BogolyubovLogunovTodorov by Bohlin T.

By Bohlin T.

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It is easy to see why all three operators belonging to the same line, or to the same column, always commute (the products of two σ’s that anti-commute are commuting operators, since the commutation introduces two −1 signs, with cancelling effects). Moreover, the products of all three operators is always +1, except the last column for which it is −1 30 . Here, instead of an infinite number of triplet of directions in space, we have 6 groups of three operators, but the same question as above arises: can we attribute a color to each of the 9 elements of matrix (23), red for result +1 and yellow for result −1, in a way that is consistent with the results of quantum mechanics?

The reason is simple: why require that theories with contrafactuality/additional variables should be explicitly local at all stages, while it is not required from standard quantum mechanics? 1), nor again the expression of the state vector itself, correspond to mathematically local calculations. In other words, even if one can discuss whether or not quantum mechanics is local or not at a fundamental level, it is perfectly clear that its formalism is not; it would therefore be just absurd to request a local formalism from a non-orthodox theory especially when the theory in question is built in order to reproduce all results of quantum mechanics!

We could not conclude honestly this section on loopholes without mentioning that, while most specialists acknowledge their existence, they do not take them too seriously because of their “ad hoc” character. Indeed, one should keep in mind that the explanations in question remain artificial, 33 For instance, in the proof that makes uses of a probability density ρ(λ), if one assumes that a and b become two functions a(λ) and b(λ), it makes no sense to compare the average values for different fixed values of a and b.

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