The statistics of particles in local quantum theories

Elliot W. Montroll, John Ward

Oscar Dahlsten, Andrew J. P. Garner, Jayne E. Thompson +2 more

In quantum theory, particles in three spatial dimensions come in two different types: bosons or fermions, which exhibit sharply contrasting behaviours due to their different exchange statistics. Could more general forms of probabilistic theories admit more exotic types of particles? Here, we propose a thought experiment to identify more exotic particles in general post-quantum theories. We consider how in quantum theory the phase introduced by swapping indistinguishable particles can be measured. We generalise this to post-quantum scenarios whilst imposing indistinguishability and locality principles. We show that our ability to witness exotic particle exchange statistics depends on which symmetries are admitted within a theory. These exotic particles can manifest unusual behaviour, such as non-abelianicity even in topologically simple three-dimensional space.

Werner A. Hofer

Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown intrinsic energy components, they depend on the physical environment by way of external potentials. Due to these statistical qualities and wave function normalization, non-locality is inherent to the fundamental relations of Planck, de Broglie and Schroedinger. A local formulation of these statements is introduced and briefly assessed, the modified and local Schroedinger equation is non-linear. Quantum measurements are analyzed in detail, the exact interplay between causal and statistical reasons in a measurement process can be accounted for. Examples of individual measurement effects in quantum theory are given, the treatment of diffraction experiments, neutron interferences, quantum erasers, the quantum Zeno effect, and interaction-free measurements can be described consistent with the suggested framework. The paper additionally provides a strictly local and deterministic calculation of interactions in a magnetic field. The results suggest that quantum theory is a statistical formalism which derives its validity in measurements from considering every possible measurement of a given system. It can equally be established, that the framework of quantum physics is theoretically incomplete, because a justification of ensemble qualities is not provided.

Wesley E. Brittin, Asım Orhan Barut

Huaiyu Zhu

Existing experiments do not disprove local realistic quantum theories. To overcome logical difficulties of the standard quantum theory, a nondeterministic irreversible local realistic theory was proposed, in which the wave-particle duality is objective in contrast to the complementarity principle. The statistical characteristics of these two theories can be distinguished by a proposed experiment within presently available technology. 03.65.Bz(found), 03.75.-b(m.w), 05.30.-d(q.sm), 05.40.+j(fluct)

Edward G. Harris