Newton's Inverse square law

[geordief]

I am just wondering , in a historical way how Newton came up with his gravitational formula.

 

Was it just so simple a mathematical formula that he said to himself "let's give this a go" and "Oh it seems to work" or did he approach it in a logical way?

 

I would find it interesting to know especially as he got it wrong . So , presumably any logic he followed (if he did) would have to have been faulty too.

 

Was he able to measure parabolic trajectories and did that lead him to the formula for mutually attracting bodies?

[pavelcherepan]

I think it was based on empirical data including a lot of work done by Galileo and his own observations and also based on his laws of motion.

 

 

I would find it interesting to know especially as he got it wrong . So , presumably any logic he followed (if he did) would have to have been faulty too.

 

Based on what was known at the time he got it right. If you don't need an extreme precision you can use Newton's formula to calculate all kinds of stuff with enough accuracy for all day-to-day applications.

 

 

Was he able to measure parabolic trajectories and did that lead him to the formula for mutually attracting bodies?

 

What in particular are you referring to?

[geordief]

 

 

 

What in particular are you referring to?

Well I am thinking of the military context where you have to calculate the place on the earth where a cannon ball would come to land. It's trajectory can be described mathematically (discarding wind and air conditions) by a parabola .

 

This must have been know by Newton . and the formula ,as I recall contains the term for acceleration as well as the initial speed of the trajectile.

 

This formula is the closest one that I learned (many years ago) to the formula to gravitational attraction based on mass and distance.

 

I wondered if there was a connection between the two formulae or would it be because I learned both around the same time academically?

 

Actually I think there is an interesting description of this trajectory by Feynman where he explains how his tutor gave a different reasoning behind the trajectory (I could try and dig it out if you like but I think it is quite well known)

 

Edit: found it

 

http://www.feynmanlectures.caltech.edu/II_19.html

Edited November 13, 2015 by geordief

[swansont]

 

I would find it interesting to know especially as he got it wrong . So , presumably any logic he followed (if he did) would have to have been faulty too.

 

Wait, what?

[geordief]

Wait, what?

Sorry I don't follow.

 

I know he got it "right" in his own context but "got it wrong" is layman's speak for "he was later proved wrong" ,isn't it?

Edited November 13, 2015 by geordief

[Reg Prescott]

Geordief, you are quite correct. Newton did indeed get it wrong, assuming we take a law to be that which holds in all times and all places.

 

Otherwise we end up having to countenance absurdities like "It's a law that it never snows... erm, as long as you stay in Singapore."

 

Another member posted above: "Based on what was known at the time he got it right", implying the law was true in the 17th or 18th century, but no longer true, which really doesn't make much sense at all. It was not true then, and it's not true now.

 

Generally I find scientists very reluctant to concede that their forebears were wrong, preferring circumlocutions like "... he was almost right".

 

Newton was a genius; he needs no defense. There's no disgrace in being wrong. Let's not be coy, I say.

Edited November 13, 2015 by Reg Prescott

[swansont]

Sorry I don't follow.

 

I know he got it "right" in his own context but "got it wrong" is layman's speak for "he was later proved wrong" ,isn't it?

 

Wrong is probably the wrong word for it. Relativity reduces to Newtonian gravity except in extreme cases, and none of the data available to Newton showed him to be wrong. Given the latter, how could he have had a failure of logic?

 

Science in general (and physics in particular) is based on models. As the saying goes, all models are flawed, but some are useful. It's not so much right vs wrong as useful vs not useful.

 

Another member posted above: "Based on what was known at the time he got it right", implying the law was true in the 17th or 18th century, but no longer true, which really doesn't make much sense at all. It was not true then, and it's not true now.

 

No. Science is always limited to/by the best data that's available to you, and the data you get is interpreted in light of the best understanding of science that you have. And in the majority of circumstances, Newtonian gravity holds true.

[Reg Prescott]

No. Science is always limited to/by the best data that's available to you, and the data you get is interpreted in light of the best understanding of science that you have. And in the majority of circumstances, Newtonian gravity holds true.

