Anti-matter. Seeing the previous word, you immediately glance back at the title, right? Strangely, it has been 80 years since the discovery of anti-matter, and we use it routinely in our technology. Nevertheless, anti-matter is still thought of as something from science fiction (and mostly bad science fiction at that).
It all goes back to one of my favourite theoretical physicists, Paul Dirac, and you might like how he found it (roughly). He essentially did it by taking the square root of an existing equation (the “Klein-Gordon” equation) to get a new equation*, now called the Dirac equation (I’ve scribbled it over on the right, just for fun).
So here’s something you’ll know very well from your own journeys in mathematics. Pick a number, like 9, and ask what its square root is. The answer that immediately comes back is 3, and then maybe a moment or two later on you also realize that -3 is also a solution. In other words, both 3 and -3 square to give the same number. In much the same way, Dirac found that there were two choice for what equation squares to the thing he was trying to take the square root of! Turns out that they are very similar things, but opposites in other senses. In fact, the presence of one is rather like the absence of another. Huh? If you started with no particles at all, there’s a sense in which you can take away an electron, for example. What do you get? A positron, the anti-electron. Positrons are used in PET-scans, by the way, very useful in medical diagnosis (and nothing whatsoever to do with small furry animals.)
Yes, it is true that if you combine matter and its anti-matter they will “cancel each other out”, leaving only the energy they had (matter anti-matter pairs have equal mass, not opposite mass) – that’s the thing used most in science fiction.
Yes, the analogy with numbers above has led you to a correct conclusion: the case of the number 0 suggest that there must be matter that is its own anti-matter. Do we know any examples of this? Yes! Quite familiar in fact – the photon (particle of light, carrier/quantum of the electromagnetic force) is also an anti-photon.
So then there’s the next question you’ve thought of. A big one. Why is there more matter around here (that we see around us in our universe) than there is anti-matter? In fact, when matter was created, why was anti-matter not created in the same amount too, and if so, what stopped them from just canceling each other out and leaving nothing (except their energy)? In other words, there’s that Big Question again – “Why is there something and not nothing?”
As usual in this exciting field, it is easy to get to a very deep question that sits right on the frontier. The answer is that we don’t yet have an answer. We’re hoping that future experiments, current and future theories that pertain to the physics of the early universe might shed some light on this issue.
Ok, I’ll stop here by pointing you to a lovely discussion that you can listen to while you get on with things. It is an episode of the excellent BBC Radio 4 series “In Our Time”, where the host Melvyn Bragg chats with three physicists (including, to my pleasant surprise, my dear friend and colleague – and once close colleague from my Durham (the one in England) days – Ruth Gregory) about anti-matter, past, present and future. It’s a really good conversation! Link here.
-cvj
*Why? Well, being slightly technical for a moment, for those who are interested: It has to do with wanting a new wave equation that was first order in time derivatives -like Schrodinger’s equation- rather than second order. Schrodinger’s itself would not do since it did not incorporate Special Relativity.
(Cross-posted yesterday to Correlations.)
So was this formulated before or after positrons were discovered?
’cause, what the science fiction antimatter promoters never seem to remember is that bananas produce antimatter from e+ decay of 40K.
Of course, since the electron capture and b- decays are much more common, your average banana only cranks out one positron every 2 hours. If you want one to appear during a 50 minute university lecture, you should probably bring a whole hand to class.
wow, that’s intense. haha i’m going to have to take a break, then come back and read it again 🙂 …looking forward to hearing the BBC anti-matter conversation!
Oh, cool! Thanks, EJ! And, uh, I’m pretty sure Ambitwister’s comment wasn’t there when I posted my second one… 😛
The way it’s written now is for a “free” particle. Just replace the zero on the right-hand side with E*psi, or for arbitrary potential V(x) use (E – V(x))*psi.
But wait… I don’t see anything that looks like a potential! Where does the potential term go if you want to solve for, say, an electron in a box?
Ohhh… now I see that the gamma^mu are actually the Dirac matrices in disguise. Tricky tricky!
Aaron: no, the gamma^mu aren’t relativistic dilation factors, they’re Dirac matrices.
That’s the Dirac equation? I thought it was supposed to be complicated! Am I to understand that gamma^mu = 1/sqrt(c^2 – v_mu^2), as usual?