Part #02: How an equation predicted antimatter

Following on the heels of the groundbreaking publications by Heisenberg and Schrödinger in 1925, physicists such as Max Born and Paul Dirac succeeded in developing a mathematically coherent formalism of quantum mechanics. “And shortly afterwards, Dirac managed to reconcile quantum mechanics with Einstein’s special theory of relativity,” explains Heinemann. The result was the famous Dirac equation. “Just looking at it is incredibly exciting,” says Heinemann enthusiastically. The Dirac equation paves the way for quantum field theory, which allows the collective behavior of particles to be described using quantum mechanics. “Quantum field theory ultimately describes the elementary particles and their interactions via quantized fields that interact with each other.” Particles manifest themselves as excitations of these fields. But what do these excitations look like? Heinemann laughs. “We humans are naturally very limited in our perception. Quantum mechanical processes remain hidden from us; ultimately, we can’t perceive or understand them using our senses.” Our macroscopic world is simply not quantum mechanical, which is why we have no intuitive feel for the quantum realm. “However, if you do a lot of quantum physics calculations,” Heinemann adds with a wink, “then you can develop a certain intuition, at least in the physical sense.”

But back to Dirac: his equation was capable of describing ad hoc an anomaly in the magnetic moment of the electron that had been previously discovered but never explained, which Dirac saw as confirmation of his work’s validity. According to Heinemann: “But the equation also offers a second solution that appears to allow negative energies.” Yet negative energies make no sense in physics. As such, Dirac surmised that this second solution might describe a particle which, in the case of the electron, must have an opposite electric charge, i.e., a positive one. But which particle could it be? The only positively charged particle known in the 1920s, the proton, was quickly ruled out due to its much greater mass. Dirac stuck to his equation and finally postulated the existence of antiparticles that were associated with the apparently negative energy states. These ideas were all very exotic and many assumed the equation must be wrong. But in fact, only a short time later, Carl David Anderson observed elementary particles in nebula chamber experiments with cosmic rays that apparently had the same mass as electrons but the opposite charge: positrons. “This means that antimatter was first predicted in theory and then discovered in experiments shortly afterwards,” Heinemann explains. When a particle and an antiparticle collide, the result is mutual annihilation, i.e., they completely disappear, releasing energy in the process. “But surprisingly, our universe is one of pure matter, which raises another question: Why does our world consist only of matter?” Actually, the Big Bang should have created just as much matter as antimatter, which would have quickly led to the annihilation of all matter and antimatter and made the creation of our universe impossible.

The Dirac equation is fundamental to quantum field theory, which makes it possible, for example, to describe the creation and annihilation of photons in the context of quantum electrodynamics. Quantum field theory also makes statements regarding vacuum that are difficult to reconcile with our everyday concept of an “absolute void.” According to Heisenberg’s uncertainty principle, nature can create matter and antimatter from vacuum for a short time. “Consequently, quantum field theory predicts ‘Quantenzittern’ for vacuum.” – measurable quantum fluctuations in the course of which particles and antiparticles suddenly appear and disappear. “Today, quantum field theory forms the theoretical basis for describing the elementary particles and how matter in our universe developed in the first three minutes.” Accordingly, the theory applied in the Helmholtz Association’s research program “Matter and the Universe,” in which experts from the Deutsches Elektronen-Synchrotron DESY, the Karlsruhe Institute of Technology (KIT) and the GSI Helmholtzzentrum für Schwerionenforschung are involved, is essentially based on Dirac’s contribution to quantum field theory, which would subsequently be expanded from electromagnetic forces to the weak and strong nuclear forces of particle physics.

“What currently makes quantum physics research so groundbreaking,” says Beate Heinemann, “is the fact that it is beginning to be used for quantum engineering. Simply put, whereas we used to merely observe quantum physics, we are now actively applying the unique features of quantum physical systems, for example in quantum computing. This is truly new and revolutionary.” – which is why, in the next installment, we’ll shed some light on what quantum computing is all about. Stay tuned!

Series in the Quantum Year 2025