While working on a review of a book that talks about the fortuitously bio-friendly constants of nature (review forthcoming, don’t worry), I mistyped “ratio of proton to electron masses” and “ratio of proton to electron charges.” Which is, of course, 1, and thus not a terribly interesting ratio.
But that got me wondering: is there a solid fundamental reason why that ratio is one? This is, could you have a self-consistent universe in which the electron and proton had different charges– say, a proton having twice the charge of an electron? That wouldn’t be a useful sort of universe, of course, as the lightest element would be chemically more like helium than hydrogen, and that pretty effectively screws up all of chemistry, but that doesn’t necessarily mean it would be mathematically impossible.
I suspect it must be impossible, just because it wouldn’t make much sense otherwise, but I’m not sure what the argument would be. And I’m too lazy to Google it up this morning, so instead I’ll make myself look like an idiot, in hopes of getting an answer in comments.