# Why did Kaluza need to invent a new theory to unify general relativity and electromagnetism?

Wikipedia (and many other sources) say that by extending the number of spacetime dimensions from four to five, Kaluza–Klein theory unifies general relativity and electromagnetism into a single theory. But why do need to do anything as complicated as adding a new dimension? It's conceptually very easy to write down Maxwell's equations in curved spacetime without doing anything nearly as fancy. How is this any less "unified?"

In the quantum context, a compact extra dimension gives a natural justification for the quantization of electric charge, but Kaluza's original theory was entirely classical.

• Because it allows for EM to arise from a metric theory in five dimensions. – Ryan Unger Jul 19 '17 at 8:06

• Eh, I see what you're getting at, but your distinction between one and two fields seems fairly arbitrary. The metric $g_{\mu \nu}$ in $D$ spacetime dimensions could reasonably be thought of as one field, or $D(D+1)/2$ different fields, or $D^2$ different fields respecting $D(D-1)/2$ constraints, depending on how you count. – tparker Jul 20 '17 at 8:08