Notes on Relativity and Cosmology - Physics Department, UCSB

172 CHAPTER 7. RELATIVITY AND THE GRAVITATIONAL FIELD
In order to be able to talk about all of this without getting too confused, people
invented two distinct terms for the following two distinct concepts:
1) Gravitational mass m G . This is the kind of mass that interacts with the
gravitational field. Thus, we have F = m G g.
2) Inertial mass m I . This is the kind of mass that goes into Newton’s second
law. So, we have F = m I a.
Now, we can ask the question we have been thinking of in the clean form: is it
always true that gravitational mass and inertial mass are the same? That is, do
we always have m G = m I ?
7.2.2 The 2nd ingredient: The effects of gravity on light
Let’s leave aside for the moment further thought about fields as such and turn
to another favorite question: to what extent is light affected by gravity?
Now, first, why do we care? Well, we built up our entire discussion of special
relativity using light rays and we assumed in the process that light always traveled
at a constant speed in straight lines! So, what if it happens that gravity
can pull on light? If so, we may have to modify our thinking.
Clearly, there are two possible arguments:
i) No. Light has no mass (m light = 0). So, gravity cannot exert a force on
light and should not affect it.
ii) Yes. After all, all things fall at the same rate in a gravitational field, even
things with a very small mass. So, light should fall.
Well, we could go back and forth between these two points of view for quite
awhile.... but let’s proceed by introducing a third argument in order to break
the tie. We’ll do it by recalling that there is a certain equivalence between
energy and mass.
In fact, in certain situations, “pure mass” can be converted into “pure energy”
and vice versa. A nice example of this happens all the time in particle accelerators
when an electron meets a positron (it’s ‘anti-particle’).
e + e - light light
light
light
e
+
e-