Subatomic Physics

270 P , C, CP, andT
P and C, and we shall discuss one in Chapter 11. However, it is extremely difficult
to construct a Lorentz-invariant Hamiltonian that violates CPT. (These statements
are somewhat oversimplified, but the essential features are correct.)
The CPT theorem was something of a sleeper. In preliminary form, it was
discovered independently by Schwinger and by Lüders. (35) Pauli then generalized
the theorem. (36) Up to 1956, however, it was considered to be rather esoteric.
Dogma held that the three operations T , C, andP were separately conserved, and
the CPT theorem was assumed to give little experimentally usable information.
When violation of parity became a possibility, the CPT theorem suddenly acquired
more meaning (37) : Equation (9.90) states that if P is violated, some other operation
must also be violated. Indeed, we have mentioned in Section 9.4 that C is also not
conserved in the weak interaction.
The CPT theorem can be tested. For instance, it predicts that the masses and
lifetimes of weakly decaying particles and antiparticles, such as the negative and
positive muon, should be identical, even though charge conjugation invariance does
not hold in the weak interactions. No violation of the CPT theorem has been
found, despite a resurgence of interest caused by some (string) theories which try
to unify gravity with the other interactions. Tests that are as good or better than
the equality of the masses of the neutral kaons , ¯ K 0 and K 0 to about 1 part in 10 14
have been performed. (38)
After this digression, we return to the situation in 1964. The observed CP
violation in the decay of the neutral kaons together with the CPT theorem leads
nearly inescapably to one of two conclusions: either T is not conserved or the CPT
theorem is wrong. Theorists had in the meantime found even stronger proofs for
it (39) and were rather reluctant to give it up. On the other hand, time reversal is
also a cherished symmetry. Certainly the easiest way out would have been capitulation
of the experimentalists with an admission that the experiments were wrong.
Additional data, however, strengthened the earliest conclusions. Detailed analysis
of all the information from the decays of the neutral kaons at least provides some
further insight. The analysis implies that the CPT theorem holds but that not only
CP but also T invariance is violated. (40)
35J. Schwinger, Phys. Rev. 82, 914 (1951); 91, 713 (1953); G. Lüders, Kgl. Danske Videnskab
Selskab, Mat.fys. Medd. 28, No. 5 (1954).
36W. Pauli, in Niels Bohr and the Development of Physics, (W. Pauli, ed.) McGraw-Hill, New
York, 1955.
37T. D. Lee, R. Oehme, and C. N. Yang, Phys. Rev. 106, 340 (1957).
38CPT and Lorentz Symmetry III, (Alan Kostelecky, ed.), World Sci., Singapore, 2005.
39Proofs of the CPT theorem require relativistic field theory and are never easy. For the reader
who wants to convince himself of this fact, we list here a few references, approximately in order
of increasing difficulty: J. J. Sakurai, Invariance Principles and Elementary Particles, Princeton
University Press, Princeton, N.J., 1964; G. Lüders, Ann. Phys. (New York) 2, 1 (1957); R.
F. Streater and A. S. Wightman, PCT, Spin, and Statistics, and All That, Benjamin, Reading,
Mass., 1964.
40R. C. Casella, Phys. Rev. Lett. 21, 1128 (1968); 22, 554 (1969); K. R. Schubert, B. Wolff, J.
C. Chollet, J. M. Gaillard, M. R. Jane, T. J. Ratcliffe, and J.-P. Repellin, Phys. Lett. 31B, 662
(1970); G. V. Dass, Fortsch. Phys. 20, 77 (1972).