ON THE VARIATION OF VACUUM PERMITTIVITY IN FRIEDMANN UNIVERSES

Vacuum permittivity, the measure of strength of electric fields in a vacuum, is a function of the spacetime geometry of Einstein's general relativity. This dependence on geometry was noted over 40 years ago by C. Moller (1952) and has remarkable consequences. Variation in vacuum permittivity breaks the equivalence of physical measurements and mathematical coordinates postulated by Einstein. Physical lengths, as measured by a rigid rod, and physical times, as measured by an atomic clock, are not equivalent to the mathematical lengths and times of general relativity. This changes some concepts of space and time, invalidates stronger interpretations of the principle of equivalence, and requires that care be exercised in interpreting the speed of light. The laws of physics must be carefully used to understand the essential relationships between mathematical spacetime and physical measurements. For Friedmann universes, vacuum permittivity is directly proportional to the Friedmann radius and is therefore a function of time. As the size of the universe evolves, the changing strength of the electrical force between charges shifts atomic energy levels, changing the wavelengths of emitted light. This shift in photon emission due to the evolution of electrical attraction in the atom is twice as large as evolutionary photon shift. Considered together, atomic and photon evolution reverse the interpretation of Hubble redshift to imply that the Friedmann universe is presently collapsing.