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Proc Natl Acad Sci U S A. 1976 Mar; 73(3): 669–673.
PMCID: PMC335979

Theoretical foundations of the chronometric cosmology

I. E. Segal
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Abstract

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 = tan2(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.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Segal IE. A variant of special relativity and long-distance astronomy. Proc Natl Acad Sci U S A. 1974 Mar;71(3):765–768. [PMC free article] [PubMed]
  • Segal I. Positive-energy particle models with mass splitting. Proc Natl Acad Sci U S A. 1967 Feb;57(2):194–197. [PMC free article] [PubMed]
  • Segal IE. Observational validation of the chronometric cosmology: I. Preliminaries and the redshift-magnitude relation. Proc Natl Acad Sci U S A. 1975 Jul;72(7):2473–2477. [PMC free article] [PubMed]
  • Nicoll JF, Segal IE. Phenomenological analysis of observed relations for low-redshift galaxies. Proc Natl Acad Sci U S A. 1975 Dec;72(12):4691–4695. [PMC free article] [PubMed]
  • Bargmann V, Wigner EP. Group Theoretical Discussion of Relativistic Wave Equations. Proc Natl Acad Sci U S A. 1948 May;34(5):211–223. [PMC free article] [PubMed]
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