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Celebrating Einstein
"The Momentum of Light"

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?
 

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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)

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Date Modified: 01/17/2006


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