Let's assume we follow Rabbi Moshe Feinstein's ruling that hearing aids are permitted on Shabbat, but microphones are not.
What about installing an audio induction loop in the synagogue? It would send out a magnetic signal that's inaudible to naked ear, but would allow hearing aids (switched to the right mode) to turn into sound?
Is anyone aware whether its permissibility has been discussed? Or if it's been installed anywhere? (It appears this technology is more popular in the U.K., if that helps)