53 votes
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Why don't magnetic monopoles exist?

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 ...
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32 votes
Accepted

Why are magnetic monopoles "incompatible" with quantum mechanics?

The argument here is supposed to go something like this: Classical electrodynamics, as long as you don't insist on a Lagrangian formulation, is fully described by Maxwell's equations in terms of the ...
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  • 105k
27 votes
Accepted

Does magnetic monopole violate $U(1)$ gauge symmetry?

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 ...
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  • 105k
15 votes
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Magnetic monopoles in field theory

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 $\...
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  • 105k
14 votes
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How will SR EM Lagrangian change if we find a magnetic charge?

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 ...
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  • 9,241
14 votes

Is there a topological difference between an electric monopole and an magnetic monopole?

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 ...
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12 votes

Vector potential field for a hypothetical magnetic monopole

You can find a solution on most of space, but not all of space. To see why, imagine taking the flux integral of $\vec{B} = \hat{r}/r^2$ over the surface of a sphere $S$ of radius $r$. Doing this ...
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12 votes

Vector potential field for a hypothetical magnetic monopole

Describing a magnetic monopole is a problem in Classical Electromagnetism: essentially, if you have a magnetic monopole, then $\nabla \cdot \mathbf{B} \neq 0$, meaning that we can no longer define a ...
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11 votes

Magnetic monopoles and special relativity

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 ...
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11 votes

Why are magnetic monopoles "incompatible" with quantum mechanics?

For your first question, on the link between quantum mechanics and potentials is that currently, there is no formulation of QM without these potentials and only in terms of the gauge invariant EM ...
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  • 1,145
10 votes

Why isn't Dirac credited with the discovery of the Aharonov-Bohm effect?

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 ...
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8 votes
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What would Maxwell's Equations be if we had magnetic charges and magnetic currents?

By analogy (between $\mathbf{E}$ and $\mathbf{B}$ as they are pretty much equivalent) then the divergeance of $\mathbf{B}$ field wouldn't be 0 anymore, instead: $$\nabla \cdot \mathbf{B}= \frac{\rho_{\...
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8 votes
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How does a magnetic monopole break time reversal symmetry?

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_{\...
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8 votes

Why do physicists believe that there exist magnetic monopoles?

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 ...
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8 votes

What do we mean with magnetic monopole and dipole?

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes. Luckily, there exists a ...
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8 votes

Do magnetic monopoles exist?

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 ...
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8 votes
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Principle of equivalence between a magnetic dipole and a closed loop with electric current

The papers you should read for this question are Vaidman, Lev. "Torque and force on a magnetic dipole." Am. J. Phys 58.10 (1990): 978-983 (Paywall-free version) and Haus, H. A., and P. Penfield. "...
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8 votes
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This vector potential gives a magnetic monopole field, what's wrong with it?

Yes, you have problems with this potential due to the singularity. Notice that you do want the singularity in $r=0$, as you are talking about a point charge (and the electric potential is singular in ...
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8 votes

Why are magnetic monopoles "incompatible" with quantum mechanics?

You are correct. This really has nothing to do with quantum mechanics. The existence of magnetic monopoles would require a change in Maxwell's equations (i.e., the divergence of the magnetic field ...
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7 votes
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What does the non-zero divergence of $\textbf{H}$-field say about magnetic monopoles?

The short answer is yes. $\textbf{H}$-field can have sources and sinks - these are what the "poles" of a bar magnet are. In an LIH medium $\textbf{B}=\mu_0\mu_r\textbf{H}$. Even though $\boldsymbol{\...
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  • 110k
7 votes
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No monopoles in the Weinberg-Salam model

I) Consider a Yang-Mills type theory with gauge group $G$. In principle we can consider the same theory with its covering group $\tilde{G}$, with $\pi:\tilde{G}\to G$. The covering group is by ...
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7 votes

Magnetic monopole and vector potential

You seek a 1-form $A$ on $\mathbb{R} - \{0\}$ such that $\mathrm{d}A = B$. On all of $\mathbb{R} - \{0\}$, $\mathrm{d}B = 0$, so this could exist. But, since you have magnetic flux, you require that ...
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7 votes

Why are magnets in form of hollow sphere not a magnetic monopole?

A good starting point to see that gluing small magnets to a sphere doesn't work is seeing what the field of just two magnets opposed gives you. A single dipole magnet has a field that falls off as $\...
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7 votes

Why don't magnetic monopoles exist?

Within the framework of standard model (SM) magnetic monopoles are non-existent. It is quite subtle as to why this is not the case. To begin, look at the Dirac's famous charge quantization condition. ...
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  • 1,553
7 votes
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Symmetry in electricity and magnetism due to magnetic monopoles

Both of these follow from desirable properties of this hypothetical magnetic charge, namely: Magnetic charge is conserved. Magnetic field lines radiate outwards from positive magnetic charges. The ...
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7 votes

How to derive Gauss's law for magnetism?

The answer depends on the assumptions. When you ask how to derive something you must ask yourself from what you want to derive it. For example: if you experimentally find out that there are no ...
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7 votes
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Is a magnetic monopole really necessary for charge quantization?

Yes, "quantization of charge" means that all charges are a multiple of some fundamental charge unit $e$. Of course, everything being made up of electrons and protons with a fixed charge explains ...
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  • 105k
7 votes
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Breaking a gauge group through a monopole$.$

First, have a look at the papers https://arxiv.org/abs/1602.04251 and https://arxiv.org/abs/1605.02391 where the authors (Seiberg and Witten) have a more careful analysis of the properties of the ...
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6 votes
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What would be the force constant for magnetic monopoles?

This is a good question, but at first blush it is hard to answer. This is because there is always an ambiguity in where you put the meaningful definitions - you can put it in the force constant, or ...
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6 votes

What would be the force constant for magnetic monopoles?

Your new constant would probably be $k/c^2.$ $k$ is actually a simplified expression for $1/(4 \pi \varepsilon)$ which is the permittivity of free space. For magnetic fields, you use the permeability ...
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