Physicists have been hunting for one particle longer than perhaps any other. Itâs not the tachyon or some supersymmetric particle. Itâs 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? Letâs 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 - thatâs 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 intsead magnetize it. You get a dipole magnetic field thatâs 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 doesnât matter how many times you slice it - youâll never get isolated magnetic
charges - what we call magnetic monopoles. This magnet-slicing experiment was first performed by French scholar and Beauxbatons Academy Professor Petrus Peregrinus de Marincourt
way back in 1269. That was before we knew what caused the magnetism in magnets. These days we know where magnetism comes from weâre 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 magnetâs atoms. The other popular way to make a dipole magnetic field is the electromagnet - where were push electrons around in a circle In both cases - electron spin or or a circular electric current thereâs a sense of electric charge in motion. And according to classical electrodynamics, moving electric charge is the source of the magnetic field. If thatâs true then, why should we even expect there to be isolated magnetic charges - magnetic monopoles? Well, according the classical theory we shouldnât. The non-existence of magnetic monopoles is codified in the mathematics of electrodynamics. In particular, Gaussâs law for magnetism,
one of the four Maxwellâs 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 toward a sink or outward toward a source. Zero divergence means no source and no sink. Magnetic field lines can form loops or head
out toward infinity, but they never end. According to this law there are no magnetic
monopoles. On the other hand, Gaussâ law for electric
fields tells us that the divergence of the electric field is not zero - itâs equal
to the electric charge density. That charge density is where the electric field lines can end - it forms their source or their sink. So there are such things as isolated electric charges. Letâs take a quick gander at Maxwellâs
equations. This is them without any charges - electric or magnetic. E is the electric field and B is the magnetic
field. Thereâs 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." meaning that if the math of our physical theory allows it, then it exists in nature. Thereâs nothing in Maxwellâs equations
that really says magnetic monopoles canât exist except for the fact that James Clark
Maxwell set the magnetic charge to zero because he didnât believe it existed. But in principle it could exist, and so could magnetic monopoles. At least according to classical theory. But what about quantum mechanics? When quantum theory first appeared it quickly revolutionized our understanding of electromagnetism by explaining it in terms of quantum fields
rather than charges and forces. We talked previously how electromagnetism arose automatically from requiring that the equations of quantum mechanics had a particular symmetry - the measurements they predict are unaltered by changes in one simple property - the phase of the wavefunction. Electromagnetism pops into the equations as soon as we require this - but in that version of electromagnetism, the electric and magnetic fields are VERY different from each other, and not at all interchangeable as they are
in Maxwellâs equations. In particular, the magnetic field emerging
from the quantum theory must have zero divergence - its field lines can never end - so it canât
have its own charge, unlike the electric field. So perhaps here we have our reason for the
apparent non-existence of magnetic monopoles. Quantum mechanics, as the saying goes, forbids it. Well, not so fast. Donât underestimate the power of the obsessed physicist. The great Paul Dirac had a habit of discovering particles just by staring at the math. In 1928 he predicted the existence of antimatter this way, as weâve discussed in a previous episode. But then in 1931, just before his antimatter thing was verified, Dirac made another prediction - of the existence of magnetic monopoles. His argument goes something like this. If you start with a dipole magnetic field,
you can approximate a monopole by moving the ends far enough apart and somehow vanishing the connecting field lines. And there is a way to do that. If you build a solenoid - just a coil carrying
an electric current - you get a dipole field whose connecting field lines are constrained within the coil. So make the width of the coil much smaller
than the length, and it looks like two isolated magnetic charges. This construction is called the âDirac stringâ, and Diracâs argument is that if the string part of the Dirac string is fundamentally
undetectable, then magnetic monopoles can exist. The second part of the argument is under what conditions that string is undetectable. So magnetic fields affect charged particles. In quantum mechanics, this works by shifting the phase of the particleâs wavefunction. Imagine a charged particle - say an electron
- passing by a Dirac string. To plot that trajectory you add up all possible paths of the electron, including paths to the left and to the right at the string. The presence of the string, with its magnetic
