Greetings,
First, let me say that dimensions are for forming frames of reference (directionality in some sense). The dimensions do not have to be orthogonal (meet at right angles), be straight, or even be constant. A 3D curve can be represented parametrically at functions x(t), y(t), and z(t), where t is a straight constant dimension, but x, y, and z are not.
When talking about the "real" world, the first 3 dimensions do not have to be spatial, and the 4th doesn't have to be temporal. My doctoral thesis was on a 6-dimensional representation for light filling a space. This is a real representation called the plenoptic function. The first 3 dimensions were the position of a viewer. The next two dimensions represented the direction that the viewer was gazing. The last dimension represented time. The domain of the function was (space, direction and time), and the range was incident light. So I should know that you can MAKE UP any dimensions you want.

As for Einstein, relativity, and other interesting stuff, look at "Faster Than the Speed of Light: The Story of a Scientific Speculation by Joao Magueijo." It is interesting in that it expands Einstein's ideas quite nicely, in some sense mapping Einstein's theories as functions of "universe time."
I more layman terms, the book contains very interesting info on Lorentz Transforms and the speed of light. The basic idea is that light does have a constant speed at each instant in the existance of our universe. So the constant c is actually replaced by a function c(t), where t varies ever so slowly through the lifetime of the universe. Very cool theory with huge ramifications.
I have my fireproof suit on, so let me have it!
Best,
Jeff