That's a neat article. Thanks for sharing.
Much of what I'm going to talk about here comes from Weinberg's "The Quantum Theory of Fields". If you like you can look up the references there.
We really don't need to invoke an extra "anti-Universe" in order to talk about CPT. Any (relativistic) Quantum Field Theory contains CPT symmetry. If we find that CPT is not a symmetry of nature most of our theories aren't worth as much as garbage. Let's talk some.
Why do we even care about CPT invariance? Well, it is basically the principle that if we can make a physical process go "backward" then we are doing a CPT transformation. It would make a great deal of sense that the Universe should be able to go backward or forward under the same laws. (I'm ignoring things like entropy, which sets a "forward" direction for time. I read once that it was possible to reverse time and still be able to do the entropy thing but I don't recall how.)
CPT is an invariance that is broken into several pieces. First of all, parity is such an obvious symmetry of nature that it took a very long time to find out that it is not always a symmetry. A parity transformation takes a vector x into a new vector -x. Until somewhere in the early 60s it was assumed that all the laws of nature were invariant under a partity transformation. I mean, really, it shouldn't be that complicated, but it actually is. There was an experiment being done on a lump of cobalt and it was noticed that electrons were being preferentially emitted in a specific direction, which is pretty weird. Now-a-days we say that the weak nuclear force, the mechanism for radioactive decay, does not require parity invariance. So P (the parity operator) is not conserved.
To save a long conversation (I'll give more details if you request) "charge conjugation" is also not an invariant operator. (That's where you replace your particle with its anti-particle.) The decay of a neutral kaon has two pion decay channels, \(\displaystyle \pi ^0 ~ + ~ \pi ^0\) and \(\displaystyle \pi ^+ ~ + ~ \pi ^0 ~ + \pi ^- \). For a long time it was thought that there were two particles, each with its own decay channel, but it was eventually proven that there is only one of the things. Some other heavy mesons have similar decays. So charge conjugation as an invariance is down, too.
To make things even worse, if we combine P and C we find that even the CP operator (switch the parity and do charge conjugation) is also not an invariance.
That leave us with time invariance (make everything move "backward" in time), T. We don't know if this one is conserved but since we are speculating that CPT is invariant and that CP isn't then we are left with the conclusion that T is also not invariant.
These are small, but detectable, variances. All but T and CPT have been directly measured.
I can go into more detail if anyone wants.
-Dan