are separated in space, it is
    natural to think what will happen at A is independent of the
    setting of knob b and vice versa.  The principles of relativity
    seem to impose this point of view if the time at which the knobs
    are set and the time of the measurements are so close that, in
    the time laps, no light signal can travel from A to B and vice
    versa. Then, no signal can inform a measurement apparatus of
    what the knob setting on the other is. However, there are cases
    in which the predictions of quantum theory make that
    independence assumption impossible. If quantum theory is true,
    there are cases in which the results of the measurements A will
    depend on the setting of the knob b and/or the results of the
    measurements in B will depend on the setting of the knob a.[1]

 It is logically possible to deny CFD and thus to avoid Eberhard's
 proof.  This assumption can be made in Everett's interpretation.
 Everett's interpretation does not imply CFD is false and CFD can be
 assumed false in other interpretations.  I do not think it is
 reasonable to deny CFD in some experiments and not others but that is
 a judgment call on which intelligent people can differ.

 It is mathematically impossible to have a unitary relativistic wave
 function from which one can compute probabilities that will violate
 Bell's inequality. A unitary wave function does satisfy CFD and thus
 is subject to Eberhard's proof. This is a problem for some advocates
 of Everett who insist that only the wave function exists.  There is no
 wave function consistent with both quantum mechanics and relativity
 and it is mathematically impossible to construct such a function.
 Quantum field theory requires a nonlocal and thus nonrelativistic
 state model. The predications of quantum field theory are the same in
 any frame of reference but the mechanisms that generate nonlocal
 effects must operate in an absolute frame of reference. Quantum
 uncertainty makes this seemingly paradoxical situation possible. There
 is a nonlocal effect but we cannot tell if the effect went from A to B
 or B to A because of quantum uncertainty. As a result the predictions
 are the same in any frame of reference but any mechanism that produces
 these predictions must be tied to an absolute frame of reference.

 There is a certain Alice in Wonderland quality to arguments on these
 issues. Many physicists claim that classical mathematics does not
 apply to some aspects of quantum mechanics, yet there is no other
 mathematics. The wave function model is a classical causal
 deterministic model. The computation of probabilities from that model
 is as well.  The aspect of quantum mechanics that one can claim lies
 outside of classical mathematics is the interpretation of those
 probabilities.  Most physicists believe these probabilities are
 irreducible, i. e., do not come from a more fundamental deterministic
 process the way probabilities do in classical physics. Because there
 is no mathematical theory of irreducible probabilities one can invent
 new metaphysics to interpret these probabilities and here is where the
 problems and confusion rest.  Some physicists claim there is new
 metaphysics and within this metaphysics quantum mechanics is local.

 References:

 P. H. Eberhard, Bell's Theorem without Hidden Variables, Il Nuovo
 Cimento, V38 B 1, p 75, Mar 1977.

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