How does gamma-gamma pair production really work?

Question

See the Breit-Wheeler process, wherein two gamma photons are converted into an electron and a positron via a process that's the reverse of electron-positron annihilation. I do not doubt this process. However I'm less confident about the Wikipedia two-photon physics article. It talks about gamma-gamma pair production, and as far as I know it's in line with what some particle physicists say. It says this:

"From quantum electrodynamics it can be found that photons cannot couple directly to each other, since they carry no charge, but they can interact through higher-order processes^{[clarification needed]}. A photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion–antifermion pair, to either of which the other photon can couple".

However as far as I know, a 511keV photon does not spend its life magically morphing into a 511keV electron and a 511keV positron. That’s in breach of conservation of energy. In similar vein the electron and the positron cannot then magically morph back into a single 511keV photon. That's in breach of conservation of momentum. Moreover photons travel at the speed of light whilst electrons and positrons do not - a photon cannot spend its life fluctuating into fermion pairs, if it did it couldn't travel at c. Besides, virtual particles are virtual. As in not real. They aren't short-lived real particles that pop in and out of existence like magic. Instead they only exist in the mathematics of the model. Which is why hydrogen atoms don’t twinkle, and magnets don’t shine. On top of all that pair production surely does not occur because pair production occurred. Spontaneously. Like worms from mud. All in all, this explanation for pair production is woefully inadequate. A better explanation is required. So:

How does gamma-gamma pair production really work?

I will give a 500-point bounty to the least-worst answer to the question. One answer will get the bounty, even if I don't like it.

Answer 1

Quantum field theory does not offer a description of "how" its processes work, just like Newtonian mechanics doesn't offer an explanation of "how" forces impart acceleration or general relativity an explanation of "how" the spacetime metric obeys the Einstein equations.

The predictions of quantum field theory, and quantum electrodynamics (QED) in particular, are well-tested. Given two photons of sufficient energy to yield at least the rest mass of an electron-positron pair, one finds that QED predicts a non-zero amplitude for the process $\gamma\gamma \to e^+ e^-$ to happen. That is all the theory tells us. No "fluctuation", no "virtual particles", nothing. Just a cold, hard, quantitative prediction of how likely such an event is.

All other things - for instance the laughable description in the Wikipedia article you quote - are stories, in this case a human-readable interpretation of the Feynman diagrams used to compute the probability of the event, but should not be taken as the actual statement the quantitative theory makes.

There is no "how", what happens between the input and the output of a quantum field theoretic process is a black box called "time evolution" that has no direct, human-readable interpretation. If we resolve it perturbatively with Feynman diagrams, people like to tell stories of virtual particles, but no one forces us to do that - one may organize the series in another way, may be even forced to do so (e.g. at strong coupling), or one may not use a series at all to compute the probability. The only non-approximative answer to "how" the scattering processes happen in quantum field theory that QFT has to offer is to sit down and derive the LSZ formula for scattering amplitudes from scratch, as it is done in most QFT books. Which, as you may already see from the Wikipedia article, is not what passes as a good story in most circles.

But neither nature nor our models of it are required to yield good stories. Our models are required to yield accurate predictions, and that is what quantum field theory does.

Answer 2

Two photon physics goes through higher order diagrams . Depending on the energy of the gamma rays even gamma gamma colliders are envisaged.

For gamma gamma center of mass energies below the summed mass of electron and positron this is the lowest higher order diagram

This is for all photons of low energy. One can count four electromagnetic vertices which will be multiplying the integral with $(1/137)^{1/2}$, and the whole will be squared to get a crossection. This will be a very small number and that is why effectively for low energies there is no measurable two photon scattering.

When the center of mass energy of the two incoming gammas is larger than twice the electron mass, the dominant diagram will be:

Note that there are now only two electromagnetic vertices for the production of on shell electron and positron. With very energetic photons a large number of particle creation channels open and the crossection of gamma gamma interactions is expected to rise .

Answer 3

However as far as I know, a 511keV photon does not spend its life magically morphing into a 511keV electron and a 511keV positron. That’s in breach of conservation of energy. In similar vein the electron and the positron cannot then magically morph back into a single 511keV photon. That's in breach of conservation of momentum.

