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According to Dirac, theoretically, each Magnetic Monopole (North mm) is connected with their counter partner in space, the Magnetic Antimonopole (South mm) via an infinite thin and possible long undetectable string called the Dirac String. By this Dirac actually acknowledges the dipole nature of magnetism even concerning magnetic monopoles which is essential for the Dirac magnetic monopoles to be compatible with Maxwell Theory.

I am wondering what the existing theory predicts of what would happen, if a monopole and antimonopole pair, a large distance apart, and that is "apparently" due to the Dirac string (i.e infinitely thin), isolated from each other, would come close together and collide?

Will these two join forming an elementary magnetic dipole or else called the Quantum Magnet? Or merge forming something different for example a particle, and what particle is this predicted to be?

Please notice also that the term Quantum Magnet refers to the electron.

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When two Dirac monopoles annihilate they leave behind a closed loop of a Dirac string. This object (and the string itself) is not entirely undetectable. It carries one quantum of magnetic field flux. So if, for instance the string passes through a closed electric circuit, it will cause a corresponding splash in e.m.f. around it as Faraday's law prescribes. If you catch the string into your SQUID you should get a persistent current in it. If you now shunt the Josephson junction with a full proper superconductor wire (no more weak link), the Dirac string loop will get trapped around the supeconductor (Meissner effect), and won't be able to self-annihilate by shrinking down to nothing.

The closest (although not entirely faithful) "real life" analog to such object would be a closed loop vortex in a superconductor. I imagine it should have some resemblance to the roton-type excitation in a superfluid.

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  • $\begingroup$ In fluiddynamics two opposite spin vortices aligned on the same 2D plane side by side close together and fully submerged inside the same medium create a vortex ring (i.e. vortex line closed to a loop). This is easily demonstrated here: youtube.com/watch?v=_18avidXxqY . So there is in this case not such thing as opposite spin annihilation of the vortices. The two vortices are simply joined via the vortex line forming a vortex ring. My question however does not refer to this kind of side by side collision but to the head to head collision (planes of the vortices are parallel). $\endgroup$
    – Markoul11
    Sep 22, 2022 at 19:12
  • $\begingroup$ No, I am not making an analogy between a monopole and a vortex cross section. Instead I am saying that a Dirac monopole can be thought of as a ${\it termination}$ of a Dirac string whereby the flux contained in the string "spills out" (see e.g. Fig. 11.4 in Volovik's "Universe in a Helium Droplet"). A magnetic monopole is a non-local entity in that sense. Therefore when a monopole-antimonopole pair annihilates (e.g. by colliding head-on) it leaves behind a closed Dirac string loop, which can be thought of as a sort of analogous to a vortex ring in your video. $\endgroup$
    – John
    Sep 23, 2022 at 10:37
  • $\begingroup$ The different thing about the Dirac string loop is that it carries a conserved magnetic flux and can only disappear by shrinking down to a point. This should happen fast as Dirac string should have some finite per-length energy, but it can be prohibited from doing so by threading a superconducting rod through the Dirac string loop. $\endgroup$
    – John
    Sep 23, 2022 at 10:37
  • $\begingroup$ This is an interesting related to the question reference: arxiv.org/abs/1904.02257 $\endgroup$
    – Markoul11
    Sep 27, 2022 at 7:22
  • $\begingroup$ Another here: royalsocietypublishing.org/doi/10.1098/rsta.2019.0333 and here, pnas.org/doi/full/10.1073/pnas.97.6.2431 $\endgroup$
    – Markoul11
    Sep 27, 2022 at 7:43

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