Mach's Principle and Invariance under Transformation of Units

A gravitational theory compatible with Mach's principle was published recently by Brans and Dicke. It is characterized by a gravitational field of the Jordan type, tensor plus scalar field. It is shown here that a coordinate-dependent transformation of the units of measure can be used to throw the theory into a form for which the gravitational field appears in the conventional form, as a metric tensor, such that the Einstein field equation is satisfied. The scalar field appears then as a "matter field" in the theory. The invariance of physical laws under coordinate-dependent transformations of units is discussed.

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