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How does repulsion and attraction of a magnet work? I have a hypothesis. We all know that repulsion works when people throw balls at each other. This is used as an analogy of how virtual particles are used to explain how magnets repel each other in some cases. The other idea is that virtual particles have momentum and anti-momentum to explain attraction and repulsion. Is it possible to explain attraction by virtual particles leaving the south pole of one magnet at some angle, let's say less than 45 degrees and arriving at the second magnet's south pole at around 90 degrees?

As an after thought, the 45 degree angle would be obtained if the north pole particles were repelled by the south pole particles but now I seem t be creating a loop in my thinking.

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    $\begingroup$ Relevant: Feynman on magnets $\endgroup$ – David H Dec 14 '13 at 2:47
  • $\begingroup$ @DavidH Great interview. Feynman, although so scornful of philosophers and would never have admitted this, was a formidable philosopher of science himself. $\endgroup$ – WetSavannaAnimal Dec 14 '13 at 3:44
  • $\begingroup$ @david, loverly link, adds to the why and how question for a bonus:-) $\endgroup$ – Jitter Dec 14 '13 at 4:14
  • $\begingroup$ @Jitter Yes, it's quite relevant to that question as well! In fact it's almost worthy of being submitted as an answer. $\endgroup$ – David H Dec 14 '13 at 5:13
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To invoke Feynman in the interview, it can be rather unsatisfying to invoke virtual particles to explain forces in terms of something else more wonted to you. Virtual particles are wholly internal to the analysed system and so individually do not heed normal conservation laws - they are "off-shell" (i.e. off the light cone defined by $E^2-p^2 c^2 = m^2 c^4$) - but their nett effect yields the conservation of momentum laws, which manifest themselves as "force" (i.e. impulse transfer needed to uphold momentum conservation).

You can think of virtual particles more literally as Feynman liked to do, or you can think of them simply as mathematical terms in a perturbation series. Indeed, witness Barut and Kraus, "Nonperturbative Quantum Electrodynamics: The Lamb Shift"; here the system of one electron, one photon (Maxwell-Dirac coupled system) is solved nonperturbatively, and it gives an infinite series of terms corresponding to virtual pairs too. Here the analysis gives the "right answer" (for the Lamb shift) and the virtual pairs drop out of the Maxwell-Dirac equation description - other than this you can think of them as something not really explicable in other ideas more wonted to you. Similar ideas come from the Dyson series, which can either be thought of as being "made of" the actions of virtual particles, or it can simply be thought of as a standard, rigorous technique for finding the fixed points of certain integro-differential operators when they are contraction mappings: mathematicians call this the Peano-Baker series (see Baake and Schlaegel, "The Peano Baker Series" and many mathematicians highly adept at applying it would never have heard of thinking of its terms as "particles".

Another tack: you can think of the force arising from impulse transfer through the "magnetic field" needed to uphold the conservation of momentum and energy, which itself follows through Noether's theorem from basic symmetries of the World - the time shift and spatial shift invariance of physical laws.

However, I'm sure someone will answer with the handwaving argument as to how the idea of throwing balls between two people can - with a stretch - motivate an attractive force. I myself can't even recall the argument properly - I have always found it so unsatisfying that it never sticks in my head and I would ultimately rather stick with the description of the magnetic force in more abstract terms: we don't expect to understand it in terms more wonted to us.

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  • $\begingroup$ I wont upgrade you or downgrade you yet, until I getaround to reading your links ;-) Have a look at my hypothisis and tell me if it would work or not, preferably with some simple maths or correct it to work with some simple maths. I' m interested in the angle on the angle ofthe thought train. $\endgroup$ – Jitter Dec 14 '13 at 4:27
  • $\begingroup$ @Jitter I don't really think so: like I said virtual particles are off shell and violate conservation laws if thought of as disembodied from their perturbative series: the series as a whole and the particles that go into and leave the Feynman diagram are what's real. In your example, you see this nonconservation - a virtual particle leaving and entering at different directions clearly does not conserve momentum in its "flight", so I don't find it a very fulfilling way to think: if you're going to go along these lines then you're left with the baffling question: okay, where did the impulse ... $\endgroup$ – WetSavannaAnimal Dec 14 '13 at 4:41
  • $\begingroup$ @Jitter ... come from that shifted the momentum state of the virtual particle "in its flight"? All these problems vanish when the series is put together as a whole. BTW, +1 for your question because it does bring into sharp focus the limitations of virtual particles. $\endgroup$ – WetSavannaAnimal Dec 14 '13 at 4:43
  • $\begingroup$ @Jitter Now that I think about it, it's vaguely wonted to me: I think you're argument is not unlike the simple argument often given for attraction - it's argued that the virtual particles have an uncertainty in momentum by HUP and therefore can reach the sink particle from the opposite direction they left the source particle from, IIRC. $\endgroup$ – WetSavannaAnimal Dec 14 '13 at 4:47

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