In skimming through my physics text book, I realised how many things in 3D follow an inverse square law. Magnetic fields, electric fields, sound waves, light (when described as a wave, not a particle), gravity, and possibly friction all seem to follow it.
Clearly most of these will follow an inverse cube law in 4D. I'd like to discuss whether this will have disastrous effects on stability, just like gravity does.
The biggest problem is the electric field. In classical mechanics, electrons orbit the nucleus of an atom in a similar way to planets orbiting the sun. If the electric field obeyed an inverse cube law, the electrons would surely spiral inwards just like the planets.
I've heard that this happens before, but I didn't believe it until now. Isn't there any way around this? Can we still have a vaguely sensible 4D universe?