Re: The problem of relativistic synchronisation

Le 06/09/2024 à 14:21, Mikko a écrit :

On 2024-09-05 14:15:28 +0000, Richard Hachel said:
 

Le 05/09/2024 à 14:24, "Paul.B.Andersen" a écrit :

Den 05.09.2024 01:23, skrev Richard Hachel:

 Vo=0.8c
 Vapp=Vo/(1+cosµ.Vo/c)
 Vapp'=(4/9)c
 Vapp"=4c
 R.H.

 

 BTW, your equation above is wrong.
 It should be:
Vapp = v⋅sin(μ)/(1 - (v/c)⋅cos(μ))
 where μ is the angle between the observed object's
velocity and the line of sight.
 That is because we can only observe the transverse
component of the object's velocity.
 If the object is coming right at us, μ = 0⁰, and Vapp = 0.

 What do you say, Paul?

Note that v_app > c when v > c/(sin(μ)+cos(μ))

 What's the matter with you?
Are you drunk, or just insane?

 No, Paul just knows and understands certain simple things.

I am willing for Paul to know and understand certain simple things.
For example, he knows and understands perfectly the notion of reciprocal relativity of internal chronotropies.
He is not a thug, he is not a moron, he is not a criminal.
But there are things that he does not understand, and, not understanding them, assumes that those who say them do not have all their mental faculties.
I explained to him correctly why he was making a colossal relativistic blunder when he thought he could integrate (Leibniz) improper times into accelerated frames of reference.
The blunder is of the same type as the poorly understood addition of relativistic speeds, and which some consider very simple, and of the type W=v+u.
I explained the blunder clearly, and showed that by ricochet, an observable time measured too large would induce in the opposite direction, a proper time measured too small.
Paul takes this as a joke, because "that's not what relativists say".
It's a shame that he's stubborn, because a good understanding of things could necessarily earn him a better judgment.
When two parties confront each other, they must be heard both clearly and completely. We can then judge.
Problem: Paul doesn't understand anything I'm telling him.
So he only judges with one hand.
It's not scientific.
For those who want to understand: what is observable time?
If we set To²=Tr²+Et², we see that it is the diagonal of proper time and anisochrony.
It's visible to everyone.
However, this diagonal will stretch as proper time increases, or as the distance traveled increases.
What Paul does not understand (and neither do physicists) is that we must constantly take into account the length of this diagonal,
and not the path taken by the end of this diagonal (which forms a curve).
If we take the path, we have too large a value of the improper time.
This is not serious as it stands, since we easily have To=(x/c).sqrt(2c²/ax)
But the problem will arise when we want to calculate Tr (the proper time) with respect to this curve. We will inevitably imagine a proper time that is much too short, whereas if we refer to the simple progression of the length of the diagonal without taking into account its progressive rotation, but simply its value,
there is absolutely no possible error.
I am providing the little diagram explaining the difference between the blue curve and the red diagonal, and the dramatic confusion that we make by confusing the two values.
<http://nemoweb.net/jntp?l17hZFcqtPdgFMEzX69soViAgkM@jntp/Data.Media:1>
R.H.