Re: Proper time differences

On 08-July-24 10:45 pm, Stefan Ram wrote:

   From various sources I gather,
 dt = "gamma" d"tau".
    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".
    I believe 0<="gamma"<=1, so, for an example, we can assume
   "gamma" to be 0.5:
 Dt = 0.5 D"tau",
    which means just,
 D"tau" = 2 Dt.
    So, that would mean: For a moving thing the proper time
   difference D"tau" (I assume: between two fixed events) is
   /larger/ than the coordinate time difference.
    But since falling muons live longer, the proper time distance
   should be /smaller/, not larger!
    What's wrong here? TIA!

"Time dilation" is a special case of the Lorentz transform, and due to continued lack of clarity on this point in popular science media, people tie themselves in knots by trying to use time dilation in situations that do not match the special case.
Apply the complete Lorentz transform to your problem, and any apparent contradictions will go away.
Sylvia.