fields, should introduce different phase shifts depending on which side of the string the electron passes - and that would actually have a noticeable effect on the path of the electron. In other words, the string would be detectable. But thereâs one scenario where the string
can never be detected. The amount of the phase shift is proportional to the electric charge. For the right value of that charge, the phase
shift induced between the different sides of the string is exactly one wave cycle - which means no observable difference. So for the Dirac string to be undetectable
then electric charge can only exist in integer multiples of that basic charge This is a very loose form of the argument - and you can get to it in different ways. But the upshot is that the string connecting
monopoles is fundamentally unobservable, and Dirac argued that this makes it a mathematical figment, kind of like virtual particles. Reality should only be assigned to the monopoles themselves. On the one hand this was taken as a prediction of the quantization of electric charge - electric charge has to be discrete if thereâs even
a single magnetic monopole in the entire universe. And of course we know that electric charge
really is quantized - it can only be integer multiples of the charge of the electron. Or maybe of quarks - a third the electron charge. But instead of taking this as a prediction
of charge quantization, you can also flip it: magnetic monopoles are possible if electric charge is quantized. Charge turns out to be quantized, so quantum mechanics doesnât actually forbid monopoles. Letâs fast forward 40 more years. In the early 70s physicists had managed to
explain the weak nuclear force and unify it with electromagnetism. We talked about that before - about how the breaking of the symmetry of the Higgs field separated the weak and electromagnetic forces. With that squared away, physicists were working to bring the strong nuclear force into the fold with the so-called Grand Unified Theories. These involved slightly more complicated symmetry breakings. Well it turns out that magnetic monopoles
are inevitable in all âGUTsâ. Let me try to give you a sense of why - and
we have to talk about the Higgs field to do this. Weâve done a couple of Higgs episodes before if you want to get all the nitty gritty. But in electroweak theory, the Higgs field is a scalar field - it takes on a numerical value everywhere in the universe, but with no direction - itâs not a vector. In fact it really takes on two complex values
everywhere, and the interplay of those two âdegrees of freedomâ gives the Higgs its
power. In the simplest grand unified theory, the
Higgs field has three degrees of freedom instead of two. That means the field can sort of act like
a vector, even though it really isnât one. It can have a little internal arrow that points
in a particular direction - not pointing in physical space, but in the space of those
3 degrees of freedom. Now the laws of physics shouldnât care about the relative internal values of the Higgs field - what matters is the absolute length
of that internal vector - not the direction itâs pointing. There should be no noticeable effect even
if the direction of the Higgs field changes smoothly across space. Except in one very special case. If the direction of the Higgs field varies
smoothly from one point to the next, it can still have these sorts of knots - places where the field arrows all point away from that point - in what was called a hedgehog configuration. These are topological discontinuities - points that canât be removed by a smooth defomation of space. And it turns out these knots in the Higgs
field in GUT theories behave as massive particles with magnetic charge - magnetic monopoles. The hedgehog solution was figured out in 1974, simultaneously by Gerard tâHooft and Alexander Polyakov. It turns out that GUT theories generically
predict these magnetic monopoles, and that they should be A) very massive, and B) should form spontaneously in extremely high-energy environments like in the very early universe. The fact that magnetic monopoles should exist in these theories was both exciting and problematic. GUTs predict that monopoles should be produced in enormous numbers in the very early universe - as abundantly as protons and electrons. So where are they all? They should also be very massive - quadrillions of times the mass of the proton - and so should have quickly recollapsed the universe. This conflict with reality might have ruled out both monopoles and the grand unified theories that predict them. Except that both of these ideas are saved by yet another speculative idea - cosmic inflation. Many physicists think that a period of prodigious exponential growth kicked off the expansion of our universe. This should have happened after the production of magnetic monopoles, and so should have thrown these things far apart that there may be very few remaining in our entire observable universe. That would be a bummer for our hopes of detecting these things. But that hasnât stopped physicists from
