There is no axiomatic system for the quantum theory

Details There is no axiomatic system for the quantum theory There is no axiomatic system for the quantum theory

2007-11-20

arxiv.org/abs/0711.3130v4

Physics

General Physics

Journal of Mathematical Physics, (2007), (accepted for publication)

Scientific paper

Recently, [arXiv:0810.3134] is accepted and published. We derive an inequality with two settings as tests for the existence of the Bloch sphere in a spin-1/2 system. The probability theory of measurement outcome within the formalism of von Neumann projective measurement violates the inequality. Namely, we have to give up the existence of the Bloch sphere. Or, we have to give up the probability theory of measurement outcome within the formalism of von Neumann projective measurement. Hence it turns out that there is a contradiction in the Hilbert space formalism of the quantum theory, viz., there is no axiomatic system for the theory.

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