The hole in the heart of quantum electrodynamics

Pair production is the creation of a particle and its antiparticle. Some say it was first observed in 1929, but it’s usually accredited to Carl Anderson in 1932. He used a cloud chamber and an electromagnet to investigate cosmic rays. He effectively split a gamma photon over an atomic nucleus to create an electron and an antielectron. He called the latter the positive electron, which was soon shortened to positron:

Image from schoolphysics

However whilst he realised that he’d discovered the positron, he didn’t realise that he’d performed pair production. See the APS physics article Focus: Landmarks: The First Antiparticle. It tells how “learning of Anderson’s discovery, Patrick Blackett and Giuseppe Occhialini, also at Cambridge, conducted cloud-chamber experiments in which they saw simultaneous production of positive and negative electron pairs in cosmic ray collisions”. Also see Blackett and Occhialini’s paper presenting some photographs of the tracks of penetrating radiation. You need a gamma photon with an energy of over 1022 keV to perform electron-positron pair production, because the electron and positron have a mass of 511keV/c² each. They also need some kinetic energy to fly apart, and some energy is lost to the nucleus by virtue of conservation of momentum.

Dirac’s 1931 prediction

The experimental discoveries were timely. They confirmed Dirac’s 1931 prediction. This was perhaps a lucky break for Dirac, who had arguably moved the goalposts in response to Oppenheimer’s 1930 paper on the theory of electrons and protons. But no matter, in his quantised singularities in the electromagnetic field, Dirac said this: “we may call such a particle an anti–electron. We should not expect to find any of them in nature, on account of their rapid rate of recombination with electrons, but if they could be produced experimentally in high vacuum they would be quite stable and amenable to observation. An encounter between two hard γ–rays (of energy at least half a million volts) could lead to the creation simultaneously of an electron and anti-electron”. Dirac referred to an encounter between “two hard γ–rays” or two gamma photons. It’s a more purist procedure than splitting one gamma photon over a nucleus and turning it into an electron and a positron. It’s known as gamma-gamma pair production or two-photon physics, and is typified by the Breit-Wheeler process dating from 1934. Two gamma photons are converted into an electron and a positron via a process that’s the reverse of electron-positron annihilation. It was performed indirectly at SLAC in 1997. More recently physicists at Imperial College London have proposed a more direct method. See the press-release article scientists discover how to turn light into matter after 80-year quest. It says “this experiment would recreate a process that was important in the first 100 seconds of the universe and that is also seen in gamma ray bursts, which are the biggest explosions in the universe and one of physics’ greatest unsolved mysteries”. The light-into-matter quest has been going for more than 80 years since those heady days of the nineteen thirties. If you go back to Skobeltsyn in 1929 it’s 89 years. If you go back to Einstein’s E=mc² paper in 1905 it’s 113 years. And if you go back to Newton’s Opticks query 30 in 1704, it’s 314 years and counting: “are not gross bodies and light convertible into one another?” Yes they are, in pair production and annihilation:

Images from Ethan Siegel’s starts with a bang, image credit © Addison-Wesley, retrieved from J Imamura / U of Oregon

Gross bodies are also converted into light in gamma ray bursts. They aren’t much of a mystery once you know why matter falls down, but we’ll come back to that. Meanwhile the important question is how does pair production actually work? Perhaps surprisingly, there seems to be no official answer to this at present. Perhaps even more surprisingly, there seems to be no official question either. Back in 1927 Dirac came up with second quantization, which includes creation and annihilation operators, which add or remove a particle from the many-body system”. In gamma-gamma pair production, the annihilation operator makes the photons disappear, and the creation operator makes the electron and positron appear. It might be beautiful mathematics, but it isn’t physics. It offers no explanation of how pair production works, and as such is no better than magic. In fact, it’s worse, because the story goes that particles materialise and dematerialise, which is lies to children.

