The Strange Teory of Light and Matter

April 16, 2013

Richard P. Feynman in 1965 jointly received the Nobel Prize in Physics for his contributions to the theory of Quantum Electrodynamics (QED). The other receivers of the prize were Julian Schwinger and Sin-Itiro Tomonaga who also contributed to the development of the theory of QED.

While the two other Nobel Laureates had a more formalistic approach to the complicated theories and concepts in QED, Feynman was a man of intuition, exemplified by his development of the so-called Feynman diagrams; pictorial representations of the interactions that QED describes. Schwinger banned the use of Feynman diagrams in his classes which illustrates the fundamentally different approaches of him and Feynman.

In a short book titled The Strange Theory of Light and Matter Feynman explains the fundamentals of QED. The book contains four chapters, each corresponding to a lecture that Feynman gave on the topic, and is aimed at an audience without any prior experience with photonics and quantum mechanics. Since quantum descriptions of light-matter interactions are not trivial, this seems like an impossible task! However, Feynman conveys an understanding and intuition, as always, but not the techniques and tricks that are needed to efficiently make use of the QED theory; or to quote the introductory chapter:

“I’m going to explain to you what the physicists are doing when they are predicting how Nature will behave, but I’m not going to teach you any tricks so you can do it efficiently (…) It takes seven years – four undergraduate and three graduate – to train our physics students to that in a tricky, efficient way.”

Essentially, Feynman gives a single rule and uses this one rule throughout the analyses of physics problems that people would normally approach with a bulky machinery of mathematics. The rule is that physical events occur with a certain probability that is the square of the length of an arrow (a vector), the so-called probability amplitude. If the event can occur in several ways, the probability amplitude of the event is obtained by adding the probability amplitudes of the individual ways.

In the second chapter, Feynman uses the above rule to analyze light in various well-known settings; reflection off a mirror, diffraction at an interface, diffraction through a slit and focusing via a lens. Feynman also explains dispersion (that, for instance, red and blue light behave differently) in the simple framework of addition of probability amplitudes, and likewise he derives Fermat’s principle in the limit of ray optics. These are nice demonstrations of the versatility of the basic rules of QED to explain any phenomenon involving light.

In the subsequent chapter, the interaction of photons with electrons is analyzed using three simple processes: photon propagation, electron propagation and electron absorption or emission of a photon. Introducing space-time Feynman analyzes these processes using the probability amplitudes, and the Feynman diagrams are introduced; electrons as straight lines and photons as wiggly lines.

As an interesting example, the reflection and transmission of light from a slab of glass is analyzed. The slab is represented by a number of layers, each containing electrons, and the photons scatter with the electrons inside each layer. From this analysis Feynman concludes:

“Thus we can get the correct answer for the probability of partial reflection by imaging (falsely) that all reflection comes from only the front and the back surfaces. In this intuitively easy analysis, the “front surface” and “back surface” arrows are mathematical constructions that give us the right answer, whereas the analysis we just did (…) is a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.”

In optics and photonics, we usually think of light scattering as happening at interfaces between different media. But obviously light scatters with the electrons inside the media and not only with the interfaces, and Feynman with this example beautifully demonstrates how these views are in good agreement.

Having taken graduate courses on quantum mechanics, nanophotonics and many-body quantum theory – that all contained enormously many equations – it is striking how Feynman in this little book analyzes similarly difficult problems without any equations!

The simplicity with which Feynman explains the curious nature of light-matter-interactions demonstrates his profound understanding, and I vividly recommend anyone who wants to be inspired and gain a bit of Feynman’s intuition to read this book.

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