Could the Electromagnetic Field extend into higher dimensions?

Question

DId the concept of higher physical dimensions exist in Maxwell's time? Has anyone explored the ramifications of modern GU theories on EM propogation or has it been somehow established that it is bound to ordinary 3D spacetime? What would be a test to determine if it was or not?

Answer 1

If you represent Maxwell's Equations in a Minkowski frame, they simplify to

dF = 0, d*F = 4 pi *J

In a sense, you are using math in higher dimensions to characterize a 4-dimensional phenomenon.

In 1919, the Kaluza-Klein model was proposed. It is considered the first supradimensional spacetime model, the first baby step toward string theory / M-brane theory.

Such a model is overkill for electromagnetism. It's more than you need. But any successful GU theory of any kind must include EM.