54 votes
Accepted

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 ...
John Rennie's user avatar
31 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 ...
ACuriousMind's user avatar
  • 125k
16 votes
Accepted

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 $\...
ACuriousMind's user avatar
  • 125k
16 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 ...
ACuriousMind's user avatar
  • 125k
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 ...
Michael Seifert's user avatar
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 ...
Philip's user avatar
  • 11.4k
11 votes
Accepted

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 ...
ACuriousMind's user avatar
  • 125k
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 ...
LPZ's user avatar
  • 11.6k
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 ...
David Bar Moshe's user avatar
10 votes
Accepted

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 ...
Salvatore Baldino's user avatar
9 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. ...
Mass's user avatar
  • 2,020
9 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 ...
Yashas's user avatar
  • 7,173
9 votes
Accepted

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. "...
Robin Ekman's user avatar
  • 14.8k
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 ...
garyp's user avatar
  • 22.2k
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 ...
KF Gauss's user avatar
  • 7,833
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 $\...
Chris's user avatar
  • 17.2k
7 votes
Accepted

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 ...
Michael Seifert's user avatar
7 votes

Symmetry in electricity and magnetism due to magnetic monopoles

You actually noticed something that is called electromagnetic duality. A duality correspond to two different theories which give the same physical results as long as we make specific mappings among ...
Diracology's user avatar
  • 17.7k
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 ...
Gold's user avatar
  • 35.9k
7 votes
Accepted

Question about Charge and Gauge Transformation

You are right of course! Physical observables must be gauge invariant. But this does not mean that they must be neutral. They could be charged under the global symmetry and be neutral under the local ...
Prahar's user avatar
  • 26.1k
7 votes
Accepted

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 ...
Weicheng Ye's user avatar
6 votes
Accepted

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 ...
Emilio Pisanty's user avatar
6 votes
Accepted

Why are electric monopoles not interpreted as topological defects but magnetic monopoles are?

Recall that electric-magnetic duality involves an $S$-transformation, namely the coupling constant undergoes $e\leftrightarrow 1/e$. This constant is very different from $1$ (in particular, $e\ll1$), ...
AccidentalFourierTransform's user avatar
6 votes

Is this case a failure of Stokes' theorem?

In this kind of cohomology-related things, physicists tend to say that “Stokes theorem always holds,” while allowing the possibility of delta-function sources. On the other hand, mathematicians ...
L-C's user avatar
  • 544
6 votes
Accepted

Why would magnetic monopoles not violate the law of conservation of energy?

Since the magnetic monopole acquires a significant amount of energy, you cannot just treat it like a (magnetic) test charge that moves passively on and on in the supposedly constant solenoidal ...
oliver's user avatar
  • 7,462
6 votes
Accepted

Is it possible to introduce magnetic monopoles without breaking $∇ · B = 0$?

No, it is not possible. If you have a magnetic monopole then, by definition, there is some closed Gaussian surface $S$ over which $$\oint_S \vec B \cdot d\vec S \ne 0$$ which by implies that $$\int_V \...
Dale's user avatar
  • 100k
6 votes
Accepted

Magnetic field lines are closed lines?

In general, it is not true that the magnetic field lines will form closed loops—although that it what happens in a lot of simple geometries. What is true instead is that the magnetic field lines ...
Buzz's user avatar
  • 16.1k
6 votes

EM radiation from monopole v.s. dipole

Please read the exact wording in the cited source carefully. The forbidden thing is the monopole radiation, not radiation from a monopole. "Monopole radiation" is the radiation due to time ...
John's user avatar
  • 3,491
5 votes
Accepted

Which charge to use in the Dirac quantization condition?

The answer can be found in section 6 of http://www.sciencedirect.com/science/article/pii/0550321381902376. Above the Hagedorn temperature, the strong interaction becomes long-ranged and falls of as $...
tparker's user avatar
  • 47.5k
5 votes
Accepted

Magnetic monopoles and special relativity

The idea that magnetism is a side-effect of electricity is deeply mistaken. The sooner you forget about that idea, the better. Electricity and magnetism are the two aspects of a single phenomenon, ...
Steve Byrnes's user avatar
  • 16.6k

Only top scored, non community-wiki answers of a minimum length are eligible