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Wikipedia describes how assuming the existence of a single magnetic monopole leads to electric charge quantization. But what if there's more than one? The same argument would apply to each of them separately, wouldn't it? If their magnetic charges are rationally related everything's alright, but if they aren't satisfying both quantization conditions is impossible. So in order to explain electric charge quantization you have to assume either magnetic charge quantization or that there's exactly one magnetic monopole in the universe, neither of which seems to be much of an improvement. Am I missing something here?

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OP wrote (v1):

If their magnetic charges are rationally related everything's alright, but if they aren't [rationally related, then] satisfying both quantization conditions is impossible.

Correct.

So in order to explain electric charge quantization you have to assume either magnetic charge quantization or that there's exactly one magnetic monopole in the universe.

Well, one doesn't have to a priori assume that. One can derive that. The argument is symmetric in electric and magnetic charges. In the same way that the existence of magnetic charge leads to electric charge quantization, the existence of electric charge leads to magnetic charge quantization.

See also this Phys.SE post.

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