Because of the recent results from CERN where anti-Hydrogen atoms were first trapped for any appreciable period of time, I was asked to write a little bit about anti-matter.

CL this is for you.

Antimatter was first predicted by Dirac in the late 1920’s. Dirac was attempting to formulate a relativistic quantum theory. Quantum Mechanics is a theory of the very small. It would be very easy to go off into any number of very long tangents here, to talk about how QM works and what it applies to, and the very many interesting and counter intuitive things that we have learned from it. There is a whole discussion of things like the ultraviolet catastrophe, the persistence of atoms (as in why orbiting electrons didn’t fall into the nucleus) and the photo-electric effect which demanded the new paradigm. So I ask my reader to accept that this thing called Quantum Mechanics is out there and well verified and leave it at that. Any proper discussion would take a very long time to get into.

What needs to be taken from this is that the observations of the day demanded that certain new principles (other than those of classical mechanics) be devised for goings on, on the very small scale - specifically, for this discussion, that there was some sort of wave nature associated with the small particles.

In those days, in terms of particles with mass, the theoretical work focussed on the orbits of electrons in atoms. QM was (and still is) wildly successful at describing this correctly. The wave nature of the electron demanded that certain orbits were available and that others weren’t. The electrons did not orbit like planets orbit a star, which can do so at an infinite number of possible distances on a continuum. The electrons could only orbit a distances where the wave nature of them didn’t interfere with themselves. That sentence may sound awkward and have you going “Huh?” Please let me explain.

Picture a guitar. The strings on the guitar only play certain notes for any given tuning. Once one picks a string of a certain material and tension, and sets the length of the string and where the endpoints are, fixing the string down, it can only play one note (and harmonics). The string literally moves in a wave form and that waveform goes up and down at a certain frequency, which pushes air at a certain frequency, which you hear as a note. The waves on the string also have a fixed wavelength. This is because the string vibrates in a wave form (just picture a sine wave here) and only waves of that half wavelength or wavelength or other harmonics can fit between the endpoints. A half wavelength is one “hump.”

That may sound complicated, but it really says nothing more than a wave needs some space to go up and down in. Once I fix the endpoints, only certain waves of certain wavelengths can finish going up and down before reaching the endpoints. One hump means it went up and came down. Two humps is a harmonic etc… This is why a guitar or, any stringed instrument, plays one note when plucked and not all other possible notes. Each note has its own wave. The other notes literally don’t fit.

Analogous to this, once you fix the potential of an atomic nucleus (as in the charge and how strongly the nucleus will pull on an electron) the wave associated with an electron can only “fit” evenly at certain radii. What this means is that the charge of the nucleus once fixed, is like fixing the endpoints of a guitar string. The wave of an electron, as it whizzes around the atom, needs a certain amount of space to “go up and down” in. Only certain radii allow that to fit. If the radius is too small, the wave doesn’t fit. If it is too big, it doesn’t fit. I should point out that when I say this is analogous to a guitar, I am not making a fluffy analogy. The mathematics is exactly the same. It just lives in three dimensions instead of one, and uses other functions than sine waves as a basis. I should also say that unlike a guitar, the electron wave here is not a physical movement of a string, but rather a wave in probability space. Even so, the math really is exactly the same at a fundamental level. The different orbits can be thought of like harmonics. This is also why electron orbits don’t collapse.

The different specific orbits all correspond to different specific amounts of energy needed to get into one of those orbits. Going from one allowed orbit to another is what is is quantized in the quantum mechanics. This is the “quantum leap” which ironically, given the way media uses it, is really quite small, and is described as a leap in energy level and not exactly distance. As electrons go up and down, from one orbit to another, they take or give up energy to do so. When they go down in energy, they release that energy as light. The light only has a specific wavelength and frequency itself and it corresponds to only one energy. Please re-read that, it is really important to the discussion. This means that all of the orbits around an atom are classifiable by an energy level and the difference in energy levels in terms of energy is the amount of energy you get out as light when an electron changes its orbit. This is the spectra of a given atom. I should point out, that the allowed levels are determined by the nucleus or nuclei of an atom or molecule. Not only does this turn out to be the fundamental mechanism behind chemical bonds, but it is the reason that certain atoms and molecules absorb or give off only certain frequencies of light. This is the basis that makes a greenhouse gas into a greenhouse gas.

One of the first triumphs of QM was completely calculating and predicting the energy levels of hydrogen.

One other thing about waves before going on to anti matter and why we care about anti hydrogen. Picture two waves. Make it simple, and picture two sine waves. Now imagine that where one is “up,” the other is “down.” If you were to put them on top of each other, the “up” of one wave would cancel out the “down” of the other. This is destructive interference.

There is also something called spin. For the sake of this discussion, see it as another mathematical wrinkle. Electrons have spin 1/2.

At the time of Dirac (remember him?) Quantum Mechanics was still quite new and was formulated in a non-relativistic way (For the cognoscenti, the Klein-Gordon equation was abandoned and then revived after Dirac). What that means is that it did not take Einstein’s Special Relativity into account. It talked about electrons whizzing around at very fast, but not near light, speeds.

It turns out that if you want to make a theory that obeys Einstein’s math and also takes whatever is “quantum” in the math of QM for electrons (which have spin 1/2) and put it all together, there is only one way you can do it. It is a hard math problem, but there is a solution. When Dirac solved the problem, he found that flopping right out of his math for his relativistic electrons, was also math for other things that had spin 1/2, the same mass as electrons, and the same charge, only they were positively charged instead of negatively charged. It was an electron in every way except the charge. It was an anti-electron! Antimatter was born theoretically! Positrons (anti-electrons) were directly observed in the lab shortly there after.

Remember that bit about waves cancelling? It turns out that there is something about the waves of an electron and an anti-electron that when you bring them together, their wave forms cancel. They annihilate. Sure enough in the lab, if you bring them together, they destroy each other and give off their energy.

The theory advanced after Dirac, added the work of others who worked on particles of different spins, and expanded into new interpretations of the mathematics itself. This became what is known today as Quantum Field Theory. I am not going there in this post.

Now we have some very important questions. If you look at Dirac’s math, or any QFT, you find that everytime you can make matter - you should also be able to make an equal amount of anti-matter. And for lots of things, that is exactly what happens, all the time! However, the universe we live in is mostly, if not all, composed of matter. If there were equal amounts of matter and antimatter in the universe, it all would have annihilated. Yet, we are here. Why did the early universe favor matter? We do not know.

This gets back to why you might want to make anti hydrogen. Remember how I said that hydrogen has energy bands that are like notes on a guitar? Well you can do stuff to them like put them in big electromagnetic fields that is something analogous to changing the tuning. One of the things that happens is that those energy bands split into sub bands. We know exactly how that works for regular hydrogen. If it works slightly differently for anti-hydrogen, knowing what it does differently, and by how much, could shed important light on the big question of “why more matter.” Now everyone expects it will be exactly the same. There are many strong reasons to expect this. We have, after all, been playing with antimatter for 80 years now. Antiparticles are easy to produce in many different ways. However, no one has been able to check anti-atoms directly, because it is very hard to make anti-atoms and then hold them still long enough to look at the spectra.

What CERN did was a very large step into developing the technology to do just that.