How can antimatter exist at all? What amount of math had to be done until someone realized they can create it?
In: 4430
Since no one is answering the second part of your question, I’ll mention the history of its mathematical discovery.
We were at a point in physics where special relativity was well-understood, but quantum mechanics was still being developed. One of the important “fathers” of QM, Paul Dirac, was attempting to create an equation to describe charged, relativistic particles with mass (so eg really fast moving electrons). We knew there had to be an equation, because the theory (Maxwell’s equations) that describes electric fields is relativistic (in fact Einstein used Maxwell’s equation to determine that the measured speed of light in a vacuum was the same in all inertial reference frames, which is the fundamental observation that leads to special relativity). Dirac was really hoping to describe some observations about the light emitted by Hydrogen when you excite its electron, because up until that time we had a really poor understanding of atomic spectra.
I won’t detail how he got his equation, but we already had the time-dependent Schrödinger equation. Dirac was only looking for a wave function to describe an electron, which would match with the Schrödinger equation, and which would match with some consequences of special relativity. The wave function can be thought of as something that describes the thing you’re interested in, eg, a spin-up electron. The equation reads something like:
(Energy) * (wave function) = i * h/(2 * pi) * (the change in the wave function with time).
(actually Dirac was probably using the Klein-Gordon equation, a known version of the Schrödinger equation that included relativistic momentum, but I can’t verify now if he specifically looked at this when deriving his equation).
Here, “i” is the imaginary unit, and “h” is Planck’s constant (an important unit of quantum mechanics). Dirac already had all of this, he just needed to write the correct relativistic energy for the electron, and find solutions (ie wave functions) using this equation.
Dirac was big on using matrices in QM. What he did was start by looking at “free” particles, and introduce new matrices to describe the free electron. He needed to incorporate spin (a fundamental property of particles, like charge), and he needed to incorporate charge. For a “free” particle, there’s no potential energy. So Dirac just focussed on the momentum of such a particle, because objects with momentum have a corresponding kinetic energy. You can see this if you’ve ever had to stop a moving object—it takes energy to do this! In special relativity we also have the concept of a “rest mass”, which is the energy you can extract from mass if you convert it completely into energy. This is the energy a nuclear bomb uses to go *boom*. It’s a LOT of energy
Since there was “rest mass” energy, and since there was energy from motion, Dirac figured he needed four matrices to describe his energy: one for the rest mass, three for the motion in three dimensions. He came up with these matrices, partly by knowing they had to satisfy certain observations, and partly through guesswork/creativity. When he solved the Schrödinger equation using this energy, he found that it matched the observations he was trying to explain extraordinarily well. However, he found *four* solutions, not two. We expect two (- charge, spin up, and – charge, spin down), but there were also + charge, spin up, and + charge, spin down. Dirac wrote this off at the time as a purely mathematical result, but some physicists were so sure that these “anti-electrons” were real that they wanted to find it. We soon found out the positrons (ie anti-electrons) indeed exist, and that Dirac’s equation could describe positrons just as they described electrons. So in fact, the Dirac equation predicted the existence of antimatter.
I’ve simplified and skipped over things because it gets very technical otherwise, but hope that answers your question.
Tl:dr: scientists stand on the shoulders of giants. Dirac was just trying to explain some properties of atomic spectra using the known maths of special relativity and QM, and accidentally discovered equations that also describe antimatter.
Latest Answers