Question

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist.

Is there any direct or indirect evidence supporting a fourth dimension?

Answer 1

No. Unless you consider time as the fourth dimension. Also current research suggests that spacetime becomes two dimensional at high energies and very small distances. So, yes, dimensionality of spacetime is a mutable concept in modern physics. But no experimental evidence, indirect or direct, has been found for a fourth spacelike or a second timelike direction.

Someone is bound to question my statement that "spacetime becomes two dimensional at high energies and very small distances". My backup reference for this is Carlip's recent paper The Small Scale Structure of Spacetime, where he considers inputs from five or six different theoretical lines of research. Of course, there is bound to be a spectrum of opinion on this issue.