CPT symmetry
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CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously.
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History
Efforts in the late 1950s revealed the violation of P-symmetry by some phenomena that involve weak nuclear force fields, and there are well known violations of C-symmetry and T-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too. There is a theorem that derives the preservation of CPT symmetry for all of physical phenomena assuming the correctness of quantum laws. Specifically, the CPT theorem, by John Stewart Bell, states that any Lorentz invariant local quantum field theory with a Hermitean Hamiltonian must have CPT symmetry.
Derivation
For a handwaving argument, take a Lorentz boost in a fixed direction, let's call it z. If we complexify the Lorentz group, an imaginary boost with a boost parameter of iπ will result in t going to -t and z going to -z. If we later perform an addition rotation by π in the xy-plane, we get a combination of P and CT. The combination CT appears here instead of T because we are dealing with a unitary transformation, not an antiunitary one. Assuming that the operation of taking a complex boost is valid as a symmetry, we still get a state which is described by the same laws. This gives us the CPT theorem.
Consequences and Implications
A consequence of this derivation is that a violation of CPT automatically indicates a Lorentz violation.
The implication of CPT symmetry is that a mirror-image of our universe — with all objects having momenta and positions reflected by an imaginary plane (corresponding to a parity inversion), with all matter replaced by antimatter (corresponding to a charge inversion), and reversed in time — would evolve exactly like our universe. At any moment, the two universes would be identical, and the CPT transformation would simply turn one into the other. CPT symmetry is recognized to be a fundamental property of physical laws.
The CPT theorem can be generalized to take into account pin groups.
See also
- Poincare symmetry and Quantum field theory
- Parity (physics), Charge conjugation and Time reversal symmetry
- CP violation and Kaon