Quantum field theory and pair creation/annihilation

The creation and annihilation of matter-antimatter pairs is usually taken as proof that, somehow, fields can condense into matter-particles or, conversely, that matter-particles can somehow turn into light-particles (photons), which are nothing but traveling electromagnetic fields. However, pair creation always requires the presence of another particle and one may, therefore, legitimately wonder whether the electron and positron were not already present, somehow.

Carl Anderson’s original discovery of the positron involved cosmic rays hitting atmospheric molecules, a process which involves the creation of unstable particles including pions. Cosmic rays themselves are, unlike what the name suggests, no rays – not like gamma rays, at least – but highly energetic protons and atomic nuclei. Hence, they consist of matter-particles, not of photons. The creation of electron-positron pairs from cosmic rays also involves pions as intermediate particles:

1. The π+ and π particles have net positive and negative charge of 1 e+ and 1 e respectively. According to mainstream theory, this is because they combine a u and d quark but – abandoning the quark hypothesis[1] – we may want to think their charge could be explained, perhaps, by the presence of an electron![2]

2. The neutral pion, in turn, might, perhaps, consist of an electron and a positron, which should annihilate but take some time to do so!

Neutral pions have a much shorter lifetime – in the order of 10-18 s only – than π+ and π particles, whose lifetime is a much more respectable 2.6 times 10-8 s. Something you can effectively measure, in order words.[3] In short, despite similar energies, neutral pions do not seem to have a lot in common with π+ and π particles. Even the energy difference is quite substantial when measured in terms of the electron mass: the neutral pion has an energy of about 135 MeV, while π+ and π particles have an energy of almost 140 MeV. To be precise, the difference is about 4.6 MeV. That is quite a lot: the electron rest energy is 0.511 MeV only.[4] So it is not stupid to think that π+ and π particles might carry an extra positron or electron, somehow. In our not-so-humble view, this is as legitimate as thinking – like Rutherford did – that a neutron should, somehow, combine a proton and an electron.[5]

The whole analysis – both in the QED as well as in the QCD sector of quantum physics – would radically alter when thinking of neutral particles – such as neutrons and π0 particles – not as consisting of quarks but of protons/antiprotons and/or electrons/positrons cancelling each other’s charges out. We have not seen much – if anything – which convinces us this cannot be correct. We, therefore, believe a more realist interpretation of quantum physics should be possible for high-energy phenomena as well. With a more realist theory, we mean one that does not involve quantum field and/or renormalization theory.

Such new theory would not be contradictory to the principle that, in Nature, the number of charged particles is no longer conserved, but that total (net) charge is actually being conserved, always. Hence, charged particles could appear and disappear, but they would be part of neutral particles. All particles in such processes are very short-lived anyway, so what is a particle here? We should probably think of these things as an unstable combination of various bits and bobs, isn’t it? 😊

So, yes, we did a paper on this. And we like it. Have a look: it’s on ResearchGate, academia.edu, and – as usual – Phil Gibb’s site (which has all of our papers, including our very early ones, which you might want to take with a pinch of salt). 🙂


[1] You may be so familiar with quarks that you do not want to question this hypothesis anymore. If so, let me ask you: where do the quarks go when a π± particle disintegrates into a muon-e±?

[2] They disintegrate into muons (muon-electrons or muon-positrons), which themselves then decay into an electron or a positron respectively.

[3] The point estimate of the lifetime of a neutral pion of the Particle Data Group (PDG) is about 8.5 times 10-17 s. Such short lifetimes cannot measured in a classical sense: such particles are usually referred to as resonances (rather than particles) and the lifetime is calculated from a so-called resonance width. We may discuss this approach in more detail later.

[4] Of course, it is much smaller when compared to the proton (rest) energy, which it is about 938 MeV.

[5] See our short history of quantum-mechanical ideas or our paper on protons and neutrons.

The Charge Conservation Principle and Pair Production

The creation of an electron-positron pair out of a highly energetic photon – the most common example of pair production – is often presented as an example of how energy can be converted into matter. Vice versa, electron-positron annihilation then amounts to the destruction of matter. However, if John Wheeler’s concept of ‘mass without mass’ is correct – or if Schrödinger’s trivial solution to Dirac’s equation for an electron in free space (the Zitterbewegung interpretation of an electron) is correct – then what might actually be happening is probably simpler—but also far more intriguing.

John Wheeler’s intuitive ‘mass without mass’ idea is that matter and energy are just two sides of the same coin. That was Einstein’s intuition too: mass is just a measure of inertia—a measure of the resistance to a change in the state of motion. Energy itself is motion: the motion of a charge. Some force over some distance, and we associate a force with a charge. Not with mass. In this interpretation of physics, an electron is nothing but a pointlike charge whizzing about some center. It’s a charge caught in an electromagnetic oscillation. The pointlike charge itself has zero rest mass, which is why it moves about at the speed of light.[1]

This electron model is easy and intuitive. Developing a similar model for a nucleon – a proton or a neutron – is much more complicated because nucleons are held together by another force, which we commonly refer to as the strong force.

