CPT-symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. 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 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.
Stephen Hawking explains this, considering 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 of matter replaced by anti-matter (corresponding to a charge inversion), and reversed in time. The preservation of CPT-symmetry would mean that both the universes will evolve alike, in the sense that, at any moment, they are identical and the CPT transformation would simply take one into another. The symmetry is recognized to be a very fundamental property of physical laws.
See also