This is a related, but opposite question to this one

I have heard about a lot of things regarding elementary and GUT magnetic monopoles, as well the quasiparticle monopoles in spin ice

Since there's like 50 years of non detection of magnetic monopoles, I started to wonder whether monopoles searches have tried to approach the problem from the opposite direction. That is

What physical phenomenon that if observed by experiment, will guarantee that (elementary or GUT) monopoles cannot exist?

Attempt for a partial answer

I have discussed this problem with my professors today and we arrived at some sort of partial answer in that our current electrodynamic, Standard Model and QED theories have been well tested (particularly for QED which is tested up to the order of $10^{-26}$ from the memory of the discussion) and they all seemed to work fine without monopoles seems to be a sign that monopoles cannot exist, as Maxwell equations with the monopole terms added will result in a host of phenomenon that we never have observed

However since most theories can be easily generalised to include monopoles (that is there is no currently established theories (such as our classical electrodynamics and QED) that cannot function without monopoles, and that Maxwell Equations can be easily fixed and electrodynamics will not need to be completely reformulated to incorporate magnetic monopoles), I am wondering if our partial answer is actually strong enough to be used as some sort of "negative prove" that monopoles cannot exist

  • $\begingroup$ I think you can only set lower limits on the masses of these monopoles with these observations. $\endgroup$
    – pfnuesel
    Mar 12 '15 at 12:43
  • 3
    $\begingroup$ The existence of a non-quantized charge would probably do the trick. $\endgroup$
    – innisfree
    Mar 12 '15 at 12:54
  • $\begingroup$ @innisfree I'm sure that an explanation of that comment would be an excellent answer, well understandable by a broad audience. I'm sure it would be as interesting to anyone who hasn't heard of the Dirac string as it was to me when I first met it. $\endgroup$ May 31 '15 at 11:42
  • $\begingroup$ You can ask what would happen if we create stronger and stronger magnetic fields. As pointed out in this article: "We argued above that a uniformly magnetized vacuum is stable against spontaneous electron-positron pair production. Nevertheless, at sufficiently high B the vacuum must break down. Magnetic monopoles with mass $m_\eta$ and magnetic charge $\eta$ are spontaneously created when the energy they acquire in falling across a monopole Compton wavelength, $\epsilon\sim\eta B\frac{\hbar}{m_\eta c}$, exceeds their rest energy $m_ηc^2$". $\endgroup$ Aug 22 '15 at 4:20

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