Q-reeus wrote:Below is a direct cut-and-paste from an entry I just made at Physics.Stack.Exchange. Maybe it will help kick start some life and diversity here. And if it belongs in another sub-forum well I'm fine with it being moved.
Many years ago I considered the situation of a genuine monopole continually threading through the middle of a wholly superconducting loop. So we have two interlocking Roman rings - one an electric charge circuit, the other a magnetic charge circuit. Depending on the relative sense of circulation, either the monopole gains energy at the expense of the supercurrent, or vice versa. Well actually, it might not be that simple.
Thing is, superconductivity is intimately associated with the usual vector potential A, and a supercurrent will only change in response to a change in an externally applied A. Such as to maintain the line integral of net A around the supercurrent invariant. But A is only generated by moving electric charge. The hypothetical 'back emf' of circulating monopole would be owing to an E field the analog of the B field of moving electric charge. On a time-average basis it would be steady given a steady monopole current. Hence of a fundamentally different character to an E=−dA/dt owing to time-varying electric current, that the supercurrent would know and respect.
Hence regardless of whether circulating monopole gains or loses energy in following along the lines of B generated by the supercurrent, the supercurrent itself will do squat. There is a similar dilemma when it comes to the predicted net force/torque balance - or rather imbalance.
Upshot is, one either accepts that energy-momentum conservation would dramatically fail, or take the scenario as proof that a genuine monopole cannot exist!
Mikko wrote:The description in terms of A is based of the assumption that there are no magnetic monopoles, and therefore not valid here.
One can use more potentials or work directly with (modified) Maxwell's equations.
Q-reeus wrote:Mikko wrote:The description in terms of A is based of the assumption that there are no magnetic monopoles, and therefore not valid here.
Where do you get that idea from?
Mikko wrote:As magnetic field = curl A and magnetic charge density = div magnetic field by definitions,
but div curl V = 0 for any vector field V, including A. Therefore use of A as the only description of the magnetic field clearly says that there are no magnetic monopoles.
Q-reeus wrote:Mikko wrote:As magnetic field = curl A and magnetic charge density = div magnetic field by definitions,
but div curl V = 0 for any vector field V, including A. Therefore use of A as the only description of the magnetic field clearly says that there are no magnetic monopoles.
No disagreement on that point (∇.B = 0 in absence of monopoles), but it is completely skew of the issue I have been arguing.
Which is that any change in a closed supercurrent circuit can only be in response to an externally applied dA/dt. And always acts so as to maintain A constant within the supercurrent. A hypothetical impinging solenoidal E field owing to a threading circulating monopole current cannot therefore alter said supercurrent without violating constancy of A. Principle of supercurrent wavefunction stationary phase. Simple. Well not quite.
Just to clarify my earlier remarks about quantization of flux (more precisely fluxoid, but for a macroscopic circuit the two are essentially synonymous). It means that supercurrent net line integral of A can change slightly but only up to the value of a single flux quantum h/(2e), In a microscopic sized circuit that translates into significant allowable variation in an applied B field thus threading flux thus line integral of A, before the supercurrent jumps to a new level. Essentially unobservable though in a macroscopic circuit that fapp exhibits perfect diamagnetism.
None of that in any way helps an argument in favor of a monopole sourced E field - having no connection to A - changing the supercurrent. Such event would imply the triumph of classical physics - Maxwell's equations augmented to include monopoles - over quantum mechanics. Alas any staggering upset looks terribly unlikely given no evidence of genuine monopoles with which to conduct an actual experiment.
Mikko wrote:None of that is relevant to my first observation that your assumptions are inconsistent.
Q-reeus wrote:Mikko wrote:None of that is relevant to my first observation that your assumptions are inconsistent.
I'm calling you out on this. One line 'refutations' or rather bald assertions like that just don't cut it. While there are further aspects to the monopole/supercurrent general situation not yet covered, what has been covered is laid out plainly enough above. You claim it's wrong. I assume you can furnish a fully self-consistent alternate account of just what will happen in the given scenario?
Well lets have it then! Prove me wrong with a coherent and detailed rebuttal and I'll admit it. But that has to apply both ways. And it would be nice to get feedback from others here. Looking at the post count one could be forgiven for thinking this site is set up purely to deal with a single issue.
Mikko wrote:One needs no detailed refutation in order to observe that you have not derived a single equation from the modified Maxwell equations, or even shown them so that someting could be derived.
