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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 Nutshel

• philzook 7y ago
  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
  • nabla9 7y ago
    But does the inverse square law hold in non-euclidean space?
    • FreeFull 7y ago
      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 7y ago
        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 7y ago
          That's a short-distance effect, though, not a long-distance one.
  • evanb 7y ago
    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 7y ago
      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.