Allow me to hearken momentarily back to Newton's picture of
light as particles.
Actually the following analysis pertains to any
particles whose rest mass is zero.
If m = 0 then
Eq. (E=mc2.3)
is absurd, except in the rather useless sense that we may let
become infinite.
On the other hand,
Eq. (E=mc2.14)
works fine if m = 0. Then we just have
- that is, the energy and momentum of a
massless particle differ only by a factor of
c, its speed of propagation. Although we cannot
define 
because the massless particle always
moves at c relative to any observer [this was,
after all, one of the original postulates of the ],
we can talk about its effective mass, which is the
same as its kinetic energy divided by c2.
Thus, even though light has no rest mass (because it can never be at rest!), it does have an effective mass which (it turns out) has all the properties one expects from mass - in particular, it has weight in a gravitational field [photons can ``fall''] and exerts a gravitational attraction of its own on other masses. The classic Gedankenexperiment on this topic is one in which the net mass of a closed box with mirrored sides increases if it is filled with light bouncing back and forth off the mirrors!
Is that weird, or what?
