TITLE:
Galilean-Like Transformation Allowed by General Covariance and Consistent with Special Relativity
AUTHORS:
Frank R. Tangherlini
KEYWORDS:
General Covariance; Transformations; Synchronization; Complementarity
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.5,
March
28,
2014
ABSTRACT: As shown
earlier, a linear transformation with the same form for the spatial coordinates
as the Lorentz transformation (LT), and that allows for time dilation, but
leaves simultaneity invariant instead of the one-way speed of light, predicts
the same results as the LT for the usual tests of special relativity. Such a
transformation is allowed by general covariance. A complementarity between the
invariance of the one-way speed of light and the invariance of simultaneity is
discussed. Using this transformation, interpreted as involving external
synchronization, it is shown that two frames moving uniformly with equal and
opposite velocities, v and –v relative to a third inertial frame, in
which clocks are synchronized so that the one-way speed of light is c, can be related by a Galilean-like
transformation with a relative velocity 2v/(1-(v/c)2).These
transformations do not form a group, hence the term “pseudo-Galilean” is used
to distinguish them from the Galilean transformations. An analogy with the
Sagnac effect is discussed, and consistency with the LT for stellar aberration,
and the Doppler effect is shown. Implication of the above complementarity for
the possible unification of quantum theory and gravitation is briefly
discussed, as well as the inferred physical significance of general covariance.