It is the conservation of quark and lepton number that prevents processes like the decay of the three quarks in a proton into a positron and a photon, and thus it is this conservation law that ensures the stability of ordinary matter. But we now think that the complicated nonrenormalizable terms in the field equations that could violate the conservation of quark and lepton number are really present but just very small. These small terms in the field equations would make the proton decay (e.g., into a positron and a photon or some other neutral particle), but with a very long average lifetime,
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