Steve- It's always fun to try to answer a question that somebody's
really been wondering about. This answer will be biref, so if you need
more info you can try googling this site under 'relativity'. If the
answer isn't good enough try again, because this question at least has
definite answers, known now for 100 years.
" the light will still reach me in the same time as if I were
standing still." That depends by what you mean by 'at the same time'.
The person shining the flashlight sees the light travelling at c away
from him. If you are traveling at c/2 away from him, he sees the light
gaining on you at only c/2. So he says the light takes twice as long to
reach you as it would take if you were standing still at the distance
from him at which, according to him, you were when he turned on the
Now according to you, this guy is traveling away from you at c/2
and the light is traveling toward you at c. You say that the light take
sthe same time to reavch you that it would have taken if the guy was
stationary at the same distance he was when according to you he turned
on the light.
How can that be? You and he disagree not only about who is moving
but also about the distances and time intervals between various events.
The rules for calculating what coordinates one of you sees in terms of
the other guy's coordinates are called the Lorentz transforms, and were
figured out by Lorentz before they were nicely explained by Einstein.
The colors of light from the bulb of course are unchanged according
to the guy holding the light. However, according to you they HAVE
changed. They are Doppler shifted, toward lower frequencies. Wait, you
ask: the Doppler formula gives different results for sound depending on
if the source is moving away from the listener or vice versa (x2/3 or
x1/2 for the frequency reduction factor when the relative speed is 1/2
the sound speed.) But here we're saying that there is no air to use as
the stationary medium, so which of those results is right? It turns out
that the answer is just the square root of their product, or sqrt(1/3)
in this case. So this is called the 'relativistic Doppler shift'.
(published on 10/22/2007)