## Friday, July 04, 2014

### Science Friday: Dirac's Antiparticles

Not long now. Here's chapter 5 of George Gamow's classic, Thirty Years That Shook Physics.

The previous posts were:

1a. Planck's Quantum
1b. Jumping Photons (Einstein and the Photoelectric Effect)
1c. The Compton Effect (Proof of Energy Packets)

2a. Thomson and Rutherford's Atoms
2b. Bohr's Contributions (How electrons fill the atom)

3a. Pauli Exclusion Principle (no two electrons at any one energy state)
3b. The Pauli Neutrino

4a. De Broglie's Wavy Particles
4b. Schrödinger's Wave Equation

5. Heisenberg's Uncertainty Principle

When I was at Florida State University in the summer of 1983 for Boy's State, I used some free time to find the office of P. A. M. Dirac and touch his door. He would die the next year.

One of the challenges of the burgeoning quantum mechanics of the late 1920s was that the Schrodinger equation did not account for relativistic factors that came into play with particles that might approach the speed of light. One factor that kept anyone from "relativizing" it was that the derivatives in the equation were of different orders, if I am understanding correctly. So part consisted of a first order derivative and another part of a second order derivative. It proved difficult to introduce Einstein's famous Lorentz transformation to such a mixed order equation.

So one evening in 1928 while Dirac sat in his Cambridge study at St. John's College, he thought to reduce the second order derivatives in such a way that the equation would consist entirely of first order derivatives. The hesitation to do this is that Schrodinger's equation, when of a first order level, includes imaginary numbers, that is, numbers that include the square root of -1 (i), which is difficult to conceptualize or really know what it means.

Nevertheless, it not only worked, allowing Dirac to create a relativistic version of Schrodinger's equation that would work when particles were approaching the speed light. It also accounted for another dimension of atomic description that had been discovered, namely, spin. The equation predicted that there were two values of spin that any electron could have in any orbital.

Another thing that his equation predicted were antiparticles. If one solution to his equation involved a negatively charged electron with positive mass, then another might be a positively charged electron. Dirac initially wondered if this "positive electron" might be the proton, but he did not have to wait long. In 1932, the existence of the "positron" was officially verified.

Richard Feymann would later suggest that a positron was an electron moving back in time, one of his many quirky ideas. When electron and positron meet, they annihilate and release 2mc squared of energy. Feymann suggested this was the electron changing directions in time.

The antiproton and antineutron would be discovered later. The question would arise. Are there equal portions of matter and antimatter in the universe? Might whole galaxies out there consist of antimatter, just as ours consists of matter?

Fun story about when Dirac first met Richard Feymann. Apparently he asked him, rather matter of factly, "I have an equation. Do you?"