It all started with an article on Habr titled "What is Electricity? Five Levels of Understanding, from Maxwell to Purple." The author—a physics enthusiast—describes how he first saw Maxwell's equations in full form at university and was struck by their beauty, and then... disappointed. The equations practically begged for one symmetric addition: add magnetic monopoles! Lone north and south poles, existing on their own, just like electric charges are supposed to. "It's so logical," he wrote.
And then—the phrase that sent me diving into the literature: "Only now I understand that this is a logical trap." The issue lies in a subtlety rarely discussed: the electric field E is a vector, while the magnetic field B is a pseudovector. They're not a complete pair, they're different in a mirror. Nature seems to deliberately refuse to do what mathematics considers obvious. The author ended the article with the phrase "Oh yes, and the monopole. Ask Ani"—as if it were a joke, not a century-old unsolved problem.
What hooked me wasn't "found or not found." What hooked me was that one logical hole—"should be, but isn't"—rolled through twentieth-century physics like a destructive wave: it demanded a new conservation law, spawned a new cosmology, and ultimately... still found monopoles. Just not where anyone was looking.
Let's start with that very "trap." Scalars and vectors behave differently if you look at the world in a mirror. An ordinary vector (position, velocity, force) changes sign in a mirror. A pseudovector (angular momentum, torque, magnetic field)—doesn't. The reason is simple: angular momentum is the cross product of two real vectors (position × momentum), and the cross product is an operation of pseudo-nature: it assigns an extra minus sign with each permutation of factors.
The magnetic field behaves as a pseudovector for good reason. It's generated by circulating currents or spins—meaning it's always tied to rotation. If rotation changes direction in a mirror, then the magnetic field sort of "evolves mirror-wise" too. And here's where the strangeness surfaces: if real magnetic charges with density ρ_M existed, then the equation ∇·B = ρ_M would require this density to be a pseudoscalar—an odd-in-time quantity. We know nothing like this in nature.
Honestly: this is an argument of "inconvenience," not strict prohibition. The real prohibition is formal—the vector potential A exists if and only if ∇·B = 0 (no magnetic singularities). The pseudovector nature of B merely hints that the asymmetry of E and B is not accidental, but something fundamental. Twentieth-century theoretical physicists pulled this hint apart into two different stories, and both turned out to be remarkable.
In 1931, Paul Dirac published a paper in Proceedings of the Royal Society with a very honest title: "Quantised Singularities in the Electromagnetic Field." He showed something that still fascinates: if at least one magnetic monopole exists in the Universe—somewhere, even just one per universe—then quantum mechanics implies that all electric charges in the Universe must be multiples of the same elementary unit.
The mathematics is elegant: charge + monopole together have angular momentum "stored" in the electromagnetic field around them, and its contribution equals eg/4π—independent of the distance between them. Quantization of angular momentum (the foundation of all atomic physics) requires eg/4π = nħ/2. Hence—Dirac's condition:
e·g = n·ħc/2
If you plug in the electron's charge, the monopole's magnetic charge comes out to g ≈ 68.5·e in CGS units. The number is unwieldy, and it immediately breaks the illusion of perfect symmetry: the magnetic "charge" is 68 times larger than the electric one. This means the monopole is a monstrously strongly interacting particle.
Dirac himself was as amazed as he was excited. He wrote in the article that this "reciprocity" between electricity and magnetism is mathematically flawless, but "under these circumstances one would be surprised if Nature had made no use of it." At the same time he honestly admits: explaining charge quantization through the monopole is not final, for that "some entirely new idea would be required."
And the final, almost detective-like twist from that same article: the attractive force between two monopoles of opposite signs equals (137/2)² ≈ 4692 times the attractive force between an electron and a proton. Dirac writes that this monstrous force "would perhaps account for why poles of opposite sign have never been separated." In other words, the monopole could exist somewhere deep within matter, but such forces glue them together permanently—and we'll never see them individually.
For forty years the monopole remained pure theory. And then came a night that all of particle physics remembers.
Blas Cabrera at Stanford built the cleanest possible experiment: a superconducting loop of four turns, 5 cm diameter, connected to a SQUID magnetometer—a device that registers changes in magnetic flux with single-quantum precision. All of this inside a superconducting shield one meter long, screening external fields by 180 decibels, with a background field of 5·10⁻⁸ gauss. The idea is simple: if a monopole flies through the loop, it creates a current in it—exactly eight flux quanta, independent of velocity, mass, and trajectory. This is a rare case in physics where the response doesn't depend on anything except the fact that "the particle exists."
