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

[suckstobeyou]

F= G (mM)/r^2

I'm interested in knowing why people are so obssessed with the gravitational constant G? It is obviously true that it is perfectly tuned so planets and solar system and life could form but why do we even ask this question to begin with and not others? Obviously if you know for a fact that this is the only formula that could explain the gravitational force between two objects, then yes that would be the right question. But why do we not entertain the possibility for the existence of other equations and this one being wrong? Is it just because we haven't found others yet or does this one have to be the one and only one? For example why do we have r squared in the bottom of the equation? why could that not be some other complex term such as r to the 1.9834983484344? which then in turn could account for that weird G? Or even the equation itself could be fundamentally wrong in that it is missing another variable or something or maybe instead of multiplying the masses we should divide the larger one by the smaller one and multiply by some power of r and so on...

Are we just happy to have this formula and therefore ignoring everything else just because so far this is the only one that works?

am I wrong in saying: until we are convinced this is the only formula (THE right formula) to explain gravitational force we should avoid requiring an answer to the question "why is G so well tuned?"

 

[Janus]

But G isn't perfectly tuned. A different value of G wouldn't have that profound a effect on the formation of planets, the Solar system etc. It is just a proportionality constant that has the value it does because of the units we use. If we used different units, G would equal 1 and vanish from the equation.

 

[HallsofIvy]

I'm not at all sure I understand your question. I, at least, don't know anyone who is "obsessed" with G!

As far as the r² is concerned, the reason that is called "Newon's" equation is that Newton showed (and he had to invent calculus to do it!) that only a "1 over r²" formula would satisfy all of Kepler's laws of planetary motion.

Actually, as is the case with all scientific formulas, that one is not perfect. It is now known that the planets do not perfectly match Kepler's laws and, even allowing for iteraction between the planets, Newton's equation does not perfectly reflect their motion. Einstein produced other equations that do a better job. Of course, he didn't just alter r slightly- he produced a tensor equation that is far different even in theoretical basis.

 

[rbj]

But G isn't perfectly tuned. A different value of G wouldn't have that profound a effect on the formation of planets, the Solar system etc.

actually, Janus, a change in dimensionful constants like $G$ or $c$ or $\hbar$ or $\epsilon_0$ is, in the words of Micheal Duff, "operationally meaningless".

http://www.arxiv.org/abs/hep-th/0208093
http://en.wikipedia.org/wiki/Planck_units

It is just a proportionality constant that has the value it does because of the units we use. If we used different units, G would equal 1 and vanish from the equation.

of course, that is absolutely right. now if the dimensionless number of Planck lengths per meter stick has changed significantly, we would know the difference. likewise, if the dimensionless number of Planck times per clock tick changes significantly, we would know the difference, but there is no way any change of a dimensionful "constant" made by some "god", would be noticed by us. if some change was noticed, it would always boil down to some dimensionless quantity or ratio of like dimensioned quantities that would have changed.

 

[suckstobeyou]

But G isn't perfectly tuned. A different value of G wouldn't have that profound a effect on the formation of planets, the Solar system etc.

read and listen to #4 on this page: http://www.bbc.co.uk/radio4/science/further5.shtml

The Astronomer Royal Martin Rees explains that a large value for G would mean that stars would burn too quickly and a low value would mean that the stars would not form in the first place, so is G perfectly tuned for life? Is God a mathematician?

I also read it somewhere else that in fact G is precisely tuned and if it was more than 2% different than its current value either we would not have any stars or planets at all, or stars would be so compact they would burn all their mass so quickly which in result there wouldn't be enough time for evolution and life to take place.

I'm not at all sure I understand your question. I, at least, don't know anyone who is "obsessed" with G!

a lot of peolpe must be obsessed with G that's why they ask does there have to be a God to fine tune G for our universe. Some also came up with multiple deminsions and universes to increase the possibility for G to happen to be just the right number to allow for life, in our case. (listen to that audio from the link above)

if some change was noticed, it would always boil down to some dimensionless quantity or ratio of like dimensioned quantities that would have changed.

Are you saying if we changed G we would not feel anything different in the universe at all? would the gravitational forces between stars and planets not change?! would we not weigh either more or less on Earth?

