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If an observer approaches a clock at a significant fraction of the speed of light, would they see the clock's hands moving at a faster or slower than usual rate?

I figure there are two competing effects at play - time dilation and diminishing distance.

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2 Answers 2

up vote 4 down vote accepted

You can see this as an example of the relativistic Doppler shift (for equations, see eg: http://en.wikipedia.org/wiki/Relativistic_Doppler_effect ).

The hands of the clock are moving with some angular frequency and you are moving with a velocity v towards the clock. It follows that the frequency you are seeing will be higher, thus the clocks hands will move faster.

Conceptually this makes sense. Suppose a picture of the clock is emitted each second. Since you're moving towards the clock, you will pick up one of those pictures more often than once per second, thus making the clock seem to run faster.

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but then what about Time Dilation –  Jack Jan 11 '12 at 8:53
This is included in the derivation in the reference I gave. –  Bernhard Jan 11 '12 at 8:55
My bad , yes u r right –  Jack Jan 11 '12 at 8:57

Time dilation says moving clocks run slow, therefore, in the reference frame of the observer, the clock (that is moving toward him/her) appears to run more slowly than his/her own.

I don't think the doppler effect is important here, because it is a traditionally longitudinal effect (and the so-called relativistic transverse doppler effect is simply time dilation).

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