Notes on Relativity and Cosmology - Physics Department, UCSB

7.2. SOME OBSERVATIONS 171
to imply that my version is more accurate than the one in your readings (or vice
versa) – the readings and I are simply stressing different aspects of the various
thoughts that were rattling around inside Albert Einstein’s head in the early
1900’s. BTW, figuring out General Relativity was much harder than figuring
out special relativity. Einstein worked out special relativity is about a year (and
he did many other things in that year). In contrast, the development of general
relativity required more or less continuous work from 1905 to 1916.
In fact, I’m going to stress several important ingredients, of which we have just
seen the first. For future reference, they are:
a) Free fall and the gravitational field.
b) The question of whether light is affected by gravity.
c) Further reflection on inertial frames.
7.2.1 Free Fall
Before going on to the other important ingredients, let’s take a moment to make
a few observations about gravitational fields and to introduce some terminology.
Notice an important property of the gravitational field. The gravitational force
on an object of mass m is given by F = mg. But, in Newtonian physics, we
also have F = ma. Thus, we have
a = mg
m
= g. (7.2)
The result is that all objects in a given gravitational field accelerate at the same
rate (if no other forces act on them). The condition where gravity is the only
influence on an object is known as “free fall.” So, the gravitational field g has
a direct meaning: it gives the acceleration of “freely falling” objects.
A particularly impressive example of this is called the ‘quarter and feather
experiment.’ Imagine taking all of the air out of a cylinder (to remove air
resistance which would be an extra force), and then releasing a quarter and a
feather at the same time. The feather would then then “drops like a rock.” In
particular, the quarter and the feather fall together in exactly the same way. I
have put a video of this experiment (from when I did it live for my PHY211
class in fall 1999) on the PHY312 web site for you to check it out.
Now, people over the years have wondered if it was really true that all objects fall
at exactly the same rate in a gravitational field, or if this was only approximately
true. If it is exactly correct, they wondered why it should be so. It is certainly
a striking fact.
For example, we have seen that energy is related to mass through E = mc 2 . So,
sometimes in order to figure out the exact mass of an object (like a hot wall
that a laser has been shining on....) you have to include some things (like heat)
that we used to count separately as ‘energy’ .... Does this E/c 2 have the same
effect on gravity as the more familiar notion of mass?