Magnetic monopole + supercurrent = apparent dilemma

Classical Electrodynamics, Maxwell, etc.

Magnetic monopole + supercurrent = apparent dilemma

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!
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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!

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.
Mikko

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Re: Magnetic monopole + supercurrent = apparent dilemma

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? Certainly it's not what I wrote above. Please go back and carefully read what I actually state. Also, have a read of:
https://en.wikipedia.org/wiki/London_equations
[Better still: https://en.wikipedia.org/wiki/Magnetic_flux_quantum]
Supercurrents relate specifically to the magnetic vector potential A. Which is only generated by moving electric charge There is no room for anything like a hypothetical 'magnetic scalar potential' or 'electric vector potential' owing to a hypothetical monopole. If you claim the E field of a circulating monopole can induce a change in supercurrent - recognize this implies a direct violation of the quantum mechanical flux quantization condition upon which superconductivity fundamentally depends!
One can use more potentials or work directly with (modified) Maxwell's equations.

Then please show just precisely how you can get a hypothetical monopole to influence a supercurrent - given how such is defined in above reference. Good luck.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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?

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.
Mikko

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

None of that is relevant to my first observation that your assumptions are inconsistent.
Mikko

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

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.
Mikko

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

PS: Again, my by now usual experience at sciphysicsforums - only caught your above post by accident. There being no supposedly automatic email notification. Why?
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

There is no need to modify Maxwell's equations. Magnetism is a pure relativistic effect. Electrons are magnetic monopoles to a "free" photon.

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?

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.
FrediFizzx
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Re: Magnetic monopole + supercurrent = apparent dilemma

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....

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.

I have done so on every previous occasion this situation has arisen and every time my personal settings were set for automatic email notification.
Same story this time. Something else is going on needing investigating further. As evidenced by my receiving notification of your above post, but not that of Mikko's earlier one.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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....

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 $\hbar = c = 1$, 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
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Re: Magnetic monopole + supercurrent = apparent dilemma

FrediFizzx wrote:From the "viewpoint" of the photon, the electron is approaching it at the speed of light and ec is magnetic charge.

As you surely know, there can be no viewpoint of a photon owing to it's zero rest energy. Nevertheless one can consider the case of an ultrarelativistic electron in some inertial frame. The fields approach that of an infinitely thin pancake pulse. Radial E and azimuthal B fields of essentially equal energy density at all points.

Which contrasts to the equivalent case of an ultrarelativistic point monopole. One then has the dual of above - radial B and azimuthal E fields.
There is no way of relativistically transforming one case into the other. Neither is there need to go ultrarelativistic - the differences are fundamental at any relative speed.

To repeat: IF one assumes that a point monopole as the dual of electric charge exists, and that further both types of charge can 'feel' the relevant fields generated bu the other, then the scenario given in #1 automatically implies energy-momentum conservation will fail.

As far as I'm aware, no-one else has discovered or at least publicly presented that insight. Which is strange given how obvious an extension it is of Alvarez's idea of using superconducting coils as detectors of monopoles: http://aip.scitation.org/doi/abs/10.1063/1.1685086
...In natural units of h = c - 1, electric and magnetic charge have the same dimension; dimensionless.

I have no idea where you get that idea from, but it doesn't correspond to any system of units I'm aware of. See e.g.:
http://www.xml-cml.org/unit/si/#coulomb
https://en.wikipedia.org/wiki/Statcoulomb
Etc. Normalization is quite distinct from 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.

Evidently the answer is a flaky hosting company email server, as the issue for me is unique to this forum. Such is life.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.
FrediFizzx
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Re: Magnetic monopole + supercurrent = apparent dilemma

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!
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.

Ummm....given that pov, best we agree to fundamentally disagree Fred.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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!

Those are not natural units because they don't have $\hbar = c =1$. That $e = \sqrt{4\pi\alpha}$ is certainly dimensionless.
.
FrediFizzx
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Re: Magnetic monopole + supercurrent = apparent dilemma

FrediFizzx wrote:Those are not natural units because they don't have $\hbar = c =1$. That $e = \sqrt{4\pi\alpha}$ 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!
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

Q-reeus wrote:
FrediFizzx wrote:Those are not natural units because they don't have $\hbar = c =1$. That $e = \sqrt{4\pi\alpha}$ 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!

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.
FrediFizzx
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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

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.
Q-reeus

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Re: Magnetic monopole + supercurrent = apparent dilemma

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.

Hmm... you shouldn't be disagreeing if you would like a better and more complete understanding of physics. A choice of a man-made unit system can't change physics. It can only change the perspective. In the perspective I have presented, your OP is silly because you are chasing after something that couldn't ever possibly be true. I do believe we agree that it can't be true.
FrediFizzx
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