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# Quantum Magellan theorem(the simplest NO-GO Theorem for hidden variables)

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### Abstract

In this work we study time reversal (that can be realistically simulated using two total mirrors) of the interaction between single photon and beam splitter, without any measuring apparatus (detector). For description of this effect we use, on the one hand, standard quantum mechanical formalism, $$SQM$$. On the other hand, for description of the same effect, we use a hypothetical extension of the standard quantum mechanical formalism, so-called hidden variables theory, $$HVT$$, that should satisfy only few following general propositions. First proposition is that at the $$SQM$$ level of the analysis accuracy there are no effective distinctions between experimental facts, $$SQM$$ predictions and $$HVT$$ predictions. Second proposition is that at the hypothetically more accurate $$HVT$$ level of the analysis accuracy there is deterministic, one-to-one correspondence between initial and final dynamical state of the physical system so that $$HVT$$ dynamics is principally symmetric in respect to $$HVT$$ characteristic time reversal transformation. However, we simply demonstrate on mentioned example that such $$HVT$$ cannon exist that can be simply called quantum Magellan theorem (quantum mechanics represents "unique, Magellan straight" between "Atlantic ocean" of the macroscopic phenomena and "Great, Pacific ocean" of the microscopic phenomena). Obviously Magellan theorem can be considered as the simplest no-go theorem for a wide (potentially physically realistic) class of the hidden variables theories.

### Author and article information

###### Journal
13 October 2009
2014-06-18
###### Article
0910.2328