Nonequivalence of equivalence principles

Equivalence principles played a central role in the development of general relativity. Furthermore, they have provided operative procedures for testing the validity of general relativity, or constraining competing theories of gravitation. This has led to a flourishing of different, and inequivalent, formulations of these principles, with the undesired consequence that often the same name, "equivalence principle", is associated with statements having a quite different physical meaning. In this paper we provide a precise formulation of the several incarnations of the equivalence principle, clarifying their uses and reciprocal relations. We also discuss their possible role as selecting principles in the design and classification of viable theories of gravitation.

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11 pages, no figures

equivalence principle
general relativity
gravitation

References(51)

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There are notable exceptions. Some authors prefer to replace heuristic principles by sound mathematical postulates, on the ground that the former are not welldefined. A champion of this attitude was the Irish mathematical physicist John Lighton Synge, who wrote with characteristic wit: "When, in a relativistic discussion, I try to make things clearer by a spacetime diagram, the other participants look at it with polite detachment and, after a pause of embarrassment as if some childish indecency had been exhibited, resume the debate in their own terms. Perhaps they speak of the Principle of Equivalence. If so, it is my turn to have a blank mind, for I have never been able to understand this Principle. Does it mean that the signature of the space-time metric is +

[2]

(or - 2 if you prefer the other convention)? If so, it is important, but hardly a Principle. Does it mean that the effects of a gravitational field are indistinguishable from the effects of an observer’s acceleration? If so, it is false. In Einstein’s theory, either there is a gravitational field or there is none, according as the Riemann tensor does not or does vanish. This is an absolute property

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For example, r could be defined as the radius of the smallest sphere containing the body, evaluated as r = ( A/ 4 π ) 1 / 2, where A is the area of the sphere

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For instance, in Bohmian dynamics the equation of motion for a particle in the presence of a gravitational field is m i ̈ x = - m g ∇ Φ - ∇ Q, where Q is the so-called quantum potential, which contains m i but is not proportional to it

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Incidentally, this implies that there is no need to include the WEP explicitly in the statement of EEP. The condition that a gravitational field be locally eliminable (usually implemented through the requirements of local position invariance and local Lorentz invariance) is entirely sufficient

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