CPT Theorem

Core Idea

The CPT theorem states that any local, Lorentz-invariant quantum field theory with a Hermitian Hamiltonian is invariant under the combined operation of charge conjugation (C), parity (P), and time reversal (T). This is an exact symmetry -- not approximate -- and implies that particles and antiparticles have exactly equal masses, lifetimes, and (opposite) charges. No violation of CPT has ever been observed.

Explainer

The CPT theorem is one of the most fundamental results in quantum field theory. It states that any local, Lorentz-invariant quantum field theory with a Hermitian Hamiltonian is automatically invariant under the combined operation CPT: charge conjugation (replacing every particle with its antiparticle), parity (reflecting all spatial coordinates), and time reversal (reversing the direction of time). This is not an assumption or an observed symmetry -- it is a theorem, provable from the axioms of QFT.

The individual operations C, P, and T need not be symmetries. The weak interaction violates P maximally (only left-handed fermions feel the weak force) and violates C (the charge-conjugate process has a different rate). It even violates CP, as observed in kaon decays (1964) and B-meson decays (2001). But the CPT theorem guarantees that the triple product is always conserved. If CP is violated, then T must be violated in exactly the compensating way, and this prediction has been verified experimentally.

The physical consequences of CPT invariance are remarkably concrete. Particles and antiparticles must have: exactly equal masses (tested to parts per trillion for proton/antiproton and electron/positron), exactly equal lifetimes (tested to parts per thousand for muon/antimuon and kaon/antikaon), and exactly equal and opposite charges (tested to extraordinary precision for electron/positron). Any observed difference would signal CPT violation and would require abandoning locality, Lorentz invariance, or unitarity -- any of which would be revolutionary.

The theorem also connects to the matter-antimatter asymmetry of the universe. CPT invariance means the laws of physics do not prefer matter over antimatter in any absolute sense. The observed preponderance of matter must therefore be generated dynamically from an initially symmetric state, through processes that violate CP (and hence T, by CPT) -- the Sakharov conditions. The CP violation in the Standard Model (from the CKM matrix) is too small to account for the observed asymmetry, implying new sources of CP violation beyond the Standard Model.