MAXWELLS EQUATIONS IN THE EINSTEIN UNIVERSE AND CHRONOMETRIC COSMOLOGY

The theoretical basis for chronometric cosmology is developed from gen eral physical principles of causality, cosmic uniformity, and quantum phenomenology. Empty spacetime M is assumed to be the unique alternati ve to Minkowski space M(0) that enjoys similar properties of causality , isotropy, and separability into time X space. At any given point in M(0) there is a unique Poincare-invariant imbedding of M(0) into M, an d every normalizable free photon wave function on M(0) extends uniquel y to the same on M. These features provide a basis for the comparison of astronomical observables in the respective spacetimes. Temporal evo lution on a cosmic timescale differs greatly in M from temporal evolut ion in M(0), but on a microscopic scale the difference appears unobser vably small. M is conformally equivalent to the Einstein universe E = R(1) X S-3 (where R(1) denotes the time axis and S-3 the space consist ing of a three-dimensional sphere). Temporal evolution in M is equival ent to that in E; i.e., simple translation along the time axis R(1). T his is materially inequivalent to time evolution in M(0). The ''Einste in'' and ''Minkowski'' energies in M and M(0) (i.e., conjugate quantit ies to the respective times) are correspondingly materially different on a cosmic timescale, although microscopically they differ by unobser vably little. Chronometric cosmology (CC) proposes that the Einstein e nergy is the driving energy of the universe, while the Minkowski energ y is the locally observed energy, as required for coincidence with the local frequency of oscillation. The redshift is correspondingly the e xcess of the Einstein over the Minkowski energy. CC is devoid of adjus table cosmological parameters, luminosity, or density evolution, impli es conservation of the Einstein (but not Minkowski) energy, and predic ts that remnant radiation will be in an isotropic Planck-law state. Th e redshift-distance law in CC, which takes the form z = tan(2) (rho/2) , where rho is the distance in radians on S-3, is derived rigorously f or photons of localized spatial support. This relation departs locally from the Hubble law, which, however, appears seriously flawed (e.g., Segal 1993; Segal et al. 1993, 1994a,b). The chronometric redshift is directly proportional to the space curvature, exemplifying the proposa l by Hubble & Tolman (1935), for an alternative to the Doppler explana tion.