Wednesday, June 19, 2013


I should not post late at night.

A few things might make the 4-quark post a little clearer.

Quantum mechanics assumes that an object can be described by a linear combination of states, where a state can be such things as:

  • an electron and a positron orbiting each other with a specific angular momentum
  • an up quark and an anti-up quark orbiting each other with that specific angular momentum
  • a neutrino and an anti-neutrino orbiting each other with that specific angular momentum
  • an electron and a positron and a photon, with the photon going between the two
  • a top quark and an anti-top quark orbiting each other with that specific angular momentum
  • a neutron and an anti-neutron orbiting each other ditto
  • other combinations that have the same quantum numbers (charge, angular momentum, etc)

The experienced reader will have noticed that the masses of these combinations seem a little disproportionate: the top quark is perhaps a hundred billion times heavier than a neutrino. Can it be in the same mix? Yes: but its contribution will be correspondingly tiny. Or if you want to try to interpret that statement, you might say something like: "It only exists a little bit there, or it only exists for a tiny amount of time."

Interpretations are controversial, and these are no exception. But one way to understand it goes like this. Particles that only exist for a small amount of time have (thanks to the Uncertainty Principle) some fuzziness in their energy. For a big fuzziness in energy/mass (being "off the mass shell"(*)) the particle can only exist for a proportionately tiny amount of time. (δE δT > h).

If a particle is unstable, it typically winds up in a final state based on one of those component states. If possible. One way to think of a positive pion (mass 140 MeV/c^2) is as a combination of a proton (mass 938 MeV/c^2) and an anti-neutron (mass 940 MeV/c^2). That is handy for describing some of its interactions, but you'll notice the mass numbers don't add up--it is the proverbial gallon of frogs in a pint jar--so it never decays into a proton and neutron. It doesn't decay into a positron and electron neutrino either, but instead into a positive muon and muon neutrino, but that's a topic for another day.

(*) The term "mass shell" comes from the description of the possible particle momenta in momentum 4-space (Px,Py,Pz,Energy). For a particle of known mass, the possible momenta are restricted to a 3-dimensional "cone" or shell in the 4-space. If there's fuzziness in the mass because of the Uncertainty Principle, the momentum can be away from that cone/shell: "off the mass shell."


Texan99 said...

I've always wondered if a legitimate way to think about these puzzling not-quite-there wavicles, with their strangely cyclical properties, was that they rotate in and and out of our plane of existence from "somewhere else." Maybe they're not here much of the time, and they can get from here to there without crossing the intervening space in the conventional way.

james said...

That's one interpretation, but not a popular one, because it requires a "somewhere else" that isn't defined either. "Anyone who is not shocked by quantum theory has not understood it." Niels Bohr (variant: "If you think you can talk about quantum theory without feeling dizzy, you haven't understood the first thing about it.")

Texan99 said...

"Defined"! heavens, no. Nothing but a flyer of a speculative thought. Might make a good scifi story.