Time-symmetric relativistic and quantum theories. 1. Time-symmetric theories of special and general relativity
Abstract
In relativistic theory, particles have negative energy pairs, which were considered unphysical, but Dirac (1930) linked them with antiparticles, Zisman (1940) and Stueckelberg (1941) showed that they formally evolve backward in ordinary time t, and Feynman (1949) developed a covariant diagram technique based on them. However, the description of antiparticles in terms of negative energy states remained incomplete, and a number of problems arose. In this article, a time-symmetric relativity theory (TSRT) is formulated based on this interpretation, eliminating the previous problems. In TSRT, the proper time of a negative-energy particle is measured in its rest frame, the basis of which has negative energy and also evolves backward along t axis. Specifically, in antihydrogen, a negative-energy proton realizes the basis of such a frame. In TSRT, the principle of relativity is extended to reference frames going backwards along t-axis, and in time-symmetric special relativity, the symmetry group becomes the general Lorentz group O(1,3), which includes 4-inversion. Including translations leads to the general Poincaré group. In time-symmetric general relativity, the O(1,3) group acts locally, and the Einstein equations and their solutions remain unchanged. In TSRT, the 4-vectors of the probability current and interaction currents change sign under 4-inversion, and in time-symmetric relativistic quantum theory, this resolves a number of problems (see Articles 2 and 3).