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Talk:Essay:Quantifying Openmindedness (view source)
Revision as of 03:31, October 2, 2009
, 03:31, October 2, 2009interesting question: inverse square laws
: I do think it is quite possible that the power of 2 in Newtonian gravity is not precisely exact, and that a slight deviation from 2 (such as 2.0000001) is to be expected. The physical world is not a perfect in a mathematical sense.--[[User:Aschlafly|Andy Schlafly]] 23:05, 1 October 2009 (EDT)
: I do think it is quite possible that the power of 2 in Newtonian gravity is not precisely exact, and that a slight deviation from 2 (such as 2.0000001) is to be expected. The physical world is not a perfect in a mathematical sense.--[[User:Aschlafly|Andy Schlafly]] 23:05, 1 October 2009 (EDT)
:: Hmmm, that's an interesting question. It seems to me that the power of 2 would be forced to be exact if we take two other facts for granted, which seem plausible:
* The universe is a 3-dimensional Euclidean space
* Gravitational fields are divergence-free away from a source. This physically means that there is no contribution to the gravitational field of a mass from any point that's not part of the mass.
::This is basically a consequence of the [[divergence theorem]] (if I'm thinking straight). These are both basic tenets of the Newtonian picture. It's really not possible to do Newtonian mechanics where gravity is an inverse-2.00001 law: it would look to bodies as if gravitational force was being exerted by a body outside the mass in question! Similarly the fact that Coulomb's law is precisely an inverse-square law is a consequence of Gauss's law, which also follows from very basic assumptions. On the other hand, Newtonian physics isn't exact in the first place. I think I have read that gravity seems to be weaker than an inverse square law over extremely large distances (on the astronomical scale). This is because of some non-Newtonian, and perhaps not fully understood, physics. But there's no way to describe gravity in GR by something as simple as an inverse-square law anyway! --[[User:MarkGall|MarkGall]] 23:31, 1 October 2009 (EDT)