# Suppose there is an extra compact dimension, and suppose

• Spinnor
In summary, Kaluza-Klein theory proposes the existence of an extra compact spatial dimension in addition to the familiar three dimensions. Matter is described as a 3-dimensional surface moving in these 4 spatial dimensions in a cyclical manner. The shape of this surface determines the physics. As observers, we only perceive the three dimensions of x, y, and z. At a given instant, matter is distributed in 4-space, appearing as a 2-dimensional surface in 3-space. The theory was originally intended to unify electromagnetism and gravity, but has fallen out of favor due to its treatment of fermions and the prediction of a hypothetical particle, the dilaton, that has not been observed. However, it has influenced many

#### Spinnor

Gold Member
Suppose there is an extra compact spatial dimension in addition to familiar space dimensions x, y, and z. Let us suppose that matter is some kind of 3 dimensional surface moving in these 4 spatial dimensions, 4-space, in some cyclical manner. Let us suppose that from the shape of the surface we can get physics. Assume as an observer we ourselves are some complicated 3 dimensional surface in 4-space. Now as observers we only notice the dimensions x, y, and z. At a given instant matter is "distributed" about in 4-space so that in 3-space at a given instant matter is but a 2 dimensional surface in 3-space. Matter is nowhere and in time everywhere.

Thanks for any thoughts or help making this more interesting.

@Spinnor did you find any more insight on this topic?

Kaluza-Klein theory:
https://en.m.wikipedia.org/wiki/Kaluza–Klein_theoryIt was originally formulated as a way to geometrically unify electromagnetism with gravity. Solving the Einstein field equations in 4+1 dimensions (where one of the spatial dimensions is periodic) gives the 10 original EFEs for 3+1 dimensions along with Maxwell’s equations. There’s also an extra scalar equation that predicts the existence of a hypothetical particle called the dilaton which has never been observed. KK theory has fallen somewhat out of favor because it only treats fermions in an ad hoc manner, but it is an important jumping off point for many modern beyond-Standard-Model theories that incorporate dimensional compactification.

Spinnor