QED Summary

Richard P. Feynman’s QED: The Strange Theory of Light and Matter is a book about the theory quantum electrodynamics . This is not so much a book review as it is just me badly rewording what Feynman says.

The book opens with a sort of contextual introduction to QED, or just to physics theories in general. In fact, instead of struggling to describe it, I’ll just tell you what he calls it: “a physicist’s history of physics.” He takes us on a quick tour, starting with Mayans—how they counted beans—and finally, reaching our destination, ending with QED.

The first aspect of QED that he establishes is that light is made of particles. He shows us this by describing a ‘photomultiplier’: a machine which, when connected to an amplifier, produces a click each time a photon hits it. As a light source gets dimmer, clicks of equal volume are still produced, just less frequently.

The next thing he talks about is partial reflection in glass. He begins by introducing the ‘holes and spots theory’, a theory stating that glass has holes to let photons in, and reflective patches which reflect them back out. He invalidates this theory, though, and concludes that, even with the theory of QED, there isn’t a way of predicting which photons will reflect; you can only calculate the probability (four per cent.)

He then talks about partial reflection with more surfaces. One would intuit that two surfaces would reflect about eight per cent of the photons (100 – 100 ∗ 0.96²), he says, and yet this isn’t the case: strangely enough, the extent of reflection fluctuates from 0-16% depending on the thickness of the glass.

Next, he shows us how to actually calculate this probability: you do it by adding arrows together to produce a final arrow, and then squaring the length of that arrow to get the probability. (This is a very common technique used in other areas of physics concerning adding vectors.) This is also where Feynman introduces his legendary stopwatch! This imaginary stopwatch indicates the direction of the arrow in that its hand corresponds to the way an arrow is facing. You start the stopwatch as a photon leaves the light source, and stop it when it you hear the photomultiplier click.

The final thing he mentions in this chapter is iridescence. Essentially, each colour of light travels at a different speed, to which the rotational speed of the stopwatch corresponds (that is to say, the hand of the red-light stopwatch will spin much slower than the blue-light stopwatch.) This, combined with the uneven thickness of a surface, leads to the arrows of light pointing in different directions, leading to varying probabilities and hence varying degrees of reflection of each colour throughout the surface: iridescence!

Chapter 2 is where Feynman really begins to deconstruct the familiar laws of light, such as ‘the angle of incidence always equals angle of reflection’. The truth is, he explains, photons could theoretically reflect from any point on a mirror, but it’s only where the paths are shortest and most similar, where the angle of incidence indeed happens to equal the angle of reflection, that the probability arrows add up substantially, producing a larger final arrow and hence large final probability. The arrows corresponding to other parts of the mirror cancel out, producing no/a very small final arrow.

The next part was not a law of light, but rather a familiar phenomenon: diffraction gratings. Well, 'familiar' might be a stretch. He offered something about shiny silver license plates—maybe it's an American thing; maybe it's a '70s thing, but, either way, I had no idea to what he was referring—and also about vinyl records, which I do actually own but have never observed being anything but black (again, this is perhaps a American phenomenon; you see, the UK is not the brightest place in the world.) The final example he gave was something called a 'videodisc', which I initally misinterpreted as a CD, before realising the book, and QED, actually predated the CD. So, you know, he managed to provide a comically very unfamiliar list of examples.

Anyway, diffraction gratings (of which CDs are actually an example): you take a part of the mirror where the arrows cancel out (like the edges) and precisely scrape away some of it to eliminate arrows pointing in the opposite direction. Because all the remaining arrows are generally pointing in a similar direction, they add up and form a substantial final arrow, and therefore reflection occurs. He then goes on to explain how gratings work with white light which was very interesting, but this is getting too long (you may as well read the book at this point!) so I have to move on.

The next law he explains is refraction. Here, he mentions how mirages work. Mirages occur when the temperature near the ground is very different to the temperature higher up. Light always takes the path of least time, so it will bend towards the warmer part of the air, which is less dense and therefore easier (and quicker) for the light to travel through. Our eyes, however, always perceive light as if it's travelled in a straight line, and so it may appear to us, on an exceptionally hot day, that the light is coming from the road.

