# Causality in CPT symmetry analogue of free electron laser (stimulated absorbtion)?

While 2nd law of thermodynamics emphasizes past->future time direction, CPT theorem says that at least microscopic physics has some symmetry between past and future. For example the Feynman-Stueckelberg interpretation suggests to imagine antiparticles as traveling back in time.

Thermodynamics is one of many examples of symmetry breaking: while the fundamental equations fulfill some symmetry, the solution often breaks it. Even for (time-symmetric) classical mechanics there is Boltzmann H-theorem "proving" that entropy should grow. However, we could reverse time and use the same "proof" to show entropy decrease - getting contradiction. The problem is a subtle hidden assumption of some uniformity ("Stoßzahlansatz") - this issue is very nicely presented in Kac ring model: entropy grows as it should, but then it surprisingly decreases due to symmetry of the model.

Anyway, the CPT symmetry suggests that a CPT analogue of a device should also work (?) Very interesting would be a CPT analogue of a laser - its stimulated emission should be transformed into stimulated absorption (?) - getting lasar.

Free electron laser (FEL) is conceptually simple - just particle traveling in alternating magnetic field. We could realize its CPT analogue:

So in FEL we have high energy electrons, which go through a sequence of opposite magnets, what leads to photons from synchrotron radiation. These photons travel through the optical path and finally hit a deexcited target, exciting it.

CPT analogue of this picture is: excited target emits photons, which travel toward that lasar (stimulated absorption instead of emission), and are absorbed by traveling positron. What is nontrivial here is that deexication of the target is stimulated by turning the lasar on - earlier by optical path time.

So imagine we take a sodium lamp surrounded by detectors. The lamp is continuously excited, and this energy is seen by detectors.

Now shoot the lasar (stimulated absorption) through a small hole in the detectors (of frequency of sodium lamp) - shouldn't turning the lasar on change the energy balance of lamp-detectors?