I.e. charge is conserved.
How? Why?
Background
I am coming here with only my intuition, and a desire to learn. My intuition "feels" that if an electron keeps on repelling other electrons, eventually it will lose its ability to do that. Maybe my intuition comes from the fact that there is entropy. That nature isn't "perfect", or "ideal". That this involves forces, and energy, which are things that generally have to "come from somewhere", "get spent", "run out" or "decay". It feels like an activity or an action, and generally activities and actions affect the essence of the actor, in my intuition! Here, they do not.
The combination of all these things and more leads me to surprise when I find out that electrons truly do conserve their charge eternally. I am very interested in getting a better intuition on this, if someone would be able to "explain" it to me (some maths and formulae are welcome, even undergraduate level, but ideally a prose and intuitive explanation if possible).
Many thanks and apologies if this is a stupid question. More background as to why I am asking in this chat.
Best Answer
There's really not much to explain here. The conservation of electric charge is consistent with every experiment which has ever been performed, and so it is built in to essentially all of our models (for a recent test, see this open-access summary, or the full paper on the arxiv). It is possible to construct a model which does not have this feature, but if you do so, then you will find that it does not accurately predict the results of experiments.
There's really no deeper explanation required than that your intuition is simply wrong. You don't need to go all the way down to electrons or quantum mechanics to encounter this. Does your intuition also say that it requires a continuous input of energy to hold a box suspended over the floor? Because that is also not true, as you would learn in physics 101.
There's nothing wrong with having incorrect intuition. Your intuition was not developed for doing physics, it was developed for climbing trees and opening nuts with rocks and all of the other survival-related activities our ancestors engaged in. The reason you might expect that holding a box above the floor requires energy is because the human musculoskeletal system works via microscopic contractions and extensions of muscle fibers, and it is this inefficiency which necessitates energy while holding a box. The reason you might expect an electron to eventually lose its charge is because if you charge up a balloon (e.g. by rubbing it on your hair), then the electrons which are "stuck" to the surface of the balloon eventually wander away, and therefore the balloon loses its charge. Bad intuition is usually born from genuine experience.
So the goal is not to explain why the world doesn't fit your intuition - it is to explain why your intuition doesn't fit the world. If charged particles gradually lost their charge, then atoms would fly apart, molecules wouldn't exist, and chemistry would not be possible. Given that we are all still here some ~ 14 billion years after atoms first started to form, it would seem that this doesn't happen, at least not in the most naive picture. If you can come up with a model of charge non-conservation which is consistent with experiment while differing from current theories in measurable ways, then I would be interested to see it.