I don't know where this huge misconception comes from. Surely not from any of the wiki articles that you linked, or anything written by a physicist ever. Both pair production and particle-antiparticle annihilation are valid physic processes and happen according to all conservation laws known:

• In particle-antiparticle annihilation, the product is always two or more photons. In the rest frame, the electron and positron have the following 4-momentum $$p_{e^-}=(\sqrt{m_e^2+k^2},\vec{k})\qquad p_{e^+}=(\sqrt{m_e^2+k^2},-\vec{k})$$ and the 4-momentum of the two photons is $$p_{\gamma_1}= (q, \vec{q})\qquad p_{\gamma_2}=(q, -\vec{q}) $$ with $q=|\vec{q}|=\sqrt{m_e^2+k^2}$, so energy and momentum are conserved, and the photons travel at $c$ while electron are positron are slower.

• In the Breit-Wheeler pair production, the kinematics is exactly the same (you only have to exchange initial and final states), and therefore all conservation laws are fulfilled.

• The term 'pair-production' is frequently used for another process, which involves only a photon which propagate through a material medium. The photon scatters with an atom with a huge mass, so it can absorb a huge momentum with a neglible change in energy. This setting is a standard exercise in relativistic kinematics, and is left as an exercise for the reader.

In any case, the electron and positron are emitted in oposite directions (in the rest frame), so they're not expected to meet again. Exactly the same goes for the two photons, whith the additional caveat that their paths are much harder to curve. Therefore, it is almost impossible (if not completely impossible) that a pair of photons oscillate into a pair of electron-positron. I guess that your confusion comes from the photon self-energy Feynman diagram

But you have to remember that (real) physics doesn't claim that those internal lines represent anything with ontological meaning. Even if you read the pop-sci articles about virtual particles (don't do that!), they will explain that virtual particles are off-shell, so their energy and momentum are independent, and can be both conserved.

On top of all that pair production surely does not occur because pair production occurred. Spontaneously. Like worms from mud. All in all, this explanation for pair production is woefully inadequate.

Quantum mechanics is a probabilistic theory. Every process has a probability to happen, ranging from 0 (impossible) to 1 (always). But $\{0\}$ is a set of measure 0, so it is incredibly strange for a process to have exactly 0 probability. Unless something else forbids it. The only "something else" that we know is that some conservation law doesn't hold. In the words of Gell-Mann:

Everything not forbidden is compulsory.

We've alredy settled that pair production abides all conservation laws. Therefore, the most plausible conclusion is that pair production happens with a non-zero probability. (Spoiler: If you do the calculations, you will find out that the probability is quite high at high energies).

If you're not convinced of the probabilistic nature of pair production, you have to know that the analysis of electromagnetic showers (which include pair production) in detectors for cosmic rays and particle colliders consists in a Monte Carlo (probabilistic) reconstruction of the processes.

This is the closest to an answer to "why pair production happens?" that science can offer you (and ACuriousMind's answer is the closest to an answer to "how it happens?"). I'm sorry if you're disappointed. The mission of science is to make models of everything that we can observe or detect. Testable models. We cannot see Russell's teapot, or Sagan's garage dragon, or the interior of an event horizon, or what happened before the Big Bang, or what happens during a particle scattering. Not even in principle. Any model that only tried to explain any of those is not testable, and therefore, unscientific. It would be beyond the realm of physics, and if you know something about ethymology, "meta" means beyond, so it is metaphysics.

Why can't we see what happens during an interaction? The only tool that we have to explore the subatomic world are particle detectors, that work by measuring the energy that some particles deposit on them. So, in order to be detected, a particle must be in an (almost) asymptotic final state and its energy and momentum are drastically changed. By measuring, you destroy all the information about any future collision. It is like Achilles-the particle detector trying to chase the tortoise-interaction.

Do you know any non-invasive method to probe the interaction? Congratulations! A Nobel prize and lots of billionaire grants are waiting for you!

Answer 4

I like to offer a simple physical description. Mathematics is perfect for predictions but not very satisfying to the mind who wants to compare everything to normal logic and life experiences, and flatly refuses to believe that nature is not obliged to be logical or simple. Pair production and annihilation is nature's gift to help us explain what is going on not complicate it further.

