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1. On the notion of simultaneity in special relativityYou can't define that way unless you first define what "at the same time"
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 componentsThe words "ablsolute", "universal" and "common" should not be used for
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 couldWe also can do otherwise. It is best to define simultaneity so that it
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.
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