Two Particles Enter, No Particles Leave!

Seriously, if you don't read xkcd regularly, you need to examine your life.

In an ordinary copper wire such as you might find in power cords and running through the walls of your house, electrons carry current, flowing around the atoms of the copper. One of the ironies in the history of science (which has frustrated students of physics and electrical engineering for over a century) is that even though electrons are negatively-charged in our system, we think of current as a flow of positive charge. In other words, our standard model for the flow of electricity is opposite to the actual motion of the particles that carry the current. (We ultimately have Benjamin Franklin to blame for this problem, though we shouldn’t be too hard on him: when he established the convention for positive and negative charges in the 18th century, he didn’t know about the existence of electrons.)

Negative charges moving to the right and (equal) positive charges moving to the left both represent a current flowing to the left. Changing the direction of motion is a change in parity.

Most of the time, it doesn’t matter that we think of current as the motion of positive charges: in introductory physics and in many advanced physics classes, we ignore the microscopic reality because the math works out either way. The reason we can cheat is because simultaneously swapping the direction of charge motion and the type of charge cancels out the discrepancy. It’s like if you multiply two negative numbers together: (-2)×(-5) = 2×5 = 10. Simultaneously changing the sign of both numbers you multiply doesn’t change the product.

The change in direction is known as parity, which we write as P, and the change in charge is C. We could imagine a universe in which electrons do have positive charge, and protons are negatively charged. This is an antimatter universe: we would be exchanging electrons for positron and protons for antiprotons, and it might surprise you how little changes in such a universe. Electric current would flow the same way it does in our world, so changing both C and P at once keeps things the same as far as the wiring in our houses is concerned—and also for the structure of atoms. The combined symmetry is (shockingly!) known as CP. Nevertheless, while a universe with CP reversed would look very similar to ours, it turns out some types of particle decays would not be the same. In other words, if the cosmos mischievously swapped matter for antimatter, we still would be able to experimentally distinguish it from the universe we live in now.

From a fundamental physics point of view, whether CP is violated or not depends on what kind of forces are involved: electromagnetic interactions (which govern the structure of atoms and the flow of electricity in your house), gravity, and the strong nuclear force all preserve CP, while in rare cases the weak nuclear force doesn’t respect CP. The weak interactions also separately violate C and P, but that’s a story for another day; the main thing we care about is the combination of the two symmetries, and nearly every interaction we’ll ever run across, even in exotic experiments, will respect CP.

Antimatter and Spacetime

To put things another way: the behavior of particles is deeply connected to the structure of spacetime. In the 1920s and ’30s, when physicists began working out how relativity and quantum physics could be combined, they found a problem: matter as it was understood was unstable. In quantum mechanics, particles seek a state with the lowest amount of energy (known as the “ground state”), but in relativity, there is no such thing: energy can keep going lower and lower forever. That means a particle would keep decreasing in energy, emitting photons—violating everything we know about Nature.

English physicist Paul Dirac solved that problem by introducing antimatter, which is the mirror image of matter: now instead of energy plummeting forever, the negative energies correspond to a different set of particles. When one of these new particles meets the ordinary sort, they annihilate, producing a burst of energy corresponding to their masses and how fast they are moving relative to each other. Antimatter particles have the opposite charge to their ordinary matter companions, but everything else is the same: positrons are positively charged, but they have exactly the same mass as electrons.

So far, I’ve been talking about matter, but what about photons? Much of what I’ve said is true for photons as well, but there’s a big twist: photons have no mass and no charge. That means photons must be their own antiparticles: if two photons meet, they can annihilate each other. Since the product of this annihilation is often more photons, this isn’t as big a deal as it might sound, but under some conditions, the annihilation can make pairs of particles and antiparticles. Pair-production (as it is called) is the key to a number of physical phenomena.

The Varieties of Fermions

There’s another difference between photons and matter, however: photons are bosons and matter as we know it is made of fermions, a distinction based on the type of spin they have. Photons are spin-1 particles, which is what we think of as “normal”: a rotation by 360° brings them back to their original configuration. Fermions like electrons, on the other hand, are spin-1/2 particles: two full rotations are required to restore them to their initial orientation. (For more information about this, see my earlier post “Spinning Electron Got to Go Round“.) The spin in turn dictates how they interact: bosons can all pile together into a single quantum state, but only one fermion can fit into a single quantum state, a property known as the Pauli exclusion principle.

