The theory of relativity suggested that the energy quanta of light should
also be quanta of momentum as well. Yet the new quantum theories of the day were proving accurate even though the
momenta of light quanta hadn't been accounted for. Would these quantum theories still prove accurate when momentum was
included?
A B C
A. Momentum
Any material object is a lump of energy. That is a
major implication of Einstein's equation "E=mc2".
Einstein showed how the mass of an object is a measure of the amount of energy
it contains. The more massive an object is, the more energy you can
extract from it (with appropriate means) to do some work; the more energy an
object has, the more massive it is and the harder it is to change its motion or
lack of motion.
Any mass, whether stationary or moving, has energy.
But a moving mass also has another quality, called momentum. The object's
motion and mass both contribute to this quality. Two equally massive
objects moving at different speeds will have different momenta, the faster
object having the larger momentum; and two equally fast-moving objects of
different mass will have different momenta, the more massive object's momentum
being the larger in this case.
One important feature of momentum is that objects that have
more of it will produce larger effects on anything they happen to run
into. If a soccer player barely taps the ball into the net, the ball will
barely flex the net before rebounding. If the player kicks the ball hard,
the ball, with its greater momentum, will plow much further into the net before
the net bounces the ball back.
Another feature of momentum is that it has
direction as well as size. A soccer ball falling through the air has the
same-sized momentum as one rising through the air with the same speed, but the
momenta are still different because the directions are different. One way
we can take account of this feature is by treating some directions as positive
and their opposites as negative. Thus a soccer ball moving in one of the
positive directions would have a positive momentum, while the same ball moving
opposite to that direction would have a negative momentum.
So far, we've just been giving names to certain features of
moving objects. But these features turn out to be worth naming. We
find that in any physical process, no matter how many objects are involved or
how they interact with each other, the total momentum of all the objects
combined always stays the same. If one object runs into another and slows
down or stops as a result, it loses momentum, but the momentum doesn't just
disappear: it simply passes to the object run into. If an object
acquires a certain momentum because something increases its speed or its mass,
the something that causes this will lose an equal momentum. If two objects
interact so that they change each other's directions of motion in some way, each
object's directional change will be the exact opposite of the other's. And
if an object slows down as it moves through air or slides over a surface, its
momentum goes into the molecules of the air or the surface that it
encounters. This constancy of momentum appears, from centuries of
experimental evidence, to be a law of nature, and we can use it as a clue to
distinguish possible and impossible outcomes for any physical process.
In this respect, momentum is like energy. Centuries
of experimental evidence also indicate that the total energy of any system of
objects stays the same, no matter how much energy the individual objects gain or
lose. In a closed system of objects, energy and momentum can both be
exchanged, but cannot appear from nowhere or disappear into nothing.
The association of momentum and energy is even closer that
this. In accordance with Einstein's relativity theory, momentum and energy
are two sides of one thing, the way space and time are two features of a single
entity that we now call "spacetime". Energy is to time what
momentum is to space. Briefly put, any physical process involving energy
will also involve momentum, at least in some frame of reference.
And yet, while previously unrealized facts about energy
were coming to physicists' attention, these facts' relation to momentum remained
to be taken into account.
By December 1900, Max Planck found that the energy of light
was produced and absorbed as discontinuous lumps, or quanta. This was a
surprising discovery, because many other experiments agreed with equations that
suggested light was a continuous stream of momentum and energy. Planck's
early view was that, while light appeared and disappeared in energy quanta, it
traveled through space as a continuous stream of energy. But a few years
later, in 1905, Albert Einstein showed how certain experiments could be
understood if the energy of light also existed as quanta while traveling through
space. Later, Einstein pointed out that the existence of light quanta
suggested a property of matter: luminous matter could only contain certain
amounts of energy, but no amounts in between. This property of matter was a feature of Niels
Bohr's early model of atoms' structure and their interaction with light.
In all of this, the energy of light was a prime
consideration. The momentum of light was nowhere accounted for. Yet
somehow, the new theories of light and matter were proving accurate in their
descriptions of various phenomena. But if the new quantum theory really
were consistent, it would have to describe such phenomena accurately even when
momentum was included in its equations.
In a 1916 paper, Einstein reviewed the behavior of light
quanta. This time Einstein assumed that these were quanta of momentum as
well as energy. His results about the energy of light were consistent with
what Planck had already found in 1900 and with what experiments always
demonstrated. But by accounting for momentum too, Einstein provided us
with a more detailed theory of how light and matter interact.
(.....continued)
A B C