In regard to the latter, the reader should note that I am very hesitant to take the quark-gluon model of this strong force seriously. I entirely subscribe to Dirac’s rather skeptical evaluation of it:

“Now there are other kinds of interactions, which are revealed in high-energy physics and are important for the description of atomic nuclei. These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion. Theories of them have been set up and much developed and useful results obtained from them. But in the absence of equations of motion these theories cannot be presented as a logical development of the principles set up in this book. We are effectively in the pre-Bohr era with regard to these other interactions.”[2]

I readily admit he wrote this in 1967 (so that’s a very long time ago). He was reacting, most probably, to the invention of a new conservation law (the conservation of strangeness, as proposed by Gell-Mann, Nishijima, Pais and others) and the introduction of many other ad hoc QCD quantum numbers to explain why this or that disintegration path does or does not occur. It was all part of the Great Sense-Making Exercise at the time: how to explain the particle zoo?[3] In short, I am very reluctant to take the quark-gluon model of the strong force seriously.

However, I do acknowledge the experimental discovery of the fact that pairs of matter and anti-matter particles could be created out of highly energetic photons may well be the most significant discovery in post-WW II physics. Dirac’s preface to the 4th edition of the Principles of Quantum Mechanics summarized this as follows:

“In present-day high-energy physics, the creation and annihilation of charged particles is a frequent occurrence. A quantum electrodynamics which demands conservation of the number of charged particles is, therefore, out of touch with physical reality. So I have replaced it by a quantum electrodynamics which includes creation and annihilation of electron-positron pairs. […] It seems that the classical concept of an electron is no longer a useful model in physics, except possibly for elementary theories that are restricted to low-energy phenomena.”

Having said this, I think it’s useful to downplay Dr. Dirac’s excitement somewhat. Our world is governed by low-energy phenomena: if our Universe was created in a Big Bang – some extremely high-energy environment – then it happened 14 billion years or so ago, and the Universe has cooled down since. Hence, these high-energy experiments in labs and colliders are what they are: high-energy collisions followed by disintegration processes. They emulate the conditions of what might have happened in the first second – or the first minute, perhaps (surely not the first day or week or so) – after Creation.[4]

I am, therefore, a bit puzzled by Dr. Dirac’s sentiment. Why would he think the classical concept of an electron is no longer useful? An electron is a permanent fixture. We can create and destroy it in our high-energy colliders, but that doesn’t mean it’s no longer useful as a concept.

Pair production only happens when the photon is fired into a nucleus, and the generalization to ‘other’ bosons ‘spontaneously’ disintegrating into a particle and an anti-particle is outright pathetic. What happens is this: we fire an enormous amount of electromagnetic energy into a nucleus (the equivalent mass of the photon has to match the mass of the electron and the positron that’s being produced) and, hence, we destabilize the stable nucleus. However, Nature is strong. The strong force is strong. Some intermediate energy state emerges but Nature throws out the spanner in the works. The end result is that all can be analyzed, once again, in terms of the Planck-Einstein relation: we have stable particles, once again. [Of course, the positron finds itself in the anti-Universe and will, therefore, quickly disappear in the reverse process: electron-positron annihilation.]

No magic here. And – surely – no need for strange QCD quantum numbers.

Jean Louis Van Belle, 28 July 2019

[1] Erwin Schrödinger stumbled upon the Zitterbewegung interpretation of an electron when he was exploring solutions to Dirac’s wave equation for free electrons. It’s worth quoting Dirac’s summary of it: “The variables give rise to some rather unexpected phenomena concerning the motion of the electron. These have been fully worked out by Schrödinger. It is found that an electron which seems to us to be moving slowly, must actually have a very high frequency oscillatory motion of small amplitude superposed on the regular motion which appears to us. As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light. This is a prediction which cannot be directly verified by experiment, since the frequency of the oscillatory motion is so high and its amplitude is so small. But one must believe in this consequence of the theory, since other consequences of the theory which are inseparably bound up with this one, such as the law of scattering of light by an electron, are confirmed by experiment.” (Paul A.M. Dirac, Theory of Electrons and Positrons, Nobel Lecture, December 12, 1933)

[2] P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 4th revised edition, Chapter XII (Quantum Electrodynamics), p. 312.

[3] Feynman’s 1963 Lecture on K-mesons (http://www.feynmanlectures.caltech.edu/III_11.html#Ch11-S5) is an excellent summary of the state of affairs at the time. The new colliders had, effectively, generated a ‘particle zoo’, and it had to be explained. We think physicists should first have acknowledged that these short-lived particles should, perhaps, not be associated with the idea of a (fundamental) particle: they’re unstable. Transients, at best. Many of them are just resonances.

[4] I use the term ‘Creation’ as an absolutely non-religious concept here: it’s just a synonym of the presumed ‘Big Bang’. To be very clear on this, I am rather appalled by semi-scientific accounts of the creation of our world in terms of the biblical week.