 

No. One's epistemic context is irrelevant to the question of whether one is right or wrong. You may have the best reasons in the world for believing X, but if X is not true, you're wrong.

 

We can all agree Newton and his contemporaries had good reasons for thinking he had "got it right". Nonetheless he was wrong.

Edited November 13, 2015 by Reg Prescott

[geordief]

 

Wrong is probably the wrong word for it. Relativity reduces to Newtonian gravity except in extreme cases, and none of the data available to Newton showed him to be wrong. Given the latter, how could he have had a failure of logic?

I follow you but I am still interested as to why there seem to be 2 separate paths to the same result. Why was it that Newton's formula "worked" ? Is it enough to say that it did ? I don't suppose he took an inventory of all possible simple or fairly simple mathematical formulas ,tried them all and discarded those that failed leaving him with one that did work.

 

 

By the way ,without meaning to come across like A Hopkins (no disgrace either) , "love your cartoons"

 

Edit : I didn't pay attention to the second part of your reply where you brought in the idea of "useful models". Ophiolite will have my hide as he has noted that I tend to "cherry pick" answers to suit my bias......(unless you post edited )

Edited November 13, 2015 by geordief

[swansont]

 

No. One's epistemic context is irrelevant to the question of whether one is right or wrong. You may have the best reasons in the world for believing X, but if X is not true, you're wrong.

 

We can all agree Newton and his contemporaries had good reasons for thinking he had "got it right". Nonetheless he was wrong.

 

For it to be wrong, doesn't that mean you have to show that F = GMm/r^2 is not right? But we know that it works in most cases.

 

If you take "wrong" to mean "does not work in all cases", then every theory is wrong, which means that "wrong" kinda loses its value in evaluating a model. As I said before, it's the wrong word to use. There's a spectrum of correctness, and right vs wrong is Boolean. No theory will ever be right if it has to work in every possible case. Theories have limits of application.

I follow you but I am still interested as to why there seem to be 2 separate paths to the same result. Why was it that Newton's formula "worked" ? Is it enough to say that it did ? I don't suppose he took an inventory of all possible simple or fairly simple mathematical formulas ,tried them all and discarded those that failed leaving him with one that did work.

If you scroll about halfway down your Feynman link, you'll see where he says that minimizing the action is just another way of saying F=ma

 

You also need to realize that the parabolic trajectory does not rely on Newtonian gravity being correct. Just that you have a constant acceleration. These are two separate issues.

 

By the way ,without meaning to come across like A Hopkins (no disgrace either) , "love your cartoons"

 

Edit : I didn't pay attention to the second part of your reply where you brought in the idea of "useful models". Ophiolite will have my hide as he has noted that I tend to "cherry pick" answers to suit my bias......(unless you post edited )

 

No worries. I edited right after I made my other reply, since it was more appropriate for that comment to be directed to you than SB.

[pwagen]

I've posted this before, but I guess it's relevant here as well. Especially considering the recent influx of nitpicking - right, wrong, truth, reality.

 

http://chem.tufts.edu/answersinscience/relativityofwrong.htm

 

And after that, I hope we can go back to the other part of the OP - how did he come about his discoveries? The practicality of it all is an interesting question in itself, and would probably be quite enlightening as long as we don't let the issues of semantics spill over into this thread.

[pavelcherepan]

 

Another member posted above: "Based on what was known at the time he got it right", implying the law was true in the 17th or 18th century, but no longer true, which really doesn't make much sense at all.

 

That was not what I had in mind at all. One of the main reasons relativity was developed was that new data on electromagnetism didn't agree with classical mechanics at all. If Newton had known of electromagnetism to the extent Einstein knew, who knows what he would've come up with. That was what I meant.

 

Also it would be rather strange to assume that sort of meaning from that line because in the very nxt sentence I said that Newton's formula stands well in most day-to-day situations as long as you don't need extreme precision. Duh.

[geordief]

I've posted this before, but I guess it's relevant here as well. Especially considering the recent influx of nitpicking - right, wrong, truth, reality.