Two-photon physics

Take a look at the Wikipedia two-photon physics article. It talks about gamma-gamma pair production, and it’s in line with what particle physicists say. It originates from the HEP group at UCL. Their 1997 small tutorial in gamma-gamma physics says this: “From classical electrodynamics we know that EM waves pass through each other without any interference. From Quantum Electro Dynamics (QED) we know that photons cannot couple directly to each other, since they don’t carry charge, but they can interact through higher order processes: a photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion/anti-fermion pair, to either of which the other photon can couple”. It sounds reasonable enough, especially since it matches the Feynman diagram:

Twisted Feynman diagrams from Rod Nave’s hyperphysics

See the diagram on the right. Two photons enter from the bottom, then the leftmost photon fluctuates into a positron and an electron. This electron then absorbs the other photon, whereupon the positron and the electron depart the scene. However when you stop and think for a minute, this is most definitely lies-to-children. It’s fairy tale physics. Not just because the positron has an arrowhead going the wrong way because it’s supposed to be an electron going back in time. But because a 511keV photon does not spend its life fluctuating into a fermion/antifermion pair. A 511KeV photon does not magically morph into a 511keV electron and a 511keV positron. That’s in breach of conservation of energy. In similar vein a 511keV electron and a 511keV positron cannot magically morph back into a single 511keV photon. That’s in breach of conservation of energy and conservation of momentum. And conservation of angular momentum too. Moreover photons travel at the speed of light whilst electrons and positrons don’t. So if a photon did somehow manage to fluctuate into a fermion pair and back again, it couldn’t be travelling at the speed of light. Some will say that’s OK, the initial electron was off shell, so we don’t have to trouble ourselves with tedious little matters like conservation of energy. Only we do, because there are no perpetual motion machines. And because virtual particles are virtual. As in not real. The clue is in the name. Virtual particles aren’t short-lived real particles that obligingly pop in and out of existence spontaneously, like worms from mud. Instead they only exist in the mathematics of the model. That’s why hydrogen atoms don’t twinkle, and why magnets don’t shine. And for the cherry on top, pair production does not occur because pair production occurred. Spontaneously, like worms from mud. That’s what this official explanation of pair production is saying. It is not satisfactory. Not by a long chalk.

The hole in the heart of quantum electrodynamics

When you probe further you find that there are no other explanations forthcoming. Some particle physicists will say pair production occurs because two-photon physics goes through higher-order processes. Some will say it occurs because pair production is probabilistic. Some will even say physics only needs to yield accurate predictions, and doesn’t need to offer any explanation or understanding. Some physicists are emphatic about this, and dismiss any call for explanation or understanding as mere philosophy. It’s a strange state of affairs. Particularly when it’s clear that photons interact with photons. You started with two photons, you ended up with an electron and a positron. Ergo the two photons interacted, QED. That’s the quod erat demonstrandum QED. The quantum electrodynamics QED says they don’t. It says electron-positron attraction occurs because the electron and the positron are exchanging photons. They aren’t. And when they annihilate it isn’t because they exchange an electron. Electron-positron pair production does not occur because one of the photons turns into a positron and an electron which then interacts with the other photon. QED even gets Compton scattering wrong. The electron doesn’t emit one photon then absorb another photon and change direction. The electron and the photon interact directly, and when you understand the photon and the electron you can understand how. Just as you can understand how photons interact directly and how gamma-gamma pair production works. Sadly Feynman called QED the strange theory of light and matter. He said “my physics students don’t understand it either. That is because I don’t understand it. Nobody does”. It would seem this situation persists. Even though we do physics to understand the world, not to shut up and calculate.

