On May 8, 6:50 am, Tom Roberts wrote:

Do you have an equation, dimensionally consistent, where one
could see what you are talking about?

Consider an object moving relative to an inertial frame with a velocity
v(t) (= dr/dt where r is its position 3-vector relative to that frame,
and t is the time coordinate of the frame); v(t) can be an arbitrary
function of time. Its elapsed proper time between t=T1 and t=T2 is:

\tau = \integral_T1^T2 sqrt(1-v(t)^2/c^2) dt

(This is easily obtained by integrating the metric along the path of the
object.)

One trivially obtains \tau=T2-T1 for an object at rest in this frame.
And one clearly obtains \tauT2-T1 for nonzero v(t). Note that |v(t)| is
constrained to be less than c, so there is never a numerical problem
with the sqrt(.).

Proper time is utter nonsense. It is an abstract excuse to validate
the Loretnz transform. What a person ages, the measure of aging is in
time and not in proper time. It is time for you as an experimental
physicist to do your job. Michelson also an experimental physicist
understood this point. That is why he rejected the Lorentz transform
because the Lorentz transform is just nonsense. It manifests the
twin’s paradox.