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When I try to understand magnetic reconnection, I have a fundamental conflict with my intuition of magnetic fields.

I think it is literally a case of cognitive dissonance, my intuition and any kind of disconnection of magnetic field lines, even temporary, can not coexist.

In my intuition, a magnetic field line is a closed loop, and that is a fundamental property of it. But I conclude that can not be strictly correct.

What am I missing? In what way can a magnetic field line become something different than a closed loop?

(Related questions are about what a magnetic reconnection is, but I do not doubt that it is a real phenomenon. My disconnect is about "how does that even make sense")

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Magnetic field lines always form closed loops. In a reconnection event, the so called breaking and re-connecting of field lines take place in no time. If you look at the reconnection event, the divergence of magnetic field always comes out to be zero and there is no need of a monopole to explain reconnection.