Light is electromagnetic radiation, according to what I have learned so far essentially a changing magnetic field inducing an electric field which induces a magnetic field and so on.
The equations for magnetic induction include the cross product, and the cross product does seem to appear in Maxwell’s equations aswell (though I haven’t studied those yet so this might be a misinterpretation).
Now, vector cross product is only defined in 3-dimensional space. So my question is whether these induction phenomena (and maybe electromagnetism in general) would also work in general n-dimensional space, or whether there is something special about 3D that allows light to exist as an electromagnetic wave.
Is the cross product just a special notation for some overarching phenomenon that would produce light-like behaviour in other dimensions, or really a 3-dimensional uniqueness?
