There is no axiomatic system for the quantum theory
General Physics
2008-11-28 v4
Abstract
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.
Cite
@article{arxiv.0711.3130,
title = {There is no axiomatic system for the quantum theory},
author = {Koji Nagata},
journal= {arXiv preprint arXiv:0711.3130},
year = {2008}
}
Comments
Journal of Mathematical Physics, (2007), (accepted for publication)