Unraveling the Mystery of G: Newton's Equation F= G (mM)/r^2

[rbj]

...We cannot prove that Newton's Equation is the right one, but we can, for example, prove that there are infinitely many prime numbers.

i think you are not considering the fundamental difference between the disciplines of physics (or science) and mathematics. physics uses mathematics and a mathematical proof can certainly have a consequence in what is understood in some (or many) physical theories. but mathematics exists, in and of itself, without any reference to physics or science or really anything, except maybe philosophy.

when you prove something mathematically, you do it based on axioms (the rules we all agree on before starting) and logic and what had been proven prior. when you prove something in physics (or some other science), you do it with experiment. actually you don't really prove anything in physics (other than mathematical consequences) but you verify things in physics with experiement. you verify that the observation of some phenomena is or is not consistent with some theory. even if it is verified to be consistent with some theory does not mean the theory (or equation in this case) is "proven" because it does not mean that it is not also consistent with another theory. maybe that other theory (that might yet to be discovered) is the "right" one.

the only way to verify Newton's Eq. of gravitation, is with experiment, and then only to the degree possible by the finite precision measurements in the experiment (which turn out to be sort of difficult because, in our human scale of things, gravity seems pretty weak and difficult to measure quantitatively). for the most part, Newton's Eq. of gravitation has been verified beautifully, but it has actually failed in some subtle observations such as the precession of planetary orbits. the apsides of orbits precess more than expected under Newton's theory of gravity. this has been confirmed for Mercury and observed in several binary pulsars. and it turns out that the theory of General Relativity has done much better explaining it than Newtonian gravitation.

so, in a sense, we (well, not you or me, but us humans) have already proven that Newton's Eq. is the wrong one. it is only an approximation to reality for weak gravitational fields and slow (w.r.t. light) speeds. Newton did pretty good for a couple of hundred years until GR came along. maybe in another 200 years, some other theory will displace GR because of some failure (not yet discovered) of GR to be consistent with some observation.

Therefore until we haven't found a proof for that equation we should not go any further by encouraging ideas such as requiring multi-universes or an intelligent designer to account for the G constant.

that's a different issue completely. even though it has nothing to do with proving Newtonian theory of gravitation or not, i agree with you that either speculation about an Intelligent Designer (a.k.a. "God" but the damn creationists don't want to admit that because they know they lose in court if they do) or the application of the Anthropic Principle (which is, for the most part, a tautology) to this theory of the multiverse where our universe is just one of the products of a singularity therein, both are only speculation or a statement of faith (which is fine for what it is, but it ain't really science, it's philosophy).

 

[SGT]

Elegantly said. I think McQueen really got my question. We cannot prove that Newton's Equation is the right one, but we can, for example, prove that there are infinitely many prime numbers. Therefore until we haven't found a proof for that equation we should not go any further by encouraging ideas such as requiring multi-universes or an intelligent designer to account for the G constant.

No law of Physics can be proved in the way mathematical priniples are. Mathematical theorems are derived from a set of axioms, that are accepted without proof. If you change one axiom, the whole theory changes. For instance, if we change Euclides' fifth postulate and allow two parallels to a line pass through a point, the sum of the angles of a triangle is no longer 180 degrees.
Laws of Physics are the best explanation we can presently find to an observable phenomenon. If new observations don't fit the law, it must be changed. Newton's law of gravitation confirms all observations,from the fall of a leave from a tree on Earth to the movement of planets. Einstein's Theory of Relativity does not contradict Newton's law, it only focus the problem under a geometric point of view, but the inverse square relationship is still valid.
Are Newton's and Einstein's theories the truth? Certainly not, they are only our best understanding at the present. Are we shure that new observations won't put in doubt those theories? No, again! There is no truth in observational sciences.
Edit to add: Damn, rbj beat me in the answer.

 

[rbj]

Damn, rbj beat me in the answer.

sorry. anyway, i think i have to disagree with you if you say that GR does not contradict Newton's theory of gravitation. of course it must in some contexts or it wouldn't be necessary. if two competing theories have no contradiction in any result, they must be equivalent. one place where Newton's and Einstein's theory make different predictions is with the precession of planet's orbits. and the observation of Mercury's precession supports Einstein over Newton. but the difference is subtle. we still use Newton exclusively to compute rocket trajectories, tension in bridge members, etc.

 

[SGT]

sorry. anyway, i think i have to disagree with you if you say that GR does not contradict Newton's theory of gravitation. of course it must in some contexts or it wouldn't be necessary. if two competing theories have no contradiction in any result, they must be equivalent. one place where Newton's and Einstein's theory make different predictions is with the precession of planet's orbits. and the observation of Mercury's precession supports Einstein over Newton. but the difference is subtle. we still use Newton exclusively to compute rocket trajectories, tension in bridge members, etc.

When I say the two theories don't contradict, I mean they both use the inverse square factor. I agree with you that Newton's theory is not applicable in all cases where we use GR, or else Einstein's theory would be superfluous, but in the cases where both are applicable, there is no contradiction.