Although most particles disintegrate [the technical term is ``decay''] into other particles, a few types of particles do not. Why not?
The world exhibits many types of particles — you can read about a lot of the (apparently-)elementary particles here, and there are lots of other particles which you can build out of more elementary ones, like protons and neutrons and atomic nuclei — but most of them decay in a tiny fraction of a second. I’ve explained in a previous article why most particles decay; it’s actually a form of dissipation, something we have some intuition for, from our experience of waves and vibrations. But why is it that a few types of particles do not decay at all, or at least live much longer than the 13.7 billion-year age of the (current) universe?
The only known stable particles in nature are the electron (and anti-electron), the lightest of the three types of neutrinos (and its anti-particle), and the photon and (presumed) graviton (which are their own anti-particles). The presumed graviton, too, is stable. The other neutrinos, the proton, and many atomic nuclei (and their anti-particles … I’m going to stop mentioning the anti-stuff, it goes without saying) are probably not stable but are very, very, very long-lived. Protons, for instance, are so long-lived that at most a minuscule fraction of them have decayed since the Big Bang, so for all practical purposes they are probably stable. The other rather long-lived particle is the neutron, which when on its own, outside an atomic nucleus, lives just 15 minutes or so. But neutrons inside many atomic nuclei can live far longer than the age of the universe; such nuclei provide them with a stable home. Finally, I should add that if dark matter is made from particles, then those particles, too, must be stable or very, very long-lived.
Why are these particles stable? It turns out that our world imposes some rules on particle behavior, ones not visible to us in the physics of waves and vibrations that we encounter in daily life, that prevent some particles from decaying, either rapidly or at all. The fundamental rules are “conservation laws”, statements that certain quantities in the universe never change in any physical process. (These quantities include energy, momentum, electric charge, and a few others.) There are also some approximate conservation laws, stating that certain quantities only change very rarely. Conservation laws do not appear from nowhere, imposed out of thin air by theorists; they are related to other properties of the world. For example, if the laws of nature do not change over time, then it follows (thanks to a theorem of the mathematician Emmy Noether) that energy is conserved. Meanwhile, the stability of the matter out of which we are made provides strong tests of these conservation laws, as we’ll see.
Combining these laws with the properties of particles leads to a set of simple rules that determine when particles simply cannot decay, or when they can at most decay very rarely. And these rules are (almost) entirely sufficient to explain the stability of the particles out of which we are made, and those that we interact with most often.
Here are the main ones. Their most important consequences for our universe and our lives are written in bold-face.
Rules of Nature Believed (for deep reasons) To Be Exact
1) A PARTICLE MUST DECAY TO TWO OR MORE PARTICLES.
This is why every decay that we see in nature involves two or more particles emerging from a single one. It follows simply from the laws of nature that the total energy and total momentum must stay constant in any physical process (or as physicists say, “energy and momentum are conserved.”) And Rule #1 follows directly from these conservation laws. Here’s the argument, if you are interested:
Suppose a particle of type 1 could decay to a particle of type 2 and nothing else. Let’s see there’s a contradiction: take a particle 1 and put it in front of you, sitting at rest. All of its energy is in mass energy. Now imagine it decays to particle 2. Conservation of energy says
Mass Energy of Particle 1 = Mass Energy of Particle 2 + Motion Energy of Particle 2
Since motion energy is positive, particle 2 must have mass energy less than or equal to the mass energy of particle 1. But the motion energy of particle 2 is positive, so if the mass energy of particle 2 is less than that of particle 1 that means particle 2 must be moving. But particle 1 started out at rest, so that means it had NO momentum. Particle 2 is moving, so it has SOME momentum. That’s impossible; momentum is conserved. Therefore the decay is impossible unless the two particles have equal mass. But in this case, if particle 1 could decay to particle 2, the reverse would also be true: particle 2 could decay to particle 1. Well, that’s not a decay at all; it is a mixing between the two types of particles, which is a qualitatively different phenomenon.
2) THE MASS OF A DECAYING PARTICLE MUST EXCEED THE SUM OF THE MASSES OF THE PARTICLES PRODUCED IN ITS DECAY
Total energy and total momentum are conserved in a decay, but total mass always decreases. A particle (“parent”) with a mass m1 may only decay to particles 2 and 3 (“children”) if the sum of masses of the children is less than the mass of the parent: m2 plus m3 must be less than m1. This is a simple consequence of the law of nature that the total energy must stay constant in any physical process. Here’s the argument, if you want to see it:
Imagine you are watching particle 1 at rest — just sitting there in front of you. Its energy is all mass energy m1c2. Then it decays to particles 2 and 3. Each one has mass energy AND motion energy. Since energy is conserved
Mass Energy of Particle 1 = Mass Energy of Particle 2 + Mass Energy of Particle 3 + Motion Energy of Particle 2 + Motion Energy of Particle 3
But since motion energy is always positive, we learn that the initial mass energy is more than the final mass energy, and thus m1c2 is bigger than m2c2 + m3c2, implying m1 is bigger than m2 + m3.
Since the photon is (as far as any experiment can tell) massless, there is nothing to which it can decay. That is why light waves can travel across a room, across space from the sun, and across the universe without disintegrating in flight. The same is presumably true for the graviton.
3) THE TOTAL ELECTRIC CHARGE BEFORE AND AFTER A DECAY MUST MATCH
Another conserved quantity is electric charge. A W- particle, which is very heavy and has negative electric charge -e, can decay to an electron of negative charge -e and an anti-neutrino of zero charge. But a W- cannot decay to a positron of positive charge +e and a neutrino of zero charge, because the total charge would then have changed from -e to +e. Not can a W- decay to an electron of negative charge and a positron (or “anti-electron”) of positive charge, because that combination would have total charge zero.
