How does the elapsed time for a process seem to be longer, an observer moving with the process or observer moving relative to the process? Which observer measures proper time? Explain your answer.
The process of measuring longer time is called time dilation
consider the following examples
If you are driving during rush hour, traveling by surface streets will feel relatively faster because motion, even at slower speeds, always feels faster than intermittent faster speeds with standstills in between.
If you are standing in line somewhere, courthouse, social services, etc, you may actually experience time stop, or move very slowly backward.
The explanation is as follows
The Earth-bound observer sees time dilate (get longer) for a system moving relative to the Earth.
In contrarily, according to the Earth-bound observer, time slows in the moving frame, since less time passes there.
Everyone measures the correct time but in different frames i.e Each observer has their own proper time measured by the clock in their rest frame. However, one man's proper time is not another man's proper time.
Time dilation means that each observer will see the other observer's clock running slower
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