Image based on US Postal service stamp, see The Story Behind the Stamp by Kate Repantis

The issue here is that QED describes the interaction between light and matter, but not the interaction between light and light. On page 193 of their book climbing the mountain: the scientific biography of Julian Schwinger, Jagdish Mehra and Kimball Milton say Wolfgang Pauli proposed a solution for the infinite charge density problem. They also say this: “in the resulting improved theory, not only was the picture of the vacuum simple again, but there were now only three fundamental interactions between the electrons, the positrons, and the photons: the scattering of the fermion with the emission or absorption of the photon, and the annihilation or creation of the electron–positron pair with the emission or absorption of the photon”. The interaction between photons had gone. Pauli had thrown out the baby and kept the dirty bathwater. Because that new improved picture wasn’t just simple, it was wrong. Because it didn’t describe what actually happens in gamma-gamma pair production. It still doesn’t. Even to this day quantum electrodynamics offers no picture of what happens in gamma-gamma pair production, and hides this deficiency with lies to children. Because it still relies on its canonical creation and annihilation operators, and so absolutely misses the crucial point that waves interact.


This Post Has 8 Comments

  1. John Duffield

    As for how they interact, I fear it’s simpler than people think. Much simpler…

  2. CG

    1.) “You are not authorized to access this page “content/139/839/699″.” – that’s what it says, for me, under the link hiding behind “some photographs of the tracks of penetrating radiation.” (2nd paragraph)

    2.) link behind “paper on the theory of electrons and protons” demands a subscription to read; now — maybe that’s just me, but I usually avoid signing up everywhere for one-time-purposes; not even sure, if just anybody was allowed to sign up there.

    3.) on behalf of this article itself:
    ““this experiment would recreate a process that was important in the first 100 seconds of the universe” – I never quite understood that logic. Physicists seem hard-pressed to give an answer, where all the supposed antimatter went (later on), how we could have ended up with so much matter, but hardly any/no natural occurring antimatter (at least none that presents itself to us, visibly, in large quantities; some suggest antimatter galaxies, but that seems like a strange idea; for matter to gobble up here, antimatter there, and matter after that again, all neatly separated… was there some gathering-cry of racist particles, to flock together with “their own kin”, only? – bizarre!); which always left me baffled, as it would logically follow, that they have it backwards about the big bang creating matter via such a pair-method… if this method was the way to go, and you cannot explain how the antimatter supposedly “disappeared” [while matter, oddly, did not] – doesn’t that strongly (!) imply, that your premise must be wrong? – prompting the conclusion, that matter DID NOT in fact form in pairs during the big bang and its supposed aftermath, but through some [entirely] different process?!?

    4.) ” And because virtual particles are virtual. As in not real. ” you wrote that paragraph – for the most part – under another article, also; with that exact wording…

    5.) “Some will say it occurs because pair production is probabilistic.” – so… does that concern “vacuum fluctuations” (i.e. as a mere mathematical probability)? – which is to say: do you claim, vacuum fluctuations aren’t real?

    6.) “…He said “my physics students don’t understand it either. That is because I don’t understand it. Nobody does”. It would seem this situation persists. Even though we do physics to understand the world, not to shut up and calculate…” huh… that strangely reminds me of my physics-teacher in 12th/13th grade; he also never cared much to make us understand anything; we just needed to learn the formulas [w/o much of an in-depth explanation to it] and calculate… and keep our workbooks in order, for he would collect them and grade us for it . When form trumps understanding [in natural sciences], something’s amiss…
    He was even cocky about any attempts of mine to ask in-depth questions (that “that’s philosophy”-sentiment could have come from him; but he wasn’t even THAT quick-witted in embellishing his ignorance) … boy, that teacher really ruined the fun I once felt for that subject…

    … which reminds me: may I ask you, who your preferred target-audience was?

    PS: sorry for the length

    1. the physics detective

      1) Fixed. Maybe it was just my typo.
      2) Click on “paper” preceding the title.
      3) I think I know where the antimatter is.
      4) I like saying virtual particles are virtual. As in not real.
      5) Vacuum fluctuations are real. But they aren’t the same thing as virtual particles.
      6.) All points noted. Understanding is not mere philosophy. You can understand it. And rediscover the fun.
      I don’t really have a preferred target audience. I’d just like to do something useful. If pushed I would say I’d like to reach out to non-particle-physics physicists.
      NB: I had a problem with the recaptcha not responding. Sorry about that. I’ll look into it, but later. I have to go out now. Oh, it worked when I tried again. Humble apologies to anybody who has lost a comment.

