The start of World War II threw quantum theory research into disarray. Many of the European physicists left Europe all together, and research moved across the ocean to the shores of the United States. The advent of the atomic bomb thrust American physicists into the spotlight, and physicists began to meet on Shelter Island to discuss the future of quantum theory. By this time one thing was certain: the Copenhagen interpretation of quantum theory had triumphed and challenges to it had mostly died off.

This allowed physicists to focus on a different kind of problem. At this point in time quantum theory was not able to deal with transitional states of particles when they are created and destroyed. It was well known that when an electron came into contact with a positron, the two particles were destroyed and formed at least two photons with a very high energy, known as gamma rays. On the flip side, gamma ray photons could spontaneously turn into positron-electron pairs.

No one could explain why this occurred. It had become obvious to the physicists of the day that a quantum version of Maxwell’s electromagnetic field theory was needed to explain the phenomenon. This would eventually give rise to QED, short for quantum electrodynamics. This is a severely condensed  story of how that happened.

Quantum Fields

Richard Feynman (1918 – 1988)

It’s easy to visualize what a particle is. Visualizing fields is not so easy as they cannot be seen with the unaided eye. They are, however, just as real as particles in every sense. We’ve all felt the repulsive force of two like poles of a magnet. Many of us have sprinkled metal flakes over a piece of paper to visualize the magnetic field of the magnet underneath it. When you rest your hand on a table, your hand is not actually contacting the table. The electrons in your hand repulse the electrons in the table — just the same as like poles of a magnet do. That force is a barrier between your hand and the table, or anything you grab or touch for that matter. Fields are very much a part of our reality.

During the first Shelter Island conference in 1947, it was assumed that the electromagnetic field, photons and electron/positrons were all related to each other in some fashion. Quantum mechanics could deal with photons and electrons, but it was yet to be able to deal with them turning into one another. It became apparent that fields were actually more fundamental than particles, and that particles could be thought of as the ‘quanta’ of the field associated with it. For instance, the photon could be thought of as the quantum of the electromagnetic field.

Early attempts at a Quantum Field theory ran into major hurdles. The equations were based on a perturbation expansion. This is a complex math that is well beyond the scope of this article. But to summarize so you have a vague idea of what happens, an equation is written in a zero order, where it can be solved exactly. Then additional terms are added to form a power series, so you have a first order, second order, third… etc.  Each series provides a smaller and smaller correction to the zero order result. When everything is over, the accuracy of the final result is dependent on the number of orders (perturbations).

Early QED equations predicted infinite corrections in some cases. This was due to treating particles as points, without volume or shape, which is essential to quantum mechanics. There was no clear solution. It would take an eccentric American physicist to paint a clearer picture for all to see.

Feynman Diagrams

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Richard Feynman and a few other physicists were in a race to solve the infinite correction problem and get QED back on track. While others were locked into rigorous mathematical structures, Feynman preferred a more pictorial approach. Basically, he was visualizing particle-photon interaction with a sort of 2-dimensional graph approach. This did not sit well with many of the other physicists, as it seemed Feynman did not understand the uncertainty principle. But his genius was obvious, as he was able to come to the same conclusions that the others did without the rigorous math, so they listened to him. His pictorial approaches were called Feynman Diagrams, one of which can be seen to the right.

They have two dimensions: time and space. Time is the y axis and space is the x axis. There are particles that come in, which are angled toward the center of the diagram. When they change into something else or interact with another particle, they change angles to move away from the center. The changes in particles are caused by a force carrying particle, known as virtual photons or gauge bosons. The force carrier particles are represented by squiggly lines.

To explain the repulsion of electrons for instance, we have two electrons coming toward each other. When they get close enough, a virtual photon is exchanged between them, giving them the information to repel. And then they move away from one another.

Virtual Particles?

Virtual Particles are a key component in quantum electrodynamics. They’re virtual in that they cannot be detected. They are the force carrying particles that allow electrons to repel and allow protons to bind together in the nucleus of an atom.  A free electron is actually surrounded by virtual particles created by interactions within its own electromagnetic field. Virtual particles can be created and destroyed without the constraints of conservation laws thanks to Heisenberg’s uncertainty principle. Photons and electron/position pairs can be created “out of thin air” so long as the energy can be accounted for within the time frame determined by uncertainty.

And that’s how QED got off the ground. Richard Feynman and his diagrams, virtual particles and perturbation expansions. QED consists of interactions between particles and virtual particles, which are represented mathematically as corrections in a perturbation expansion, which can be understood more easily with Feynman diagrams. In the next article, we’ll go into a bit more detail about the particles themselves — the six quarks, the six leptons and the four force carriers which make up the mighty gauge bosons. This is essential for understanding QED in more detail. Stay tuned!

Sources:

The Quantum Story, by Jim Baggott. Chapters 18 &19  ISBN-978-0199566846



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