CPT invariance is the hypothesis that the fundamental laws of physics do not change under the combined operation of charge conjugation (C), parity reversal (P), and time reversal (T). It is most often invoked in the context of particle physics. Unlike parity invariance and CP invariance before it, CPT has been proven to be an exact symmetry of nature under a very general set of conditions.

Intuitively, the universe seems like it should be invariant under parity reversal, which is the operation of replacing everything with its mirror image; left becomes right, up becomes down, and so on. However, it was discovered in the 1950's that this symmetry is actually violated completely in processes mediated by the weak nuclear force. Most notably, neutrinos are only made with left-handed spin^{1}, despite that the mirror image of a left-handed particle is a right-handed particle. So particle physicists were sent in search of a new fundamental symmetry of nature, because these things are just too useful a handle on the catalogue of allowed and forbidden processes involving fundamental particles.

The next choice that we made was CP symmetry, the operation of parity reversal followed by charge conjugation: a swap of all particles for their corresponding antiparticles. In effect, what this is saying is that we think the 'true' mirror-image of a left-handed electron is not a right-handed electron but rather a right-handed positron. Initially this appeared to be an exact symmetry, but precision experiments on kaons in 1964 by Cronin and Fitch showed a small violation of CP symmetry.

In the 1970's the Standard Model of particle physics was formulated, based on the remarkable if difficult building block of quantum field theory. One component of the Standard Model is the CPT theorem, which proves that any quantum field theory meeting a set of three very general requirements must be invariant under the combined operation of CPT. These requirements are that the field theory obey special relativity (Lorentz invariance), that the field's behavior at a given point only depends on its state at and adjacent to that point and not on its state anywhere else (locality), and that the energy of the system is physically observable without ambiguity (Hermitian Hamiltonian). All of these are bedrock assumptions of most, if not all, of modern physics.

Naturally, this grandiose prediction inspired several experimental tests. These tests are ongoing, but CPT invariance is remarkably difficult to test. The most promising test being considered presently concerns the structure of antimatter atoms. Since an atom is a stable bound state, it is trivially invariant under time reversal, and CP transformation of a matter atom provides an anti-atom. Thus the structure of an anti-hydrogen atom should be exactly the same as that of a hydrogen atom if CPT is an exact symmetry.

An indirect lever on the possibility of CPT violation is the observation of time reversal violation. Since CP violation is a known part of the Standard Model, for CPT to hold there must be a corresponding violation of T symmetry to cancel it out. Time reversal is the most difficult of the three discrete symmetries to test; unlike parity and charge conjugation it is not within our power to directly reverse the situation. Nevertheless, there are situations where an effective time reversal may be performed in the theory with a measurable consequence.

One important example of this kind of observable is the electric dipole moment of an elementary particle, or even a nucleus. If an electron, say, were to have a permanent electric dipole moment, it would have no direction to follow except the direction of its magnetic dipole moment, either parallel to it or anti-parallel. However, under time reversal an electric dipole moment is unchanged, whereas a magnetic dipole moment reverses its direction. Clearly the two cases are distinguishable if the electric dipole moment is nonzero, hence an observation of a nonzero electric dipole moment is most likely an observation of time reversal violation. This measurement is complicated, though, by the ability of compound objects like nuclei and atoms to form temporary electric dipoles when exposed to an electric field.

CPT invariance is an important topic in modern-day particle physics. Were it shown to not occur, 'all hell would break loose' in the world of fundamental particle theory, with one or more of the fundamental assumptions of the theories necessarily invalid. Nevertheless, the form of CPT violation would suggest the direction a new theory would take, and although it would be disruptive, CPT violation would open the door to a vast new area of unexplored subatomic physics.

^{1}: We define the handedness (or

helicity) of a particle by the hand whose fingers curl in the direction of the spin while the thumb points in the direction of motion.

Sources include my undergraduate and graduate particle physics courses, conversations with my thesis supervisor, David Griffiths's text Introduction to Elementary Particles, and the Wikipedia article CPT Theorem.

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This writeup is copyright 2006 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence. Details can be found at http://creativecommons.org/licenses/by-nd-nc/2.0/ .