Notes on Relativity and Cosmology - Physics Department, UCSB

148 CHAPTER 6. DYNAMICS: ENERGY AND ...
However, that way of getting at the answer is a bit technical. So, for the
moment, we’re going to approach the question from a different standpoint.
You see, Einstein noticed that, even within electromagnetism, there was still
something funny going on. Momentum was conserved, but this did not necessarily
seem to keep isolated boxes (initially at rest) from running away! The
example he had in mind was connected with the observation that light can exert
pressure. This was well known in Einstein’s time and could even be measured.
The measurements were made as early as 1900, while Einstein published his theory
of special relativity in 1905. It was known, for example, that pressure caused
by light from the sun was responsible for the long and lovely tails on comets:
light pressure (also called radiation pressure or solar wind) pushed droplets of
water and bits of dust and ice backwards from the comet making a long and
highly reflective tail. Nowadays, we can use lasers to lift grains of sand, or to
smash things together to induce nuclear fusion.
6.3.1 Lasers in a box
Anyway, suppose that we start with a box having a powerful laser 5 at one end.
When the laser fires a pulse of light, the light is near the left end and pressure
from this light pushes the box to the left. The box moves to the left while
the pulse is traveling to the right. Then, when the pulse hits the far wall, its
pressure stops the motion of the box. The light itself is absorbed by the wall
and disappears.
Before
After
Now, momentum conservation says that the total momentum is always zero.
Nevertheless, the entire box seems to have moved a bit to the left. With a large
5 Of course, lasers did not exist when Einstein was working on this. He just used a regular
light source but, if lasers had been around, that’s what he would have used in his example.