Notes on Relativity and Cosmology - Physics Department, UCSB

158 CHAPTER 6. DYNAMICS: ENERGY AND ...
as measured by us. One might ask if the same is true for light.
The easy way to discover that it is in fact true for light as well is to use the
fact (which we have not yet discussed, and which really belongs to a separate
subject called ‘quantum mechanics,’ but what the heck...) that light actually
comes in small chunks called ‘photons.’ The momentum and energy of a single
photon are both proportional to its frequency f, which is the number of times
that the corresponding wave shakes up and down every second.
Remember the Doppler effect from problem (3-13? This is also the effect seen in
problem (4-4) when our twins Alphonse and Gaston sent pulses of light toward
each other. The frequency with which the light was emitted in, say, Alphonse’s
frame of reference was not the same as the frequency at which the light was
received in the other frame (Gaston’s).
The result was that if Gaston was moving toward Alphonse, the frequency was
higher in Gaston’s frame of reference. Using the relation between frequency and
energy (and momentum), we see that for this case the energy and momentum
of the light is indeed higher in Gaston’s frame of reference than in Alphonse’s
frame of reference. So, moving toward a ray of light has a similar effect on how
we measure its energy and momentum as does moving toward a massive object.
G
a
s
t
o
n
Alphonse
t A =5
t =0 A
x =0
A
x A
=4
Alpha
Centauri