What is a photon?

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.

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This Post Has 12 Comments

  1. Interesting story, John, thank you.
    I think that idea of Einstein to supplement wave theory with corpuscular approach was useful. His explanation of photoelectric effect may be incorrect, but still, that was very good contribution.
    Again, the problem in blind parroting of followers.
    The most strange belief of them is spin 1 for photon. Another strange belief is to call photon (wave propagation) as particle.
    Soliton is interesting solution for light, but soliton is eccess or ‘hole’ propagation case. No negative phase and only positive or no positive phase and only negative. Just one peak.
    A little bit more complicated wavelet with both positive and negative part could be a compact solution of Maxwell equations.
    Finally, the exact shape of that wave must depend on the way it were emitted – between many shapes possible.
    Mexican hat type of wavelet, say, could be close to point. Simplest analogue of soliton, but having both positive and negative phase of wave.
    Negative phase of wave is principal for diffraction and interferention.

  2. I think that between wavelets, Morlet wavelet will like you very much, John 🙂 Please, enjoy :
    https://en.m.wikipedia.org/wiki/Morlet_wavelet
    Very beautyful, is not it? 🙂
    Complex types of wavelets like that is especially cool if you are thinking about spin 1/2 wave propagation. Also not complex types of wavelets are possible, of course 🙂

    1. I think the photon is a “corpuscle” because it’s a soliton. It’s isn’t some billiard ball thing, it’s just a wave that doesn’t dissipate.
      .
      I don’t think the spin 0 is so wrong. There is a rotation associated with a sine wave. See for example the picture here: https://tex.stackexchange.com/questions/233132/diagramming-unit-circle-and-sine-wave-with-tikz. The phase can be represented by an arrowhead going round and round inside the circle. Rather like Feynman’s clock hand and your tumbling arrow.
      .
      I don’t think it’s too wrong to call a photon a particle either, provided you remember that a particle is a wave. Only it’s a wave of electromagnetic four-potential, not a wave of electric field and another wave of magnetic field. Like I said, there’s only one wave there. With one peak. Don’t forget that Maxwell unified electricity and magnetism and gave us electromagnetism. Why some people still think an electromagnetic wave is two orthogonal waves I do not know. Do you understand the canoe analogy now?
      .
      Perhaps many shapes are possible. But if it wasn’t sinusoidal, we wouldn’t call it a photon. We might call it a neutrino instead. Or something else.
      .
      I do not like those Mexican hats. It’s used to “explain” the Higgs mechanism, which contradicts E=mc².

      But yes, the Morlet wavelet is beautiful. It reminds me of a travelling breather, see the picture on the right here: https://en.wikipedia.org/wiki/Breather#Example_of_a_breather_solution_for_the_nonlinear_Schrödinger_equation. And the travelling breather reminds me of a neutrino. So yes, complex waves like that are cool if you are thinking about spin 1/2 wave propagation. You are getting the hang of this, Pavel!

  3. But the problem that they expect spin 1 for photon, John. Not spin 0.
    Also agree, that mexican hat is something crude. But comparing to soliton, it have one advantage. Soliton is not like sin-function. Phase and antiphase needed. Soliton is either phase either antiphase. Shapes like mexican hat has both.
    But sin-like functon limited in space like Morlet is something more perfect which we could expect for emitting of energy quant by atom, as it is very quick process.
    Breather is also very beautiful, John 🙂

    1. Sorry Pavel, I meant spin 1. But I’m not sorry about not liking that Mexican hat. The photon is not a Mexican hat! I do however like the Morlet wavelet. Imagine it was made out of wire and you pulled the ends apart. It would stretch outwards. If you let go of one end, it would contract. I can envisage a wave like this that concertinas in and out as it moves through space at c. That reminds me of the classical analogue of neutrino oscillations.

      1. By the way. Also soliton does not look good solution for Maxwell-like field oscillation, something like Morlet looks more natural, but for Kiehn propagation topological singularity model soliton looks as good solution.
        As soliton was motivated for similar applications. Hole ‘walking’ in semiconductor or some crystal deffects. Soliton may be understood as excess or a lack of something moving in the matrix. Not as wave oscillating – from positive to negative – phase / antiphase.

  4. Exactly – complex type of Morlet for neutrino and Morlet for photon, for example, if photon spin were 0.
    Probably, bosonic photons with spin +/-1 and 0 would be OK for me (both planar and circular polarisations are possible). But absence of 0 option shocks me, as 0 spin mean Maxwell’s type of wave propagation. Planar polarisation.
    Agree, mexican hat is ugly. I just mentioned it for contrast with soliton, as simplest shape having both positive and negative parts.

    1. Pavel: The moot point is that we’ve had a hundred years of quantum mechanics, and if you ask a particle physicist what is a photon? you don’t get a sensible reply. So maths can’t tell you what a photon is. Detective work can tell you something. Perhaps simulation can tell you more. I’d like to see some lattice simulations for this sort of thing.

  5. Yes, John. Photon is extremely important. And interesting. But nothing sensible for 100 years 🙁

    1. It’s the same for the whole of particle physics, Pavel. And for gravity. Trust me, in the future, people will talk about these times as the dark ages of physics.

  6. Alchemy was similar age for chemistry. A lot of hubris, a bit of real knowledge. The reason is same – mixing together different things and fairy tales instead of explanations.
    But, I’m optimistic.
    After alchemy loosed, chemistry began.
    Properties of that complicated particles – molecules and atoms – were investigated and understood. Together by chemists and physicists, from both points of view.
    Atoms and molecules were very complicated objects, but still mankind understood them, it gives hope, John.
    I believe, that chemical and physical approaches, used correctly, are good enough to easily solve also next task in that chain – to learn how and from which the atomic nuclei are constructed.
    The problem exists, of course. Not problem of scientific methods. But tendency of people to go blindly by the way of fairy tales and speculations instead of realistic science.
    Misconceptions are the barriers to true, not methods 🙂

    1. I’m optimistic too, Pavel. Because we have the internet. It means more and more people can “do their own research and think for themself”. And talk to one another. So more and more people know that many of the so-called explanations in physics are fairy tales and lies-to-children. I think the dark-age impasse we’ve suffered from in the last fifty years won’t last much longer.

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