Re: Proper time differences

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