      1. CG

        “Understanding is not mere philosophy.” — where did I say something was “MERE philosophy”? – that’s your line of thinking, not mine (or at least your words, not mine). I think way too fondly of the greats of philosophy, to ever feel like that (and, to be frank, I wouldn’t give too much about Einstein, if it wasn’t for his second nature as a philosophical mind; rather than a “mere” scientist), besides the fact, that academic philosophy seems to be overrun by quacks and blatherskites. All I alluded to was, that OTHERS think that lowly of philosophy, and others, yet again, contribute to a bad reputation of said “field”; and as it stands, I lost the eagerness to always clarify that difference in advance, but just let it slide, that some don’t understand or want to understand, what love for wisdom means…
        “You can understand it. And rediscover the fun.” – brains structure themselves in certain ways, which are better suited to answer some problems rather than others. Deviating from something, that once teased your brain, like in reaction to boring/bad teachers, depression, trauma or a new, different, all encroaching objects of fascination, can, if it happens early on in one’s path, shut oneself out from the “natural” access one once had to those sort of problems one left behind, and keep you stranded in a totally different universe of thought… – if that doesn’t sound to philosophical.
        – no offense!

        1. The physics detective (John Duffield)

          You didn’t say understanding was mere philosophy. Others do. I share your sentiments re philosophy, and I remind those others that a doctorate is a PhD.

  3. CG

    I should really avoid the “smaller than/larger than” operators for comment-brackets… they just disappear :/

  4. Andy Hall

    John, having read the paper by Dirac on Quantised singularities in the magnetic field it gives a quite profound insight into the mind of a mathematician who tinkers with the idea of what nature might be doing. Instead of entertaining a model where a region in total that has an entry point and an exit point for magnetic potential, with those two point being the positive and negative or north and south poles, he likes to imagine that because he can describe the field strength at each point individually that “Nature” would also make the same observation and therefore we could expect to find magnetic monopoles. He is obsessed with the form of the mathematical description and contains each term he can define as a physically seperate entity, real in its own right. So just because the mathematics has terms for North and South poles they do not need to occur in pairs. This is a bit like saying a need just the end of hose pipe because that is the bit that squirts out the water. It would make a perfect supply for a showerhead. By the same token I could manufacture the inlet ends of hose pipes and supply them to mariners for use as bilge pumps. Better than ordinary bilge pumps because they take in water and make it disappear. It we reconnect the bilge pump inlet to the shower head outlet though a wormhole or some other connection at a distance device, readily unavailable in your local hardware store we can satisfy the conservation of water laws and everyone is happy. The means of transference only needs to be a conservative statement representing a zero sum and the mathematicians are happy, I don’t understand how the two parts are connected and the physical means by which the water disappears at one point and reappears somewhere else, but that is a mere inconvenience of otherwise perfect mathematics. Which is all a mathematician moonlighting as a physicist needs to concretely justify his position. Electromagnetic waves move quite happily through vacuum space without needing electrons to create the magnetic effect that is coupled with the change in electric potential with distance that defines the wave. The electric and magnetic potential variations are mutually causal, if phase shifted, and comprise the physical mechanism of the propagation of energy in vacuum. Vacuum is the medium that support the propagation. Hence, the interaction of changes in electric magnetic fields in vacuum, which is not nothing, just space with very low energy density, precedes to formation of electromagnetic structures of higher density. If you take the right frequency of energy say 511 KeV and loop it back on itself in 2 dimensions it will form an electromagnetic structure that is a standing wave of electromagnetic wave potential. Understanding that any propagation of electromagnetic potential has a helical magnetic field associated with it leads to a much simpler understanding of how the magnetic field of an electron arises. In structure it is like a bar magnet in terms of it magnetic field and its charge is the variation of electromagnetic potential around its equator. When, als consider that it has mass and therefore sinks into a potential box of its own making, you have that origin of the beginnings of the box that Schroedinger put the electron in. That particular box is an atom but it the suggestion that mass is a persientent local dip in electromagnetic potential from the reference of electromagnetic potential at the speed of light in your local vacuum is an appealing one for me. It is the beginning of a potential well that you can pump more electromagnetic waves into and trap them as more dense standing wave forms.