The fact that an electron and a positron pair can end up into pure radiation with full efficiency and no losses and in a fully reversible process in the form of pair creation, tells us that radiation and matter are two phases of the same thing. The common phrase; radiation condensing to create matter is very expressive in this regard. So let's consider radiation to be evaporated matter, and Einstein equation E=mc^2 as describing this change of phase.

For radiation and matter to be two phases of the same thing however, they need to carry the same attributes.. like water and steam for example. And indeed this is the case. Radiation like matter carries mechanical and electrical attributes. Mechanical attributes in the form of momentum and energy, and electrical attributes in the form of electric and magnetic fields. But it doesn't have a rest mass like matter. However, trap radiation between two mirrors and you get rest mass. Or trap it by making it go round in closed circles for ever, and you also get a rest mass. This last possibility is how radiation turns into matter.

There are many respectable articles speaking of circulating energy fluxes inside the electron, like the work of Hestene for example. The process resembles that of vortex pair creation. There are big similarities between the two, which have been noted by many, with some have even tried to apply the creation and annihilation operators of QM to the vortex generation in fluids. Vortex generation produces a vortex and an anti vortex, and the two on meeting do annihilate each other. What is more, vortex creation need a boundary or a discontinuity in the fluid flow field in order to happen. And in radiation you need a nucleus for condensation to happen. While vortex annihilation does not need a catalyst to happen, so is pair annihilation.

The explanation given is that the catalyst is needed to conserve momentum- true for both vortex and pair creation. But a more mathematical explanation to this is also possible. A free fluid flow follows hyperbolic equations, whereas vortices follow elliptic pdes. The catalyst is what helps the flow to curl and change equation. In pair production, the nucleus is what helps radiation to curl and become matter, as radiation is described by hyperbolic equations(Maxwell), whereas particles are described by elliptic equations(Dirac).

Resulting from the curling of radiation is the appearance of the rest-mass and the rest of the other properties of matter. The rest mass is a result of confinement, and with mass comes gravity too. Trapped radiation need to be in the form of standing waves to avoid annihilation by destructive interference (very much like what de Broglie imagined for the atom). Now standing waves have their electric field pointing in two opposite directions, not in one direction as in waves. Upon circulation the direction becomes radial with a non vanishing divergence as a result- or an electric charge(Gauss theorem). The spin and magnetic dipole moment follows, and the ticking clock of the electron- the Zitterbewegung of Dirac follows too.

Note that the created pair need not annihilate and they could escape each other attractive forces if they had enough kinetic energy. They can even trap each other in motion as in the unstable positronium, which has all the characteristic of an atom. In more favorable conditions higher masses could be created too. The neutron being unstable when free but stable inside a nucleus could be the parallel example.

Answer 5

While scientists have observed photons smashing together and "creating" matter we're just observing matter after photons collide, we really don't know whats happening but we can observe matter that seems to magically appear. We can't see that small and scientists may draw diagrams of photons colliding with lots of fancy arrows and say "yay we made matter"

Whats really happening?

Scientists have drawn up images like these to explain colliding gamma rays creating particles like these.

Evidence for this exists in bubble chambers because this is what we can see. Gamma rays colliding just turn into matter. Poof.

Lets look at Electron-Positron annihilation to start out with.

Above we can see an electron and a positron flying towards each other about to collide. This pair will soon be turned into gamma rays. Right, no wrong!

How exactly does this take place? Standard science texts are silent on the question; only reporting that it happens, but without providing any explanation of the possible mechanisms involved. Unfortunately this is not very helpful. What we need is a slow-motion version of events, particularly what happens at the moment the particles ‘make contact’. There is no way of seeing anything on such a small scale. The best we can do is look at the available evidence and speculate on what could be taking place. Ideally this speculation should be something that makes sense in terms of a classical model. With that in mind, the following is a version of what might be happening.

Close up look:

At this point it appears that the process will repeat itself, then again, and again. Basically the particles will oscillate through each other, as though connected via a spring. Will the oscillation continue forever? This appears to be a frictionless system. As it happens, they won’t oscillate forever. The VDCL (Velocity Dependant Coulomb’s Law) tells us that as oppositely-charged particles move together the force between them decreases. As they move apart the force increases. This effectively acts as a form of damping which will slowly bring the oscillation to a stop.

Eventually stops moving.

After the oscillations have stopped we are left with a sort of ghost particle. It has twice the mass of an electron but more importantly a charge of zero.