While combinations of fermions can be bosons (which is why it doesn’t take a human being two full rotations to return to our original configuration), every bit of ordinary matter is built up of fermions. Quarks are fermions: combinations of them create protons and neutrons (themselves fermions) and mesons (which are bosons). Electrons are fermions, as are neutrinos. Atoms can be either fermionic or bosonic, but if you have enough of them together, they almost always act like bosons. (When my friends and I get together, we act like bosons too.) Dark matter may or may not be fermionic—we don’t know enough about it to tell one way or the other—but it’s certainly not made of quarks.

Even within spin-1/2 fermions, there are distinctions where things can get even more fun. The normal type are known Dirac fermions, which means that they have mass and that the particles and antiparticles are distinguishable from each other. Quarks and electrons are Dirac fermions: they all have mass and since they are charged, their antiparticles have opposite electric charge. If any massless fermions exist, they fall into the category of Weyl fermions (for the German mathematician Hermann Weyl usually pronounced “vile” in English, unfortunately); for many years, neutrinos were commonly considered to be Weyl fermions, but we know now they have mass.

However, there’s still one option: a third type of fermion is its own antiparticle. These are the Majorana fermions, named for Italian physicist Ettore Majorana (whose death is still a bizarre mystery decades later). Majorana fermions are electrically neutral, which is a necessary requirement for a particle being its own antiparticle, though not a sufficient one: after all, neutrons are neutral, but they are decidedly Dirac fermions. One way to tell if neutrinos and antineutrinos are the same is by observing a particular type of nuclear process known as “double beta decay”. In this process, a single nucleus emits two electrons and two (anti)neutrinos; if the neutrinos are missing, then that’s a pretty good clue they annihilated each other, meaning they are Majorana fermions. Since neutrinos are difficult to detect, all double beta decay experiments to date are inconclusive.

Dirac, Weyl, and Majorana fermions all reflect different symmetries—including spacetime symmetries, due to the CP symmetries or lack thereof, as mentioned above.

Fun With Quasiparticles

To summarize: the only types of elementary fermions known are Dirac fermions, with neutrinos possibly being either Dirac or Majorana. But elementary particles aren’t the only place where the fun can happen! Within materials, electrons and atoms can interact in ways that aren’t available to free particles, largely due to the density. Especially at low temperatures, electrons can act collectively, producing quantum states that are bizarre and wonderful. These quantum states themselves act like particles, so they are known as quasiparticles. They can move around, interact with each other, be created and destroyed (even without antimatter anywhere in the system!). They can have mass or be massless, charge or be neutral. While some people may disagree, I think of quasiparticles as being every bit as real as the electrons that give rise to them: you can do experiments on them and they have definite measurable properties.

So, while Majorana fermions may or may not exist as elementary particles, they may exist as quasiparticles. I recently covered a story for Ars Technica about the possible creation of Majorana quasiparticles in a hybrid semiconductor-superconductor system. These were particle-like states that were trapped at two locations in the material; they didn’t budge when prodded with electric or magnetic fields, which means they are electrically neutral. The researchers didn’t make them annihilate each other (since they were trapped, after all), so they will have to do further measurements to confirm these are actually Majorana fermions and not some other type of quasiparticle. However, since Dirac quasiparticles are known to exist in some materials, I have high hopes that Majorana fermions will be found.

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8 Responses to “Two Particles Enter, No Particles Leave!”


  1. 1 bryansanctuary April 26, 2012 at 13:47

    Nice summary: question: Spin emerges from the Dirac field. It can only be found in the presence of an interaction, a small magnetic probe. How do we know that as observed is the same as the spin in the absence of the probe?

    The probe changes the symmetry of the space, so does this symmetry change the observed spin and if so, how?

    • 2 Matthew R. Francis April 26, 2012 at 14:49

      Well, I’d turn this question around slightly: I do think of the electron as having spin apart from measurement, and spin is intimately connected to the geometry of spacetime. The interaction between the spin and the magnetic probe is what we measure, but there’s no change in symmetry: we’re just measuring with respect to our apparatus. Does that make sense?


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