# CPT theorem and annihilation of matter and antimatter after the big bang

Is the hypothesis that antimatter is moving backwards in time compatible with the hypothesis of annihilation of matter and antimatter after the big bang?

It is said that the big bang should have produced equal amounts of matter and antimatter. Matter and antimatter annihilated (at the exception of a small part of matter) so that there seems to be not much antimatter in today’s universe.

Is the above-mentioned hypothesis compatible with these assumptions? It seems that it is not compatible: if we would presume that matter and antimatter have different time directions, would not be the consequence that the matter and the antimatter generated by the big bang never met each other (??) so that there was -timely- no possibility for annihilation?

• The CPT theorem says that every relativistic local QFT must obey the CPT symmetry. Where does it say that "matter and antimatter have different time directions"? – ACuriousMind Aug 14 '14 at 18:30
• It seems that there was a bug in my question. I edited. – Moonraker Aug 14 '14 at 18:48
• I think your original question was actually better, now I'm debating whether this is "physics" or "idle speculation". – Kyle Oman Aug 14 '14 at 19:09
• @Kyle : The edited question is not far from the original question, see e.g. en.wikipedia.org/wiki/CPT_symmetry : “The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected by an imaginary plane (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion)— would evolve under exactly our physical laws." – Moonraker Aug 14 '14 at 19:40

The most common explanation for the "matter-antimatter asymmetry of the Universe" is $\rm CP$ violation in interactions involving leptons. This scenario is usually called leptogenesis because it generates a net excess of leptons compared to anti-leptons. This $\rm CP$ violation is currently unconfirmed by experiment (though there is also not yet any evidence against it - just upper limits which fail to settle the question).

Assuming $\rm CPT$ symmetry, $\rm CP$ violation implies simultaneous $\rm T$ violation, but any system that is not in thermodynamic equilibrium violates $\rm T$. So as long as leptogenesis occurs during a portion of cosmic history when the Universe is not in thermodynamic equilibrium (which fits in nicely with our understanding of the early Universe), matter-antimatter asymmetry is not in conflict with the $\rm CPT$ theorem.

• My question was not well formulated - could you answer to the edited question? – Moonraker Aug 14 '14 at 18:57
• Not really - see here for why, your "hypothesis" doesn't really work. – Kyle Oman Aug 14 '14 at 19:01
• So, as I understand, there is no compatibility with this hypothesis - thank you! – Moonraker Aug 14 '14 at 19:18

CPT does exchange particles with their antiparticles, so if there were a time direction associated with particles then it might make sense to say that, by CPT, the antiparticles would have to have the opposite time direction.

But there's no time direction associated with particles. It doesn't even make sense to say that something is "going forward in time"; it's like saying that time increases with increasing time. If you have two different arrows of time—for example, the thermodynamic arrow of time and the away-from-the-big-bang arrow of time—then in principle you can imagine a situation where they point in opposite directions. But these arrows are not properties of individual particles, and they are not reversed in a system made of antimatter.

It's also worth pointing out that "antiparticle" isn't a kind of particle. Antielectrons and antiquarks are called "anti" simply because they're less common than their CPT duals. Some particles are their own CPT duals (e.g. photon, uncharged pion) and some particles are CPT duals of each other but neither is called "anti" (e.g. W±, π±). So even if you could assign some meaning to "going backward in time" as a property of particles, it wouldn't make sense to assign that property to antiparticles as a class; there's no such class.

• What does "time inversion" and "momenta reversed" in the a.m. wikipedia article mean? Does it not refer to antimatter? – Moonraker Aug 14 '14 at 21:39
• @Moonraker: It refers to CPT "reflection", not specifically to antimatter. As an analogy, in a world with perfect spatial reflection symmetry, that symmetry exchanges left- and right-handed gloves. The gloves are mirror images of each other, but neither one is a mirror image in some absolute sense. – benrg Aug 14 '14 at 22:20

Yes, CPT is compatible with the idea that matter and antimatter are created at equal amounts. CPT is a basic theorem of quantum field theories, QFT:s. QED i a QFT and thus obeys CPT. The original QED is a theory of electrons, positrons and photons. In QCD, when a positron is produced an electron is produced at the same time (pair production). Likewise, when a positron is annihilated so is an electron, only photons remain.

@Moonraker asks a reasonable question. See Feynman "The Theory of Positrons". Here is Wikipedia's statement:

"Feynman, and earlier Ernst Stueckelberg, proposed an interpretation of the positron as an electron moving backward in time,[15] reinterpreting the negative-energy solutions of the Dirac equation. Electrons moving backward in time would have a positive electric charge. Wheeler invoked this concept to explain the identical properties shared by all electrons, suggesting that they are all the same electron" with a complex, self-intersecting world line.[16] Yoichiro Nambu later applied it to all production and annihilation of particle-antiparticle pairs, stating that "the eventual creation and annihilation of pairs that may occur now and then is no creation or annihilation, but only a change of direction of moving particles, from past to future, or from future to past.[17] The backwards-in-time point of view is nowadays accepted as completely equivalent to other pictures,[18] " Note: Wikipedia is not always a reliable source, so read the original papers it refers to.