 

[Danger]

We exist because physical laws are what they are, so it's no surprise whatsoever that they are suitable for life.

 

[rbj]

Are you saying if we changed G we would not feel anything different in the universe at all? would the gravitational forces between stars and planets not change?! would we not weigh either more or less on Earth?

well, "we" don't change $G$ or even the constants like $\alpha$ http://en.wikipedia.org/wiki/Fine-structure_constant that we could notice a change.
i am saying that we measure $G$ against our previous defined notions of what a meter, kilogram, and second are (or whatever units we choose to measure physical things with). now, i hope you do not object to the notion that the "strength of gravity" does not give a rat's ass about what set of units we choose to use. so then if we measure $G$ in terms of Planck Units http://en.wikipedia.org/wiki/Planck_units , then the value always comes out to be 1. so if God (or some "god-like being") turns the knob on $G$, we will still measure it to be 1 in terms of the Planck units. now if, for some reason, we measure it to be different, in terms of our meter sticks, cesium clocks, and kilogram prototype, then what changed is a dimensionless physical quantity such as how many Planck lengths there are in our meter.
the same song-and-dance applies to the speed of light $c$ or any other dimensionful physical quantity.

 

[suckstobeyou]

well, "we" don't change $G$ or even the constants like $\alpha$ http://en.wikipedia.org/wiki/Fine-structure_constant that we could notice a change.
i am saying that we measure $G$ against our previous defined notions of what a meter, kilogram, and second are (or whatever units we choose to measure physical things with). now, i hope you do not object to the notion that the "strength of gravity" does not give a rat's ass about what set of units we choose to use. so then if we measure $G$ in terms of Planck Units http://en.wikipedia.org/wiki/Planck_units , then the value always comes out to be 1. so if God (or some "god-like being") turns the knob on $G$, we will still measure it to be 1 in terms of the Planck units. now if, for some reason, we measure it to be different, in terms of our meter sticks, cesium clocks, and kilogram prototype, then what changed is a dimensionless physical quantity such as how many Planck lengths there are in our meter.
the same song-and-dance applies to the speed of light $c$ or any other dimensionful physical quantity.

ok I think you're completely off track regarding what my question actually is.I think you're trying to explani how we measure units in physics and how to write them in terms of planks. Again I don't care whether G is 1 or something else. forget about Planck's units... and let's get back to my question. let me pose the question in this way why is gravity as strong as it is? why not more or less?

if the speed of lights was different we wouldn't notice that much of a change and life most likely would still evolve and planets would still form and so on, the same could be true for other similar fundamental contants, they wouldn't stop life if their values were different, but gravity would... so I guess I kind of answered my own question... any comments?

 

[rbj]

ok I think you're completely off track regarding what my question actually is.

you can think that, but you'ld be wrong...

... and let's get back to my question. let me pose the question in this way why is gravity as strong as it is? why not more or less?

this is precisely the question i was addressing. take a look at the Planck units article on wikipedia http://en.wikipedia.org/wiki/Planck_units and read the Frank Wilczek quote. oh hell, i'll just paste it in for you:

...We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in Natural (Planck) Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)]... (June 2001 Physics Today) http://www.physicstoday.org/pt/vol-54/iss-6/p12.html

we have the history of how the meter, kilogram, and second were originally defined. they are quantities that are not too many orders of magnitude different from the dimensions or sizes of us (human beings). but physics doesn't give a rat's ass about human beings.

the salient questions to ask (and answer, someday) is: why is it that there are about $10^{25}$ Planck Lengths in the size of an atom? and why is it that there are about $10^{5}$ atoms across the diameter of a biological cell? why is it that there are about $10^{5}$ biological cells across the length of an organism such as us? and, effectively why is it that there are about $10^{44}$ Planck Times in the time of a clock tick (or about a human heartbeat)? and why is it that there are about $10^{8}$ Planck Masses in a mass we commonly call a kilogram (originally defined to be the mass of 1000 cubic centimeters of water)? if you answer those questions, you will answer why the speed of light is what it is (or perceived to be what it is perceived to be by us). why the gravitational constant and Planck's constant are what they are.

let these concepts mull around in your cranium for a while. i think you'll get it eventually.

