关于爱因斯坦、伯格曼和第五维度的注记

A Note on Einstein, Bergmann, and the Fifth Dimension

在1938年的论文中,爱因斯坦和伯格曼证明了,在远距情况下,与爱因斯坦-麦克斯韦理论相容的四维理论其实是一个五维理论的推论,而且这个五维理论关于每个维度都是对称的。他们因此而成为以此为基础的现代观点的先驱。但过了不久,他们却将论点撤回了,还用一种对现代读者来说相当不自然的方式修改了这理论,破坏了它关于五个维度的对称性。这是为什么?笔者从彼得·伯格曼的回信中得知,原来这是因为,那个更对称的五维理论会导致存在一个新的远距作用场(一个无质量的标量场)。而在1938年,爱因斯坦和伯格曼并不想让这种作用场出现。

This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unified theories of electromagnetism and gravitation in five dimensions. In their paper of 1938, Einstein and Bergmann were among the first to introduce the modern viewpoint in which a four-dimensional theory that coincides with Einstein-Maxwell theory at long distances is derived from a five-dimensional theory with complete symmetry among all five dimensions. But then they drew back, modifying the theory in a way that spoiled the five-dimensional symmetry and looks contrived to modern readers. Why？ According to correspondence of Peter Bergmann with the author, the reason was that the more symmetric version of the theory predicts the existence of a new long range field （a massless scalar field）. In 1938, Einstein and Bergmann did not wish to make this prediction.