Re: Proper time differences

Le 08/07/2024 à 19:38, Mikko a écrit :

On 2024-07-08 14:45:12 +0000, Stefan Ram said:
 

  From various sources I gather,
 dt = "gamma" d"tau".

 The defining equation of proper duration is
   dτ² = dt² - dx²

I think it is better to write:
To²=Tr²+Et²
This is a beautiful Pythagirism that not only can we teach in high school classes, but which will prove magnificent when we move on to the study of uniformly accelerated frames of reference.
For accelerated repositories it's the same:
To²=Tr²+Et²
To²=Tr²+(1/2a.Tr²)²/c²
To²=Tr²(1+1/4Vr²/c²) where Vr is the speed at a given time at a given location.
To=Tr.sqrt(1+(1/4)Vr²/c²)
On the other hand, I do not recommend putting this equation on your exam papers.
You would systematically have zero. The correctors do not joke with the SR taught by Doctor Hachel.
R.H.