关于动能与引力能之间形式对称性的破缺
On a Broken Formal Symmetry between Kinetic and Gravitational Energy
摘要：
从历史上看，对称性的发现在我们对自然的基本理解的进步中发挥了重要作用。本文将证明在牛顿理论中，在球形引力场中，试验质量的动能（KE）和引力势能（GPE）之间存在形式对称性。换句话说，存在一种表达GPE的方式，使得数学表达式的形式在KE和GPE的互换下保持不变。当通过一个适当的假设扩展到相对论时，它会导致一个框架，将广义相对论和牛顿的引力能概念联系起来，即使对称性被打破，除了在无穷小的极限。在无限小尺度下认识到这种对称性，就有可能写出单个引力子的相对论性方程，根据一种解释，它的性质可能是意想不到的。
英文摘要：
Historically, the discovery of symmetries has played an important role in the progress of our fundamental understanding of nature. This paper will demonstrate that there exists in Newtonian theory in a spherical gravitational field a formal symmetry between the kinetic (KE) and gravitational potential energy (GPE) of a test mass. Put differently, there exists a way of expressing GPE such that the form of the mathematical expression remains invariant under an interchange of KE and GPE. When extended to relativity by a suitable assumption, it leads to a framework that bridges the general relativistic and Newtonian conceptions of gravitational energy, even though the symmetry is broken except in the infinitesimal limit. Recognizing this symmetry at infinitesimal scales makes it possible to write a relativistic equation of an individual graviton, the properties of which under under one interpretation may be unexpected.
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