# The Electromagnetic Force

All four forces operate by way of the same basic mechanism: the exchange of virtual particles, usually the gauge bosons. (Physicists have observed real versions of these gauge bosons in the case of the strong, weak, and electromagnetic forces. Most physicists assume it's true for gravity, too.) And yet these forces behave very differently. What gives each force its distinctive character are the properties of its gauge bosons, and the way the gauge bosons interacts with matter particles. So let's start with the electromagnetic force, and see how its behavior is shaped by its gauge boson, the photon.

## Electric Charge

The photon interacts with ("couples to" in the jargon) matter particles with electric charge. These are the quarks and the charged leptons: electron, muon, and tau. (And, of course, their anti­particles.) Hence, these particles are capable of electromagnetic interactions, while neutrinos aren't. In addition, particles that are made up of charged particles also interact electromagnetically. For example, the proton is made up of three quarks, each of which has charge. The proton itself has charge, and so interacts electromagnetically. The neutron is also made up of three quarks, but in such a way that the result is electrically neutral. Hence, the neutron has electromagnetism, not due to any net electric charge, but due to the charged particles that make it up. This is sometimes referred to as "residual electromagnetism," and the effect is rather weak.

## Range

The strength of the electric force between two charged particles decreases as they get farther apart, according to the square of the distance. That is, if you double the distance between two charged particles, the force decreases by a factor of four. Because the force between two charged particles never drops all the way to zero, regardless of how far apart they are, we say that the range of the electromagnetic force is infinite.

This feature of the electromagnetic force is related to the photon's mass. It doesn't have any! * The reason this is important has to do with a combination of the Heisenberg uncertainty principle, the theory of relativity, and the law of conservation of energy. The exact details can be found in any book on quantum field theory, but I'm guessing that you don't have any of these on your reading list for the near future. So instead, we'll go with the stripped-down, oversimplified, math-free explanation.

The theory of relativity implies a very specific relationship betwen a particle's mass and it's energy: E = mc2gamma. (See Dave's Relativity Page for more on this.) But in the case of a virtual particle, the law of conservation of energy prevents this relation from holding. The result is an irreconcilable difference between the energy of a virtual particle and its mass. And the larger the mass, the larger this discrepancy has to be.

The Heisenberg uncertainty principle says that this discrepancy is allowed to occur, but only for a short amount of time. The larger the discrepancy, the shorter the time. But since the discrepancy is proportional to the mass, for a massless particle there's no limit to how small the discrepancy can be, and so there's no limit to how long it can occur.

The reason this leads to a force with an infinite range is that given a limitless amount of time, a virtual photon can wander infinitely far from the charged particle it sprung up from, before being absorbed by some other charged particle. A virtual particle with mass will have only a finite lifetime (the heavier it is, the shorter the lifetime) and so it will only have a finite range. We'll see this with some of the other forces.

## Other Features

We can say lots of other things about the electromagnetic force. For example, it's what holds the electrons near the nucleus in an atom. It's what holds atoms together into molecules or crystals. It holds molecules together into cells, and holds cells together into people or plants or pasta. It keeps two solid objects, such as you and the chair you're sitting on, from passing through each other, and so on. But we won't. The features I've chosen to emphasize on this page, are the ones that distinguish electromagnetism from the other forces covered on the next few pages. Such as, the strong force.

The Strong Force
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* Well, it has no mass as far as we know. It turns out that it's really impossible to prove that something is completely massless, since a particle that's completely massless behaves exactly the same as a particle whose mass is simply too small to notice. Hence all we can really say about the photon's mass is to quote an upper limit. That is, "I don't know if it's massless, but I do know it's lighter than...," followed by some number. And for the photon, that number is really small. About 6 x 10-16 eV (.0000000000000006 electron-Volts). And at least one group of physicists claims to have established an upper limit on the photon mass that's about ten orders of magnitude smaller than this! For reference, the lightest particle that we know does have mass, is the electron, which has a mass of about half a million eV. So with that in mind, I'll go ahead and refer to the photon as "massless." (There are theoretical reasons to believe that the photon is exactly massless, as well.) Back