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Physics + MathPhysics & Math

The Good Vibrations of Quantum Field Theories

ByDon LincolnThe Nature of RealityThe Nature of Reality

It’s not unusual for me to receive mail questioning quantum mechanics and special relativity. I’ll admit, these ideas can sound a bit crazy. For some people, these ideas are simply too counterintuitive to accept. Occasionally, I can convince a correspondent that they accurately describe the universe. But I have some bad news for my pen pals: physicists no longer think about the universe in these simple terms. Our experiments have long shown the subatomic realm to be far more mind-blowing than those modestly-perplexing ideas. It has been nearly a century after all. In the words of my teenage daughter, those ideas are

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soooooooo 1920s.

Quantum mechanics tells us that an electron is both a particle and a wave and you can never be certain what it will do. Relativity tells us that clocks aren’t absolute, distances depend on the observer, and that energy can be converted into matter and back again. These ideas are still correct, but they’re just the tip of the iceberg.

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Physicists now use a class of theories called quantum field theories, or QFTs, which were first postulated in the late 1920s and developed over the following decades. QFTs are intriguing, but they take some getting used to. To start, let’s think only about electrons. Everywhere in the universe there is a field called the electron field. A physical electron isn’t the field, but rather a localized vibration in the field. In fact, every electron in the universe is a similar localized vibration of that single field.

Electrons aren’t the only particles to consist of localized vibrations of a field; all particles do. There is a photon field, an up quark field, a gluon field, a muon field; indeed there is a field for every known particle. And, for all of them, the thing that we visualize as a particle is just a localized vibration of that field. Even the recently discovered Higgs boson is like this. The Higgs field interacts with particles and gives them their mass, but it is hard to observe this field directly. Instead, we supply energy to the field in particle collisions and cause it to vibrate. When we say “we’ve discovered the Higgs boson,” you should think “we’ve caused the Higgs field to vibrate and observed the vibrations.”

This idea gives an entirely different view of how the subatomic world works. Spanning all of space are a great variety of different fields that exist everywhere, just like how a certain spot can simultaneously have a smell, a sound, and a color. What we think of as a particle is simply a vibration of its associated field.

This has significant consequences on how we think about how particles interact. For instance, consider a simple process whereby two electrons are fired at one another and are scattered. In the quasi-classical view of scattering, one electron emits a photon and then recoils. The photon travels to the other electron, which also recoils. This is like having two people in boats and having one of them throw a sack to the other—the thrower’s boat moves in response to the mass of the sack, as does the catcher’s boat.

The Good Vibrations of Quantum Field Theories-qft_figure.png

A traditional Feynman diagram (top) and the same subatomic process using quantum field thinking (bottom). On the left, a photon field is vibrating and the quark and gluon fields are quiescent. When the photon makes a quark and antiquark pair, the quark field is vibrating while the other two fields have no excitation. Finally, when the quark and antiquark combine to make a gluon, only the gluon field has a vibration.

In the QFT approach, a vibration in the electron field induces a vibration in the photon field. The photon field vibration transports energy and momentum to another electron vibration and is absorbed.

In the well-known process where a photon converts into an electron and an antimatter electron, the photon field vibrations are transferred to the electron field and two sets of vibrations are set up—one consistent with an electron vibration and the other consistent with the antimatter electron.

This idea of fields and vibrations explains how the universe works at a deep and fundamental level. These fields span all of space. Some fields can “see” other fields, while being blind to others. The photon field can interact with the fields of charged particles but cannot see gluon or neutrino fields. On the other hand, a photon can interact indirectly with the gluon field, first by making quark vibrations which then make gluon vibrations. It’s kind of like when two quarrelling siblings use a third to pass messages.

Quantum fields are really a mind-bending way of thinking. Everything—and I mean everything —is just a consequence of many infinitely-large fields vibrating. The entire universe is made of fields playing a vast, subatomic symphony. Physicsts are trying to understand the melody.

Go Deeper
Author’s picks for further reading

QED . Richard P. Feynman.

The Particle at the End of the Universe . Sean Carroll.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.