A type of unified-field theory that postulates a generalization of the general theory of relativity to higher than four space–time dimensions. In five space–time dimensions this gives general relativity and electromagnetic interactions. In higher space–time dimensions Kaluza–Klein theories give general relativity and more general gauge theories. A combination of Kaluza–Klein theory and supersymmetry gives rise to supergravity, which needs eleven space–time dimensions. In these theories it is proposed that the higher dimensions are ‘rolled up’ to become microscopically small (a process known as spontaneous compactification), with four macroscopic space–time dimensions remaining. It has been suggested by Sir Roger Penrose that the higher dimensions in Kaluza–Klein theory and other theories with compact higher dimensions might be unstable, leading to singularities. The question of how higher dimensions can be stabilized is very fundamental to any higher-dimensional theory, because changes in the sizes of higher dimensions would correspond to changes in the fundamental constants with time. Several suggestions have been made as to how this stabilization might be achieved. It has been suggested that the reason that there are four large space-time dimensions should be sought in the early universe, rather than using theories of elementary particles to investigate why the higher dimensions are very small. It has also been suggested that in Kaluza–Klein theory there may be particles (Kaluza–Klein particles) that could contribute to the missing mass of the universe. Kaluza–Klein theory is named after the German mathematician and physicist Theodor Kaluza (1885–1954), who proposed it in a paper published in 1921, and the Swedish physicist Oskar Klein (1894–1977), who modified it to take account of quantum theory in 1926.

Kaluza–Klein theory. The theory suggests that space–time is analogous to an object that appears to be one-dimensional from far away but is seen to have a compact extra dimension when viewed close up.