This is getting way too long and we haven’t even reached Chapter 3! I’ll try to be more concise. The explanation for light traveling in straight lines is similar to before: the shortest paths produce the largest final arrow; the longer paths cancel out. I don’t really know how to summarise the next part without a diagram, but, basically, you can restrict a ray of light in a way that allows a photomultiplier to to the side of the source to click, suggesting that light has not travelled in a straight line. This works similarly to the grating: if you eliminate some of the probability arrows, the remaining arrows add up to produce a substantial final amplitude.

Next he explains how a focusing lens works. By placing a convex piece of glass between the source and the multiplier, you can modify the duration of each path so that they are all the same (the shortest paths are slowed down by the thickest part of the glass.) You end up with a huge final arrow because all the small arrows are pointing in the exact same direction.

Finally, in this chapter, he introduces the method which allows you to calculate probability from a sequence of several events, rather than alternative events. It’s called multiplying arrows. One thing which I found a bit confusing here was the fact that he started using the word ‘amplitude’, which he hadn’t been using before. Anyway, what you do is you get the arrows for each step and multiply them in succession. He refers to ‘shrinking and turning’—‘shrinking’ corresponds to the length of the arrow and ‘turning’ to the angle determined by the stopwatch (I think.) Light traveling involves only turning; interactions with a surface, only shrinking.

Let's move on to Chapter 3! I don’t know how I’m going to summarise this chapter. Where to even begin? I’ll skip straight to the main part of the lecture, where he talks about ‘the three basic actions’, and draws some strange diagrams within axes, space on 𝑥 and time on 𝑦.

He explains there’s a formula to calculate P(A to B), the first action: a photon getting from point A to point B. He also talks about ‘the Interval’, I, which I didn’t really understand. The second action is an electron getting from point A to point B; the last action is coupling: emission or absorption of a photon by an electron, referred to as 𝑗. The point of the chapter is that you need to consider all possible ways A to B could happen, and then multiply and add the amplitudes to work out a final probability. This includes electrons going backwards in time, and photons disintegrating into electron-positron pairs (similar to how a neutron can decay into an electron and a proton).

He then re-explains partial reflection, going into more detail regarding what's really happening in the glass. For some reason, the stopwatch is no longer applicable, but the turning concept remains, only in the opposite direction, and this time the arrow spins only until a photon is emitted; as soon as it starts traveling, the arrow stops spinning—meaning the angle of the arrow indicates when the photon was emitted. It’s all very confusing. Anyway, these new arrows of light entering the glass add up and form an arc, from which you can draw a chord (final arrow), resulting in the same four percent probability we learned about in the first chapter.

He goes on to talk about refraction in more detail, and polarization of electrons.

Ok, Chapter 4 now! Chapter 4 has two parts: QED’s flaws and subnuclear particles. The main problem with QED is the difference between m & e and n & j and lack of mathematical connection needed to legitimize such a discrepancy. m is the mass of an electron and e is the charge; n and j are theoretical values used in the aforementioned calculations. This part, admittedly, did not make a great deal of sense to me, so please excuse the rather scanty synopsis.

The last thing Feynman talks about is the tiny subatomic particles: quarks, gluons, neutrinos, Ws and electrons again. He talks about how scientists keep discovering new cycles of particles with greater masses. He also talks about flavours and colours of quarks. This part was rather overwhelming; the new particles just kept coming, and I also read this book before I'd learned anything about subatomic particles at school.

In conclusion, I thoroughly enjoyed this book. I picked up the Feynman Lectures a few months after reading it. I believe I managed to get through about seventeen chapters, but decided to put it back on my shelf until I'd finished the first year of my undergraduate degree. Anyway, do pick up QED if you get the chance! This meagre summary has not done it anything close to justice. I, too, will be picking it up soon, to reread it.