Theoretical Frameworks for Testing Relativistic Gravity; The Parametrized Post-Newtonian Formalism

• Main Author: Will, Clifford Martin
• Format: Others
• Published: 1971
• Online Access: https://thesis.library.caltech.edu/3839/1/Will_cm_1971.pdf; Will, Clifford Martin (1971) Theoretical Frameworks for Testing Relativistic Gravity; The Parametrized Post-Newtonian Formalism. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NQNB-RK02. https://resolver.caltech.edu/CaltechETD:etd-09302005-113319 <https://resolver.caltech.edu/CaltechETD:etd-09302005-113319>

Increasing sophistication and precision of experimental tests of relativistic gravitation theories has led to the need for a detailed theoretical framework for analysing and interpreting these experiments. Such a framework is the Parametrized Post-Newtonian (PPN) formalism, which treats the post-Newtonian limit of arbitrary metric theories of gravity in terms of nine metric parameters, whose values vary from theory to theory. The theoretical and experimental foundations of the PPN formalism are laid out and discussed, and the detailed definitions and equations for the formalism are given. It is shown that some metric theories of gravity predict that a massive, self-gravitating body's passive gravitational mass should not be equal to its inertial mass, but should be an anisotropic tensor which depends on the body's self-gravitational energy (violation of the "principle of equivalence"). Two theorems are presented which probe the theoretical structure of the PPN formalism. They state that (i) a metric theory of gravity possesses post-Newtonian integral conservation laws if and only if its nine PP parameters have values which satisfy a set of seven constraint equations, and (ii) a metric theory of gravity is invariant under asymptotic Lorentz transformations if and only if its PPN parameters satisfy a set of three constraint equations. Some theories of gravity (including Whitehead's theory and theories which violate one of the "Lorentz-invariance" parameter constraints) are shown to predict an anisotropy in the Newtonian gravitational constant. Gravimeter data on the tides of the solid Earth are used to put an upper limit on the magnitude of the predicted anisotropy, and thence to rule out such theories.