As a child, the Nobel Prize-winning physicist Richard Feynman asked his father
why a ball in his toy wagon moved backward whenever he pulled the wagon forward.
His father said that the answer lay in the tendency of moving things to keep moving,
and of stationary things to stay put. "This tendency is called inertia," said
Feynman senior. Then, with uncommon wisdom, he added: "But nobody knows why it is
true."
This question comes up in the context of wondering whether photons are really
"massless," since, after all, they have nonzero energy and energy is equivalent
to mass according to Einstein's equation E=mc
^{2}. The problem is simply
that people are using two different definitions of mass.The overwhelming consensus
among physicists today is to say that photons are massless. However, it is possible
to assign a "relativistic mass" to a photon which depends upon its wavelength.
This is based upon an old usage of the word "mass" which, though not strictly
wrong, is not used much today.
The old definition of mass, called "relativistic mass," assigns a mass to a
particle proportional to its total energy E, and involved the speed of light, c,
in the proportionality constant:
m = E / c^{2}.(1)
This definition gives every object a velocity-dependent mass.
The modern definition assigns every object just one mass, an
invariant quantity that does not depend on velocity.This is given by
m = E_0 / c^{2}, (2)
where E_0 is the total energy of that object at rest.
The first definition is often used in popularizations, and in some
elementary textbooks.It was once used by practicing physicists, but for
the last few decades, the vast majority of physicists have instead used the
second definition.Sometimes people will use the phrase "rest mass," or
"invariant mass," but this is just for emphasis: mass is mass.The
"relativistic mass" is never used at all.(If you see "relativistic mass"
in your first-year physics textbook, complain! There is no reason for books
to teach obsolete terminology.)
Note, by the way, that using the standard definition of mass, the
one given by Eq. (2), the equation "E = m c
^{2}" is
not correct.Using the
standard definition, the relation between the mass and energy of an object
can be written as
E = m c^{2} / sqrt(1 -v^{2}/c^{2}), (3)
or as
E^{2} = m^{2} c^{4}+p^{2} c^{2},(4)
where v is the object's velocity, and p is its momentum.
In one sense, any definition is just a matter of
convention. In practice, though, physicists now use this definition because
it is much more convenient. The "relativistic mass" of an object is really
just the same as its energy, and there isn't any reason to have another word
for energy: "energy" is a perfectly good word. The mass of an object,
though, is a fundamental and invariant property, and one for which we do
need a word.
There are people who still want to use
relativistic mass and it is not easy to settle an argument
over semantic issues because there is no absolute right or wrong,
just conventions of terminology.
[Relativity FAQ]
This is an error. There