This has been asked before but I need to be clear on what kind of answer I'm looking for. All the other posts are just water analogies.
I get it, you add the voltages together. And there's a magical unicorn pumping it aka the water pump and hill-tilts on hill-tilts with meatballs rolling on meatballs.
Seriously though, how does it REALLY work? I don't need any analogies to tell me WHAT it does, because I can sum that up in a simple formula. And I really really do not want any false quasi-explanations.
If you must use analogies to convince yourself of its workings, you simply do not understand it. Electricity is NOT water.
So if we have two batteries of the same chemistry in series, why do we get higher Fermi levels? The chemistry shouldn't support that, the chemistry has a set Fermi level: you get 1.5V of some materials. But somehow, by having them in series you get e.g. 6V. How does that work in terms of particle physics? That is very crucial here: how do we chemically and electrically get that higher fermi level.