Kaluza

Kaluza refers to Theodor Kaluza, a German mathematician and physicist who lived from 1885 to 1954. In 1921 he proposed a five-dimensional unified field theory that aimed to merge gravity and electromagnetism within the framework of general relativity extended to an extra spatial dimension. In Kaluza’s formulation, the familiar four-dimensional spacetime is supplemented by a compact fifth dimension. By applying a cylinder condition—that physical fields do not depend on the fifth coordinate—the five-dimensional Einstein equations can be decomposed into four-dimensional gravity plus Maxwell’s equations, with the electromagnetic potential emerging from the off-diagonal components of the five-dimensional metric. A scalar field associated with the size of the extra dimension also enters the description.

Oskar Klein later contributed a key refinement in 1926 by proposing that the extra dimension is not extended but compactified on a tiny circle, rendering it unobservable at ordinary energies. This idea, known as the Klein modification, helps explain why the fifth dimension has not been detected. The combined approach is known as Kaluza–Klein theory, and it is considered an important early step toward modern higher-dimensional theories that geometrize gauge fields and forces.

Impact and legacy: Kaluza–Klein theory introduced the concept that physical forces can arise from geometric properties of extra dimensions. While it faced challenges, including the presence of a scalar field without a clear experimental role and the lack of a complete quantum framework at the time, the core idea influenced later developments in gauge theory, extra dimensions, and string theory.