Why Magnetic Monopoles SHOULD Exist

**SPEAKER_1** (0:01)
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**SPEAKER_2** (0:26)
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**Matt O'Dowd** (0:56)
Physicists have been hunting for one particle longer than perhaps any other. It's not the tachyon or some supersymmetric particle, it's the magnetic monopole. And of all the fantastical beasts of particle physics, this is perhaps the most likely to actually exist. So, where are they all?
Let's try an experiment. Take a metal bar, and force all the electrons to one end. The electric field of the bar now looks like this. That's a dipole field. Now, cut the bar in half, and you get a pair of electric charges, one negative and one positive, both of which have electric fields that radiate straight out. Now, take a metal bar, and instead magnetize it. You get a dipole magnetic field that's very similar to the dipole electric field. So if we cut this bar in half, surely we get a pair of magnetic charges similar to our electric charges, right?
Wrong. The ends of the split magnet still have north and south poles and still generate a dipole field. And according to classical electromagnetism, it doesn't matter how many times you slice it, you'll never get isolated magnetic charges, what we call magnetic monopoles. This magnet slicing experiment was first performed by French scholar and Bo Batten's Academy professor, Petrus Peregrinus de Maroncourt, way back in 1269
That was before we knew what caused the magnetism in magnets. These days we know where magnetism comes from, and we're not so surprised that a halved magnet just makes two smaller magnets. In a ferromagnet, the field is the sum of the countless tiny aligned dipole fields of electrons in the magnet's atoms. The other popular way to make a dipole magnetic field is the electromagnet, where we push electrons around in a circle. In both cases, electron spin or a circular electric current, there's a sense of electric charge in motion. And according to classical electrodynamics, moving electric charge is the source of the magnetic field. If that's true then, why should we even expect there to be isolated magnetic charges, magnetic monopoles? Well, according to the classical theory, we shouldn't. The non-existence of magnetic monopoles is codified in the mathematics of electrodynamics. In particular, Gauss' law for magnetism, one of the four Maxwell's equations. It states that the divergence of a magnetic field is zero. The divergence is just this mathy term for the amount that a field points inward towards a sink or outwards from a source.
Zero divergence means no source and no sink.
Magnetic field lines can form loops or head out towards infinity, but they never end. According to this law, there are no magnetic monopoles. On the other hand, Gauss' law for electric fields tells us that the divergence of the electric field is not zero. It's equal to the electric charge density. That charge density is where the electric field lines can end, and they form their source or their sink. So there are such things as isolated electric charges. Let's take a quick gander at Maxwell's equations.
This is them without any charges, electric or magnetic. E is the electric field and B is the magnetic field. There's a near perfect symmetry between electricity and magnetism, which only gets screwed up when you put in the electric charge, here in the form of charge density and current density. You could also have symmetry between these equations if there was such a thing as magnetic charge. If you add magnetic charges to these equations, then you get a magnetic force that looks exactly like the electrostatic force. The physicist Murray Gell-Mann said that everything not forbidden is compulsory.

**SPEAKER_6** (4:57)
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