Theory of gravitation theories: a no-progress report

TL;DR

This paper reviews historical efforts to establish criteria for viable gravitational theories, highlighting fundamental ambiguities and misconceptions that hinder progress in formulating alternatives to general relativity.

Contribution

It critically examines the foundations of proposed gravitational theory criteria, revealing their dependence on representations and clarifying common misconceptions.

Findings

Qualitative principles like the Einstein Equivalence Principle lack robust quantitative foundations.

Ambiguities in defining matter and gravitational fields affect theory viability assessments.

Misconceptions about conformal frames and theory equivalence persist in the field.

Abstract

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of the present paper could be ``why are we still unable to write a guide on how to propose viable alternatives to general relativity?''. Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein Equivalence Principle, into quantitative ones, such as the metric postulates, stand on rather shaky grounds -- probably contrary to popular belief -- as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions, such as those of the stress-energy tensor or classical vacuum, on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the Equivalence Principle, the use of conformal frames and equivalence between theories are clarified.