1. On the notion of simultaneity in special relativity

1. On the notion of simultaneity in special relativity
The notion of simultaneity being defined by the coincident existence of all events occurring
at the same time, or even, being characterized by the set of all physical phenomena occurring
at the same instant, one should be able, at least by considering all the fixed components found
in a given inertial system, to speak of "absolute simultaneity", "universal synchronization", or
"common calendar" - these terms then being capable of acquiring a real physical meaning - if
one could, without it varying, transpose the simultaneity proper to a particular observer to all
other inertial observers present in the same frame of reference.
It would suffice to find any signal, or any action, by which a body A could
interact instantaneously with a body B, that is to say by means of information propagating infinitely quickly, for this notion of "absolute simultaneity" to be experimentally proven. We could then say that
the action induced by body A was instantly transmitted to body B, or that the action produced by
body A was carried out at the same time as its detection by body B, and that there exists, de facto, between A and B, a sort of reciprocal and absolute simultaneity.
We could also imagine a round-trip signal carried out over the distance x separating A and B, and carried out by means of infinitely rapid information, in such a way that the instants Ta (departure noted by watch A) and Ta' (return noted by watch A) are simultaneous. It would easily come that if the two watches A and B are "correctly" tuned (for example by using an electromagnetic signal from the medium M of AB,
or by slowly moving apart the two watches that we would have previously synchronized at the same place)
then the instant Tb (instant noted by B for the reflection of the signal) would be the same as the instants Ta and Ta',
since if Ta'-Ta = 0 by definition, then |Tb-Ta| + |Ta'-Tb| = 0, hence Ta =Ta'=Tb, and, by practicing in this way
step by step, for a multitude of other points C, D, E, F, G, H, I and so on, the notion of general coexistence
in perfect absolute simultaneity of all the fixed components of a given inertial frame R
could be demonstrated.
 However, this proof does not exist: we know that a body can act at a distance on another body - for example in the
form of an electromagnetic wave, in the form of a mechanical shock transmitted along a rigid rod, or
in the form of a gravitational interaction - but we have never found a signal that is infinitely fast,
or an action at a distance that is instantaneous. It seems rather, in fact, that there exists, in nature, a sort of
uncrossable limit speed that we will find for any Galilean frame of reference considered - a limit
observable speed, the true keystone of modern science - and which will extend to all particles and all
properties of physics.
We can then suppose, and state, in light of what we have just said, the following fundamental principle:
"the notion of simultaneity is relative by any change of observer; even fixed between them, different
observers placed in different places, build different systems of simultaneity"; and, thus, generally, in a given system, two or more simultaneous events for an observer A will no longer be so, and reciprocally, for an observer B, even perfectly inertial.
From there, the physical impossibility of covering any landmark with fixed clocks
"absolutely" synchronized with each other will inevitably appear, since they will never be able to agree on the notion of simultaneity:
two benches placed in a public garden, two stations arranged on a national railway network, will never be able to agree on what could be abstractly called "the notion of universal present time", and, at best of a desired "coherent" synchronization - for example, by using one of the two adjustment methods
mentioned above - each of the two watches thus synchronized will always consider that the other watch
is behind it by a value equal to T = x/c; a real, physical measurement, absolutely indicative of itself, and
implying that the same calendar cannot be valid for the entire universe, nor even simply for any given
geographical landmark.
R.H.