  A 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 field-free 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 conservations laws of
classical and quantum-electrodynamical fields established by Cunningham and by
Bialynicki-Birula.
