Different Aspects of Spin in Quantum Mechanics and General Relativity

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES
Symmetry-Basel Pub Date : 2023-11-03 DOI:10.3390/sym15112016
Martin Tamm
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Abstract

In this paper, different aspects of the concept of spin are studied. The most well-established one is, of course, the quantum mechanical aspect: spin is a broken symmetry in the sense that the solutions of the Dirac equation tend to have directional properties that cannot be seen in the equation itself. It has been clear since the early days of quantum mechanics that this has something to do with the indefinite metric in Lorentz geometry, but the mechanism behind this connection is elusive. Although spin is not the same as rotation in the usual sense, there must certainly be a close relationship between these concepts. And, a possible way to investigate this connection is to instead start from the underlying geometry in general relativity. Is there a reason why rotating motion in Lorentz geometry should be more natural than non-rotating motion? In a certain sense, the answer turns out to be yes. But, it is by no means easy to see what this should correspond to in the usual quantum mechanical picture. On the other hand, it seems very unlikely that the similarities should be just coincidental. The interpretation of the author is that this can be a golden opportunity to investigate the interplay between these two theories.
量子力学和广义相对论中自旋的不同方面
本文对自旋概念的不同方面进行了研究。最完善的一个当然是量子力学方面:自旋是一种对称性破缺,因为狄拉克方程的解往往具有在方程本身中看不到的方向性。从量子力学的早期就很清楚,这与洛伦兹几何中的不定度规有关,但这种联系背后的机制是难以捉摸的。虽然自旋与通常意义上的旋转不一样,但这两个概念之间肯定有密切的关系。研究这种联系的一种可能的方法是从广义相对论的基础几何开始。在洛伦兹几何中,旋转运动比非旋转运动更自然,有什么原因吗?从某种意义上说,答案是肯定的。但是,要看出这在通常的量子力学图像中应该对应什么并不容易。另一方面,相似之处似乎不太可能只是巧合。作者的解释是,这可能是研究这两种理论之间相互作用的黄金机会。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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