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I understand that the frequency of light (or any electromagnetic
wave) decreases when it "climbs" higher from the ground. This means
that period of the wave motion increases. Is there a way to "see"
that this (decrease in f, increase in T) implies that time passes
faster at higher altitude? For some reason I can't see it :-). Could
you come up with an explanation which would be suitable at the high
school level?