Ie. Segal et Z. Zhou, MAXWELLS EQUATIONS IN THE EINSTEIN UNIVERSE AND CHRONOMETRIC COSMOLOGY, The Astrophysical journal. Supplement series, 100(2), 1995, pp. 307-324
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.