Failure of Bell's theorem over a functional space

Márton Gömöri, Tomasz Placek

Gregor Weihs

Guang-Liang Li

According to quantum mechanics in its current form, quantum randomness is an intrinsic property of the physical world. The legitimacy of such interpretation is the essence of the Einstein-Bohr debate. Bell’s theorem implies that local realism should be responsible for the experimental invalidation of Bell inequalities. In this paper, it is shown that quantum randomness is due to the unattainability of precise space and time coordinates, and the failure of Bell inequalities is irrelevant to local realism. Furthermore, by reconsidering Bell’s theorem in the context of the mathematical setting for quantum physics, namely, Hilbert space, it is shown that, whether a measurement is performed on a system or not, the logical relation between orthogonal vectors corresponding to mutually exclusive properties of the system must be disjunction (“or”) rather than conjunction (“and”). Moreover, if the unattainability of precise space and time coordinates is taken into account, and if disjunction is used to serve as the logical relation between the orthogonal vectors, then it is possible to render quantum mechanics complete in the sense considered by Einstein while not essentially modifying the mathematical setting for quantum physics.

Gyula Bene

Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.