tag:blogger.com,1999:blog-8666091.post8425319373865136760..comments2021-05-03T21:54:48.969+02:00Comments on The Reference Frame: Magnetic monopoles seen in CM physicsLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8666091.post-77107510008072686882009-09-07T06:20:55.492+02:002009-09-07T06:20:55.492+02:00Dear Neil,
indeed, one can always formulate elect...Dear Neil,<br /><br />indeed, one can always formulate electromagnetism in terms of the "A for E" field which is known the "dual gauge potential" and labeled "A tilde" or by similar symbols.<br /><br />You also correctly determine why this is not a convenient choice for ordinary electromagnetism: there are too many normal electric charges and Dirac strings for "A tilde" would have to run from each of them - which would be a lot of unphysical choices etc.<br /><br />But the logic would otherwise be identical. You could do it and these dual Dirac strings would have to be invisible, i.e. the A-B effect would have to lead to a trivial phase for (now:) magnetic monopoles that orbit such dual Dirac strings.<br /><br />The role of the electric and magnetic charge would be exactly reverted, relatively to the formalism with the normal "A for B" potential. At any rate, the phase in the Aharonov-Bohm effect for one charge orbiting the Dirac string coming from the other type of charge is always of the kind<br /><br />exp(i.Q_{electric}.Q_{magnetic}) <br /><br />which is already symmetric with respect to the electric and magnetic "worlds", "indices", or 'adjectives", so nothing would change about it. You would still conclude that Q_{e}.Q_{m} must be a multiple of 2.pi in the quantum relativistic (electromagnetically rationalized) units.<br /><br />So it's about convenience, not about the truth: we know quite a lot of el. charges but have seen no magnetic ones, so we use the "A for B" vector potential and not "A for E" - "E" is determined from the (minus) gradient of the scalar potential "phi" (minus the time derivative of A).<br /><br />There is no problem here and there is also no problem with the fast comments now.<br /><br />Best wishes<br />LubosLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-12723956980383206352009-09-06T22:08:04.979+02:002009-09-06T22:08:04.979+02:00Fascinating, thanks. But here's my problem wit...Fascinating, thanks. But here's my problem with even this attempt to make monopoles reasonable, save monopoles from A-field problems etc: if E and B are truly equivalent, then there isn't even a reason for only B to have a correlated A field! There would have to be an "A for E" type field as well (per definition, "equivalent") Then charges have to be corralled within this weird scheme of being ends of dipoles, worrying about A-B effect etc. and what charge would be specified? Well, to be consistent, the same charge (in absolute, "Gaussian" terms)! Well, it isn't ... Did I miss anything?<br /><br />(I think your fast-comment section is having problems.)Neil Bateshttps://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-21506494811186378112009-09-06T15:08:19.312+02:002009-09-06T15:08:19.312+02:00No, this won't transform particle physics as w...No, this won't transform particle physics as we know it. It's the other way around. <br /><br />Morris <i>et al.</i> managed to express the properties of the magnet known as spin ice in terms of magnetic monopoles and strings connecting them. When spin ice is placed in an external magnetic field along certain directions, Dirac strings carrying the flux between pairs of magnetic charges are stretched mostly along the direction of the field but also wander aimlessly in the two perpendicular directions. In this way the properties of atomic magnetic dipoles can be calculated in terms of strings doing a random walk in 2+1 dimensions. <br /><br />The authors of that paper performed the calculations and confirmed the results experimentally by measuring spin correlations through neutron scattering. In a sense they borrowed ideas from particle physics to gain understanding of a condensed-matter system.oleghttps://www.blogger.com/profile/11644793385433232819noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-80053413896213480802009-09-05T16:14:32.149+02:002009-09-05T16:14:32.149+02:00Thanks for clearing that up! I only saw the popul...Thanks for clearing that up! I only saw the popular press blurbs which, of course, water down the gruel.Brian Oxleyhttps://www.blogger.com/profile/06617364377560752378noreply@blogger.com