 

http://chem.tufts.edu/answersinscience/relativityofwrong.htm

 

Interesting (and relevant) but I don't think Asimov had a future as a comedy script writer based on that evidence.

[Reg Prescott]

 

That was not what I had in mind at all. One of the main reasons relativity was developed was that new data on electromagnetism didn't agree with classical mechanics at all. If Newton had known of electromagnetism to the extent Einstein knew, who knows what he would've come up with. That was what I meant.

 

Also it would be rather strange to assume that sort of meaning from that line because in the very nxt sentence I said that Newton's formula stands well in most day-to-day situations as long as you don't need extreme precision. Duh.

 

Yes, it does. It works very well in day-to-day situations.... for medium-sized durable objects like, say, us. It doesn't work so well in day-to-day situations for, say, muons. Aren't we being a little anthropocentric here?

 

If your claim is that Newton produced an extremely useful rule of thumb for us, you'll hear no argument. But I thought we were discussing a law here?

 

Also, both yourself and Swansont are failing to distinguish between getting something right, and producing something that works. Plolemaic cosmology -- with a static Earth and spinning heavens -- works perfectly well if you want to navigate around the world. I don't think we'd want to say Plolemy got it right (or almost right), though, would we?

Edited November 13, 2015 by Reg Prescott

[studiot]

 

Silly Billy,

One's epistemic context is irrelevant to the question of whether one is right or wrong.

 

Neither I nor the OED can agree with you there, since epistemic can apply to gradations and you are only putting a binary case.

Edited November 13, 2015 by studiot

[swansont]

Yes, it does. It works very well in day-to-day situations.... for medium-sized durable objects like, say, us. It doesn't work so well in day-to-day situations for, say, muons. Aren't we being a little anthropocentric here?

 

If your claim is that Newton produced an extremely useful rule of thumb for us, you'll hear no argument. But I thought we were discussing a law here?

 

Muons don't follow Newtonian gravity? How big is the relativistic correction?

 

What do you think a law is, in science?

[michel123456]

I am just wondering , in a historical way how Newton came up with his gravitational formula.

Maybe he was reading books?

https://en.wikipedia.org/wiki/Inverse-square_law#History

[geordief]

Maybe he was reading books?

https://en.wikipedia.org/wiki/Inverse-square_law#History

Thanks (indeed) .

[Strange]

Wrong is probably the wrong word for it. Relativity reduces to Newtonian gravity except in extreme cases, and none of the data available to Newton showed him to be wrong. Given the latter, how could he have had a failure of logic?

 

And even if he had access to data that showed his law of gravity didn't always apply (e.g. if observations could have been made of the precession of Mercury) he would have been stumped. Einstein's work depended on a lot more than just knowing that Newton's theory was "wrong" (but that was obviously a motivating factor). It required the mathematics of differential and non-Euclidean geometry, and so depended on the work of Monge, Gauss, Riemann and many others. It was also inspired by his own theory of special relativity, which depended on Maxwell's equations as well as the work of Lorentz, Poincare and others.

 

So developments in science, as with any other area of history, depends on context, available knowledge, technology as well the work of individuals.

Maybe he was reading books?

https://en.wikipedia.org/wiki/Inverse-square_law#History

 

Interesting article:

 

By 1679, Hooke thought gravitation had inverse square dependence and communicated this in a letter to Isaac Newton.^[4] Hooke remained bitter about Newton claiming the invention of this principle, even though Newton's Principia acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the solar system,^[5] as well as giving some credit to Bullialdus.^[6]

 

I always assumed that Newton had used Kepler's observations to derive the law but apparently (I have lost the reference, I'm afraid) he didn't. But did later show that Kepler's laws could be derived from his law of gravitation.

[Reg Prescott]

Q1 : Muons don't follow Newtonian gravity? Q2 : How big is the relativistic correction?

 

Q3 : What do you think a law is, in science?

