First unification in higher dimensions

[Demystifier]

It is frequently stated in the literature that the first attempt to unify gravitation and electromagnetism through a theory in higher dimensions was attempted by Kaluza and Klein. Yet, today I have realized that this is not true. The first such attempt was done by Nordstrom in 1914
http://arxiv.org/abs/physics/0702221
BEFORE Einstein constructed his general theory of relativity.

The idea is surprisingly simple. It is a Maxwell theory in 5 dimensions, with the ansatz that the 5-component vector potential does not depend on x_5. With this ansatz the 5-dimensional Maxwell equations split into the 4-dimensional Maxwell equations and a scalar 4-dimensional theory of gravity described by A_5.

This theory can also be viewed as a first version of a brane theory (which are today popular in the context of string theory). By contrast, the Kaluza-Klein theory is a first compactified theory (which are also today popular in the context of string theory).

 

[atyy]

Indeed. Nordstrom also contructed the first relativistic theory of gravitation ("Nordstrom's second theory"). It is a field on flat space time. Einstein and Fokker studied Nordstrom's theory and rewrote it as a theory of spacetime curvature. It is experiment that chooses between the Nordstrom's theory and Einstein's general relativity: Nordstrom's theory gets the observed perihelion precession wrong. Interestingly, Clifford Will classifies Nordstrom's theory as the only known metric theory of gravity other than GR that satisfies the strong equivalence principle http://relativity.livingreviews.org/Articles/lrr-2014-4/ .

General relativity was born as a theory of spacetime curvature, but after that from Kraichnan, Gupta, Feynman, Weinberg, Deser and others, we know it is also valuable to view it as a field on a background spacetime.

Here's an article that reviews Nordstrom's work:
http://arxiv.org/abs/gr-qc/0405030
Scalar Gravitation and Extra Dimensions
Finn Ravndal