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Scalar‐Tensor Theory in Canonical Form. I. The Question of Mach's Principle

### Abstract

By first casting the scalar‐tensor theory into canonical form, the constraint equations are obtained from which it is possible to discuss the self‐energy problem of the neutral particle and the electron. With the assumptions of Minkowski space and a constant scalar field as boundary conditions at infinity, it is shown by variational arguments that the inertia of these objects is unchanged from the corresponding general relativity values. Accordingly, if the boundary value of the scalar is altered by a change of matter at infinity, the mass of the electron is unchanged. From this point of view, the scalar‐tensor theory is no more compatible with Mach's principle than is general relativity.

© 1970 The American Institute of Physics

Received 12 December 1969
Published online 28 October 2003