All Possible Paths: The Creative Genius of Richard Feynman

Today would have marked the 103rd birthday of legendary physicist, science communicator and Nobel Laureate Richard Feynman. Feynman was awarded the 1965 Nobel Prize in Physics for his work on quantum electrodynamics (QED), including the introduction of the famous Feynman diagram (discussed below). Known as the Great Explainer, he was famous for his easy-to-understand explanations of complex scientific concepts and his infectious curiosity about nature. He dedicated a large part of his life to teaching physics, mostly at Caltech, believing that he himself learnt as much from teaching as from his own research into mysteries of nature.

Feynman’s “Doddles”

Quantum electrodynamics (QED) is the theory of light and matter, or photons and electrons. In order to describe the interaction between light and matter, Richard Feynman came up with a brilliant new calculation method which he called, path integrals. With this method, he proposed that when light travels from one point to another, it takes all possible paths between the two points at the same time.

To enable physicists to track these paths in a more intuitive way, the ever-inventive Feynman came up with his famous diagrams that at first sight, look like stick figures that kids love to draw. Here’s an example of a Feynman diagram.

The cartoon-like character of these diagrams belie the fact that they are an extremely powerful tool for physicists to visualize and account for the interactions among sub-atomic particles like electrons and photons. The arrows in a Feynman diagram shows the way in which the energy flows, or rather, the direction in which the electrons are travelling, and squiggly lines represent photons and gamma ray energy, that bridge the movement of the electrons.

The above diagram is a simple one: it has only two vertices representing the emission and absorption of a field particle. An electron (e) emits a photon at V1. This photon is then absorbed slightly later by another electron at V2. The emission of the photon causes the first electron to recoil in space, while the absorption of the photon’s energy and momentum causes a comparable deflection in the second electron’s path. The upshot of this interaction is that the particles move away from each other in space.

Frank Wilczek, who won the Nobel Prize in Physics in 2004, regularly draws Feynman Diagrams as part of his research in trying to understand an idea within physics. As he puts it:

Feynman’s influence pervades physics and has contributed to how every modern physicist thinks about his or her problem. Many physicists, including me, feel that our understanding of a physics idea is incomplete until it can be expressed with Feynman Diagrams. Once you can express it in that language, you have access to a well-developed body of visual metaphors and theoretical techniques.” [1]

Discovery After Discovery

As a testament to his genius, Feynman Diagrams are still used by physicists all over the world. They have helped scores of physicists make their own discoveries, some of which went on to win prestigious prices.

Below are Feynman Diagrams depicting scientific discoveries which led to Nobel Prizes in Physics between 1936 and 2015. Most of the diagrams were drawn by Nobel laureate Frank Wilczek and were shown in an exhibition at the ArtScience Museum in Singapore, marking the centenary of Richard Feynman [2].  Among the diagrams is the Nobel Prize-winning work of Feynman himself.

1936 – POSITRON DISCOVERY

The 1936 Nobel Prize in Physics was shared equally between Victor Franz Hess “for his discovery of cosmic radiation” and Carl David Andersen “for his discovery of the positron”. See note [3] for more details on the positron.

1957 – PARITY VIOLATION

The 1957 Nobel Prize in Physics was awarded jointly to Chen Ning Yang and Tsung-Dao Lee “for their penetrating investigation of the so-called parity laws which has led to important discoveries regarding the elementary particles”. See note [4] for more details on parity violations.

1965 – QUANTUM ELECTRODYNAMICS

The 1965 Nobel Prize in Physics 1965 was awarded jointly to Sin-Itiro Tomonaga, Julian Schwinger and Richard P. Feynman “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles.” See note [5] for more details on QED.

1993 – A NEW TYPE OF PULSAR

The 1993 Nobel Prize in Physics was awarded jointly to Russell A. Hulse and Joseph H. Taylor Jr., “for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of extreme states of matter and search for planets beyond Earth’s solar system.

2004 – THE STRONG FORCE

The 2004 Nobel Prize in Physics was awarded jointly to David J. Gross, H. David Politzer and Frank Wilczek “for the discovery of asymptotic freedom in the theory of the strong interaction”. See note [6] for more details on the strong force.

