Beautiful Science: 75 Years of the Feynman Diagram

Richard Feynman (1918-1988) was a towering figure in 20th century theoretical physics, and the co-winner of the 1965 Nobel Prize for his groundbreaking work in Quantum Electrodynamics (QED), the study of how light interacts with matter.

Instrumental to the astonishing success of QED is the Feynman Diagram, a pictorial representation of the complex equations describing the interactions between subatomic particles such as electrons and photons. The beauty of Feynman diagrams is that they allow one to calculate interactions between elementary particules much more efficiently and with less mathematical drudgery than before.

Here is a very simple example of a Feynman diagram:

A simple Feynman diagram, showing particles represented by straight lines and a photon represented by a wavy line. In this case, the vertical axis is space and the horizontal axis is time © Romainbehar, CC0, via Wikimedia Commons

To understand the ingenuity of Feynman’s invention, let’s consider a somewhat more detailed diagram (note: you don’t have to understand the physical details, only where the logic leads).

The above Feynman diagram depicts a beta decay, a type of radioactive decay in which a beta ray is emitted from an atomic nucleus. Now, during a beta decay, the proton in the nucleus is either transformed into a neutron or vice versa. If a neutron is converted to a proton as shown, it is known as β- decay (the W- symbol denotes a weak boson, an extremely short-lived particle).

Reading the diagram from left to right, we see that a neutron (n) has decayed into a proton (p) and a weak boson, which in turn decays into an electron and an electron anti-neutrino. In effect, what is shown here is a weak interaction, which can be expressed mathematically as follows:

where the numbers indicate mass and charge (e.g., a proton has a mass of one and a charge of one). Without going further into details, what this diagram has done is tell us not only what goes into an interaction and what comes out but also what goes on during the interaction itself. This insight is not unique to this example; the big advantage of Feynman diagrams in general is that they help physicists keep track of the possible interactions of elementary particles, thus paving the way for more detailed calculations. It is why Feynman diagrams are still being widely used today by theoretical physicists, 75 years after its invention.

Interesting Historical Facts

Now for some interesting historical facts about Feynman’s ingenious tool. When Feynman introduced the first of his diagrams in his seminal 1948 paper, “Spacetime Approach to Nonrelativistic Quantum Mechanics”, they were were initially derided by some as something that was too good to be true. How can a simple diagram lead to a profound understanding of elementary particle interactions? Indeed, Feynman himself didn’t fully know why his method worked! Not until the distinguished physicist, Freeman Dyson (1923-2020) translated Feynman’s squiggles into rigorous mathematics were they widely accepted by the scientific community. Today, Feynman diagrams are part of everyma theoretical physicist’s toolkit and they continue to open the path to new discoveries in diverse areas of physics, from quantum mechanics to string theory to astrophysics. That Feynman could come up with such a powerful conceptual tool way before he could justify it rigorously using mathematics only adds to the mystique of Feynman’s intuitive, almost magical approach to doing physics. As the eminent mathematician Mark Kac once remarked:

“There are two kinds of geniuses. An ordinary genius is a follow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magiciansEven after we understand what they have done, the process by which they have done it is completely darkRichard Feynman is a magician of the highest caliber.”

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