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This month's Scientific American has an article about preons, which are hypothetical particles that the standard-model particles would be built out of. They discuss a problem with confinement in these models. We know that, say, an electron has a size less than x. This requires an uncertainty in momentum of at least h/x. Say for simplicity that the preon is ultrarelativistic. Then its energy has to be at least h/x (in units with c=1), and this is equivalent to a rest mass of at least h/x. Putting in x<~10^-17 m for an electron gives m>~10^-25 kg, which is much too big for an electron. All of these arguments would seem to apply equally well to any theory in which standard-models have substructure. E.g., it would seem to apply to string theory.
How is this not a showstopper for such models? The Sci Am article makes vague references to a resolution by some technical trick. The same problem occurs for a pi meson, and they say this was solved by Goldstone 1961 for bosons. Apparently 't Hooft extended the solution to fermions in 1979.
Can anyone explain what's going on, using crayons?
How is this not a showstopper for such models? The Sci Am article makes vague references to a resolution by some technical trick. The same problem occurs for a pi meson, and they say this was solved by Goldstone 1961 for bosons. Apparently 't Hooft extended the solution to fermions in 1979.
Can anyone explain what's going on, using crayons?