Kaluza–Klein theory

A framework that seeks to unify gravity and electromagnetism by treating spacetime as having an extra compact spatial dimension. In its simplest form, the extra dimension makes the four-dimensional electromagnetic field part of higher-dimensional gravity.

Kaluza's fifth dimension: The additional spatial coordinate introduced in Kaluza's attempt to derive electromagnetism from gravity. Its metric components yield the electromagnetic field when the theory is viewed in four dimensions.
Theodor Kaluza: A German mathematician and physicist who proposed deriving electromagnetism from five-dimensional general relativity. His 1921 proposal introduced the extra dimension at the heart of the theory.
String theory: A framework in which fundamental entities are one-dimensional strings whose quantum excitations include particles and forces. It also uses extra dimensions, but builds a broader quantum framework than the original theory.
Gauge–gravity correspondence: A family of relationships connecting gravitational theories to gauge theories in different dimensions. The theory is an early example of deriving gauge-field structure from higher-dimensional geometry.
Kaluza–Klein reduction: A procedure for expressing a higher-dimensional theory in terms of fields on fewer dimensions. It reveals how the five-dimensional metric separates into gravity, electromagnetism, and a scalar field.
Oskar Klein: A Swedish theoretical physicist who developed a quantum interpretation of a compact extra dimension. His 1926 work connected the fifth dimension's small size to quantized electric charge.
Einstein–Maxwell theory: A four-dimensional theory combining general relativity with classical electromagnetism as separate fields. It describes the same familiar forces without deriving electromagnetism from an extra dimension.
Kaluza–Klein monopole: A gravitational solution in higher-dimensional theories that appears as a magnetic monopole in four dimensions. It shows how extra-dimensional geometry can produce a four-dimensional magnetic-charge configuration.
Compactification: The treatment of extra spatial dimensions as curled up into small, finite geometries. A compact fifth dimension can evade observation at ordinary energies.
General relativity: Einstein's theory describing gravity as the curvature of spacetime. Kaluza extended its geometric framework by adding another spatial dimension.

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