A Question...

[Mattius_]

Why is it that heat, light, and waves all follow the inverse square law? Why not the inverse cube law? why any law? why doesnt light radiate to 100% of its horizon instead of expanding by mathematical functions?

The best explanation i can come up with is that the inverse square law is a function of the spherical nature of things... Am i anywhere near the solution?

[Tyger]

in three space dimensions that is the way that conserved things spread out. A spherical shell with twice the radius has four times the area.

[elas]

Tyger is correct in as far as he goes, it could be added that all obey the inverse square law because they are all t[products of the same force.

[HallsofIvy]

elas:Tyger is correct in as far as he goes, it could be added that all obey the inverse square law because they are all t[products of the same force.

Do you have any evidence for that? What force do you mean? I see no reason to believe that there is any connection than that they are all examples of (different) conservation laws.


When I was in high school my physics teacher had what he called a "butter gun". It was simply a squirt gun with a dowel frame coming from the muzzle. There were dowels forming a square frame at a certain distance and dowels forming 4 identical squares at twice that distance. The point was that, since area is dependent upon length squared (and "similar triangles" tells us that, twice the distance from the end of the gun, the width is twice as great) we could fit 4 "pieces of toast" at twice the distance as that at which we could fit 1. Since the "amount of butter" was fixed, at twice the distance each piece of toast got 1/4 the toast as a piece at the first position.

Anything that "spreads out" uniformly must obey a "1/r2" law.

[jeff]

Originally posted by Tyger
in three space dimensions that is the way that conserved things spread out. A spherical shell with twice the radius has four times the area.

Originally posted by HallsofIvy
...they are all examples of (different) conservation laws.

In a very real sense, you guys are both right. Tyger argued in terms of spacetime geometry while HallsofIvy in terms of conservation laws. Well there's a theorem of profound and fundamental importance in physics due to emmy noether that relates conservation laws and symmetries. In this case it's the relation between poincare symmetry of spacetime geometry and the laws of conservation of mass energy-momentum it gives rise to.

[Tyger]

spreads out that way. The field strength of a radio wave goes as 1/R, which is why they can be received over such a large distance. But field strength is related to an amplitude and not a probabilty. The probablity that something will absorb a photon from the wave still goes as R−2.

[elas]

If the same law applies to all forces then what is the difference between forces?
Your reply will probably be that it is a difference in strength or density, or both.
To which I would reply that neither is proof that there is more than on kind of force (operating at different densities).
I would like to have a definition that demonstrates the need for more than one force.