General relativity. Papers in honour of J._L._Synge.

Differential constants of motion for systems of free gravitating particles in the Newtonian frame are first defined and then determined. It is shown that they are all implied by the existence of the first integral invariants of Poincare known from classical mechanics, or by the circulation theorem known from hydrodynamics. It is proved further that the restriction to vacuum conditions does not change the set of differential constants of motion. Another consequence is that nothing can be inferred from local (in space and time) measurements about the displacement, velocity, and orientation of a laboratory in free fall relative to a fixed Galilean frame.

Differential constants of motion for systems of free gravitating particles. I. Newton's theory

We proved in a previous paper that a generalized circulation theorem characterizes Einstein's theory of gravitation as a special case of a more general theory of gravitation, which is also based on the principle of equivalence. Here we pose the question of whether it is possible to weaken this circulation theorem in such ways that it would imply more general theories than Einstein's. This problem is solved. Principally, there are two possibilities. One of them is essentially Weyl's theory.

Weak Circulation Theorems as a Way of Distinguishing between Generalized Gravitation Theories

Differential constants of motion for systems of freely gravitating particles in general relativity are first defined and then determined. It is shown that they are all consequences of the local simultaneity conservation property of general relativity. It is proved, further, that the restriction to vacuum conditions does not change the set of differential constants of motion, excluding the nonphysical cases of space-time of dimension 2 or 3. Another consequence is that nothing can be inferred from local (in space and time) measurements about the orientation of a laboratory in free fall relative to Fermi transported axes. A similar property exists in Newton's theory.

Differential constants of motion for systems of free gravitating particles. II. General relativity

It is possible, within the framework of general relativity, to define an active gravitational mass density of incoherent matter. It is not equal to the inertial mass density, except when at rest. The concept can be specialized to a single massive particle; again, its active gravitational mass is not equal to its inertial mass, except when it rests. A measurement of the impulse imparted to a test particle by a massive body passing nearby can establish the difference, and it may be possible to carry out this measurement in a laboratory. As a by-product of our computations we obtain a generalization to nonradial motion of the slowing-down effect in a Schwarzschild field.

A. Kovetz

Papers

Differential constants of motion for systems of free gravitating particles. I. Newton's theory

Weak Circulation Theorems as a Way of Distinguishing between Generalized Gravitation Theories

Is Active Gravitational Mass Equal to Inertial Mass

Differential constants of motion for systems of free gravitating particles. II. General relativity