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Luke_A_Somers comments on What was your biggest recent surprise? - Less Wrong Discussion
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All of those gluons and quark-antiquark pairs are every bit as stable as the Earth's gravitational field. They're elements of the ground state for a quark.
The process of finding the ground state for a particle from its interactions, including dragging in virtual pairs to screen high field intensities around the singularity, is called Renormalization.