 

There are some fascinating issues to be addressed here, although I'm afraid it may take us away from Georgief's original question (for philosophical analysis of your question about Newton's laws, G, the locus classicus, I believe, is Ernest Nagel's 1961 masterpiece "The Structure of Science" -- a superb read!), and I wouldn't want to derail his/her thread. Just a few brief comments, then, on Swansont's excellent questions...

Q1: One answer might be: "No, muons don't follow Newtonian gravity on the grounds that there is no such thing as Newtonian gravity."

Similarly, one might respond to a question on whether Dalton's atoms (or unicorns) are affected by such-and-such with: No, on the grounds that Dalton's atoms don't exist; according to our current understanding there is nothing in nature possessing the properties that Dalton attributed to his atoms.

Newtonian gravity, according to my layman's understanding (so please be gentle -- I'm not a physicist), is construed, among other things, as an attractive force which acts instantaneously over any distance, apparently with no expenditure of energy, against a backdrop of absolute space and absolute time. Is this correct? If so, I don't think anyone believes in Newtonian gravity these days, do they?

Swansont, you stated above "Relativity reduces to Newtonian gravity except in extreme cases". Some might object to this being asserted as an uncontroversial fact; I don't think it is. Questions of reduction in science are complex, require heavy-duty analysis from the philosophy of language, and quickly transcend my own limited competence. There is a concern, though, over so-called incommensurability, and whether Dalton's atomic theory, say, and whatever the current theory is, are both theories about the same thing (atoms), or two theories about different things (which share the name "atom").

The same applies, mutatis mutandis, to theories of gravity. Frege-Russell inspired descriptivist theories of reference seem to support the latter conclusion; reference of terms is secured via a description, and inasmuch as nothing satisfies Dalton's description of the atom, it does not refer; there is no such thing as Dalton's atom (or Newtonian gravity). Those wishing to defend inter-theory continuity, on the other hand, can appeal to the Kripke-Putnam inspired causal theory of reference whereby continuity of reference is purportedly secured by means other than a description.

I'll reproduce a passage from Larry Laudan at the bottom of this post for everyone's consideration, with apologies once again to Geordief if he/she doesn't want LL cluttering his/her thread.

Q2: Not being a physicist (as you well know - pokety-poke), I'm not competent to answer that, nor am I particularly inclined to play "Let's Watch the Non-Physicist Butcher the Physics ". If we can remain at a non-technical level, perhaps we can still enjoy an enlightening discussion of the philosophical issues involved here.

Q3: We could talk all day! -- perhaps somewhere else though. I'd just say here, however, as I've said in other places with respect to related concepts such as evidence and the so-called Scientific Method, anyone who thunks there's a simple answer to this question should probably thunk again.

Now, as promised, here's Laudan...

QUOTE

"There is a deep reason why the convergent realist is wrong about these matters [cumulationist or retentionist construals of science]. It has to do, in part, with the role of ontological frameworks in science and with the nature of limiting case relations. As scientists use the term 'limiting case', T1 can be a limiting case of T2 only if (a) all the variables (observable and theoretical) assigned a value in T1 are assigned a value by T2 and (b) the values assigned to every variable of T1 are the same as, or very close to, the values T2 assigns to the corresponding variable when certain initial and boundary conditions -consistent with T2 *** (see below) - are specified. This seems to require that T1 can be a limiting case of T2 only if all the entities postulated by T1 occur in the ontology of T2. Whenever there is a change of ontology accompanying a theory transition such that T2 (when conjoined with suitable initial and boundary conditions) fails to capture T1's ontology, then T1 cannot be a limiting case of T2. Even where the ontologies of T1 and T2 overlap appropriately (i.e., where T2's ontology embraces all of T1's), T1 is a limiting case of T2 only if all the laws of T1 can be derived from T2, given appropriate limiting conditions. It is important to stress that both these conditions (among others) must be satisfied before one theory can be a limiting case of another. Where 'closet positivists' might be content with capturing only the formal mathematical relations or only the observable consequences of T1 within a successor, T2, any genuine realist must insist that T1's underlying ontology is preserved in T2's, for it is that ontology above all which he alleges to be approximately true."

