0 Ju n 20 05 1 The roots of scalar - tensor theory : an approximate history 1

Why are there no fundamental scalar fields actually observed in physics today? Scalars are the simplest fields, but once we go beyond Galilean-Newtonian physics they appear only in speculations, as possible determinants of the gravitational constants in the so-called Scalar-Tensor theories in non-quantum physics, and as Higgs particles, dilatons, etc., in quantum physics. Actually, scalar fields have had a long and controversial life in gravity theories, with a history of deaths and resurrections. The first gravity theory of scientific interest was developed by Newton, using a scalar potential field. After developing special relativity into which electromagnetism fit so nicely, it was natural for Einstein and others to consider the possibility of incorporating gravity into special relativity as a scalar theory. Of course, in its original form this effort was not successful, but it did help in pointing the way to standard Einstein general relativistic theory of gravity as a metric field. However, the original investigation of a scalar field did reinforce Einstein’s interest in Mach’s principle, suggesting an influence of gravity on inertial mass. Also, five dimensional unified field theories as studied by Fierz, Jordan, and others suggested a spacetime scalar field that might well provide a “varying” gravitational constant. Even Einstein and Bergmann were briefly interested in such possibilities. However, Dicke, motivated by Dirac’s numbers and Mach’s principle, provided the major driving force for theoretical and experimental investigations of such a possibility. While later experimentation seems to indicate that if such a scalar exists its influence on solar system size interactions is negligible, other reincarnations of a scalar-tensor formulation have been proposed in the contexts of dilatons in string theory and inflatons in cosmology. This paper presents a brief overview of this history. A recent, and much more thorough, study of the subject of scalar-tensor theories can be found in the book by Fujii and Maeda, [1].