CPT Variance
The CPT theorem
The CPT theorem is one of the most fundamental principles in particle physics, stating that all physical processes remain invariant under the combined operation of charge conjugation (C), parity inversion (P), and time reversal (T). This result emerges from the structure of quantum field theory and special relativity, so every local, Lorentz-invariant theory with a Hermitian Hamiltonian must respect it.
Individual breaking, combined protection
Individual C, P, and the pair CP are all violated in the weak interaction, observed in cobalt-60 beta decay and in neutral kaon decay. The combined CPT symmetry, however, has never been observed to break. Any violation would overturn locality or Lorentz invariance and would carry profound implications for spacetime and the matter-antimatter asymmetry of the universe.
In this toy, C, P, and T are exact involutions. CPT sends a particle to its antiparticle with inverted position and unchanged momentum, and it preserves a scalar invariant the calibration panel checks to zero error.
What the model captures
The companion logic extracts the group-theoretic skeleton: the involution property of each operator, the CPT composition law, a protected invariant, and the linear matter-antimatter asymmetry that vanishes at exact CPT. The violation sliders are illustrative controls with no direct empirical counterpart; the established physics is kept apart from these toy dials in the assumptions below.
- state model: a particle is position, momentum, charge and a matter/antimatter label.
- C flips charge and species; P inverts position and momentum; T reverses momentum. each is an exact involution.
- CPT defined as C then P then T, with a known analytic image for any reference state.
- a CPT scalar invariant (charge times species sign, plus momentum-squared minus position-squared) that the combined operation preserves.
- matter-antimatter asymmetry modelled as linear in the CPT-violating parameter, vanishing at exact CPT.
- calibration checks the involution and invariance identities against their exact values; assumptions keep the CPT theorem apart from the illustrative violation dials.