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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.physics.relativity
Subject: Re: Proper time differences
Date: Mon, 8 Jul 2024 20:38:09 +0300
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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

which is equivalent to your equatio.

>   Where t is the coordinate time in the rest frame, "gamma"
>   is the Lorentz gamma factor and "tau" is the proper time.
> 
>   Now, if "gamma" is constant, I think we can replace the "d"
>   by "D" (triangle which is flat at its bottom), i.e., we can
>   use finite difference instead of infinitesimal ones:
> 
> Dt = "gamma" D"tau".

That's right. That happens when the moving object is not accelerated.

>   I believe 0<="gamma"<=1, so, for an example, we can assume
>   "gamma" to be 0.5:

No, gamma is 1 / sqrt(1 - v²) which is 1 when v = 0 and greater otherwise.

-- 
Mikko