That's a great question!
Particle masses are measured in a great variety of ways. If they
are big and heavy enough, you can put them on a scale. Subatomic
particles have to be measured much more carefully than that.
Typically, subatomic particle masses are determined by the
relationship between their energy and their momentum. If a particle is
not moving, its total energy is E=mc^2. If it is moving, then
E^2=(mc^2)^2+(pc)^2, where p is the momentum and c is the speed of
light.
One way to measure the mass, say, of a proton, is to put it in a
mass spectrometer. Accelerating it in a known electric field gives it
an amount of kinetic energy proportional to its charge. Causing the
proton to move in a circular path in a uniform, well-calibrated
magnetic field allows the momentum to be measured quite precisely.
Another way of measuring the proton mass is to get a very pure
sample of hydrogen molecules with a known number of protons in it,
weigh it, and subtract off the masses of the electrons and also the
binding energies of the electrons in their molecular orbits.
Some subatomic particles are heavy and unstable. You can measure
their masses by computing the total energy and momentum of their decay
products, if you happen to know the masses of their decay products and
can measure their momentum (a typical situation in a high-energy
experiment -- we usually have a big magnet and a detector inside which
can measure particle's paths. The curvature of the paths tells what the
momentum is).
Other particles are very light and do not decay. The photon is one
of them. Models of electricity and magnetism which include a small mass
for the photon predict that the electromagnetic interaction should have
a finite range, kind of like the weak nuclear force, which is mediated
by particles which are kind of like the photon, but are very massive.
No evidence has been observed that the electromagnetic force has any
range limitation, and upper limits have been set on the photon mass
that are extremely stringent.
We used to think that neutrinos were massless. The more skeptical
among us pointed out that there was no proof, experimental or
theoretical that neutrinos couldn't have a mass, and so a series of
experiments was constructed in Japan, Canada, the U. S. and Switzerland
to see if neutrinos had mass. This one's tricky because they don't
decay and interact only very seldom with matter at all. It turns out
that there are three kinds of neutrinos that we know of, one
corresponding to each kind of lepton -- the electron neutrino, the muon
neutrino, and the tau neutrino. It turns out that if (at least some of)
their masses are not zero, and some parameters called mixing angles are
not zero, then neutrinos can change spontaneously from one type to
another, and back. We call this "flavor oscillation". The rate of
flavor oscillation, which can be measured experimentally, is
proportional to the difference in the squares of the masses of the
neutrinos undergoing oscillation. We don't yet have measurements of the
masses of the neutrinos themselves, but know something about the
differences in the squares of their masses.
Similar elegant oscillation techniques can determine with
tremendous accuracy the mass difference between similar particles, for
example, in the pair of neutral kaons.
Tom
(published on 10/22/2007)
