Essays:Adding arrows

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Doos 07:09, 17 October 2007 (PDT)

This essay is largely based on Richard Feynman's book "QED - The Strange Behavior of Light and Matter" and his lectures in Auckland, New Zealand. The first being the written version of the many lectures held by Feynman at universities around the world in the 1970' and 1980's.

Quantum electrodynamics is a topic not very well understood by gemologists (or even by physic majors), but with the simple concept of "adding arrows" the strange behavior of light can, atleast partially, be explained. Nobel Prize winner Richard Feynman had the ability to teach hardcore quantum theory at a novice level maybe only to be surpassed by Walter Lewin. Throughout everything Feynman freely admits that some things just can not be explained at present, nor that anything he lectured is correct. In 10 years we might have much more insight in the strange behavior of light, but at present we will have to do with emperical knowldege and our limited understanding.

The main objective of this essay is therefor not to be authorative or correct, just to dive a little deeper in the topic of light so we may understand how light works. From why light doesn't travel in a straight line to how diffraction works, it can all be explained by the simple concept of "adding arrows".

Reflection

When a light source is pointed at a reflecting surface, we are taught that the reflection will reach a point on the opposite of the normal and that the angles of incidence and the angle of reflection are equal. The incident ray, the reflected ray and the normal all lie in the same plane. That is the "law of reflection". A logical interpretation of that might be that light will always follow that path of least distance (or even least time). That raises a few questions, as how much of the light will be reflected from the glass plate. Or even worse, if we would paint a portion of the glass black, would it still be able to reflect light from lightsource A to detector point B? According to the usual law of reflection, the latter should not occur. In reality it can.

For us to understand this, we need to let go of the idea that light travels only in a straight line from A to B or that there is only one path a light ray can take to get from A to B, via a reflecting surface, when the shortest path between A and B is blocked.

Possible paths light can take when traveling from point A to point B via a reflecting surface.

When a photon travels from point A to point B via a reflecting surface, it can take an infinite amount of paths to reach B. The shortest possible route being dictated by the law of reflection (depicted as the green arrows). However there is no reason why the photon could not take a longer path, and in fact it does. It could easily follow the red paths (which are longer paths) or the blue paths (even longer) or anything in between. If we were to place a detector at point B and measure the time it takes to get from point A to B via the reflecting glass, the time for every photon to arrive at point B will be different. A good indicator that shows that light does not always travel the shortest distance.

If we were to take a stopwatch with counter clockwise rotating hand, the hand would stop at a different "hour" for every of these paths and we can think of the direction the hand is pointing to as an "arrow" (as indicated at the bottom of the image). These stopwatches rotate very fast counter clockwise at the frequency of the photon.