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14. Is this a real FAQ?

Paul Budnik paul@mtnmath.com

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 [Note 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 [Note 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:

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


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