"Too often, philosophers (and physicists) infer the existence of a limiting case relation between T1 and T2 on substantially less than this. For instance, many writers have claimed one theory to be a limiting case of another when only some, but not all, of the laws of the former are 'derivable' from the latter. In other cases, one theory has been said to be a limiting case of a successor when the mathematical laws of the former find homologies in the latter but where the former's ontology is not fully extractable from the latter's."

"Consider one prominent example which has often been misdescribed, namely, the transition from the classical aether theory to relativistic and quantum mechanics. It can, of course, be shown that some 'laws' of classical mechanics are limiting cases of relativistic mechanics. But there are other laws and general assertions made by the classical theory (e.g., claims about the density and fine structure of the aether, general laws about the character of the interaction between aether and matter, models and mechanisms detailing the compressibility of the aether) which could not conceivably be limiting cases of modem mechanics. The reason is a simple one: a theory cannot assign values to a variable which does not occur in that theory's language (or, more colloquially, it cannot assign properties to entities whose existence it does not countenance). Classical aether physics contained a number of postulated mechanisms for dealing inter alia with the transmission of light through the aether. Such mechanisms could not possibly appear in a successor theory like the special theory of relativity which denies the very existence of an aetherial medium and which accomplishes the explanatory tasks performed by the aether via very different mechanisms."

*** above {This matter of limiting conditions consistent with the 'reducing' theory is curious. Some of the best-known expositions of limiting case relations depend (as Krajewski has observed) upon showing an earlier theory to be a limiting case of a later theory only by adopting limiting assumptions explicitly denied by the later theory. For instance, several standard textbook discussions present (a portion of) classical mechanics as a limiting case of special relativity, provided c approaches infinity. But special relativity is committed to the claim that c is a constant. Is there not something suspicious about a 'derivation' of T1 from a T2 which essentially involves an assumption inconsistent with T2? If T2 is correct, then it forbids the adoption of a premise commonly used to derive T1 as a limiting case. (It should be noted that most such proofs can be re-formulated unobjectionably, e.g., in the relativity case, by letting v --> 0 rather than c --> ∞.) }

UNQUOTE

Edited November 14, 2015 by Reg Prescott

[geordief]

Since you ask SB, no I have no objection to your seemingly sidetracking my thread . I am happy that my original question has been well answered in the main by michel123456

and , in any case I am well used to butting in on other peoples' threads in an off topic way where it is allowed or tolerated.

 

[Reg Prescott]

 

Since you ask SB, no I have no objection to your seemingly sidetracking my thread . I am happy that my original question has been well answered in the main by michel123456

and , in any case I am well used to butting in on other peoples' threads in an off topic way where it is allowed or tolerated.

 

 

 

Phew! And thanks!

 

The issues you raise are indeed fascinating. How did Newton come by his laws? And how are these laws to be construed: are they empirical discoveries? are they stipulational definitions (i.e. Newton isn't discovering the law, but laying down the law). For example, it seems implausible, to say the least, that Newton came upon his third law by leaning against walls and doors to see if every action force has an equal and opposite reaction force.

 

And is there any difference between an empirical hypothesis/law and an analytic truth (i.e. a definition, such as all bachelors are unmarried men)? Quine, for one, notoriously says no.

 

As I mentioned in my previous post, Nagel's 1961 treatment of the whole issue is magnificent, and I'll be happy to point you to other sources if you'd like to read more on it. These waters are deep! But intriguing.

 

Best regards

Edited November 14, 2015 by Reg Prescott

[swansont]

There are some fascinating issues to be addressed here, although I'm afraid it may take us away from Georgief's original question (for philosophical analysis of your question about Newton's laws, G, the locus classicus, I believe, is Ernest Nagel's 1961 masterpiece "The Structure of Science" -- a superb read!), and I wouldn't want to derail his/her thread. Just a few brief comments, then, on Swansont's excellent questions...

 

 

Q1: One answer might be: "No, muons don't follow Newtonian gravity on the grounds that there is no such thing as Newtonian gravity."

