Ambiguous red shifts

Abstract

Dedicated to the memory of Marcos Moshinsky who contributed so much to science and provided so many opportunities to so manyA one-parameter conformal invariance of Maxwell's equations allows the wavelengths of electromagnetic waves to change as they propagate, and do so even in otherwise fieldfree space. This produces an ambiguity in interpretations of stellar red shifts. Experiments that will determine the value of the group parameter, and thereby remove the ambiguity, are proposed. They are based on an analysis of the anomalous frequency shifts uncovered in the Pioneer 10 and 11 spacecraft studies, and physical interpretation of an isomorphism discovered by E. L. Hill. If the group parameter is found to be non-zero, Hubble's relations will have to be reinterpreted and space-time metrics will have to be altered. The cosmological consequences of the transformations are even more extensive because, though they change frequencies they do not alter the energy and momentum conservation laws of classical and quantum-electrodynamical fields established by Cunningham and by Bialynicki-Birula.

On the Metric of Space-Time

“…Such results would have another consequence. Tomilchik [5] and Wulfman [7,8] have both argued that the magnitudes of the "Pioneer Anomalies" roughly correspond to the value of the Hubble constant because the anomalies are primarily due to the assumption that the space-time is Minkowskian. However, Turyshev, et al [19] argue that the anomalies can be explained by a recoil effect which had not been properly accounted for.…”

“…However, the value of the group parameter γ could be determined by measuring successive return times, as well as frequency shifts within radar wave-pulses sent to receding spacecraft. The uncertainty in the resulting value of the group parameter can be expected to be less than the uncertainty in the value of Hubble's constant [7,8].…”

“…In the year 2000, unaware of it, Hoyle, Burbidge, and Narlikar used the Bateman-Cunningham Lie group in their development of a generalized relativistic cosmology [4], and in 2010, Tomilchik [5] argued that Hubble's relations are a consequence of properties of transformations of the special conformal subgroup of the Bateman-Cunningham group. Hill's paper is however listed in Kastrup's recent review of papers dealing with conformal invariance [6], which led to the research reported here, and to the realization that the value of Hill's group parameter can be determined by experiments proposed by Wulfman [7,8]. A more recent list of references to research on the physical role of conformal transformations is contained in an article on the quantum mechanics of accelerated relativistic particles written by Calixto, et al [9].…”