I understand what proper time is, I was asking what you are measuring a change in with respect to proper time. Can we represent the magnitude of the 4-velocity as [tex]d\lambda / d\tau[/tex] (or [tex]cd\lambda / d\tau[/tex], perhaps), where [tex]d\lambda[/tex] is some physically meaningful quantity? If so, what would it be?Garth said:Proper time [tex]\tau[/tex] is that time measured in the rest frame, moving and/or distant (in a gravitational field) clocks will run at a different rate, rulers will contract etc. Therefore measure the 'rate' of [tex]dt/d\tau, dx/\tau [/tex] etc.
Thanks, I didn't know that--I guess although the trick works nicely in SR it can't be generalized to GR.Garth said:BTW Although time bears the same mathematical relationship to the space dimensions as the imaginary numbers do to the real, calling time ‘imaginary ict has its own problems as MTW point out in ‘Gravitation’ page 51.