light have mass?
is one of the most common questions that keeps cropping up
are studying physics, and its actually a good question.
answer is ... yes and no.
carries energy (shine a spotlight at an object and
that object gets hot), and it also carries momentum,
that is, a lightbeam has a certain amount of "push" to it. A lightbeam
aimed at you should push on you with a certain amount of
force, and the object projecting the beam should feel
a certain amount of recoil. For
object placed in the path of the beam, we talk about it experiencing a
certain amount of light-pressure, and technically, when a body
absorbs light, and is given a small "shove" by the beam ,
that originally belonged to the light is now owned
by the (now-moving) object.
1: The energy
and momentum of light
everyday purposes, the amount of momentum carried by light is pretty
small, but it's proportional to the beam's energy, which is in
turn proportional to the quantity and frequency of the light. Higher
frequencies carry more energy, and have a correspondingly stronger
If someone shines a torch at you, and you
at the beam, the pressure of the light hitting you in the face should
be slightly be
stronger, and the apparent frequency of the signal will be higher, too,
because you're intercepting the light-signal at a faster rate.
If you try to run directly away from the lightbeam,
light-signal's apparent frequency will be lower ( thanks to
its Doppler shift), it's apparent energy
will be lower, and the amount of momentum that you feel the light to
have when it hits you should be smaller, too, by exactly the
If the person then throws
the torch at you, then the light
coming at you from the approaching torch will again have a higher
frequency, energy and momentum. But the hurled
torch itself, as a moving body, will also have kinetic energy and
momentum. So since we say that
these things, for the torch, are standard properties of
a moving mass, why don't we say
that light is made up
of little moving particles that also carry mass?
What is mass?
we look at our operational definitions for "mass", we find that they
were designed around the sorts of properties that we associate
with solid objects, and one of the most important properties that
objects have but light doesn't is persistence.
tend to stay put, and if they move, they tend to move slowly
us to be able to see them by bouncing light off them. Objects have a location,
even if that location isn't always fixed with time. We can grab a
moving object and stop it, and then poke it about to measure its
But with light, transience is
part of its very
nature. If you could stop light dead, it would cease to be light. It's
frequency would be zero, it's energy would be zero, and its
momentum would be zero. All the properties that we came across earlier
that sounded rather like the properties of matter
would disappear. We
can suggest (as Einstein did in his
E=mc² paper 
) that light can
transfer momentum between an emitting object and a receiving one, but
while the light is "in flight", it's difficult to say that it has
"mass" itself, in any conventional way. A single pulse of
light just isn't a
complicated enough thing to be able to support the properties that we
normally associate with "mass"
What we can
do, though, is to trap light, and when we do that, the rules change.
an individual "stopped" light-beam wouldn't seem to
have doesn't have energy or momentum, we can (in theory) trap
light within a mirrored capsule or container. We can imagine a complex
bouncing about within the container, exerting pressure equally
on all of the container's walls. The light-complex still has energy,
but the momentum of its different components, acting in different
directions, cancels out. The container stays put. The energy of the
light is now confined to its container, and we can now carry
out thought-experiments with it. 
we try to move
the container, our lightcomplex doesn't like it. The container wall
that's pushed against the light-complex feels a greater resistance
due the fleeting increase in light-pressure, and the wall that
moves away form the light-complex feels a reduced light-pressure. When
we push against the container, it seems to resist, just as if it
contained a piece of matter, rather than trapped light-energy.
the container is moving, and its internal light has quickly reached a
equilibrium at the container's new velocity, the moving container's
mass has momentum, and so does the light-complex inside it. The light
traveling in the same direction as the
container now has more energy and momentum that the light components
acting in the opposite direction. The trapped light-complex
has a total momentum of zero when
it is stationary, but a conventional-looking momentum when the
This is much more like the behaviour
of mass, and in fact, we find that the initial energy of the
light-complex and its net momentum change with velocity in exactly the
same way as the relationship between the rest mass of a body, and the
momentum that a body has when it's moving. If we use Newtonian
mechanics, we say that the momentum of a body, p,
is equal to its mass
times its velocity, p=mv ... and if we calculate
that Doppler shifts change the forward and rearward energies
momenta of the different light-components, we find that the overall
momentum of the complex is proportional to velocity and energy, p=E(something)v.
