Minkowski Space from Quantum Mechanics

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2024-05-04 DOI:10.1007/s10701-024-00753-x

László B. Szabados

引用次数: 0

Abstract

Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum mechanical systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems.

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量子力学中的闵科夫斯基空间

彭罗斯的 "自旋几何定理 "得到了进一步扩展，从 SU(2) 和 E(3) （欧几里得）扩展到 E(1, 3) （波恩卡莱）不变的基本量子力学系统。被视为具有正静止质量的 E(1, 3) 不变基本经典机械系统的质心世界线的明考斯基空间任意两条非平行时间直线之间的洛伦兹空间距离，可以用 E(1, 3) 不变的基本观测量（即系统的四动量和角动量）来表示。在量子力学的抽象代数表述中，用基本量子观测量给出了 E(1, 3) 不变的基本量子力学系统的类似表达式，并证明在经典极限中，它以渐近消失的不确定性再现了闵科夫斯基空间时间直线之间的洛伦兹空间距离。因此，在经典极限中，只需使用抽象量子力学系统的观测值，就能从量子力学中恢复闵科夫斯基空间的度量结构。

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

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.

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