 

[rbj]

F= G (mM)/r^2
...
For example why do we have r squared in the bottom of the equation? why could that not be some other complex term such as r to the 1.9834983484344?

i meant to address this one, too, but i got distracted with the G thing. the answer to the $r^2$ thing has to do with the surface area of a sphere (which is $4 \pi r^2$) and this concept we call "flux" or "flux density" (in this case gravitational flux) in which this other concept we call "field" or "field strength" is proportional to. (in fact, the most natural units which are almost the same definition of Planck units, would make the constant of proportionality between flux density and field strengh equal to 1, so there would be no difference between flux density and field strengh. these would be the same as Planck Units but with $4 \pi G = 1$ and $\epsilon_0 = 1$.)

check out the wikipedia articles on "inverse-square law", "flux", and "Gauss's Law" to get a more explicit explanation.

 

[daniel_i_l]

The r^2 reflects the fact that gravity spreads in 3 spatial dimentions. in 1D it would be r^0, in 2D r^1 in 3D r^2 ...

 

[thephy]

A good theory is always based on the experiment. And luckily, the result of the experiments are always can be described exactly by math, such as by formulas or by geometry. It is funny that physics can be compatible with mathematics. And therefore we can predict some phenomenas by computations.
F= G (mM)/r^2
The only 2 can make a force effective for long distances, which has been proved in classical mechanics and quantum mechanics.
The fact is that we often try to explain what we see, but sometimes we may not see the truth and then the theory need to be revised.

 

[ahrkron]

I'm pretty sure that there have been experiments to measure the exponent in the inverse square law. IIRC, they have put some very strict limits on it. I think some are cited at the beginning of "Gravitation" (Misner, Wheeler & Thorne).

 

[Fe-56]

or we can believe the simplicity and beauty of our Universe :-))
(and 2 is much more "pretty" number than 1.999874564864613513243)

 

[McQueen]

A Scientist , and more especially a physicist , seeks primarily to know how things work the way they do , while a Philosopher seeks to know why things work the way they do. Although these statements might sound semantically equivocal , in actual terms they are worlds apart , they represent two extremes . On the one hand there is the factual , empirical , tabulated experimentally proven result and on the other is the abstract , ethereal , undefined concept. To try to explain in mathematical terms why a certain line of poetry sounds better than another , makes no –sense , everybody with an opinion could be right and they could as equally be wrong , to try and put this kind of logic to work in explaining factual phenomenon is equally futile. It might be that Physicists are erring in this regard . This is just one interpretation of “suckstobeyou” comment. Again , take the recent experiments to determine “locality” or “non-locality” . The whole context of the experiment and as a result its meaning has been “altered” until the very experiment and its result has become meaningless. In the original experiment two quantum entangled particles were separated , it was known that if one of the particles had a spin up then the other would have a spin down , now, and here is the relevant part , the spin of one of the particles was changed AFTER they had undergone a space like separation. If the other spatially separated particle underwent an opposite change in spin , it would prove many statements such as the collapse of the wave function , the existence of faster than light interactions and as a direct consequence of this the whole subject of “causality”. The experiment has been carried out using SPDC (spontaneous parametric down conversion) to produce quantum entangled photons which , although of identical energy , frequency , wave-length etc., have opposite polarization , therefore if photon A of the entangled pair has a vertical polarization then it is taken for granted that Photon B will have a horizontal polarization. In fact the experiment has progressed from the purely experimental stage to one of practical application in the form of Quantum Encryption : http://www.newscientist.com/article.ns?id=dn4914 [/URL] BUT and this is the crucial point , the two entangled photons are separated and the polarization of one is [I]detected without [/I]changing its polarization at the spatially separated location. What does this prove ? Does it prove anything about locality or non-locality or the wave function or causality ? No. The single point that it proves is that quantum entangled photons possesses opposite polarization at the moment of separation , nothing else. Why is this so? How can a subject which has been so hotly debated for more than half a century be suddenly dropped or obscured in such a blatant manner? The claim now is that the state of polarization of the entangled photons is held in abeyance [I] until[/I] the polarization of one of the photons is detected at which time the wave collapses . Notice that there is nothing here about the polarization being changed after the photons are spatially separated , so the experiment tells us nothing of whether spatially separated particles can in fact interact. This passes totally out of the realm of Science or Philosophy and enters an unknown area altogether. P.S. Use of capitals for emphasis only and should not be attributed as shouting.

