A Note On Einstein, Bergmann, and the Fifth Dimension

TL;DR

This paper examines Einstein and Bergmann's 1938 work on five-dimensional unified theories, highlighting their initial symmetry approach and subsequent modifications to avoid predicting a new long-range scalar field.

Contribution

It clarifies the historical development of Einstein-Bergmann's five-dimensional theory and explains why they altered their original symmetric formulation.

Findings

Original symmetric theory predicted a new long-range scalar field.

Modifications by Einstein and Bergmann removed the scalar field prediction.

Historical analysis of Einstein-Bergmann's motivations and decisions.

Abstract

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. (Based on a lecture at the Einstein Centennial Celebration at the Library of Alexandria, June, 2005.