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.
Highlights
It was shown in the author’s Ph.D. dissertation [1] that a linear transformation that has the same form for theHow to cite this paper: Tangherlini, F.R. (2014) Galilean-Like Transformation Allowed by General Covariance and Consistent with Special Relativity
For an argument by the author involving commutators, that supports the physical significance of general covariance in the quantum domain, see [55]
The preceding analysis shows that, in accordance with the principle of general covariance, one can consistently use a linear transformation between two inertial frames based on an external synchronization that keeps simultaneity invariant, but not the one-way speed of light, while keeping the out-and-back speed invariant
Summary
It was shown in the author’s Ph.D. dissertation [1] that a linear transformation that has the same form for the. The historical motivation for the author’s work was originally based on the divergences in quantum electrodynamics, as well as general covariance, and is described in the 2009 preface to the dissertation in [32], where there is described the application to Reichenbach synchronization [33] when represented by a local time transformation, as given in Anderson et al [34]. This is omitted here for brevity, as is discussions about the ether, for the.
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