 

[SpaceTiger]

let me pose the question in this way why is gravity as strong as it is? why not more or less?

Are you perhaps trying to ask about the anthropic principle -- i.e. that the laws of physics must be tuned such that we can exist? If so, then nobody will be able to answer your question. Such discussions are more for philosophy than physics. However, this hasn't prevented such threads from popping up on PF, so if that is what you're after, I'd suggest a search of the forums.

 

[McQueen]

Are you perhaps trying to ask about the anthropic principle -- i.e. that the laws of physics must be tuned such that we can exist? If so, then nobody will be able to answer your question. Such discussions are more for philosophy than physics. However, this hasn't prevented such threads from popping up on PF, so if that is what you're after, I'd suggest a search of the forums.

I feel that suckstobeyou's post is capable of many interpretations. To give a prominent example of this take the moon landings and the Voyager spacecraft , which were phenomenally successful despite the fact that no-one till today knows for sure exactly what gravity is or why it works in the way it does. And its still getting better , Japan has launched its Hayabusha space probe which will land on an asteroid pick up samples and return to earth.

 

[SGT]

I think that what suckstobeyou is trying to do is to use the old argument that the physical constants of the Universe where finelly tuned to allow human life, so an Intelligent Designer created the Cosmos in order to give origin to some beings who would worship Him/Her.
For a good debunking of that theory, please read this article by Victor J. Stenger.

 

[alias25]

prehaps suckstobeyou is thinking about chaos theory and complex systems and that the universe is a complex system sensitive to initial conditions.

 

[rbj]

Are you perhaps trying to ask about the anthropic principle -- i.e. that the laws of physics must be tuned such that we can exist?

but the only numbers (unversal constants) where this fine-tuning has any meaning, are the dimensionless numbers. not dimensionful numbers like $G$ or $c$ or $\hbar$ or $\epsilon_0$. those numbers have meaning only in the context of the system of physical units we measure things with (in which the universe does not care).

If so, then nobody will be able to answer your question. Such discussions are more for philosophy than physics.

there are legitimate (albeit speculative) discussions in theoretical physics (like string theory and branes, etc.) about the possibility that other universes may have appeared out of this thing called the "multiverse" in which the salient dimensionless universal constants could have been different, so different that matter could not have formed or some other difference (the amount of clustering of stars, galaxies, etc.) so that nothing like life as we understand it, could have formed. it's not pure philosophy, but it is pretty speculative.

 

[SGT]

but the only numbers (unversal constants) where this fine-tuning has any meaning, are the dimensionless numbers. not dimensionful numbers like $G$ or $c$ or $\hbar$ or $\epsilon_0$. those numbers have meaning only in the context of the system of physical units we measure things with (in which the universe does not care).

No, the dimensionful constants could be ten, a hundred or a million times greater or smaller than they are in any system of units.

there are legitimate (albeit speculative) discussions in theoretical physics (like string theory and branes, etc.) about the possibility that other universes may have appeared out of this thing called the "multiverse" in which the salient dimensionless universal constants could have been different, so different that matter could not have formed or some other difference (the amount of clustering of stars, galaxies, etc.) so that nothing like life as we understand it, could have formed. it's not pure philosophy, but it is pretty speculative.

Yes, and some of those universes could give origin to different forms of life. It only happens that we live in the particular Universe where the physical constants are what they are and allowed the appearance of human beings and cockroaches. By the way, cockroaches are best suited than humans to live on Earth, so if there is an Intelligent Designer, he must have tuned the constants in the benefit of roaches and we should mention the blattopic principle.

