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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.physics.relativity
Subject: Re: 1. On the notion of simultaneity in special relativity
Date: Thu, 29 Aug 2024 11:40:47 +0300
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On 2024-08-28 11:30:01 +0000, Richard Hachel said:

> 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,

You can't define that way unless you first define what "at the same time"
means.

> 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.

The words "ablsolute", "universal" and "common" should not be used for
concepts that are specific to one inertial frame.

> 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.

We also can do otherwise. It is best to define simultaneity so that it
can be used for the construction of the time coordinate of a coordinate
system. If we can find a signal that has the same speed in all directions
we can use that. For example, sound in a metal bar that is stationary
with respect to the coordinate system being constructed.

-- 
Mikko