Cabrera monitored the system for months. On February 14, 1982, the detector registered one single large jump—exactly 8 quanta, with ±5% accuracy. It was the largest event in 151 days of observation, and it perfectly matched the passage of one Dirac unit of magnetic charge. Cabrera methodically ruled out alternatives: power spikes, radio interference from a hairdryer, vibrations, screwdriver strikes on the structure, wire heating by cosmic rays. Nothing fit.
The news flew around the world. The organizers of the Third Grand Unification Workshop tracked down Cabrera by phone in Virginia and asked him to speak the next morning. On April 16, 1982, in Chapel Hill he delivered a talk—calm, precise, careful to the last digit—and, as Physics Today later wrote, "electrified" the participants: Grand Unification theory was for the first time bringing not formulas, but a possible particle in a capital basement.
Then—drama. Cabrera expanded the detector to three loops (476 cm²) and ran for 1008 active days (1150 astronomical days). Not one event. Then an eight-loop detector—again zero. The flux upper limit dropped to 4.4·10⁻¹² cm⁻²s⁻¹sr⁻¹. That "one event in 151 days" remains in the history of physics as the Valentine's Day Monopole—the most painful discrepancy between a perfect signal and its complete absence over the next 40 years. Spontaneous release of internal mechanical stresses in the superconductor—a never fully excluded cause—has since been considered the most likely explanation.
Parallel to the search for a "live" monopole, theorists discovered that such particles are not exotic, but a mandatory consequence of the most beautiful physics models. In 1974, 't Hooft and Polyakov independently showed: in any gauge theory where a Higgs field breaks symmetry down to U(1), stable classical solutions with magnetic charge exist. Essentially—monopoles must exist.
In Grand Unified Theory (GUT), where strong and electroweak interactions merge at a scale of ~10¹⁶ GeV, these monopoles turn out heavier than any particle that could be created in an accelerator: mass on the order of 10¹⁷–10¹⁸ GeV—roughly a quadrillion proton masses. No existing or planned collider comes even close.
And then—the explosion. Alan Guth and Henry Tye calculated how many such monopoles the early Universe should have produced during the Grand Unification phase transition (the Kibble mechanism: Higgs "bubbles" merge, misaligned fields form topological knots—and the knots are monopoles). The answer: the present-day monopole density exceeds astrophysical limits by roughly 14 orders of magnitude. This means monopoles should dominate the Universe and would have collapsed it long ago.
This is precisely where the idea of cosmic inflation appears. Guth describes it like this: he was sitting at home one night in early December 1979, trying to get the equations worked out before Tye left for China, and suddenly realized that if the early Universe "supercooled" in a false vacuum, it expands exponentially—and all this time the monopole density gets diluted to zero. "That same night I realized that exponential expansion also solved the flatness problem"—the second fundamental puzzle of cosmology. Guth's 1981 paper, "Inflationary universe: A possible solution to the horizon and flatness problems," has accumulated about 13,000 citations to date. And it started with an attempt to hide monopoles.
Note the irony: inflation—the pillar of modern cosmology, the foundation of the entire "flat" Universe we observe with percent-level precision—was born as a patch to remove unwanted particles. The product of a century-long hunt for the monopole turned out to be not a particle, but a new model of the entire early Universe.
Parallel to the theoretical work came the engineering. The huge disadvantage of GUT monopoles is that they're too heavy for colliders—but if they exist as relic particles, they can be searched for in cosmic rays.
The first "can't be many" argument was the Parker bound (1970): a monopole flying through the galactic magnetic field drains energy from it (like an electric charge in an electric field). If there are too many monopoles, the galactic field will "discharge"—but it exists. Hence the upper flux limit ~10⁻¹⁵ cm⁻²s⁻¹sr⁻¹—on the order of one monopole through a square centimeter per tens of millions of years. Beyond that—only enormous detectors.
MACRO at Gran Sasso (Italy) operated from 1989 to 2000. It's a detector 76.5×12×9.3 meters under 1400 meters of rock, with three different types of subdetectors: liquid scintillator, streamer tubes, nuclear tracks. Acceptance area—about 10,000 m²·sr. Result: zero candidates, flux upper limit 1.4·10⁻¹⁶ cm⁻²s⁻¹sr⁻¹—the tightest direct limit of its time.