 

[rbj]

No, the dimensionful constants could be ten, a hundred or a million times greater or smaller than they are in any system of units.

we wouldn't know the difference if any of those dimensionful universal constants changed. they have "no operational meaning" except as a reflection of the units used to measure them. they are purely a human construction.

don't believe me? take it up with Michael Duff. you might want to check out the paper(s) he has written either explicitly about the subject or peripherally. they are cited at the Planck Units article at wikipedia (i referenced that earlier in this same thread.) just like a carpenter commonly measures length against a like dimensioned standard, so it is the same in physical experiments or even in our perception of reality. it's the dimensionless numbers that are operationally meaningful. what $G$, $\hbar$, $c$, and $\epsilon_0$ tell us (in terms of the units we chose to use to measure them) is, essentially, where Nature has put her tick marks on her ruler, clock, weighing scale, and electroscope (in terms of our anthropocentric units). if God (or some other god-like being) were to somehow change $G$ in such a way that he/she could tell the difference, we could not. we would still measure it to be the same value in terms of these things we call meters, kilograms, and seconds.

Yes, and some of those universes could give origin to different forms of life. It only happens that we live in the particular Universe where the physical constants are what they are and allowed the appearance of human beings and cockroaches. By the way, cockroaches are best suited than humans to live on Earth, so if there is an Intelligent Designer, he must have tuned the constants in the benefit of roaches and we should mention the blattopic principle.

i'm not plugging the ID thing, even if, as a matter of faith some of us might choose to believe something like that. this whole ID mess in the public schools is simply a damn shame. i wish the creationists would simple get out of the science classroom and let the scientists do science.

 

[SGT]

we wouldn't know the difference if any of those dimensionful universal constants changed. they have "no operational meaning" except as a reflection of the units used to measure them. they are purely a human construction.
.

I am not talking about different unit systems. Do you think that if instead of $$6.672x10^{-11}Nm^2kg^{-2}$$ G was $$6.672x10^{-14}Nm^2kg^{-2}$$ or $$6.672x10^{-8}Nm^2kg^{-2}$$ we would have the same Universe? I don´t think so. In the first case gravity would be probably too low to allow star formation and in the second, stars would be so massive that they would probably burn their hydrogen in a few million years.

 

[McQueen]

I think that what suckstobeyou is trying to do is to use the old argument that the physical constants of the Universe where finelly tuned to allow human life, so an Intelligent Designer created the Cosmos in order to give origin to some beings who would worship Him/Her.

On the contrary , I think that far from being a post which should be relegated to Forum limbo , suckstobeyou’s post is intelligent , amusing and thought provoking. Imagine for instance , just for a second , if by some quirk of fate , after all these years Gravity was found to have an electromagnetic solution ! Say for instance it had something to do with the number of self interactions taking place within atoms of different types. Just speculating , mind you. It would , at one stroke get rid of the awkward 4 pi r^^2 factor ,it would also be a welcome turn of events to scientists like Lorentz and Einstein who both believed that Gravity was in some way related to electromagnetism. In fact Einstein said that such an “electromagnetic “ based ether would iron out all the kinks in his General relativity Theory.

 

[rbj]

I am not talking about different unit systems. Do you think that if instead of $$6.672x10^{-11}Nm^2kg^{-2}$$ G was $$6.672x10^{-14}Nm^2kg^{-2}$$ or $$6.672x10^{-8}Nm^2kg^{-2}$$ we would have the same Universe?

i'm saying that, unless some dimesionless universal constant changes, we would not know the difference, and then the salient number that changed is that dimensionless constant. say, if the Fine-Structure Constant $$\alpha$$ changed, eilther the fundamental charge, or Planck's contstant, or the speed of light (which is defined in SI), or the permittivity (which is defined in SI) changed. you might think it was c that changed but the important number is alpha.

likewise, there are some 20 something fundamental universal parameters that John Baez indentifies http://math.ucr.edu/home/baez/constants.html , some of these are masses of particles. but they are referenced against another mass (probably Planck mass). and if it isn't some dimensionless quantity like these has not changed, there is no way you or anyone else would know if G were different. if G apparently changes relative to how we measure it, there is a fundamental dimensionless parameter that is more primary that is at the root of it.

I don´t think so. In the first case gravity would be probably too low to allow star formation and in the second, stars would be so massive that they would probably burn their hydrogen in a few million years.

read the Duff paper. please.

