[论文解读] An Analysis of States in the Phase Space: From Quantum Mechanics to General Relativity

Sebastiano Tosto|arXiv (Cornell University)|Jul 7, 2008

Quantum Mechanics and Applications参考文献 15被引用 3

一句话总结

本文提出了一种新框架，将量子不确定性扩展至时空坐标，将粒子视为在空间和时间上均非定域化的。通过仅关注共轭变量的非定域化范围，而非其局域值，该方法将量子力学、狭义相对论和广义相对论的结果作为推论重现，表明引力本质上是通过时空非定域化而涌现的量子现象。

ABSTRACT

The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D, vol. 18, n.12, 1996]. Instead of attempting to increase the accuracy of some existing computational model through a new kind of approximation, these papers acknowledge since the beginning the lack of deterministic information about the local properties of the constituent particles, considered random, unknown and unpredictable and thus ignored in principle. The leading idea is that the physical properties of quantum systems could be inferred merely considering the delocalization ranges of dynamical variables, rather than their local values. In effect, despite the agnostic character of the approach proposed, both papers show that the kind of physical information reachable reproduces exactly in all cases examined that obtained solving the pertinent wave equations. The concept of quantum uncertainty is further extended in the present paper to both space and time coordinates, considering thus a unique spacetime delocalization range and still discarding since the beginning the local values of the conjugate dynamical variables. The paper shows an unexpected wealth of information obtainable simply extending the concept of space uncertainty to that of spacetime uncertainty: the results are inherently consistent with that of the operator formalism of wave mechanics and with the basic postulates of special relativity, both inferred as corollaries. Moreover, even the gravity appears to be essentially a quantum phenomenon. The most relevant outcomes of special and general relativity are achieved as straightforward consequence of the space-time delocalization of particles using the simple quantum formalism first introduced in the early papers.

研究动机与目标

• 探索是否可从一个最小假设出发推导出量子力学与相对论中的物理定律：即时空坐标中的量子不确定性。
• 通过从一开始就摒弃共轭变量的局域值，解决对粒子局域性质缺乏确定性知识的问题。
• 证明仅通过时空非定域化即可获得与波动力学和狭义相对论一致的结果。
• 探究是否可通过该形式化体系将引力理解为一种由时空非定域化所导致的涌现量子效应。
• 在基于非定域化范围的单一概念框架下，统一量子与相对论现象。

提出的方法

• 该方法假设动力学变量（如位置与动量）的局域值在本质上未知且被忽略，仅关注其非定域化范围。
• 通过将量子不确定性扩展至空间与时间坐标，引入时空不确定性，将其视为统一的非定域化范围。
• 形式化体系基于不确定性原理的简单量子力学框架，不以波方程或算符形式为起点。
• 物理预测从相空间的几何结构中推导，强调范围而非点值。
• 该模型将所有物理信息编码于非定域化程度之中，而非精确的局域测量。
• 结果与狭义相对论和量子力学一致，广义相对论作为推论自然出现。

实验结果

研究问题

• RQ1 是否可从一种摒弃对粒子局域性质的已知信息、仅关注非定域化范围的形式化体系中，推导出量子力学的基本原理？
• RQ2 将量子不确定性扩展至时空坐标，对相对论性与引力现象的推导有何影响？
• RQ3 在多大程度上可将狭义与广义相对论作为时空非定域化框架的推论重新获得？
• RQ4 是否可将引力解释为由时空中的量子非定域化所引发的涌现效应？
• RQ5 标准的算符形式化体系是否为必需，还是可被仅基于不确定性范围的相空间描述所取代？

主要发现

• 该形式化体系在不求解波方程的前提下重现了波动力学的所有结果，仅依赖于非定域化范围。
• 狭义相对论作为时空非定域化框架的自然推论出现，与其实验假设一致。
• 广义相对论的核心预言，包括时空曲率，作为同一时空不确定性原理的后果被推导而出。
• 该方法表明引力本质上是量子现象，源于粒子在时空中的非定域化。
• 该模型在不引入动力学变量局域值的前提下，与既有的物理定律保持一致。
• 结果本身具有内在自洽性，除时空中的量子不确定性外，无需额外假设。