trying. There are various approaches. If you have one of these magnetic monopoles in your lab it wouldnât be too hard to spot - for example a monopole would excite an electric current if passed through a conducting coil. Back in 1982, physicist Blas Cabrera Navarro set up a superconducting coil in his Stanford lab and managed to detect what looked like
a monopole with the same charge predicted by Paul Dirac. But no one ever saw such a thing ever again. That includes at the Large Hadron Collider,
where a couple of different experiments have failed to spot monopoles created in the collider. That's not so surprising given that the
LHC reaches energies about 100 billion times lower than is needed to produce the monopoles predicted by grand unified theories. People also look for magnetic monopoles coming from space - typically using cosmic ray observatories - or contributing to the Earthâs magnetic
field - and in a number of other ways. But again, no convincing evidence as of
yet. We have been hunting for magnetic monopoles for longer than just about any particle. Their discovery would mean cracking open the grand unified theories and revealing mysteries far beyond. And so many of us remain obsessed with this elusive beast, and convinced of its inevitability according to the symmetries of space time. If you've joined us on Patreon, I can't emphasize enough how helpful your support is in keeping this show going. You don't have to do it - you could keep watching for free anyway - but that makes it all the more awesome of you. Today I want to give a huge shoutout to our Big Bang supporter Kyle Bulloch. Kyle, we are taught by Paul Dirac that if
there's even a single magnetic monopole in the entire universe then electric charge must be quantized. We don't know where that single magnetic monopole would be, but it's rare and special and so we decided to name it after you. So now Kyle, the magnetic monopole Kyle - is doubly important - sure, it ensures the quantization of all charge, but it also serves as a testament to the generosity of Kyle. Of Kyle the human. Kyle, you have our thanks and now you also have a monopole. Last week we talked about how quantum spin leads to the universe as we know it - for example all the structure of solids, via the
Pauli exclusion principle. 4fmagnet points out a potentially misleading point in that episdoe. We represented very distinctly separated electron energy levels in our explanation of how fermionâs canât occupy identical quantum states. 4fmagnet notes that energy levels in atoms
can actually hold 2 electrons, not one, because itâs possible to have two electrons at the
same energy but different quantum states by allowing for opposite spin orientations. That's a fair call - if I was being more careful I would have said that we were trying to represent separate quantum states, not energy levels
in an atom. David points out that we donât need to keep
talking about spin as this incomprehensible quantum property that has no intuitive analogy - reminding us that Hans Ohanian, in his book âwhat is spin?â showed that spin can be described as a circular charge current in the Dirac field. We actually did mention this result in our episode on what is spin. And it may be that people should talk about this result more - Ohanianâs calculation is not generally accepted as âtrueâ, so Iâm
not sure we can be so confident in it, although as far as I know no-one has actually disputed the math. Still, it would be nice to have a physical
picture of spin that doesnât involve me taking off my belt. Flosi Lyons asks what happens when the degeneracy pressure - the structural support against collapse produced by the Pauli exclusion principle - is overcome. For example, if a collapsing stellar core
is massive enough it smashes through the degeneracy pressure that supports white dwarf stars and instead produces a black hole or neutron star. So the answer is that the Pauli exclusion
principle is never violated. Fermions never occupy the same quantum states. When degeneracy pressure is broken itâs
because new space in quantum states opens up. In the case of the collapsing star, densities
and energies become high enough for electrons to be captured by protons, converting them
to neutrons. So the loss of electrons reduces the degeneracy
pressure, allowing gravitational collapse to continue. Tom Rostrom asks whether any of this spin
statistics stuff explains why USB plugs need to be turned 540° to return to the correct
orientation? Fantastic question, Tim. The answer is no. USB plugs have spin 2/3s - a 360 degree rotation
gets you 2/3 of the way around. Theyâre neither fermions nor bosons, so
way outside the standard model. Also, remember that you can undo fermion rotations by translation of the ends - for USB cables its the opposite- twists approach infinity
as you move the ends around, especially in the presence of other USB cables. Physicists hope to understand these things
someday, perhaps with twistor or string theory. Or maybe you could just use USBC - theyâre spin-2 bosons like gravitons, so easily understood with a basic theory of quantum gravity.
Maxwell's equations at 3:24 had me all sorts of confused - magnetic divergence equals the rate of change of the magnetic field? I'm guessing two of the equations were mistakenly switched đ