- #1

- 271

- 10

Kaluza–Klein theory - Wikipedia

I assume the Einstein equations is same as the Einstein Field Equations (because when I clicked the highlight, the EFE came out).The five-dimensional (5D) theory developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919,[2] and published them in 1921.[3] Kaluza presented a purely classical extension of general relativity to 5D, with a metric tensor of 15 components. 10 components are identified with the 4D spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the "radion" or the "dilaton". Correspondingly, the 5D Einstein equations yield the 4D Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the "cylinder condition" hypothesis, that no component of the five-dimensional metric depends on the fifth dimension. Without this assumption, terms are introduced that involve derivatives of the fields with respect to the fifth coordinate. This extra degree of freedom is such that the field equations of fully variable 5D relativity grow enormous in complexity. Standard 4D physics seems to manifest the cylinder condition, and the corresponding simpler mathematics.

<snip>

The field equations are obtained from five-dimensional Einstein equations, and the equations of motion from the five-dimensional geodesic hypothesis.

If EFE can work above 4D. Up to what D can it be valid? Can it be made to work in the compactified dimensions too?

Remember Lisa Randall RS1 and RS2 seem to use General Relativity above 4D too (doesnt it?).