CPT Symmetry

So, this is a random post on some background physics I felt like looking into. I've heard lots of talk about CPT symmetry, so I figured a post on it was reason enough to research it a little.

Physics requires that certain processes behave the same under specific transformations. Fundamental to our understanding of the universe is CPT-symmetry, which essentially says that if we replace a system of particles with their antiparticles, flipped the sign on the spatial axes, and ran time backwards, the same laws of physics would hold. Violating CPT-symmetry causes relativity itself to break down, so most physicists are big into maintaining CPT-symmetry, and working out how to test it. The first process most people talk about is charge symmetry (c-symmetry).
In charge symmetry, all of the positive charges are replaced by negative charges, and all of the positive charges are replaced with negative charges. In essence, we replace all of the particles of the system with their anti-particles. If everything still behaves the same, then the system is charge-symmetric, which would be nice. For gravity, the nuclear strong force, and the electromagnetic force, charge parity holds. However, the weak interaction (the same one that let's us break strange, charm, top, and bottom conservation in this post) is not charge invariant. Due to something called chirality (or handedness), the weak force can tell the difference between the particle system, and the antiparticle system. Only left-handed particles and right-handed antiparticles are allowed to interact by the weak force. Charge symmetry doesn't affect the handedness of the particle, but does affect whether it's a particle or antiparticle. Thus, charge symmetry can change whether something should or shouldn't interact via the weak force. Therefore, in particle physics, charge symmetry does not hold, something you might not expect from a classical (non-quantum mechanical) understanding of electricity and magnetism.
The second major symmetry is parity symmetry (p-symmetry). Parity symmetry essentially takes the original system and dumps it in a mirror universe. Where we assign a particle the position (x,y,z), the reflected world gives it the position (-x,-y,-z). If the laws of nature still hold, the world is parity symmetric. Gravity, the strong force, and the electromagnetic force all have no problem with parity symmetry. But, the weak force does. Here, the handedness of the particle gets flipped, but not whether it's a particle or an antiparticle. So, again, the major issue is that something that would originally interact weakly no longer interacts via the weak force after the transformation.
However, we have complimentary problems here. C-symmetry gives us the wrong class of particle (normal matter or antimatter) while maintaining handedness, while p-symmetry gives us the wrong handedness while maintaining the class of particle. So some theorists had a bright idea: since it would be really nice and simple for our universe to be symmetric, let's combine the two. Hence, physicists talk a lot about CP-symmetry. For a CP-symmetric process, both the spatial dimension and the charge get flipped, so our problem of particle-type and handedness gets fixed.
However, from experiment, we know that there are times when CP-violation is violated. So, CP-symmetry does not always hold. Thus, for CPT-symmetry to hold, we need to find some T-symmetry violating processes.
Time symmetry seems counter-intuitive. We know time to be asymmetric, eggs fall to the ground and shatter, but no egg fragments come together and fly up onto a table. However, the individual processes acting on the egg at very small scales are time-symmetric. When we look at all of the tiny interactions, each is reversible on it's own. It's the macroscopic behavior, and the second law of thermodynamics, that provide our macroscopic sense of time as an arrow pointed in one direction only. However, there are some theoretical ways to violate time symmetry. One of these is a non-zero electric dipole moment of the neutron. If the neutron has a non-zero electric dipole moment, it wouldn't behave the same if you flipped the direction of time. So, lots of experiments are currently attempting to measure the nEDM, as it's called. I was involved in one last summer, and a friend is involved in the planning stages of one now. If physics does manage to measure a non-zero nEDM, it would set constraints on how much CP-symmetry is allowable, or it would point to a model of physics outside the Standard Model. But more on that later.