Anti-Matter and Quantum Relativity

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It's 1928 Over the past quarter century, the greatest geniuses of the modern era discovered the two keys to the fundamental nature of reality. Einstein's theory of special and general relativity had changed forever the way we think about motion, space, and time. And the emerging field of quantum mechanics had radically altered our understanding of the fundamental building blocks of the universe. Yet this year, 1928, one brilliant insight would bring these theories together and unveil the quantum fabric of reality. It would also predict the existence of antimatter.

By the late 1920s, Einstein and Planck had already shown that light is a particle as well as a wave. And Louis de Broglie had shown that all matter has this dual wave particle nature. Bohr, Heisenberg, Born, Pauli and others pieced together a mathematical description for the weird nature of subatomic particles. Then, in 1926, Erwin Schrödinger wrote down his famous equation, the Schrödinger equation, which breathed life into this emerging model. It describes how these matter waves, represented as wave functions, change over time and allowed physicists to predict the evolution of quantum systems, such as the strange interference pattern in the famous double slit experiment. Yet, everyone knew there was a problem. First and most obvious, the Schrödinger equation is totally incompatible with Einstein's relativity. In relativity, the dimensions of space and time are intrinsically connected and they flow into each other as frames of reference change.

But the Schrödinger equation tracks the evolution of a particle's wave function according to one and only one clock, typically the clock in the reference frame of the observer.

Relativity tells us that the passage of time depends on velocity. So the Schrödinger equation only works for slow moving objects. That's a problem. Subatomic particles are often moving at close to the speed of light. The other problem with the Schrödinger equation is that it describes particles as simple wave functions, distributions of possible positions and momenta that have no internal properties. Yet we now know that many elementary particles have an internal property called spin. That doesn't mean that they're actually rotating, but spin does result in a sort of quantum angular momentum. For example, electrons spin causes them to align themselves with magnetic fields, just like a rotating electric charge would. The axis of spin can point in different directions, for example, up or down. The discovery of quantum spin starts with an Austrian physicist named Wolfgang Pauli. Pauli realized that to explain electron energy levels in atoms, those electrons must obey a rule that we call the Pauli exclusion principle. It states that no electron can occupy the same quantum state as another electron. In fact, it applies to all particles called fermions. In the case of electrons in atoms, it suggests that we should only find one electron per atomic orbital if we count each orbital as a quantum state. However, we actually observe two electrons per orbital. And so Pauli realized there must exist a hidden quantum state. Pauli introduced what we call a new degree of freedom internal to electrons. One that could take on one of two values. Let's call those values up and down.

That would allow two separate electrons, one up, one down, to occupy the same atomic energy level without occupying the same quantum state and therefore violating the Pauli exclusion principle. Other physicists soon figured out that this new quantum state represented spin. And the up and down degrees of freedom were the direction of pointing of the angular momentum axis. We now call these two-component wavefunctions spinors.

Now, it's okay to ignore spin in the old Schrodinger equation and get approximate answers. But when a magnetic field is present, spin direction becomes very important. So, for fast-moving electrons and for electrons in electromagnetic fields, the Schrodinger equation gives the wrong answers. The problem consumed a brilliant British physicist, Paul Dirac.