This suggests a simple scaling factor between light-energy E
and the equivalent amount of mass, m.
we then do the same exercise under special relativity, the Doppler
the mass-momentum relationships are both a little bit more complicated
than under Newtonian physics, but again, we get the result that the
captive light-complex has
properties equivalent to that of a body, with the amount of equivalent
mass being proportional to the amount of trapped energy.
the proportionality between the energy and the apparent mass that it
gives to its container?
if we calculate the exact amount of momentum for a moving light-complex
based on its initial "rest-frame" energy, and work out how much mass
would have to be in the container to have the same momentum, we find
that with either Newtonian physics or special relativity 
= E / c2
if the apparent total mass of a container and its
trapped light reduces by an amount m when we open
the container and we allow its energy to escape, the amount of escaping
energy should be found to be
Generality of E=mc2
here, we can show that the relationship should be general. Let's take
our moving container of light, the one whose apparent mass and momentum
is increased by the amount of light-energy that it contains. Does the
energy have to be in the form of light?
that the container has an internal mechanism that suddenly
exposes solar panels that soak up the light and use it to
charge an internal
battery. Should the container's speed or momentum change? What if that
stored energy is then used to drive an internal lightsource that
replaces the original lightcomplex? Should the container's speed or
momentum change again?
For an external observer, we
want to say say that the
total energy and momentum (and apparent mass) that the sealed box
presents to the outside
world should remain the same, regardless of what might be
going on inside.
The energy and momentum of the box-system should be conserved.
the fact that this trapped energy is in the form of light shouldn't
be relevant. If the light is absorbed by the walls of the box,
and the energy is turned into the additional thermal energy of the
molecules that make up the box structure, then this heat energy
should again contribute the same amount of mass, according to the same
E=mc² formula. If that heat is absorbed by chemical
the box, then the energy of those chemical bonds will again contribute
mass, according to E=mc².
and energy are interchangeable,
just as Newton had suggested a few hundred years
"Opticks"  ... what E=mc²
gives us is the conversion factor (or
"exchange rate") that applies when we want to convert one into the
other. Although Einstein's famous paper on E=mc²
was originally presented as a followup to his paper on special
relativity, the relationship is a general one. 
Michell tried (and failed) to measure the momentum
of sunlight in the Eighteenth Century.
Einstein, " Does the Inertia of a Body depend upon its
Energy-Content?" ("Ist die
Trägheit eines Körpes von seinem Energiegehalt abhänging? ")
Annalen der Physik 18 639-641 (1905)
before Einstein's paper, a number of other researchers had already been
asking, "What effect does radiation-pressure have on a moving cavity
containing trapped electromagnetic energy?". Some of these researchers
came tantalisingly close to Einstein's result, but stopped short of
actually saying, as Einstein did, that the resulting "mass-like"
effects should be considered as real.
Baird, Relativity in Curved Spacetime
(2007), chapter 2, " Gravity, Energy and Mass "
Baird, " Two exact derivations of the mass/energy
relationship, E=mc² " physics/0009062
Baird, Relativity in Curved Spacetime
(2007), " Calculations 2: E=mc² from
Newtonian mechanics "
Newton, Opticks, Query 30:
Are not gross Bodies and Light convertible into one another, and may
not Bodies receive much of their Activity from the Particles of Light
which enter their Composition? ... "
Einstein, " An Elementary Derivation of the
Equivalence of Mass and Energy " Bull. Am. Math. Soc.
41 223-230 www.ams.org/bull/2000-37-01/
- Albert Einstein "E=mc²:
The most urgent problem of our time " Science
Illustrated (April 1946)
J. Feigenbaum and N. David Mermin "E=mc² "
Am.J.Phys. 56 18-21 (1988)
Fadner "Did Einstein really discover "E=mc²
?"Am.J.Phys. 56 114-122 (1988)
all original material
copyright © Eric Baird 2007/2008