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Every magnet broken in half produces two complete magnets. North and south poles exist only in pairs. Electric charges, however, exist in isolation -- electrons carry negative charge alone, protons carry positive charge alone. This asymmetry is encoded in Maxwell's equations, where the magnetic field has no source term analogous to electric charge.

The absence of magnetic charges is not predicted by any fundamental principle. It is simply observed. The question of whether this absence is a deep truth about nature or merely a gap in our observation remains one of the most important open problems in theoretical physics.

Dirac's approach was characteristically elegant. Rather than asking why monopoles do not exist, he asked what would follow if they did. The answer was extraordinary: the mere existence of a single magnetic monopole, anywhere in the universe, would require electric charge to be quantized -- to come in discrete integer multiples of a fundamental unit.

Charge quantization is one of the most precisely verified facts in physics. The electron's charge has been measured to extraordinary precision, and every charged particle carries an exact integer multiple of this value. Dirac showed that a single monopole provides a natural explanation for this otherwise unexplained observation.

The Dirac quantization condition states that the product of electric charge and magnetic charge must equal an integer multiple of Planck's constant divided by four pi. This relationship links the fundamental constants of electricity and magnetism in an equation of remarkable simplicity.

In February 1982, Blas Cabrera's superconducting quantum interference device at Stanford recorded a single event consistent with a monopole passing through the detector. The signal matched theoretical predictions exactly. Cabrera expanded his detector eightfold and continued observations. The event was never repeated.

Modern searches use a variety of techniques. The MoEDAL experiment at CERN's Large Hadron Collider searches for monopoles produced in high-energy collisions. The IceCube Neutrino Observatory in Antarctica searches for monopoles in cosmic radiation. Deep underground detectors search for the characteristic Cherenkov radiation a monopole would produce.

No confirmed detection has been made. The absence places ever-tighter constraints on monopole abundance and mass, narrowing the parameter space where they might exist.

Grand unified theories predict that monopoles were produced copiously in the extreme temperatures of the early universe. At the moment the unified force separated into the electromagnetic, weak, and strong forces, topological defects in the vacuum would have created monopoles of immense mass.

The predicted abundance was problematic. Standard cosmology suggested monopoles should be common enough to dominate the mass of the universe. Their observed absence required explanation.

Alan Guth's theory of cosmic inflation was partly motivated by this monopole problem. If the universe underwent a period of exponential expansion in its first fraction of a second, the monopole density would be diluted to negligible levels. Inflation solved the monopole problem while simultaneously explaining the observed flatness and homogeneity of the cosmos.

The magnetic monopole remains one of the most well-motivated predictions in theoretical physics that has not yet been confirmed by experiment. Every grand unified theory predicts their existence. Their discovery would confirm that the electromagnetic, weak, and strong forces were once a single unified force.

The MoEDAL experiment continues to search at collider energies. Astrophysical observations constrain the cosmic monopole flux. Theoretical work explores whether monopoles might be lighter or more exotic than originally predicted.

The monopole stands at the intersection of quantum mechanics and classical field theory, of cosmology and particle physics, of mathematical elegance and experimental persistence.

• P. A. M. Dirac, "Quantised Singularities in the Electromagnetic Field," Proceedings of the Royal Society A, 1931.
• G. 't Hooft, "Magnetic Monopoles in Unified Gauge Theories," Nuclear Physics B, 1974.
• A. M. Polyakov, "Particle Spectrum in Quantum Field Theory," JETP Letters, 1974.
• B. Cabrera, "First Results from a Superconductive Detector for Moving Magnetic Monopoles," Physical Review Letters, 1982.
• A. H. Guth, "Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems," Physical Review D, 1981.
• MoEDAL Collaboration, "Search for Magnetic Monopoles with the MoEDAL Prototype Trapping Detector," JHEP, 2016.