Theoretical foundations of the chronometric cosmology.

The derivation of the redshift (z)-distance (r) relation in the chronometric theory of the Cosmos is amplified. The basic physical quantities are represented by precisely defined self-adjoint operators in global Hilbert spaces. Computations yielding explicit bounds for the deviation of the theoretical prediction from the relation z = tan(2)(r/2R) (where R denotes the radius of the universe), earlier derived employing less formal procedures, are carried out for: (a) a cut-off plane wave in two dimensions; (b) a scalar spherical wave in four dimensions; (c) the same as (b) with appropriate incorporation of the photon spin. Both this deviation and the (quantum) dispersion in redshift are shown to be unobservably small. A parallel classical treatment is possible and leads to similar results.