The field of particle physics is full of what can be confusing dichotomies: fermion vs. boson, hadron vs. lepton, paper vs. plastic (okay, not that last one). You can add yet another to the list: extended particles vs. point-like particles.
The quarks, leptons and bosons of the Standard Model are point-like particles. Every other subatomic particle you’ve heard of is an extended particle. The most familiar are the protons and neutrons that make up the nucleus of an atom, but there are many others—pions, kaons, Lambda particles, omegas and lots more. The defining feature of these kinds of particles is that they have a reasonably measurable size (which happens to be about the size of a proton).
Now extended particles don’t have a well-defined surface like a marble does. They’re a bit more like the Earth and its atmosphere. The atmosphere of the Earth is thickest near the surface of the Earth and it gets thinner with altitude. So the exact point at which you can say that you are no longer in the Earth’s atmosphere is a bit fuzzy, but you can still safely say that the boundary between inside and outside the Earth’s atmosphere is 10 or 20 miles straight up. Independent of the exact point at which you say something is inside or outside, extended particles have a size.
Point particles are much more bizarre and are sometimes said to have zero size. This statement has raised more than one eyebrow. How can something have no size at all? And if it has mass, does the zero size mean it has infinite density? (And by the way, as you read on, you’ll see the answer to that last one is no.) You begin to see why some people are skeptical when a scientist says a particle is point-like.
Yet there is a sense in which it’s true. So how can that be?
Let’s start with the easiest point-like particle we know, the electron. Assume it has zero size. Although we know that the quantum realm differs from the familiar world, in which things are measured in inches and feet, we can still get a reasonable mental image of what happens as we imagine looking at an electron with a perfect microscope. To begin with, since it has zero size, you can never actually see the electron itself.
However, you notice the electron does have an electric charge, and that sets up an electric field around it. That’s the first crucial point. The second crucial point is an idea called the quantum foam, which refers to the fact that empty space isn’t actually empty. Matter and antimatter particles appear and disappear with utter abandon, willfully flouting what seems like a principle of common sense. Empty space is actually pretty complicated.
Now if you combine those two ideas—that there is an electric field and that space consists of a writhing, bubbling mix of particles—then you can imagine what a point particle is like. At a large distance from the particle, its electric field is weak and doesn’t much affect the quantum foam. However, as you get closer to the point particle, the field becomes stronger. The stronger field affects the ephemeral virtual particles to a greater and greater degree, eventually lining up other particles with its point particle. (For example, the field of a positively charged point-like particle will push away other positive particles and hold negative particles close.)
Thus if you collide two point-like particles, while the two particles might never actually collide, the cloud of particles surrounding them will likely interact. The point-like particle is the mathematical abstraction at the center of the particle, but the extended field in essence makes even a point particle not so point-like.
While the quarks, leptons and force-causing bosons of the Standard Model are all currently treated as point-like, there is no guarantee that this will always be true. It may be that as we probe to smaller and smaller sizes, we will eventually find that the particles we thought were point-like are actually extended particles with smaller things inside them. However, because the core particle is surrounded by this extended cloud, determining whether the core is point-like or extended is a real challenge.
In summary, extended particles have a fixed size, although they may have a fuzzy edge; point-like particles are mathematical abstractions with zero size. But even zero-size particles have an extended effect, due to the effect of the field surrounding them.
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