The author shows in this article that a coherent description of
the Sagnac effect for massive particles, which takes account of
length contraction and time dilation can only be obtained with
a so called ?absolute? clock synchronization parameter. Any
other synchronization leads to an incoherent description
between the point of view of an observer on the rotating
platform and a non-rotating observer. This demonstration
generalises the one made by Selleri and the author for the
Sagnac effect with electromagnetic waves.
Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way speed of light. The conventionality of some features of relativity theory allows full compatibility with existing experimental evidence.
The conventional nature of synchronisation is discussed in inertial frames, where it is found that theories using different synchronisations are experimentally equivalent to special relativity. On the other hand, in accelerated systems only a theory maintaining an absolute simultaneity is consistent with the natural behavior of clocks. The principle of equivalence is discussed, and it is found that any synchronisation can be used locally in a freely falling frame. Whatever the synchronisation chosen, the first derivatives of the metric tensor disapear and a geodesic is locally a straight line. But it is shown that only a synchronisation maintaining absolute simultaneity makes it possible to define time consistently on circular orbits of a Schwarzschild metric.