Mysteries of Magnetism

The ancient Greeks thought of atoms as the smallest, indivisible bits of matter. By the twentieth century, experiments showed that (what we nowadays call) atoms have internal structure; a key early experiment was the Geiger-Marsden experiment, performed under the supervision of Rutherford, about which we’ll have more to say in a future post.

But the desire to know the fundamental particles of nature is stronger than ever. With the tremendous technical improvements in particle accelerators in the second half of the twentieth century, the drive to probe for the smallest constituents of matter became a major theme in physics.

It’s satisfying to our modern sensibilities (reductionism, again!) to know that a macroscopic charged object has a number of elementary charged particles within it, and the net charge on the macroscopic is the algebraic sum of the charges on the elementary particles within it. (Schematically, if there are 100 protons and 99 electrons in the object, then its net charge is +1. Of course, the number of elementary particles in a macroscopic object is truly enormous, but I hope you get the idea.)

But how can we ever know that we’ve finally reached the smallest indivisible bits? I suppose we never shall know; we can continue to probe at smaller and smaller distance scales (which involves higher and higher energies, which means bigger and bigger particle accelerators), but one can never be sure that there isn’t structure at distance scales that are currently beyond our reach.

The Geiger-Marsden experiment mentioned led to Rutherford’s hypothesis that most of the mass of an atom is concentrated in a very small central region, which he dubbed the nucleus of the atom. Later experiments led to the discovery of the neutron, so it became known that the nuclei of atoms could contain both protons and neutrons. Still later scattering experiments (for recent studies, see here) led to the suggestion that protons and neutrons have internal structure. Nowadays, the standard model of particle physics hypothesizes that protons and neutrons are composed of quarks; although quarks have never been isolated, their theory is very well-developed, and there is a very large body of experimental evidence to support this theory.

But so far, all scattering experiments involving electrons have failed to detect any structure within them. Experiments have also failed to detect a lower limit to the size of an electron. This is mysterious, and also troubling. A point particle is problematic theoretically, as it would require a modification of the current theories of electromagnetism. If an electron is really a point particle, then according to Coulomb’s law, its electric field would get arbitrarily large as you approach one more and more closely. Similarly, electrons have mass, and if the mass is concentrated at a point, the density of an electron would be infinite, and its gravitational field would also increase indefinitely as you approached it more and more closely.

In any case, maybe electrons and quarks are truly fundamental particles, and therefore qualify as “atoms” in the sense of the ancient Greeks.


The first puzzle of magnetism is that magnets always occur in the form of dipoles; that is there is always a North pole and a South pole to a magnet. It is possible to have electric dipoles also, but an electric dipole consists of a positive charge and a negative charge. It’s possible to separate the two electric charges so that they are far away from each other, and study each one separately. The same cannot be said for magnetic dipoles; trying to separate the two poles of a magnet, say by cutting a metal bar magnet in half, typically results in two dipole magnets, each with its own North and South pole. Try as one might, so far no one has been able to isolate a North magnetic pole by itself, or a South magnetic pole by itself. Another way to say this is that magnetic monopoles (the analogues of individual charged particles that could be placed near each other to create an electric dipole), if they exist, have not been detected yet.

The second puzzle of magnetism is the nature of the microscopic cause, or source, of magnetism. Mass is the source of gravitational fields (at least in Newton’s classical theory; in Einstein’s modern theory of gravity, mass, energy, pressure, etc. are all sources of gravitational fields), and many fundamental particles have mass. Thus, the source of gravitational fields (at least classically) can be identified microscopically as elementary particles that have mass.

Charge is the source of electric fields. Microscopically, the source of electric fields can be traced to those elementary particles that have charge; for example, electrons and quarks.

What is the microscopic source of magnetic fields? Do some elementary particles have some intrinsic magnetism?

Well, macroscopically, electric currents are a source of magnetic fields. Around any current-carrying wire there is a magnetic field, that decreases in strength as you move away from the wire. The field can be made stronger by coiling the wire, which explains why you should never coil the speaker wires of your sound system: The resulting magnetic field could be strong enough to foul up the sound output from the speakers.

And there is some sympathy with the thought that this is the only source of magnetic fields; after all, there seems to be no fundamental magnetic particle (a hypothetical magnetic monopole, as mentioned above). Could it be that all magnetism is caused by circulating electric charges?

Well, it turns out that some fundamental particles have intrinsic magnetism. This sounds reasonable for neutrons and protons, because they are composed of quarks, which are charged. So one can imagine that perhaps the quarks are circulating inside the protons and neutrons, and the circulation (which constitutes an electric current) is the cause of the magnetism.

But what about electrons? If they are truly elementary, and have no deeper structure, then if you really want to explain all magnetism by electric current, you have a problem. Furthermore, electrons have intrinsic angular momentum, but explaining this in terms of real physical rotation (a spinning electron, assuming the electron is a sphere small enough to be compatible with experimental limits on its size) is problematic because the surface of the electron would have to be moving faster than the speed of light.

Saying that electrons just have intrinsic magnetism, and that’s just the way it is, so don’t try to understand it any further, is a little unsatisfying. However, F. J. Belinfante in 1939 came up with the idea that perhaps the origin of both the electron’s “intrinsic” angular momentum and its “intrinsic” magnetism is not intrinsic at all, but a consequence of energy flows in the electron’s electromagnetic field. A paper of Ohanian (What is Spin? American Journal of Physics, Volume 54, Number 6, June 1986, pages 500–505) explains the details and brings the idea to the attention of a modern audience.

Ohanian’s thought-provoking paper is worth checking out if you are interested.

(This post first appeared at my other (now deleted) blog, and was transferred to this blog on 22 January 2021.)