Wednesday, August 5, 2009

Einstein, light and the photoelectric effect

Einstein has blessed us with a huge quantity of scientific contributions. I'm a huge fan of the ideas he was presenting with relativity. He has also furthered our understanding of some of the properties of light. However, Einstein also said some strange things regarding the energy of light in trying to explain the photoelectric effect.

Einstein made the claim that the energy of light is proportional to the frequency of the light times a constant. This allowed for some very simple mathematics that agreed perfectly with experimental results regarding the photoelectric effect (energy of the liberated electron). But by definition the photoelectric effect is such that we measure the electrons that flow as a result of an interaction between an incoming light wave and the electron itself. Einstein neglected an amplitude term in the energy of light equation he postulated, even though he knew that light had many wave properties and that the standard equation for the energy of a wave includes an amplitude term.

It is well known that if the brightness of incoming light is too dim then no photoelectric effect will be observed (ie. if it isn't bright, your solar panel generates no electricity). It seems plausible that this is because the incoming light merely lacks the requisite amount of energy to cause the photoelectric effect due to not enough amplitude. This lack of photoelectric effect in dim lighting would probably be explained as too few photons reaching the solar detector in standard terminology. The photon was a description of light as a particle created by Einstein, he gave the photon just enough energy to cause the photoelectric effect! If the universe produced a basic particle of light, wouldn't it be weird for its basic amount of energy to happen to be the amount necessary to cause the photoelectric effect, which Einstein happened to be studying at the time that he created the concept of the photon?

One of the properties of the photoelectric effect is that if the amplitude of the incoming light wave (or the number of photons in standard terminology) increases, then the number of electrons liberated by the photoelectric effect increases though their energy does not (it's affected by the frequency of the light wave). The photon based explanation is simple: more photons cause more interations with electrons. But a wave based explanation is equally simple: a wave with more amplitude has more energy and thus has the ability to interact with more than one electron.

Compton scattering was used as evidence supporting the existince of the photon, however, I suspect the effect could also be explained with a wave model of light.
I do not believe that it is appropriate to quantize energy (in any form including light). There can always be a smaller amount of energy than whatever value we set for a quanta of energy. I believe that the interaction between light and the electron in the photoelectric effect can be best explained by modeling light as a wave.