Volume 5: Pages 133-141, 1992

Hamiltonian Geometrodynamics

Kenneth J. Epstein ¹

¹5252 Broadway, # 308, Chicago, Illinois 60640 U.S.A.

The kinematic problem of a test particle in an arbitrary metric proves highly amenable to the Hamiltonian method augmented by the orthonormal tetrad of vierbein formalism of general relativity. The concepts of potential energy, kinetic energy, and momentum are well defined and useful. The Hamiltonian method derives the gravitational redshift from energy conservation, the cosmic redshift from conservation of momentum, and the Sagnac effect from the difference between the local and global speeds of light in a rotating frame. The round‐trip speed of light in an expanding universe proves to be less than the local speed of light under existing conditions, but conditions are possible in which the round‐trip speed could exceed the local speed of light c. A gravity‐geometry dualism is suggested in which Newtonian and Einsteinian concepts are equally valid, despite the greater accuracy of Einstein's theory. The problem is formulated for quantum mechanics as well as classical dynamics, but the problem of quantum geometrodynamics is not solved.

Keywords: energy, momentum, conservation, dualism, vierbein, tetrad, local, global, anisotropy, affine connection

Received: February 4, 1991; Published Online: December 15, 2008