Q-reeus wrote:Mikko wrote:One needs no detailed refutation in order to observe that you have not derived a single equation from the modified Maxwell equations, or even shown them so that someting could be derived.
Post #1 is quite sufficient to qualitatively establish a dilemma exists. But to reiterate one point there you conveniently ignore. As implied in the standard, classical extended ME's a monopole is not bizarrely one end of a filamentary flux tube (aka Dirac 'monopole') but a genuinely point particle having dual properties to that of an electron. As such, it's fields cannot be described via a standard magnetic vector potential A. Whose only generator is by definition electric charge. Hence your criticism is wrong from the start.
To repeat the challenge - show by concrete counterexample how such a genuinely point monopole, whose fields E, B, are ostensibly described by a magnetic scalar potential and electric vector potential, would conservatively interact with an electric supercurrent in general. I say you cannot. Take it or leave it.
Q-reeus wrote:PS: Again, my by now usual experience at sciphysicsforums - only caught your above post by accident. There being no supposedly automatic email notification. Why?
FrediFizzx wrote:There is no need to modify Maxwell's equations. Magnetism is a pure relativistic effect...
...Electrons are magnetic monopoles to a "free" photon....
I have again tested the board email system and it appears to be functioning as it is supposed to be with no errors reported. Please check all your user settings and subscription settings again.
Q-reeus wrote:FrediFizzx wrote:There is no need to modify Maxwell's equations. Magnetism is a pure relativistic effect...
Which is equivalent to saying genuinely point magnetic monopoles, whose static field B = -∇φ_m cannot be owing to relativistic transformations of a standard EM field sourced from electric charge, don't exist. Well Fred, if you follow the straightforward logic of my #1, that is indeed the implication - at least if assuming energy-momentum conservation is sacrosanct....Electrons are magnetic monopoles to a "free" photon....
What??!! Elaborate please!
FrediFizzx wrote:From the "viewpoint" of the photon, the electron is approaching it at the speed of light and ec is magnetic charge.
...In natural units of h = c - 1, electric and magnetic charge have the same dimension; dimensionless.
If you got the notification of my reply then your settings must be right. But there is not much I can do if there are no errors in the email log. Either the hosting company email server is flaky or your email server is or both. You will just need to check the forum for replies from time to time.
FrediFizzx wrote:https://en.wikipedia.org/wiki/Natural_units
Which easily demonstrates that magnetism is a pure relativistic effect. Magnetic monopoles are all around us known as electrons. The search for something else is futile.
Q-reeus wrote:FrediFizzx wrote:https://en.wikipedia.org/wiki/Natural_units
And diving down to the sub-topic https://en.wikipedia.org/wiki/Natural_u ... tism_units
One has the dimensions of charge given there as....definitely not dimensionless!
FrediFizzx wrote:Those are not natural units because they don't have . That is certainly dimensionless.
Q-reeus wrote:FrediFizzx wrote:Those are not natural units because they don't have . That is certainly dimensionless.
Does normalizing either or both of h, c, actually make them dimensionless? Not at all. As the constant of quantum action h always has dimensions energy x time or equivalent as shown here: https://en.wikipedia.org/wiki/Planck_constant#Value
Likewise, c as the fundamental velocity limit in relativity continues to have dimensions of distance/time. All that changes when normalizing either is choice of units that give a net numerical value of 1. Dimensionality is unaffected by any such choices.
And of course the same general situation applies for charge. Try getting consistency for an obvious example F = qE, based on your belief q can be dimensionless!
FrediFizzx wrote:Actually having hbar and c to have dimensions is the normalization. c is just a conversion factor between length and time. hbar is just a conversion factor between energy and angular frequency, etc. Setting c = 1 just means that the magnitude of all your velocities are from 0 to 1 and dimensionless. And so forth. Nature doesn't give a hoot about our man-made dimensions and units. F = qE just means that the electric field is equivalent to force when q is dimensionless. It is not a problem.
Q-reeus wrote:Umm....once again Fred seems best we agree to fundamentally disagree.
Getting back on OP topic, which Mikko for some odd reason has revived from it's long slumber here....
Invitation is renewed to anyone (here or elsewhere - feel free to alert colleagues/friends/etc.). Try and find a relevant and coherent rebuttal to #1 post claim. Good luck folks.
Return to Sci.Physics.Electromag
Users browsing this forum: No registered users and 1 guest