There is no axiomatic system for the quantum theory
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 spin1/2 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3130
 Bibcode:
 2007arXiv0711.3130N
 Keywords:

 Physics  General Physics
 EPrint:
 Journal of Mathematical Physics, (2007), (accepted for publication)