# Tag Info

44

There is no theoretical reason why magnetic monopoles cannot exist and indeed there are good reasons for supposing that they should exist. It's just that we have never observed one. In the past there have been various experiments to detect magnetic monopoles, though I think everyone has given up on the idea by now. If you're asking why we can't get ...

21

No, a magnetic monopole a la the Dirac string does not "violate" gauge symmetry. Rather, the statement "we have a magnetic monopole" means only that we are forced to consider the gauge theory not on the whole spacetime, but on the spacetime with the location of the magnetic monopole removed. Why? Because, at the location of the magnetic monopole, the ...

16

This is interesting. You would definitely have to 'nail down' the magnets to the sphere, because it will be an unstable configuration. Also in the real world, edge-effects will destroy any chance of perfect radial field lines, so let's assume we're in an ideal scenario. Outside the sphere, the magnetic field would be that of a source monopole placed at ...

16

Let me make quite clear that the recent experiment does NOT imply the detection of a true magnetic monopole. Somehow, in all the excitement, the word "synthetic" was dropped rather quickly from the phrase "synthetic magnetic field". A synthetic magnetic field is a physical quantity that obeys the same equations as a magnetic field, typically realized in ...

14

The field would disappear completely. I think the simplest explanation is in terms of the surface currents that account for the field (assuming constant magnetization, which is reasonable for thin slices). For the initial torus magnet (your second image) the magnetic field is generated, in practice, by surface currents on the planar ends of the torus. One ...

14

In the absence of magnetic monopoles, Maxwell's equations are \begin{align} \text d F &= 0 ,\\ \text d{\star F} &= J_e , \end{align} where $J$ is the 4-current 3-form due to electric charges (assuming a metric with signature $(-,+,+,+)$). For cohomological reasons, from the first equation one can asserts that there exists a 1-...

11

i) First of all, the Dirac quantization rule $$\tag{1} \frac{qg}{2\pi\hbar} ~\in~ \mathbb{Z}$$ for magnetic monopoles can be generalized to the Dirac-Zwanziger-Schwinger quantization condition $$\tag{2} \frac{q_1g_2-q_2g_1}{2\pi\hbar} ~\in~ \mathbb{Z}$$ for dyons. (In a slight misuse of terminology, we shall in the following also include purely ...

11

Magnetic monopoles can be created according to numerous Grand Unified Theories (GUT). The idea is that at sufficiently high energies you can reach an energy range where three of the four fundamental forces (strong nuclear, weak nuclear, and electromagnetism) couple to one another and are the same force. Such a state existed in the universe a tiny fraction of ...

11

For each $r>0$, the divergence of the magnetic field of the monopole is zero as you have already checked; \begin{align} \nabla\cdot\mathbf B(\mathbf x) = 0, \qquad \text{for all $\mathbf x\neq \mathbf 0$}. \end{align} But what if we also want to find the divergence of this field at the origin? After all, that is where the point source sits. We might ...

11

The mathematical model for classical electromagnetism just doesn't forbid magnetic monopoles by construction. Consider an arbitrary vector field $X$ in 3d. Such a vector field is totally characterized by its divergence and curl. Suppose the following is true: $$\nabla \cdot X = \sigma, \quad \nabla \times X = Y$$ Then knowing $\sigma$ and $Y$ everywhere,...

10

I think Emilio Pisanty's answer is good enough. But here is another longer, 'magnetic charge' approach. ( Let's specify the coordinates first (sorry I borrow your picture). It's obvious that the toroid is symmetrical under rotation along $\hat{\phi}$ direction. Thus we can't have magnetic field along $\hat{\phi}$. Which means it is sufficient for us to ...

10

Dirac's discovery of the quantization of the magnetic charge is distinct from the Aharonov-Bohm effect. These effects depend on different topological properties of the manifold on which a charged particle moves. The Aharonov-Bohm effect appears on manifolds with a nonvanishing first cohomology group $H^1(M)$, while the Dirac quantization condition takes ...

10

The difference between the two arises because Maxwell's equations, while looking perfectly "equal", actually are not all of the same nature when we phrase electromagnetism in terms of a potential. If you think of $F$ as the dynamical variable, then $$\mathrm{d}F = 0 \quad \mathrm{d}{\star}F = 0$$ in vacuum look perfectly symmetric, and you might imagine ...

9

Another option, besides modifying the potential $A_\mu = (A_i, \phi)$ in some way, is to introduce another 4-potential $C_\mu = (C_i, \psi)$. Then the electric and magnetic field are given by $$E = - \nabla \times C - \frac{\partial A}{\partial t} - \nabla \phi$$ $$B = \nabla \times A - \frac{\partial C}{\partial t} - \nabla \psi$$ More on this 2-potential ...

