On: The Inverse Square Law (2000)

[greens]

For gravity and EM fields the inverse square law is a consequence of a massless force carrier particle and Lorentz invariance. Quantum Field Theory in a Nutshell by Zee talks about this early on.

[philzook → greens]

An interesting but rather overcomplicated seeming explanation. The posted article basically is saying inverse square laws results from conversation of flux (of any kind) in 3d. That seems like a pretty good explanation to me

[evanb → philzook]

For radiation, yes.

But for force laws, having a massless carrier is critical for an inverse-square law. With massive carriers (like the carriers of the weak force, W+Z bosons) the range of the force scales like 1/M; the force law is more like exp(-Mr)/r ---> 1/r as M-->0. The diminishing of the force with exp(-Mr) means flux isn't conserved. (note I worked in units where hbar = 1 = c, so that the W's mass ~= 80 GeV/c^2 corresponds to 1/M << 1 fm)

[philzook → evanb]

But also things that aren't radiation or high energy physics. Inverse square laws are ubiquitous in hydrodynamics, heat flow, electrostatics. Good ole fashioned 19th century physics. And I think that's its most natural arena.

[nabla9 → philzook]

But does the inverse square law hold in non-euclidean space?

[FreeFull → nabla9]

It doesn't. As far as we can tell though, our universe doesn't have much curvature, so the problem doesn't come up.

[nabla9 → FreeFull]

It comes up in our solar system. The anomalous motion of Mercury can explained only if the gravity does not follow inverse square law.

[evanb → nabla9]

That's a short-distance effect, though, not a long-distance one.