Nonlinear Phenomena in Complex Systems, 2014, Vol.17, No.4, pp.451-454

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2014, Vol.17, No.4, pp.451-454

Space–Time Non-Invariance of the Conformal Geometry and Its Possible Observable Manifestations
L. M. Tomilchik

It is supposed that the geometry of the General Relativity flat limit can be described by semi-direct product of the Special Conformal Transformations and Lorentz groups, locally isomorphic to Poincare group. The possible observable manifestations of such a supposition are considered. It is shown that the detected Universe accelerated expansion can be treated as a purely kinematic effect of the proposed space–time geometry. The radar procedure of the distance determination in conformal space–time is described. It is shown that the space intervals conformal contraction gave rise to anomalous violet frequency shift during the monochromatic signal propagation over the closed path. Its relative value equals the Hubble constant multiplied by duration of propagation. The predicted phenomenon is the local manifestation of the cosmologic expansion and, in principle, is accessible to experimental detection.

Key words: conformal geometry, Hubble law, radar distance, space–time deformation, violet frequency shift

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