Synchronization Gauges and the Principles of Special Relativity

Abstract

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of 'theories' that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl synchronization gauge and, finally, to the even more general Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light on inertial and rotating reference frames, the GPS's working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams. 1

Noninertial Observers in Special Relativity and Clock Synchronization Debates

“…for some smooth scalar function ψ of the spatial coordinates of the reference frame, lead to the velocity of light, v c , in the direction of the unit vectorn being given by v c = cn 1 − ∇ψ · cn , (2) and this still leads to the average speed of light to be c over any closed path and so is consistent with the experimental evidence [3][4][5]. It should also be noted that transformations of the form given by Eqs.…”

“…A review of the considerable literature on the conventionality of simultaneity debate is given in Anderson et al [3], who conclude that clock synchronization is "irreducibly conventional" and claim that "one cannot single out [a particular synchronization choice] without an a priori assumption about the one-way speed of light" [3, p. 99]. Some more recent contributions are given in [2,[4][5][6][9][10][11].…”

The Inertial Transformations and the Relativity Principle

“…is a merely artificial element, S 0 being just the IRF [inertial reference frame] in which, by stipulation, Einstein synchronization has been performed: as a matter of fact, any IRF S can play the role of S 0 ." [17] In spite of this conclusion, it is necessary to insist that the statements made in the initial part of the present paper are correct. The theory with the free e 1 applied to the rotating platform and to the Sagnac effect shows that only the choice e 1 = 0 gives a satisfactory formulation of the physics on the rotating disk.…”

“…We add some comments concerning the RRS article [17]. This paper provides a perfectly consistent alternative to my approach.…”

On constancy of the speed of light in the global positioning system

“…The metric tensor can be introduced into the ECEF frame for the standard synchronization [7,8] between spatially separated clocks so that the speed of light appears to be c where c is the speed of light in vacuum. It is well known that the so called Sagnac correction should be made to extract accurate positioning information from GPS signals received [2][3][4][5][6].…”