That would be a wrong answer, since the law of Newtonian gravity really exists. (Reminder: this is in the science section, not the philosophy section.

 

Newtonian gravity, according to my layman's understanding (so please be gentle -- I'm not a physicist), is construed, among other things, as an attractive force which acts instantaneously over any distance, apparently with no expenditure of energy, against a backdrop of absolute space and absolute time. Is this correct? If so, I don't think anyone believes in Newtonian gravity these days, do they?

Um, it's used all the time. By NASA, even, to send probes to planets, satellites into orbit and men to the moon. It works very well.

 

I'm aware you aren't a physicist, and yet you made a physics claim.

 

Swansont, you stated above "Relativity reduces to Newtonian gravity except in extreme cases". Some might object to this being asserted as an uncontroversial fact; I don't think it is. Questions of reduction in science are complex, require heavy-duty analysis from the philosophy of language, and quickly transcend my own limited competence. There is a concern, though, over so-called incommensurability, and whether Dalton's atomic theory, say, and whatever the current theory is, are both theories about the same thing (atoms), or two theories about different things (which share the name "atom").

It's actually a question of math, and it's not really controversial at all.

 

The same applies, mutatis mutandis, to theories of gravity. Frege-Russell inspired descriptivist theories of reference seem to support the latter conclusion; reference of terms is secured via a description, and inasmuch as nothing satisfies Dalton's description of the atom, it does not refer; there is no such thing as Dalton's atom (or Newtonian gravity). Those wishing to defend inter-theory continuity, on the other hand, can appeal to the Kripke-Putnam inspired causal theory of reference whereby continuity of reference is purportedly secured by means other than a description.

 

I'll reproduce a passage from Larry Laudan at the bottom of this post for everyone's consideration, with apologies once again to Geordief if he/she doesn't want LL cluttering his/her thread.

So I take your answer to be that you somehow know that muons don't follow Newtonian gravity ("It doesn't work so well in day-to-day situations for, say, muons.") but you can't explain how you know this, or demonstrate that is indeed true. You can't quantify how "not so well" it works.

 

 

Q2: Not being a physicist (as you well know - pokety-poke), I'm not competent to answer that, nor am I particularly inclined to play "Let's Watch the Non-Physicist Butcher the Physics ". If we can remain at a non-technical level, perhaps we can still enjoy an enlightening discussion of the philosophical issues involved here.

 

No, not really. What I asked is not a question of philosophy. The problem is you've brought philosophy to a physics discussion.

 

Q3: We could talk all day! -- perhaps somewhere else though. I'd just say here, however, as I've said in other places with respect to related concepts such as evidence and the so-called Scientific Method, anyone who thunks there's a simple answer to this question should probably thunk again.

I specifically asked for a science answer, not a philosophy one. Not even an attempt?

 

{This matter of limiting conditions consistent with the 'reducing' theory is curious. Some of the best-known expositions of limiting case relations depend (as Krajewski has observed) upon showing an earlier theory to be a limiting case of a later theory only by adopting limiting assumptions explicitly denied by the later theory. For instance, several standard textbook discussions present (a portion of) classical mechanics as a limiting case of special relativity, provided c approaches infinity. But special relativity is committed to the claim that c is a constant. Is there not something suspicious about a 'derivation' of T1 from a T2 which essentially involves an assumption inconsistent with T2? If T2 is correct, then it forbids the adoption of a premise commonly used to derive T1 as a limiting case. (It should be noted that most such proofs can be re-formulated unobjectionably, e.g., in the relativity case, by letting v --> 0 rather than c --> ∞.) }

And yet I doubt many physicists would have a problem with this; I've never run across any. Partially since the argument of letting c going to infinity and c being constant is not in conflict. Also, letting v go to zero in relativity sorta removes a lot of the interesting parts of relativity (there is nothing there to be relative to, if everything is at rest) so what's the point?

[Reg Prescott]

I've just one comment to make regarding all the above:

 

“There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.
—Daniel Dennett

[moth]

I could have sworn there is a philosophy section here.

Or maybe this is all a big solipsism.