The magnetic field is composed of closed loops (assuming there is no magnetic monopole). How does one prove any two magnetic loops do not knot to form a link?
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2$\begingroup$ What makes you think they can't form knots? $\endgroup$– Prof. LegolasovDec 25, 2020 at 2:55
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2$\begingroup$ @Hans It's obviously not true if there is magnetic material (long bendy magnet) or conductive material (long bendy solenoid) present that can be tied in a knot. This presumably includes plasma. But I'm guessing it has to be true in any empty volume where the field has to obey the Laplace equation. $\endgroup$– Roger WoodDec 25, 2020 at 6:51
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$\begingroup$ You are both right. I am embarrassed by my stupid question. $\endgroup$– HansDec 25, 2020 at 7:50
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3$\begingroup$ @RogerWood There seem to be some papers about knotted and linked vacuum solutions to Maxwell's equations, like arXiv:1502.01382. $\endgroup$– benrgDec 25, 2020 at 8:16
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$\begingroup$ @benrg: You seem to have answered my new question physics.stackexchange.com/q/602923/17354.Care to provide a detailed answer there? $\endgroup$– HansDec 25, 2020 at 8:39
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1 Answer
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You don't.
Take a set of short permanent magnets. Chain them together. Make a knot out of the chain, and connect the ends.
Or form two chains. Make them into linked closed loops.
answered Dec 25, 2020 at 5:12