[beefield]

I have never quite understood why there can't be stable stallites in dimensions above 3.

I mean, I know the argument that gravity inverse square law becomes inverse cube law in 4d, but what I do not understand is that what/why enforces that. Why in a hypothetical 4d world there just can not be a gravity-like force that is inverse square? Would that cause some kind of contradiction?

[alexey-salmin]

If you make a uniform flash of light in 3d space it spreads around you in a shape of a sphere of increasing radius. Energy gets distributed evenly across the sphere's surface which is growing with time proportional to a square of the radius. So energy density (think intensity) decreases as inverse square. In 4d space the sphere's surface grows with the cube of the radius.

This sort of intuition. Applies to electromagnetic waves, sound and gravity all alike.

[beefield]

But there are forces even in our 3d world that do not follow inverse square law (strong/weak nuclear forces). That kind of proves that all forces do not need to follow this intuition?