Feynman – The First Lecture (continued)
Professor Feynman tries to explain QED to us using the simple example of reflected light off of a glass surface (like a window). We find that if a second surface is added then the percentage of light photons reflected can either increase of decrease depending on the space between the surfaces. This is amazing. How can light photons “know” that they should reflect or not? How do they “know” there is a second surface -- since they must pass the first surface to find this out? This is all very mysterious and inexplicable. Feynman admits that he doesn’t know why either … nor does anyone else. Nevertheless, it is a fact. QED is a theory which holds up very precisely to experimentation. It is as close to scientific truth as any scientific theory can be. How does Feynman explain QED?
He uses very complicated mathematical tools to calculate these percentages. Fortunately, he can explain things using visual aids; viz. arrows and back-running clocks. Here is what happens.
He tells us that we must breakdown the phenomena into two parts.
Suppose a single photon is emitted from a light source. It can bounce off the first surface (first arrow) or it can pass through the first surface and bounce off the second surface (second arrow). So, we have two arrows (which he calls amplitudes). The first arrow starts out horizontally pointing to the right. Now let the QED clock start running backward extremely quickly (about 1,000,000,000,000,000 revolutions per second!). The first arrow turns counterclockwise around and around. The first arrow turns around many times during the time the photon leaves the light source, bounces off the first glass surface, and hits the photomultiplier. Next, start the second arrow horizontally pointing to the left and let it turn, turn, and turn at the same speed during the time it takes a photon to leave the light source and bounce off the second surface and hit the photomultiplier.
Here is a diagram which shows what is happening and how to create and combine the arrows. In the end, we want the probability that a photon emitted from the light source will hit the photomultiplier. This is our goal in QED.
Putting the two arrows together as in the above diagram we get an orange line. We draw a circle using this as the radius of the circle. (see next page)
The area of this circle is the probability we are seeking (after dividing byπ). Professor Feynman summarizes QED by saying that we first see how many ways an event (e.g., a photon hitting a photomultiplier) can happen.
(1) Each way or route has an associated arrow (just like arrow one and arrow two above).
(2) The arrows spin around and around for a length of time depending on how long it takes for light to travel that particular route.
(3) You add the arrows together by placing them together head to tail and create an (orange) line.
(4) The circle formed by the orange line has an area.
(5) The area of this circle, divided by π, is the probability of the event happening.
Why is Nature like this? Why do photons act like this? Professor Feynman cannot tell us – nor can anyone else.