electrons, fields of color, quantum field theory

In June, 2014, I lectured at the Physics Department of the Czech Technical University in Prague. I started by asking the question “Just what does the electron look like?”, and I showed 2 images. The first was the familiar Rutherford image of particles orbiting a nucleus, and the second was a (very simplified) image of the electron as a field in the area around the nucleus.

Then I asked for a vote. Rather remarkably just four people in the audience chose the field image, and no one selected the particle picture. In other words, THEY DID N’T KNOW. So here we are, 117 years after the electron was discovered, and this highly educated bunch of physicists had zero idea what it looks like.

quantum field theory, dr. rodney a. brooks, fields of color

Naturally when the electron was discovered by J. J. Thomson, it was naturally pictured as a particle. After all, particles are easy to visualize, while the field concept, let alone a quantized field, is not an easy one to grasp. But this picture soon ran into problems that led Niels Bohr in 1913 to propose that the particles in orbit picture must be replaced by something new: undefined electron states that satisfy the following two postulates:

1. [They] possess a peculiarly, mechanically unexplainable [emphasis added] stability.

2. In contradiction to the classical EM theory, no radiation occurs from the atom in the stationary states themselves, [however] a process of transition among two stationary conditions can be accompanied by the emission of EM radiation.

This led Louis de Broglie to propose that the electron has wave characteristics. There then followed a type of struggle, with Paul Dirac leading the “particle side” and Erwin Schrodinger the “wave side”:.

We insist that the atom in truth is merely the … phenomenon of an electron wave caught, as it were, by the nucleus of the atom … From the point of view of wave mechanics, the [particle picture] would be merely fictitious.– E. Schrodinger.

Nevertheless the fact that a free electron acts like a particle could not be solved, and so Schrodinger gave in and Quantum Mechanics became a theory of particles that are described by probabilities.

A second struggle occurred in 1948, when Richard Feynman and Julian Schwinger (along with Hideki Tomanaga) established numerous techniques to the “renormalization” issue that afflicted physics. Once again the particle view espoused by Feynman won out, in huge part because his particle diagrams proved easier to work with than Schwinger’s field equations. And so two generations of physicists have been brought up on Feynman diagrams and led to think that nature is made from particles.

In the meantime, the theory of quantized fields was perfected by Julian Schwinger:.

My retreat started at Brookhaven National Laboratory in the summer of 1949 … Like the silicon chip of more recent years, the Feynman design was bringing computing to the masses … But eventually one must bring it all together again, and after that the piecemeal strategy loses some of its appeal … Quantum field theory must work with [force] fields and [matter] fields on a completely equal footing … Here was my obstacle.– J. Schwinger.

Schwinger’s last version of the theory was published between 1951 and 1954 in a collection of five papers entitled “The Theory of Quantized Fields”. In his words:.

It was to be the purpose of further advancements of quantum mechanics that these two distinctive classical principles [particles and fields] are merged and become transcended in something that has no classical counterpart– the quantized field that is a fresh conception of its own, an oneness that replaces the classical duality.– J. Schwinger.

I believe that the primary reason these masterpieces have been disregarded is that lots of physicists considered them too difficult to comprehend. (I know one who could not get past the initial page.).

And so the choice is all yours. You can think that the electron is a particle, despite the many inconsistencies and absurdities, in addition to questions like how significant the particles are and what are they made of. Or you can conclude it is a quantum of the electron field. The choice was described in this manner by Robert Oerter:.

Wave or particle? The answer: Both, and neither. You could think of the electron or the photon as a particle, but only if you were willing to allow particles act in the unusual way described by Feynman: showing up again, interfering with one another and cancelling out. You can also think of it as a field, or wave, but you should keep in mind that the detector always registers one electron, or none– certainly never half an electron, no matter how much the field has been broken up or spread out. Ultimately, is the field just a calculational instrument to inform you where the particle will be, or are the particles just calculational tools to tell you what the field values are? Take your pick.– R. Oerter.

What Oerter neglected to say is that QFT describes why the detector constantly registers one electron or none: the field is quantized. The Q in QFT is very important.

So when you choose, dear reader, I really hope you will not choose the image of nature that doesn’t make sense– that even its proponents call “bizarre”. I wish that, like Schwinger, Weinberg, Wilczek, Hobson (and me), you will select a reality made of quantum fields– properties of space that are illustrated by the equations of QFT, the highest philosophically appropriate image of nature that I can think of.

Find out more on the Fields of Color blog.


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