OK, so quantum electrodynamics is said to date from 1929 when it was the same thing as quantum field theory. However it immediately suffered from the “problem of infinities”. So much so that some say most workers in the field doubted its correctness, whilst others say physicists believed a conceptual change was needed. As to what, see the conceptual foundations and the philosophical aspects of renormalization theory by Tian Yu Cao and Silvan Schweber dating from 1993. They say QFT embodies a reductionist view, but “serious doubt has often been cast on the whole program, particularly when the foundations themselves were found to be in a state of confusion”. They describe QED as a conceptually unstable theory, and say a stubborn historian might reject it, or renormalization, or both.
QED image from David Butler’s YouTube Classroom Aid
They say renormalization was conservative because “it took the framework of QFT as given, and made no attempts to alter its foundations”. They talk about the locality assumption, which “is a legacy of the point model of particles”. They say Frenkel’s idea of the point-electron was quickly accepted and became the conceptual basis for QFT. And that the idea of looking for a structure of the electron was given up because, as Dirac said in 1938, the electron “is too simple a thing for the question of the laws governing its structure to arise”.
Ignorance of the structure of the electron and other entities
Cao and Schweber also say “it is clear, therefore, that what is hidden in the locality assumption is an acknowledgment of our ignorance of the structure of the electron and that of other elementary entities”. They also talk about the operator field assumption, where “local field operators have a direct physical interpretation in terms of the emission and absorption and the creation and annihilation of the quanta associated with the particles”. It’s clear that what’s hidden is the ignorance of what actually happens in pair production and annihilation. Cao and Schweber also talk about the plenum assumption of the bare vacuum. They say the vacuum isn’t some state of nothingness, but is a polarizable medium. That’s good. But they also say it’s the scene of wild activities wherein field operators result in local excitations, implying virtual processes of arbitrarily high energy resulting in infinite quantities. That isn’t good. But what is, is this: “there exists essentially no empirical evidence for believing the correctness of the theory at these energies”. And this: “thus the divergence difficulties are not external. They are internal to the very nature of QFT: they are constitutive within the canonical formulation of QFT. In this sense the occurrence of the divergences clearly pointed to a deep instability in the conceptual structure of QFT”. In other words the divergences and infinities are there because the foundations are not. Because people like Bohr, Heisenberg, Pauli, and Dirac didn’t understand what a photon was, or an electron, or a positron.
What is a photon?
Nor did Tomonaga, Schwinger, and Feynman. So the $64,000 dollar question is this: how can you come up with a theory describing the interaction of light and matter when you have no concept of the entities that comprise light and matter? Surely you have to start at the beginning and gain some kind of understanding before you bet the farm on point particles and renormalization? By taking note of things like the photoelectric effect and photon polarization, where an angled filter rotates the plane of polarization:
Crossed polarizer image from Rod Nave’s hyperphysics
Then you can take note of the hard scientific evidence provided by pair production, the Einstein-de Haas effect and the Stern-Gerlach experiment. Along with the Davisson-Germer experiment and the Thomson and Reid diffraction experiment. Then you won’t end up painting yourself into a corner and resorting to hocus pocus to dig yourself out of a hole, only to find you’ve dug the hole even deeper. Instead you stop digging, you start at the beginning, and you ask yourself a simple question: what is a photon? It has to start there. If you don’t have any idea what a photon is, how can you ever understand how light interacts with light? How can you ever understand what happens in gamma gamma pair production? How can you ever understand the electron? Or the positron? Or the electromagnetic forces between an electron and a positron? How can you ever understand how a magnet works?
The nature of light
People have tried to address this issue, see for example The Nature of Light: What is a Photon? It’s a book edited by Chandra Roychoudhuri, Al Kracklauer, and Kathy Creath. It dates from 2008 and contains 27 essays on the subject. At £122 it’s expensive, but you can find the first five essays online in the October 2003 issue of Optics and Photonics News:
Partial contents page from the October 2003 issue of Optics and Photonics News
You can also find Kracklauer’s essay Oh photon, photon, whither art thou gone? Plus the essay on the Bohr model of the photon by Geoffrey Hunter, Marian Kowalski, and Camil Alexandrescu. And the essay on Propagating topological singularities: the photon by Robert Kiehn, as well as the essay from quantum to classical: watching a single photon become a wave by Marco Bellini, Alessandro Zavatta, and Silvia Viciani. You can also find The Maxwell wave function of the photon by Michael Raymer and Brian Smith on the arXiv. And an essay by Roychoudhuri called the nature of light: what are photons? on the SPIE website. Yes, there’s perhaps a sense in which one can ask three different experts and get four different opinions, but something shines through. Such as “the photon is modelled as a monochromatic solution of Maxwell’s equations confined as a soliton wave”. That’s by Hunter, Kowalski, and Alexandrescu.
The photon has a wave nature
It’s enough to make you dissatisfied with the answers you usually hear. Especially after hearing Chandra Roychoudhuri say this in 2016: “SPIE has decided that our “Special Conference” series on “The nature of light: What are photons?” is no longer serving the interests of the society. It has been cancelled. I have tried to get it re-instated. But, I have failed to convince them otherwise”. Especially when you ask what is a photon? and the answer is “an excitation of the photon field”. Because that’s a non-answer, one that turns one unanswered question into two. What’s an excitation? What’s the photon field? It’s similar for “the propagator of Aμ and “the quantum of electromagnetic four-potential”. Sadly Wikipedia isn’t much help here. It says “the photon cannot be described by any mechanical model”, a claim which dates back to George Joos in 1951. But at least Wikipedia talks about the photon’s physical properties. It refers to wavelength lambda λ in expressions like energy E = hc/λ, where h is Planck’s constant and c is the speed of light. The photon is not some point-particle. See what Willis Lamb said in his historical essay Anti-photon: “radiation does not consist of particles”. He didn’t like the word photon because it came with billiard-ball baggage, but I’m stuck with it. So I’ll say this: radio-wave photons can have a wavelength a hundred kilometers long. That’s the starting position: the photon has a wave nature.
It just comes down to reformulating the wave theory in quantum mechanics
This isn’t something new, it dates back to 1925, before the photon got its name. See Pascual Jordan’s resolution of the conundrum of the wave-particle duality of light by Anthony Duncan and Michel Janssen. On page 47 they quote Jordan saying this: “Einstein drew the conclusion that the wave theory would necessarily have to be replaced or at least supplemented by the corpuscular picture. With our findings, however, the problem has taken a completely different turn. We see that it is not necessary after all to abandon or restrict the wave theory in favour of other models; instead it just comes down to reformulating the wave theory in quantum mechanics”. Easier said than done perhaps, but you’ve got to start somewhere. Like I said, with the photon. Buckle up.