As noted many years ago by Sciama, and more recently by Nordtvedt, Lorentz invariant (relativistic) gravitation at linear order involves a vector potential that is required to properly account for large inertial effects as well as the correct prediction of the classical tests of general relativity theory (GRT). It is pointed out that the linear-order vector aspect of the gravitational potential makes possible a simple, powerful and inexpensive technique for testing the predictions of GRT and associated issues. An experiment using this technique gives preliminary results that, to order of magnitude, corroborate GRT.
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1. If one demands a theory that satisfies Mach's Principle irrespective of the particular value ofρ c, one must go to a theory that contains GRT with “critical” cosmic matter density as a special case. Such a theory (an Einstein-Cartan theory with teleparallelism) has been developed by Treder .
2. Equation (4) here is Nordtvedt's Eq. (14), in Ref. 3, with GRT PPN parameters chosen.
3. The exact value of this correction factor that depends on the way in which energy is distributed between field and sources in turn depends on how the source term for the gravitational field equations is constructed. At least two different source terms that give correct predictions for the various tests of GRT exist. In this connection see Peters . This ambiguity does not mean that it is impossible in principle to determine how energy is distributed between sources and field. Indeed, if one posits the existence of “critical” cosmic matter density, this experiment can decide the issue.
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Woodward, J.F. A new experimental approach to Mach's principle and relativistic graviation. Found Phys Lett 3, 497–506 (1990). https://doi.org/10.1007/BF00665932
- general relativity
- Mach's principle
- experimental gravitation