Re: I dare to relativists to explain local time: t-vx/c²

Le 05/10/2024 à 19:32, hertz778@gmail.com (rhertz) a écrit :

Explain this:
 1905 EINSTEIN'S MODIFIED LORENTZ TRANSFORMS
t' = γ (t - vx/c²)
x' = γ (x - vt)

 Attention.
I have always said, against Einstein's advice, that the theory of relativity was mathematically very simple, but that it was full of non-obvious concepts and frequent traps.
All the mathematical tools of special relativity are in the baggage of an average 16-year-old student.
What is missing today is mainly semantics.
It is not Minkowski, Grossmann or Lorentz who are missing,
but Hugo, Dante, or Shakespeare.
That is to say, people who know how to say things and explain them.

 IF
 v = 11 Km/sec
x = 400 Km
 γ = 1.00000000067222
  t' ≈ t - 48.89 nsec
 48.89 nanoseconds meaning WHAT?

Vo=11000m/s
x'=400 kms.
γ = 1.00000000067222
t' ≈ t - 48.89 nsec
(je ne vérifie pas le calcul mais si cela est correct, cela veut dire que l'événement e1 qui s'est produit en x, s'est produit, pour l'observateur O,
à 400km, et il y a To=1333333 ns.
Vo=0.0000366666c
C'est ça que ça veut dire.
Passons à la distance notée par O' qui est x'.
x'=(x-Vo.To)/sqrt(1-Vo²/c²)     Attention To négatif, e1 s'est produit "avant". Je ne fais pas le calcul, mais e1 s'est produit légèrement plus loin que pour x. Et aussi légèrement plus loin dans le passé puisque To'=x'/c

     Worse yet.
 IF x' = 0, then x = vt

 If x=0 then x'=0 and To=0 and To'=0, this is the moment when the watches are triggered.

 t' = γ (t - vx/c²) = γ (t - v²/c² t) = t/γ
 t' = γ (t - vx/c²) = γ (t - v²/c² t) = t/γ
 t' = 0.999999998655556 t (now t' run slower than t!)
 Any explanations about these numerical examples of
the ridiculous results when applying SR?

If x=0 then x'=0 and To=0 and To'=0 , this is the moment when we trigger the watches.
Before the crossing, the watches that are coming towards us always turn reciprocally faster.
Once the crossing has taken place, the watches that are moving away always turn reciprocally slower than ours. This is a simple relativistic Doppler effect (to which we must not forget to add the gamma effect of reciprocal expansion of the internal mechanisms).
R.H.