I think we may need some mathematics to clear up some questions. The following are called Lorentz transformations, they can be used for all properties of coordinate systems x, y, z, and time,t , but I am just going to include the transformations for time, t, since this seems to be a point of confusion.
t is time as it passes for the observer which is assummed to be at rest (galileian body) and t' is time for another object, person, coordinate system that is moving relative to us with time t. In order to find how time passes for this other object we can use this equation:
t'=[1-(v/c)]t/[sqrt(1-(v^2/c^2))]
where v is velocity of the obect, as it appears to us, t is time elapsed for us, sqrt is the square root. c is the constant for the speed of light or 300,000 km/sec.
What this equation shows is that for a light particle time has no significance because 0/0 is indeterminate. You can use this equation to see how slow time is moving for that car speeding 120 miles down the road.
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