基于扩展最小作用原理与信息度量的自旋理论：量子化、纠缠与时延贝尔实验
摘要
本文基于扩展最小作用原理及电子内禀角动量具有随机取向的假设，发展了电子自旋的量子理论。该表述的新颖之处在于引入相对熵来处理内禀角动量的随机取向，从而进行作用总量的极值化。通过递归应用这一扩展最小作用原理，我们展示当相对熵的阶数趋于某个极限时，电子自旋的量子化是数学上的必然结果。此外，成功恢复了当第二个斯特恩-格拉赫实验装置相对于第一个斯特恩-格拉赫实验装置旋转时，的测量概率公式以及Schr"{o}dinger-Pauli方程。Furthermore, the principle allows us to provide an intuitive physical model and formulation to explain the entanglement phenomenon between two electron spins. In this model, spin entanglement is the consequence of the correlation between the random orientations of the intrinsic angular momenta of the two electrons. Since spin orientation is an intrinsic local property of the electron, the correlation of spin orientations can be preserved and manifested even when the two electrons are remotely separated. The entanglement of a spin singlet state is represented by two joint probability density functions that reflect the orientation correlation. Using these joint probability density functions, we prove that the Bell-CHSH inequality is violated in a Bell test. To test the validity of the spin-entanglement model, a Bell test experiment with time delay is proposed. As the time delay increases, we predict that the Bell-CHSH inequality changes from being violated to non-violated.
引用
@article{arxiv.2404.13783,
title = {Spin Theory Based on the Extended Least Action Principle and Information Metrics: Quantization, Entanglement, and Bell Test With Time Delay},
author = {Jianhao M. Yang},
journal= {arXiv preprint arXiv:2404.13783},
year = {2025}
}
备注
Closely match the accepted version. Appendix C is added to explain the choice of relative entropy. 25 pages, 7 figures. This paper is related to arXiv:2302.14619 and arXiv:2310.02274