Magnetic monopole

A magnetic monopole is a hypothetical elementary particle that carries an isolated magnetic charge g, sourcing the dual electromagnetic field tensor *F^{μν} = ½ ε^{μνρσ} F_{ρσ} the way an electron with charge q sources F^{μν}. If magnetic monopoles existed, the symmetric Maxwell equations would read ∂_μ F^{μν} = μ₀ J_e^ν (electric four-current sourcing F) and ∂_μ F^{μν} = μ₀ J_m^ν (magnetic four-current sourcing F), restoring perfect E↔B duality at the level of the field equations. The actual second Maxwell equation in our universe, ∂_μ *F^{μν} = 0, is a statement of the experimental absence of magnetic monopoles to the precision of every search ever conducted.

Paul Dirac in 1931 showed that magnetic monopoles are consistent with quantum mechanics, with one striking consequence. The wavefunction of an electric particle in the field of a monopole cannot be globally single-valued unless the product of the electric charge q and the magnetic charge g satisfies the *Dirac quantisation condition q g = 2π n ℏ for some integer n. The smallest non-trivial monopole charge is therefore g_D = 2π ℏ / e ≈ 4.14 × 10^{−15} Wb (= Φ_0, the magnetic flux quantum). The argument turns the empirical fact of electric-charge quantisation — that every elementary particle has charge a multiple of e/3 — into a theoretical consequence* of monopole existence. For physicists who view charge quantisation as one of the deepest unexplained facts in nature, the existence of even a single magnetic monopole anywhere in the universe would make it suddenly comprehensible.

In grand-unified theories (GUTs) like SU(5) and SO(10), magnetic monopoles arise automatically as topological solitons — stable lumps of energy density that emerge whenever a non-abelian gauge group breaks to a subgroup containing an unbroken U(1). The 't Hooft-Polyakov monopole (1974) is the canonical example: a finite-energy stable solution of the SU(2)→U(1) Higgs model with magnetic charge g_D and mass on the order of M_GUT/α. Cosmological monopole production in the early universe (Kibble mechanism) would generically have produced enough monopoles to overclose the universe by many orders of magnitude — the monopole problem of GUT cosmology, which Alan Guth proposed in 1980 to solve by inflation (which dilutes the relic monopole density to negligible). Despite this rich theoretical motivation and sixty years of dedicated experimental search — the MoEDAL detector at the LHC, lunar-regolith analyses by the Maryland-Stanford collaboration, the Cabrera 1982 single-event candidate at Stanford that has never repeated — no magnetic monopole has ever been observed. We have not found one. We have not ruled them out. Dirac showed they would not break anything.