| MadSci Network: Physics |
The two great ideas of quantum mechanics, the "uncertainty principle" (which says that you can never tell exactly where anything is) and the "particle-wave duality" (which says that electrons, photons, and their friends behave like ripples on a pond when you want them to behave like billiard balls, and vice versa) conspire in a grand joke on humanity to make it impossible to answer "obvious" questions like "How big is it?" "Where is it?" "How heavy is it?" "When did it do that?" "Where did it go?" "Which one is it?"
Okay, enough philosophy: you just want an answer to your question. Here are two answers. Since the "particle-wave duality" says that all particles are actually waves, we can pretty clearly define the "wavelength" of the object. Essentially, we treat it as a ripple on water, and ask how big the ripple is. The equation is
lambda = h/p ~= h/(m v)where h is planck's constant (=6.6*10-34 Joule-seconds), and m and v are the mass and velocity of the particle. The size of the thing depends on how fast it's going! (actually, this length is less a size and more a "fuzziness" in its position.) For "typical" particles making up your body, electrons have a wavelength roughly the size of an atom (an angstrom, 10-10 meters), and a proton or neutron has a wavelength of a few femtometers (10-15 meters). However, this is a pretty useless definition: since we can increase the momentum p of a particle forever using a particle accelerator (lambda = h/mv isn't true for relativistic particles), we can make the wavelength as small as we like, which is essentially saying the particles have zero size.
Another sort of size: An electron has an electric charge. Electrical charges of the same sign repel (must like magnets), so if we say that the electron is made up of an infinite amount of tiny bits of like charge, energy is required to push the little bits together. Since Einstein says E=mc2, that energy is equivalent to a mass. If we suppose that the entire mass of an electron consists of the energy required to hold it together, then we can work out how big the whole ball of wax (err, charge) must be. This is the "Classical electron radius", and is 2.8 * 10-15 meters, or 2.8 femtometers... much smaller than its wavelength. However, this argument completely ignores all the quantum mechanical details which are so important at such a small scale.
If we could stop a photon from moving (we can't) long enough to measure its mass, that mass would be zero. The neutrino and a few other particles also probably have zero mass. How can something that doesn't weigh anything have a size?
I'd say that from a quantum-mechanical point of view, elementary particles don't have a size: if you insist on giving them one, you might as well call it zero.
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