 

[SpaceTiger]

I think that what suckstobeyou is trying to do is to use the old argument that the physical constants of the Universe where finelly tuned to allow human life, so an Intelligent Designer created the Cosmos in order to give origin to some beings who would worship Him/Her.
For a good debunking of that theory, please read this article by Victor J. Stenger.

As much as I'm sure some of us would like to, I don't think it's possible to debunk intelligent design. What that article seems to be "debunking" is the approach that many creationists take to the anthropic principle. Often, what they'll do is calculate the probability that various things (like the orbit of earth) would have lined up exactly as they did. They then go on to argue that things had to be this way in order for us to exist, and given that their probability is always small, they interpret it as evidence for a designer.

That argument is flawed two senses. First of all, if the universe really is fine-tuned to our existence, then it doesn't necessarily mean there was designer -- it could easily be that there are multiple universes and we're in one of the few that can harbor conscious life. The second, and most obnoxious, way that the argument is flawed is that they just assume that life couldn't have arisen in other ways. Although this sort of prejudice isn't surprising from creationists, it's subtle enough that most people won't get it.

Despite these things, I actually do suspect that the universe is fine-tuned such that we can exist -- I find it very hard to believe that the majority of "possible" universes would be capable of giving rise to conscious life. I tend to interpret this in the context of a multiverse. I try not to go much beyond that, however, because it is, as I said, more philosophy than physics at this point.

 

[SpaceTiger]

but the only numbers (unversal constants) where this fine-tuning has any meaning, are the dimensionless numbers. not dimensionful numbers like $G$ or $c$ or $\hbar$ or $\epsilon_0$.

I wasn't arguing with you, I was trying to take another approach to the question, since the OP seemed unsatisfied by your response. The dimensionless/dimensionful point doesn't really address the anthropic principle.

there are legitimate (albeit speculative) discussions in theoretical physics (like string theory and branes, etc.) about the possibility that other universes may have appeared out of this thing called the "multiverse" in which the salient dimensionless universal constants could have been different

Oh, I'm well aware, but as you said, this is mostly speculation. Until we actually find some evidence for these theories, I'm not going give any such discussion the status of "pure physics".

 

[rbj]

I wasn't arguing with you, I was trying to take another approach to the question, since the OP seemed unsatisfied by your response. The dimensionless/dimensionful point doesn't really address the anthropic principle.

it depends. if you are applying the AP to G, I'm saying it does. if you're applying it to the normalized masses of the (known) fundamental particles (which are dimensionless numbers, BTW), then i agree.

Oh, I'm well aware, but as you said, this is mostly speculation. Until we actually find some evidence for these theories, I'm not going give any such discussion the status of "pure physics".

i think we're on the same page. at least as far as I'm concerned (you can decide for yourself if we are or not).

 

[suckstobeyou]

On the contrary , I think that far from being a post which should be relegated to Forum limbo , suckstobeyou’s post is intelligent , amusing and thought provoking. Imagine for instance , just for a second , if by some quirk of fate , after all these years Gravity was found to have an electromagnetic solution ! Say for instance it had something to do with the number of self interactions taking place within atoms of different types. Just speculating , mind you. It would , at one stroke get rid of the awkward 4 pi r^^2 factor ,it would also be a welcome turn of events to scientists like Lorentz and Einstein who both believed that Gravity was in some way related to electromagnetism. In fact Einstein said that such an “electromagnetic “ based ether would iron out all the kinks in his General relativity Theory.

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.

 

[vanesch]

As much as I'm sure some of us would like to, I don't think it's possible to debunk intelligent design. What that article seems to be "debunking" is the approach that many creationists take to the anthropic principle. Often, what they'll do is calculate the probability that various things (like the orbit of earth) would have lined up exactly as they did. They then go on to argue that things had to be this way in order for us to exist, and given that their probability is always small, they interpret it as evidence for a designer.

As you point out, this is indeed a wrong argument. I like to take a funny example of why this is indeed flawed. Consider the small probability that I'm near a surface of a planet. If all locations in space are equally probable, I should be floating in interstellar space by an overwhelming probability! But I'm lucky, I live near an extremely unlikely place in the universe, which moreover is suited for me.

 

[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.