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Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.
The Doppler effect depends on direction---it happens when the observer is moving towards or away from the source, not when the observer is moving sideways. (It happens for light---redshift and blueshift---as well as for sound.) Time dilation, on the other hand, is a genuine clock-rate-difference which is present no matter what direction people are moving in, and it's still there even if you've tried to take Doppler shifts into account.
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