9

These are "fake monopoles", in the sense that the north and south poles are not actually separated. They are the ends of thin tubes which behave like Dirac strings - like long thin twisted magnets. The tubes are formed due to geometrical frustration, which forces the magnetic field to be orientated either toward the outside or toward the inside of the ...

9

The article is pretty poorly written. As Siva said it doesn't even link to the original paper. So I just looked up the name mentioned in the article and found this which is probably what they're talking about (though this is just a guess). They measured the magnetic dipole moment of protons and antiprotons to ~4 parts per million (and verified the CPT ...

9

There are no consequences concerning the quantization of the charge or the existence of real magnetic monopoles. The connection with the monopoles is only formal. What the experimentalists study is the (superfluid) velocity field $v$ and the corresponding vorticity $\Omega=\nabla \times v$ in the gas and the spin orientation of the atoms (the system is ...

9

You cannot just add a term to the Lagrangian to give the usual electromagnetic gauge theory magnetic charge. The reason is rather simple: The equation of motion for a magnetic four-current $j_m$ is $\mathrm{d}F = j_m$. But $\mathrm{d} F = \mathrm{d}\mathrm{d} A = 0$ independently of the equations of motion. So simply adding a term doesn't work. The first ...

8

If you have a source of radial magnetic field $B\sim Q_M/r^2$, then one may prove that the vector potential $\vec A$ can't be single-valued. It's because $\vec B={\rm curl}\vec A$ for a well-defined $\vec A$ automatically satisfies ${\rm div}~\vec B=0$. However, $Q_M/r^2$ has a curl proportional to the delta-function at the origin. Still, this delta-...

8

1) Postponing for a moment the issue of magnetic monopoles, one conventional answer is, that the gauge potential $A_{\mu}$ (as opposed to, e.g., the electric and magnetic $\vec{E}$ and $\vec{B}$ fields) constitute the true fundamental variables and (the photon field) of QED. At the classically level, by saying that $A_{\mu}$ are fundamental variables, we ...

8

As Mark M says in his answer,you cannot have a monopole magnet. You can simulate one. After all when you are at the north pole of earth, to all intents and purposes that is a monopole for magnets in the area. By spreading the magentic lines of one of the poles on a large area and concentrating the other to a very small one. Look at the images here. If you ...

8

The answer to your question, is yes, it has indeed been considered. The bound state has even been given a name "monopolium". Here is a paper discussing prospects for detection and production. I should add the caveat that they're not strictly, in your words "confined together like quarks". You could separate them if you input enough energy, unlike the ...

8

The English Wikipedia article on magnetic monopoles has the following equation for the 'extended' Lorentz-Force of a magnetic field on a electrically and magnetically charged particle: $$\vec{F}=q_{\mathrm e}\left(\vec{E}+\vec{v}\times\vec{B}\right) + q_{\mathrm m}\left(\vec{B}-\vec{v}\times\frac{\vec{E}}{c^2}\right)$$ Under time reversal ($t$ is ...

8

No free magnetic monopoles have ever been confirmed to exist. There have been experimental results that are consistent with the existence of monopoles, most famously on Valentine's Day, February 14 in 1982, but that observation has never been repeated and is now dismissed as an artifact of some kind. No experiment has confirmed the existence of magnetic ...

7

It should perhaps be stressed that the magnetic monopoles that many GUTs predict are generalized 't Hooft Polyakov monopoles (as opposed to e.g. the Dirac/Wu-Yang monopoles, which are singular in a point/exclude a point). Once a GUT action $S[A,\phi,\psi]$ is adapted, then the 't Hooft Polyakov monopoles do in principle not constitute a new independent ...

7

You cannot. B is not just a relativistic side-effect of E. Jackson, Electrodynamics, Section 12.2 has a nice discussion, in which he refutes the "proofs" given in some undergraduate texts. "The confusion arises chiefly because the Lorentz transformation properties of the force are such that a magnetic-like force term appears when the force in one ...

7

You don't hear about gravitomagnetic monopoles because they, unlike magnetic monopoles, cannot be well defined within the context of GR. Gravitomagnetism is only a weak field approximation of GR which isn't Lorentz-invariant, so it is not to be expected that everything from electromagnetism has an analogy in GR. In electromagnetism, there are two ways one ...

7

Introducing magnetic charge into Maxwell equations is not a problem at all, and it does not require any strings etc. Moreover, it makes Maxwell equations symmetric w.r.t. magnetic and electric fields/charges. The equations are as follows: \begin{split} \mathop{\mathrm{curl}} E + \frac{\partial H}{\partial t} &= -J_m \\ \mathop{\mathrm{curl}} H - \frac{\...

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