And since the electron is the lightest particle that has electric charge, there is nothing that it can decay to; only neutrinos, photons, gluons and gravitons are lighter, but they are all electrically neutral, so any combination of them would have zero electric charge. Any unknown particles that are lighter than the electron must also be electrically neutral, or we would easily have produced them in experiments. So the electron is stable.
4) THE TOTAL NUMBER OF “FERMIONS” BEFORE AND AFTER THE DECAY CAN CHANGE ONLY BY AN EVEN NUMBER
All particles are either fermions or bosons, as described here. The rule stated above follows from the fact that angular momentum, like energy and momentum, is conserved (which explains the tendency of spinning things like the earth to keep spinning.) The rule prevents a neutron from decaying to a proton and an electron; laws 1, 2 and 3 would be obeyed, but not 4, because all of these particles are fermions. Instead, a neutron decays to a proton, an electron and an anti-neutrino; then we have one fermion initially and three at the end, for a change of two.
There are three types of neutrinos, and it is now believed all three have mass (at least two of them do and probably all three — that’s a long story.) The lightest neutrino is the lightest known fermion, but the only known particles that are lighter, to which it could potentially decay, are bosons (the photon and the graviton.) Therefore it cannot decay at all: one cannot start with one fermion and end up with only bosons. [This neutrino could turn out to be unstable if there are even lighter fermion particles that we've so far missed because they interact even more weakly with ordinary matter than neutrinos do.] Incidentally, we do know neutrinos are moderately long-lived because we have observed them traveling great distances from distant star explosions, called “supernovas”.
Rules of Nature Believed (for less deep reasons) To Be Very Nearly Exact
5) THE TOTAL NUMBER OF QUARKS MINUS THE TOTAL NUMBER OF ANTIQUARKS MUST NOT CHANGE IN A DECAY
A proton contains three quarks plus many gluons and many pairs of quarks and antiquarks, so in a proton the number of quarks minus the number of antiquarks is three. A neutron also has an excess of three quarks. So a neutron, which is heavier, can potentially decay to a proton without violating rule 5 — and it does (along with an electron and an anti-neutrino).
But the proton is the lightest particle that has a more quarks than antiquarks, so it follows from this rule, along with rule 2, that it is stable. Clearly the proton cannot decay to any combination of electrons, photons, neutrinos etc. because these contain no quarks. There are some hadrons (particles made from quarks and antiquarks and gluons,) in particular pions and a few others, but these all differs from protons and neutrons in that they have equal numbers of quarks and antiquarks. Therefore a proton (which is heavier) cannot decay to any combination of pions plus non-hadrons (such as photons, electrons, neutrinos, etc.) because again the children will have the same number of quarks and anti-quarks, while the parent does not. Pions, by contrast, can decay without violating any of the rules; for example, an electrically neutral pion (which is a boson) can decay to two photons, while a positively-charged pion can decay to a neutrino and an anti-muon, a fact that is very useful in making neutrino beams.
Actually it is believed by many theorists (though not yet demonstrated experimentally) that this rule is violated by a tiny amount, and that the proton is very very very slightly unstable, with an extraordinarily long lifetime. By looking for a decade or so at huge numbers of protons (in a giant vat of water [here's a link to the Super-Kamiokande detector]) and seeing no sign of even a single one decaying, we know the proton lifetime is at least 10,000,000,000,000,000,000,000,000,000,000,000 years. I hope I didn’t miss a zero. The age of the current phase of the universe is about 13,700,000,000 years, so there will be plenty of protons around for a long time to come.
There are other rules too, but the majority of effects we see around us follow from these few alone.
Summary, and a Couple of Questions I Haven’t Yet Answered For You
In particular, we now have all the rules needed to explain:
- why photons are stable
- why electrons are stable
- why protons are stable or very long-lived
- why at least one type of neutrino is stable or very long-lived
which is basically all you need for ordinary matter, chemistry, sunlight, and lots of other processes of daily life — except for one thing. What about the unstable neutron?!
The neutron is a very curious case. There is no rule preventing neutron decay, and indeed it does decay, after on average about 15 minutes, to a proton, an electron, and an anti-neutrino. Why is it so long-lived? This is partly because the proton and the neutron have masses that are so nearly equal. Although the neutron has mass-energy of almost a GeV, the mass-energy of the neutron is only about 0.0007 GeV larger than the sum of the mass-energies of a proton, an electron and an anti-neutrino. Decay rates become very slow when the children from a decay have masses that add up very close to that of the parent; that’s not surprising, since by rule 2 the decay rate has to decrease to zero once the children have more mass than the parent.
But the really odd thing is that if you put a neutron in certain atomic nuclei, it becomes stable! Helium, for instance, has two protons and two neutrons. Even though a neutron by itself lives a quarter of an hour, a helium nucleus will live for the age of the universe and longer. In fact this is true for the neutrons in the nuclei of all of the stable elements in the periodic table. This fact is a hugely important consequence of Einstein’s theory of relativity (and some details of the strong nuclear force), for without it all the complexity of our chemically rich world would be absent. And this remarkable story deserves an article all its own.
Oh, and by the way, if dark matter is in fact made from unknown particles, why are they stable? Nobody knows for sure, but probably the list of rules I gave you above is not enough. Most likely there is a new conservation law, exact or approximate, yet to be discovered.