Nice try Michael,
In the rest frame [math]\tau=t[/math] [math]x^0=ct[/math]
for the rest frame [math]U^0= dx^0/d\tau =cdt/d\tau=c\gamma[/math]
Cancelling out the c's
[math]dt/d\tau=\gamma[/math]
Because we are in the rest frame [math]\gamma=1[/math] and [math]\tau=t[/math]
You are saying the speed of time is one second per second.
a sec per sec is not a rate.
Typically [math]dt/d\tau[/math] is considered the rate of time dilation.
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