Re: The Questin on the Missing Photons

Dear Questioner,

This is a great question and brings up a couple of very interesting 
points.  You ask about someone traveling at the speed of light.  This 
question is very much like one that Einstein asked himself which led him 
to the idea that perhaps no one can travel at the speed of light.  (This 
is a Gedanken, or thought experiment.  Einstein wondered what you would 
see if you could ride your bike at the speed of light, and then  turn on 
your headlight.)  From his Theory of Relativity, we now believe that it is 
impossible to travel at the speed which light travels in a vacuum, or 
about 300,000km/s.  But we can still talk about this question in terms of 
what happens as the person travels faster and faster, getting closer to 
the speed of light, although not getting exactly to it.

First, it is very important to keep in mind that according to the Theory 
of Relativity, all motion is relative.  To make this easier, let’s call 
the person who is stationary with respect to the Earth, “Earth-man”, and 
the person traveling relative to the Earth, “Space-man”.  Now, according 
to Earth-man, he is stationary and Space-man is moving away from him.  
However, according to Space-man, he is stationary and Earth-man, and the 
Earth, are moving away from Space-man.  Who is correct?  They both are.  
Everyone is stationary in their own frame of reference.  What happens if 
one shines a light at the other?  It really doesn’t matter which one 
shines the light, since they both see the other as moving away.  Let’s 
think about a simpler problem first, and work up to the light problem.

Let’s imagine that two people are standing near each other, and neither is 
moving.  We’ll call them E-man and S-man.  E-man throws small balls to S-
man, one ball every second.  S-man catches the balls.  Since E-man is 
throwing the balls once a second, and every ball travels the same distance 
to get to S-man, they will arrive at S-man one every second.  So S-man 
will catch one ball every second, that is, at the same frequency that E-
man is throwing them.

Let’s imaging that S-man starts to walk backwards, away from E-man, but 
still facing him to catch the balls.  Now, each ball will have to travel a 
little bit farther than the previous ball, since S-man has moved farther 
from E-man during the time between balls.  This means that S-man will 
catch the balls with a time slightly larger than one second between each, 
in other words, at a slightly lower frequency.  The faster S-man moves 
from E-man, the longer the time between balls and the lower the 
frequency.  If S-man moved away from E-man at the speed of the balls, or 
faster, S-man wouldn’t catch any of the balls.  That is, the balls would 
never reach him.

Now let’s imagine that S-man is Space-man and E-man (Earth-man) is sending 
light, or photons, at Space-man.  The faster Space-man is traveling, the 
longer the time interval between the photons he receives and the lower the 
frequency of the light.  In other words, the light as seen by Space-man 
would appear stretched out, or lengthened, so the wavelength would be 
longer and the frequency would be smaller.  In this case, however, Space-
man cannot actually go at the speed of the photons, nor faster.  So no 
photons are “lost”, they are just in the space between Earth-man and Space-
man, and will eventually reach Space-man if he can just wait long enough. 

Well, I hope I have answered your question.  If you would like some more 
information, please let us know.

Sincerely,

Jim Guinn