IceCube in Antarctica—a cubic kilometer of ice—looks for monopoles through the Cherenkov effect; Pierre Auger Observatory and ANITA (on a balloon over the South Pole) search for ultrarelativistic monopoles, excluding fluxes down to 2.5·10⁻²¹ cm⁻²s⁻¹sr⁻¹—six orders of magnitude tighter than Cabrera's limit.
And MoEDAL at the LHC—a special case: it's the only LHC experiment that in 15 years of operation has made not a single discovery and isn't embarrassed about it. It searches not in the main beams, but where magnetic fields are the strongest in the Universe: in Pb-Pb collisions at 5.02 TeV/nucleon, magnetic fields reach ~10¹⁴ tesla. In 2022, MoEDAL published in Nature the first search for monopoles via the Schwinger mechanism (quantum tunneling of pairs from strong fields) and excluded monopoles with Dirac charges 1–3 g_D and masses up to 75 GeV/c². The lower mass limit is "the first lower limit for finite-size monopoles from a collider search." So—again zero, but a very solid zero.
This is where the story makes its final turn. Magnetic monopoles exist—they're just not elementary. They're emergent.
In 2007–2009, Castelnovo, Moessner, and Sondhi formulated and substantiated: in spin ice—the material Dy₂Ti₂O₇ (dysprosium titanate)—elementary magnetic moments are organized in tetrahedra and cannot all "settle down" in agreement. Spin directions run into geometric frustration. If you flip one spin "tube," a pair of defects arises—and at the tube ends the magnetic field looks exactly like a monopole field.
In September 2009, Science published observations of these quasiparticles using neutron scattering: the crystal was cooled to 0.6–2.0 K, and magnetic moments self-organized into intertwined "tubes," indistinguishable from Dirac strings—those very ones that Dirac introduced as a mathematical abstraction in 1931. At the tube ends—monopoles. The work won the Europhysics Prize in 2012.
And on October 15, 2009, Bramwell and colleagues published in Nature a paper with the provocative title "Measurement of the charge and current of magnetic monopoles in spin ice." They introduced the term "magnetricity"—by analogy with "electricity." Through muon spin relaxation they measured the elementary magnetic charge—5 μB·Å⁻¹—and showed that it exactly matches the prediction of microscopic theory, that monopoles interact coulombically, and that magnetic current actually flows and is measurable. In 2011, physicists at UCL created a magnetic field pulse at 0.36 K and registered monopole current decaying over several minutes. There are no Dirac strings in matter—but there's all the mechanics of charges, currents, and even "Ohm's law" for magnetic current.
The authors' formulation leaves no room for doubt: "our measurement of magnetic charge and magnetic current establishes an instance of perfect symmetry between electricity and magnetism." The symmetry that nature refused to admit into fundamental law lives peacefully at the quasiparticle level—and it's worth figuring out what follows from this.
It seems to me the monopole story is a perfect detective tale about how physics deceives itself when confusing "beautiful mathematics" with "mandatory reality." The logical trap the Habr author wrote about is not in the pseudovector nature of B as such (that's an argument of inconvenience, not prohibition), but in the habit of thinking that equation symmetry obligates the Universe. Mathematics proposes; nature chooses—and doesn't explain why.
What honestly impressed me: the product of a century-long hunt turned out to be not a particle, but infrastructure. Without the monopole there would be no Dirac condition—the first explanation for why the charges of all electrons are identical. Without the "monopole problem"—possibly no inflation and no modern cosmology, which today gives us the age of the Universe with percent-level accuracy. Without monopole searches there would be no SQUID, MACRO, IceCube, MoEDAL, and all the hardware infrastructure that later proved useful for other things. Physics seems to have asked: "does the monopole exist?"—and, receiving "no," managed to build almost everything else in a century of reflection.
And the final twist, which I like best of all: fundamentality and emergence are not a hierarchy, but different floors of the same rulebook. In spin ice, magnetic monopoles behave perfectly, coulombically, with measurable current and their own "Ohm's law." Nature admits them into the effective world of materials, but not into the fundamental law of electromagnetism. As if she's saying: "you want monopoles? Fine, here you go—but only if you agree they'll live not where you looked for them." In this sense the monopole is not a failure, but a reminder: even the most "obvious" symmetries are a proposal, not a contract.