Five-dimensional space

[1] Much of the early work on five-dimensional space was in an attempt to develop a theory that unifies the four fundamental interactions in nature: strong and weak nuclear forces, gravity, and electromagnetism.

German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force.

[citation needed] The fifth dimension is difficult to directly observe, though the Large Hadron Collider provides an opportunity to record indirect evidence of its existence.

Einstein, Bergmann, and Bargmann later tried to extend the four-dimensional spacetime of general relativity into an extra physical dimension to incorporate electromagnetism, though they were unsuccessful.

[4] The main novelty of Einstein and Bergmann was to seriously consider the fifth dimension as a physical entity, rather than an excuse to combine the metric tensor and electromagnetic potential.

[5] Minkowski space and Maxwell's equations in vacuum can be embedded in a five-dimensional Riemann curvature tensor.

[6][7] Recent research suggests several alternative interpretations of the 5D extension of spacetime, most of them generalizing the earlier Kaluza-Klein theory.

[8] Another 5D representation describes quantum physics from a thermal-space-time ensemble perspective and draws connections with classical field theory as limiting cases.

[9] Yet another approach, spacekime representation, lifts the ordinary time from an event-ordering positive-real number to complex-time (kime), which effectively transforms longitudinal processes from time-series into 2D manifolds (kime-surfaces).