    Diracs talk of phase integrability and zero differences around a closed loop could easily be the conditions for a standing wave than correctly has its end join up with its beginning. Hence the various wave states he is on about can be multiple overlays of energy into the same basic structure seperating out by local potential based on the number of electron structures that are overlaid.

    You asked me what UML stood for in a previous question and I should have the courtesy to put the answer there. But for now I think it is also pertinent to this issue. UML is universal modelling language and is one of the notations that has become popular is software architecture description, meta-modelling and the effort to auto generate code from diagrammatic sources. It has also come into scope for the effort to unify the disciplines of systems and software engineering. I am a systems engineer that studied electrical and electronic engineering at university. I was always intrigued by the difference between electrical, mechanical and chemical energy because we are taught to readily convert between them and treat them as equivalent in many ways but then are told them are fundamentally different.

    The reason I have really taken to UML is that it give me that ability to clearing differentiate between a physical instantiation of a thing, a logical abstraction of it that conforms to it on a part for part basis and the concept of the thing. The concept is just it name, the logical definition provides the numerical description in purely abstract but numerically concrete form and the physical description maps the logical attributes of the concept to the real and measurable attributes of a thing in the real world. UML has sufficient power of relations for abstraction to be clear when we are talking about something real like the distribution of electric and magnetic potential in space or something abstract like the point of the centre of mass of an electron (the centre of distribution about which the standing wave of circulating electromagnetism is centred).
    Without such a formalism one is very likely to get completely and utterly lost in the maths. Atoms are not point particles just like electrons are. That is simply a convenient mathematical abstraction for many purposes. It is also the reason that the classical approaches to physics fail when effects get close to energies involving the size of atoms. Mathematicians should only be allowed to participate in physics under close supervision. Unfortunatley it appears they long since overran the field.

    1. John Duffield

      All points noted Andy. I was surprised when I actually read Dirac’s papers for the first time. I thought they’d be insightful and brilliant, but they were absolutely dire. IMHO he had no concept of what an electron was, and didn’t want one. See the Kurt Gottfried quote in Yes, all he cared about was mathematical beauty, and to hell with the physics. He proposed monopoles because he didn’t understand electromagnetism. I like your analogy of manufacturing the inlet end of hose pipe – bilge is the word all right. But note that the electric and magnetic potential variations are not mutually causal, because it’s electromagnetic wave potential. Yes, loop a 511keV wave back on itself and you’ve got a standing wave standing field thing called an electron. Or a positron. And yes, that vacuum is not nothing. But IMHO the key to it is that light is also displacement current, and displacement current does what it says on the can. Did you see what Schrodinger said about a wave group which in some way gets into a small closed path? Electron mass is just resistance to change-in-motion for a wave in a closed path. It’s that simple. The electron is light in a box of its own making. Add a photon and it’s in an asymmetric closed path, so the electron moves.
      Understood re UML. I work in IT. But it doesn’t float my boat like physics does. Yes, all those types of energy are at the fundamental level the same. (Hmmn. I don’t have an article on energy). Yes, I agree that contemporary physics is lost in maths. That’s why we have braneworld and the multiverse, but no electron model. Closer to home my nephew did a physics degree and came out disillusioned because it was all maths and no physics.

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