A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

Symmetry

AbrahamA. Ungar¹ 

[1] Department of Mathematics, North Dakota State University, Fargo, ND 58102, USA;

关键词: Einstein gyrogroups;    Galilei transformations of signature (m,n);    Lorentz transformations of signature (m,n);    pseudo-Euclidean spaces;    quantum multi-particle entanglement;    special relativity;   

DOI  :  10.3390/sym12081259

来源: DOAJ

【 摘 要 】

A Lorentz transformation group SO$(m,n)$ of signature $(m,n)$, $m,n\in \mathbb{N}$, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature $(m,n)$. Accordingly, the Lorentz group SO$(1,3)$ is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO$(m,n)$ forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature $(m,3)$ for all $m\ge 2$. The resulting enriched special relativity provides the common symmetry group SO$(1,3)$ of the $(1+3)$-dimensional spacetime of individual particles, along with the symmetry group SO$(m,3)$ of the $(m+3)$-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all $m\ge 2$. A unified parametrization of the Lorentz groups SO$(m,n)$ for all $m,n\in \mathbb{N}$, shakes down the underlying matrix algebra into elegant and transparent results. The special case is when $(m,n)=(1,3)$ is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when $(m,n)=(m,3)$ for all $m\ge 2$.

【 授权许可】

Unknown