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| related topics |
| {measurement, state, measurements} |
| {bell, inequality, local} |
| {let, theorem, proof} |
| {observables, space, algebra} |
| {cos, sin, state} |
| {particle, mechanics, theory} |
| {field, particle, equation} |
| {group, space, representation} |
| {force, casimir, field} |
| {theory, mechanics, state} |
|
On classical models of spin
Marek Czachor
abstract: The reason for recalling this old paper is the ongoing discussion on the
attempts of circumventing certain assumptions leading to the Bell theorem
(Hess-Philipp, Accardi). If I correctly understand the intentions of these
Authors, the idea is to make use of the following logical loophole inherent in
the proof of the Bell theorem: Probabilities of counterfactual events A and A'
do not have to coincide with actually measured probabilities if measurements of
A and A' disturb each other, or for any other fundamental reason cannot be
performed simulaneously. It is generally believed that in the context of
classical probability theory (i.e. realistic hidden variables) probabilities of
counterfactual events can be identified with those of actually measured events.
In the paper I give an explicit counterexample to this belief. The "first
variation" on the Aerts model shows that counterfactual and actual problems
formulated for the same classical system may be unrelated. In the model the
first probability does not violate any classical inequality whereas the second
does. Pecularity of the Bell inequality is that on the basis of an in principle
unobservable probability one derives probabilities of jointly measurable random
variables, the fact additionally obscuring the logical meaning of the
construction. The existence of the loophole does not change the fact that I was
not able to construct a local model violating the inequality with all the other
loopholes eliminated.
- oai_identifier:
- oai:arXiv.org:quant-ph/0205010
- categories:
- quant-ph
- comments:
- published as Found. Phys. Lett. 3 (1992) 249
- arxiv_id:
- quant-ph/0205010
- journal_ref:
- Found. Phys. Lett. 3 (1992) 249
- created:
- 2002-05-02
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