2

This is something I'm struggling to get a clear answer on.... So on the one hand we say $C$ is the charge inversion operator and describes a particle turning into its antiparticle.

However if this is the case, then antimatter study is not testing $CPT$ inversion, on $C$ inversion. Which we already know to be violated...

Many sources say combination of CPT is what turns a particle into it's antiparticle. But even here on physics stack exchange answers seem to contradict themselves, for example https://physics.stackexchange.com/a/17781/456501 which says both:

Antimatter is in every precise meaningful sense matter moving backward in time.

and

The "C" operator changes all particles to antiparticles

I feel like there are two opposing arguments that are both held as true throughout the sources.

  1. Antimatter is charge inversion (in which case my question is how does testing e.g. energy levels of antihydrogen provide a test of CPT theorem) or
  2. Antimatter is CPT inverted matter (in which case my question is how do we know that antimatter is time inverted and P inverted to matter? Where is the experiment proving this?)

Anyway if anyone is able to clear this up for me that would be great because I'm a little confused here and the more I read the more confused I am...

Qmechanic
  • 220,844
lukygee
  • 23

2 Answers2

4
  • C is violated almost maximally in the weak interactions, CP by a tiny amount there, and CPT not at all, to our present knowledge.

Look at the processes & quantities involved, not just the various charges of the particles. So, by itself, matter-antimatter asymmetry is humdrum, unless you drag in P and T.

I would modify the statement you misread in the linked question,

Antimatter is in every precise meaningful sense matter moving backward in time.

to something like

Antimatter, in CPT-preserving setups, for a CP-invariant theory, may be thought of as matter moving backward in time.

This holds, e.g., in QED, which preserves CP, in the context of relativistic QFT, as visualized by Feynman over 3/4 of a century ago, before the subtleties of the weak interactions (or the speculative complications of axial anomalies of the strong). As that answer you are excerpting from says, blindingly clearly,

The CPT theorem says that any process involving matter happens exactly the same, when done in reverse motion, in a mirror, to antimatter.

You are asking

And time reversal is not involved in particles or antiparticles as far as I can tell. So why does CPT suddenly appear when we talk about antimatter?

The point is, then, that the weak interactions treat left-handed electrons and positrons very differently (fully understood, so, not interesting anymore); but, if you drag in P, left-handed electrons almost behave identically to right-handed positrons in the weak interactions. Fitch & Cronin, over 60 years ago, slipped the "almost" into the above statement, first in the hadronic/quark sector: CP is violated by very little, hence also T, hard to think about―but an equivalent to CP if CPT is preserved, universally assumed by the bulk of the field dealing with Lorentz invariant theory. (Even the NR Schroedinger action is CPT invariant.)

So the interesting part of antimatter is in a mirror, with the film running backwards, which, so far, appears to behave like matter.

Cosmas Zachos
  • 67,623
1

The solution of Dirac's equation gives us a pair of answers and since Dirac's equation is a differential equation differentiated to time that means a time inversion of a particle is the antiparticle.