2015 – NEUTRINO OSCILLATION

The 2015 Nobel Prize in Physics was awarded jointly to Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass”. See note [7] for more details on neutrino oscillations.

Notes

[1] Email correspondence with the ArtScience Museum in Singapore dated 13 April 2018.

[2] The exhibition, entitled All Possible Paths (20 October 2018 – 3 March 2019) was organized by ArtScience Museum and the Nanyang Technological University in Singapore and the Nobel Centre.

[3] The positron or antielectron is the antiparticle of the electron. Predicted in theory several years earlier by Paul Dirac, it was discovered by American physicist, Carl Anderson while studying cosmic rays experimentally (cosmic rays were discovered by Victor Hess, co-winner of the 1936 Nobel Prize in Physics). Anderson had not set out to hunt antimatter. He had built a cloud chamber to determine the composition of cosmic rays, high-energy particles that rain down from space. Andersen took hundreds of photographs of the tracks of cosmic ray particles but he was stumped by the curve trajectory of a particle that was positively charged, yet far less massive than a proton. That particle was named positron on the suggestion of an editor of the journal, Physical Review. Only later did Anderson realize that the positron was identical to the electron except for the opposite charge, the very antiparticle Paul Dirac had predicted in 1931.

[4] In 1957 Yang and Lee, who had worked as guest scientists at Brookhaven during the summer of 1956 received the Nobel Prize in physics for radically questioning one of physics’ basic tenets – that weak force interactions between elementary particles do not have parity symmetry. They discovered that studies focused on two particles, the tau and the theta, which had the same masses, lifetimes and scattering behaviors, but which decayed differently in experiments at Brookhaven’s Cosmotron particle accelerator, proving that the fundamental and supposedly absolute law of parity conservation can be violated.

[5] Quantum electrodynamics (QED) treats the behavior of electromagnetic fields in the same manner as it treats the behavior of the electrons producing them—as particles, whose interactions can be described using probability theory. The so-called probability amplitude for anything more elaborate than an isolated hydrogen atom is far too complex to solve directly, so the standard quantum-mechanics approach is to start with a relatively simple equation and keep adding smaller and smaller corrections to it according to well-defined rules. The solution gets closer and closer to the actual answer as the corrections diminish in size. One then decides how accurate you need to be for the task at hand. However, this approach to describing an electromagnetic field means allowing the photons to have infinite momentum, and it had become clear by the late 1930s that such equations did not converge on the correct answer—adding corrections merely piled infinities upon infinities. While Schwinger and Tomonaga used highly mathematical approaches to the problem, Feynman characteristically took a different point of view. He drew pictures of every possible interaction between photons and electrons, including those involving “virtual” particles undetectable by the outside world. These iconic doodles, now called Feynman Diagrams, allowed him to calculate each scenario’s probability amplitude independently and add them all up to get the correct answer. As this blog shows, the use of Feynman Diagrams led to many other Nobel Prize-winning work in particle physics.

[6] The strong force – often called the color force – is one of nature’s four fundamental forces. It holds most ordinary matter together because it confines quarks into hadron particles such as protons and neutrons, and binds these hadrons together to create atomic nuclei. This research was triggered by the fact that quarks were never observed independently; they are usually found in threes or sometimes twos. Apart from the electrical plus and minus charge, some particles can also have a so-called color charge – red, green or blue. Quarks and gluons have such color charge. The quarks in a proton must have different colors, in order to make the total color charge neutral or white. Therefore, it is impossible for quarks to exist independently. However, it was discovered that with enough energy, one quark can appear to be momentarily free only to be drawn back into the proton. At the instant of separation, more can be deduced about the nature of the strong force and its function.

[7] Most particles called neutrinos found passing through Earth are created in nuclear reactions that take place in our nearest star – the Sun. However, as neutrinos rarely interact with matter, detecting them is extremely challenging. After years of research, scientists have identified three types of neutrinos that transform from one type to another while moving through space. In the language of Feynman Diagrams, we see one kind of particles turn into another, without any interaction occurring. The explanation of this phenomenon, named neutrino oscillation, can give us hints about the history, structure and future of the Universe.

Further Study:

Here is Feynman’s 1949 paper that introduced his famous diagrams: “Space-time approach to quantum electrodynamics”, Physical Review 76:769–789

Two primers on Feynman Diagrams: