Resnick on pages 470 and 471 in Physics (4th edition) states that(adsbygoogle = window.adsbygoogle || []).push({});

T = t/sqrt(1 - v^2 / c^2), where T is the time value (of an event) obtained by an observer using a moving clock, and t the value of the same event using a stationary clock.

But A. Einstein on page 49 in The Principle of Relativity states that

T = t*sqrt(1 - v^2 / c^2), where T is again the time value (of an event) obtained by an observer using a moving clock, and t the value of the same event using a stationary clock.

suppose that i have two synchronous stationary clocks. let one of them depart (the earth) with a velocity v = 0.5c at a specified direction so that i can use either Resnick's formula or Einstein's formula.

using Resnick's formula, if the current period of time (t) is 10/22/2006, 20:00:00 thru 21:00:00 universal time, in burbank, california, the current period of time (T) would be 20:00:00 thru 21:09:17. this does not mean at all that the moving clock is slower. it actually means the opposite. for example, if i am going to bed at 5:00:00 (the alarm is off, but it is also set at 5:00:00) universal time, and i want to set the alarm clock to wake up at 13:00:00, i see that in the process of setting the alarm, the period of time 5:00:00 thru 5:00:20 corresponds to 5:00:00 thru 13:00:00. this means that while setting the alarm, the clock moved much faster than the real time. the same analogy can be used here; the period of time (20:00:00 thru 21:00:00) measured using the stationary clock corresponds to the time period (20:00:00 thru 21:09:17) measured using the moving clock.

using Einstein's formula, we see indeed that the moving clock is slower. for example, the current period of time t (20:00:00 thru 21:00:00) corresponds to the current period of time T (20:00:00 thru 20:51:58).

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# Important note concerning relativity of time

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