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A Physics Puzzlement

So I reread Richard Feynman's magnificent QED: The Strange Theory of Light and Matter. At the end of which I have the warm glow that comes with understanding Quantum Electrodynamics--albeit at the level of a Mayan peasant's understanding of how the priests calculate when it's time for the festivals.

And then it hits me: I understand (kinda) how electrons and photons interact and how one electron emits and another one absorbs a photon and as a result momentum is transferred from one electron to the other and while they were getting closer together they are now drawing further apart--that is, I understand (kinda) how QED predicts that two negative charges repel each other.

But why do a positive and a negative charge attract each other? That remains a total mystery to me.

Can anybody help?