Gravity and the Tenacious Scalar Field

Abstract

Scalar fields have had a long and controversial life in gravity theories, having progressed through many deaths and resurrections. The first scientific gravity theory, Newton’s, was that of a scalar potential field, so it was natural for Einstein and others to consider the possibility of incorporating gravity into special relativity as a scalar theory. This effort, though fruitless in its original intent, nevertheless was useful in leading the way to Einstein’s general relativity, a purely two-tensor field theory. However, a universally coupled scalar field again appeared, both in the context of Dirac’s large number hypothesis and in 5-dimensional unified field theories as studied by Fierz, Jordan, and others. While later experimentation seems to indicate that if such a scalar exists its influence on solar system--size interactions is negligible, other reincarnations have been proposed under the guise of dilatons in string theory and inflatons in cosmology. This paper presents a brief overview of this history.