It goes without saying that a particle without charge is not going to have much of an impact on anything, nor will it be impacted by anything. For all practical purposes it may as well not exist. And that’s just the point. In electrical terms this composite particle is effectively invisible. The electron and positron have not been annihilated after all. They are still there.

Another quote,

There is one other aspect of the extinction process that needs explaining and that is the emission of photons. To understand this, consider radio transmissions. We know that when you oscillate electrons in an antenna it produces radio waves, which are just low frequency electromagnetic waves. What if that antenna contained both electrons and positrons, and they oscillated in opposing directions? Rather than cancel each other’s signal, the two sets of charges would combine to produce a wave of double the amplitude. Now look again at the electron-positron interaction. They are oscillating through each other, just like in the antenna. Therefore we should also expect them to produce an electromagnetic wave. In this case the frequency would be much higher due to the lightweight nature of the particles involved. It may even be so high as to be in the gamma ray spectrum. Thus the most likely explanation for the emission of photons is that the brief oscillating interaction between these particles produces an electromagnetic wave, or more correctly two waves (one for each particle), which have frequencies in the gamma ray spectrum.

So in conclusion to creating light (energy) from matter, we can't. What's actually happening is that oscillations of positrons and electrons at high speeds create these gamma rays.

So now that we know we can't turn matter into energy, how do we know we can't turn energy into matter?

How do we turn energy into matter? Scientists know (or think they know) it's possible.

For sake of discussion let’s call this composite positron-electron particle a ‘poseltron’. Is there any way for a poseltron to come undone, i.e. to be broken into its constituent particles? One method would be to expose it to a strong electric field which polarized the component particles and pulled them apart. But it would need to be extremely strong because the positron and electron are in direct contact.

So if you shook the two particles together you can possible shake them apart. If there are reactions like this happening it's likely a speeding gamma ray could easily hit a poseltron and shake it apart.

Poseltrons vibrate at the frequency of gamma rays so doesn't it make sense that that same frequency could vibrate them apart?

Lets say poseltrons exist but think about it, how often is an electron going to meet a positron. Not very often so if they do exist then they are probably very widespread.

The low density of poseltrons in nature would also explain why electron-positron pairs are only created occasionally – there needs to be an existing poseltron in place before conversion can occur. Under the current scientific model a photon with enough energy can convert into an electron-positron pair, but would do so for no apparent reason, i.e. at random without cause & effect. This model defies common sense.

Another reason why "poseltrons" exist,

There is another way in which positrons can be created, and that is via a process known as ‘proton conversion’. When Sodium-22, an unstable isotope of sodium, decays it turns into Neon-22. When it does this it also releases a positron and a gamma ray.

Standered theort tells us there are two means of proton conversion. One in wich a proton an and electron form a neutron. The other in which an electron-positron pair being created followed by the electron being absorbed and the positron ejected. When you think about it the second mean of proton conversion is more likely in this case. While protons and electrons probably can join together. According to current theories, Sodium-22 can just magically, out of no where, create this electron positron pair and converts one of its protons into a neutron. Lets say this is true, where is all that energy coming from that you need to create the electron positron pair. The nucleus can't create it unless it has an external source of energy.

So whats really happening?

First a poseltron drifts into the nucleas of the Sodium-22 atom.

The movement caused by strong forces in the atoms nucleus then tears the poseltron apart into an electron and positron. The electron gets absorbed by the proton and it becomes a neutron. The positron is ejected due to it's positive charge and it grabs an electron on the way out or stays as a positron. Gamma rays are generated by the breaking apart oscillations of the poseltron.

So in conclusion,

An electron and positron collide, they meet and pass through each other generating gamma rays and then form an undetectable zero charge poseltron. It's pretty much invisable.

Scientists: "yay we made energy from matter"

All that matter is still there, the energy they created is electromagnetic fields created by oscillation.

Some gamma rays bump into a poseltron by chance, they cause it to shake apart and break up the two particles. At the same time some of this energy has been absorbed by the particles.

Scientist: "yay we made matter from energy, we're so smart"

Nothing has actually been made, the matter just became visable again.

Therefore conservation of mass and conservation of energy have not been broken and the universe makes sense again. Yay

Sorry for spelling errors, this is so long spell check just died. ;)