Open AccessTheoretical foundations of the chronometric cosmology
Author(s) -
I. E. Segal
Publication year - 1976
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.73.3.669
Subject(s) - cosmology , redshift , physics , dispersion relation , scalar (mathematics) , mathematical physics , hilbert space , universe , theoretical physics , radius , photon , quantum mechanics , mathematics , galaxy , geometry , computer science , computer security
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 relationz = tan2 (r /2R ) (whereR 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.