Quantum Field Theory is generally accepted as an accurate description of the subatomic universe. However until recently this theory had one giant hole in it. The particles it describes had no mass! The Higgs field and the Higgs mechanism were proposed long ago in order to give particles mass, but it was only in 2012 that the existence of the field was proved with the discovery of the Higgs boson by the Large Hadron Collider.
Feynman’s path integral shows us that, to properly calculate the probability of a particle traveling from point A to point B, we need to add up the contributions from all conceivable paths between those points – including the impossible paths! In fact we can go even further: according to Feynman’s approach, every conceivable happening that leads from a measured initial state to a measured final state DOES in a sense happen.
The equations of quantum field theory allow us to calculate the behaviour of subatomic particles by expressing them as vibrations in quantum fields. But even the most elegant and complete formulations of quantum physics – like the Dirac equation or Feynman’s path integral – become impossibly complicated when we try to use them on anything but the most simple systems.
Quantum mechanics seems to imply that ALL possible properties, paths, or events that could reasonably occur between measurements DO occur. Whether or not this is true, a mathematical description of this crazy idea led to the most powerful expression of quantum mechanics ever devised: Richard Feynman’s path integral formulation.
Quantum Electrodynamics is the first true Quantum Field Theory. Part 2 in our series on Quantum Field Theory.
Paul Dirac’s insights into the nature of Quantum Mechanics laid the foundation for Quantum Field Theory and predicted the existence of anti-matter.