Quantum Theory's Most Incredible Prediction | Space Time

SPEAKER_1 (0:00)

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Matt O'Dowd (0:33)

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Let's talk about the best evidence we have that the theories of quantum physics truly represent the underlying workings of reality.

Quantum field theory is notoriously complicated, built from mind-bendingly abstract mathematics. But could it be that the underlying rules that govern reality are really so far from human intuition? Or a physicist just showing off?

For better or worse, the physicists are definitely on the right track. We know this because the predictions of quantum field theory stand up to experimental test time and time again. Quantum field theory describes a universe filled with different quantum fields in which particles are excitations, quantized vibrations. We've talked about QFT many times before, starting with the very first quantum field theory, quantum electrodynamics. QED talks about the electromagnetic field whose excitations give us the photon. The calculations of QED describe how this field interacts with charged particles to give us the electromagnetic force, which binds electrons to atoms, atoms to molecules, and therefore allows you to exist. QED is a much deeper and more complicated description of electromagnetism than the simple opposite charges attract like charges repel of classical electrodynamics. But how do we know it's right? Well, because it makes some predictions that clash with the classical theory. And those predictions are the most precisely tested and thoroughly verified in all of physics. Today we're going to talk about the theory and experiments behind one of these tests– measuring the G factor. Or in simple English, measuring the anomalous magnetic dipole moment of the electron. OK, first up, what on earth did I just say?

What is the anomalous magnetic dipole moment? Well, it's just like the regular magnetic dipole moment, but more anomalous.

OK, not helpful. Let's break down this magnetic dipole moment thing. Consider a bar magnet. It has a dipole magnetic field, basically meaning it has a north and south pole. Dipole, two poles. If we put a bar magnet in a second external magnetic field, it will feel a torque, a force causing it to rotate to align with that field. The tendency of a dipole magnet to rotate in an external magnetic field is its magnetic dipole moment. Anything with a dipole magnetic field has a magnetic dipole moment is basically a measure of how much it would interact with an external magnetic field if one existed. Let's talk about this dipole thing a bit more. Magnetic fields are produced by moving electric charges. A perfect dipole field is produced by charges moving in circles. For example, a loop of wire with an electric current or the planet Earth with its dynamo core.

But in the case of a bar magnet, the source of its magnetic field is a bit weirder. It mostly comes from the summed dipole magnetic fields of individual electrons in the outer shells of its atoms. And those electron dipole fields are indeed very weird. As we'll see, their nature is predicted by quantum theory. Measure electron magnetic moments and you verify your quantum picture of reality. Electron magnetic fields seem intuitive if you think of them as tiny balls of rotating electric charge.

Except electrons aren't balls and they aren't really rotating. As far as we know, electrons are point-like. They have no size and it doesn't really make sense to think of an infinitesimal.

SPEAKER_1 (4:30)

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Matt O'Dowd (5:00)

point as rotating.

Nonetheless, electrons do have a sort of intrinsic angular momentum, a fundamental quantum spin that is as intrinsic as mass and charge. Despite not being the same as classical rotation, this quantum spin does grant electrons a dipole magnetic field. So electrons have a magnetic dipole moment, meaning they feel magnetic fields and act as little bar magnets. Electrons in atoms feel the magnetic fields produced by their own orbits around the atom. This results in a subtle torque on these electrons, changing their energy states and resulting in the fine structure splitting of electron energy levels. The fine structure constant is named after this effect, and we talked about this fundamental constant in an earlier episode. Thinking of electrons as little bar magnets or as rotating balls of charge is a nice starting point, but in the end it's misleading. It also gives you completely the wrong answer if you try to calculate the electron's magnetic moment. So that electron diagram you did in middle school, it's time to kill that idea, just like you kill your Tamagotchi. In fact, weirdly, if you measure the magnetic dipole moment of an electron, you get almost exactly twice the value you'd expect for a tiny classical sphere with the same charge and angular momentum as an electron.