A quark is an elementary subatomic particle; three of them make up a proton or a neutron. Some scientists base the suggested existence of quark stars (which would be made of quarks instead of complete protons or neutrons) on a famous conjecture by the eminent Princeton physicist Ed Witten. He said the true ground state of matter (in the sense of the lowest energy per particle) consists of a mixture of roughly equal numbers of up, down, and strange quarks, with enough electrons thrown in to ensure that this soup is electrically neutral.
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