# Did Newton assume matter was atomic?

Hello all, I was talking to a friend of mine earlier explaining why a force acts as if all the mass is concentrated at the center of mass. I know of no other proof than taking the time derivatives of the center of mass. Seeing as this was long before definitive proof of the atomic structure of matter...

My question is, did Newton assume or imply the system must be divided into atoms?

For one to even be able to consider the internal forces canceling due to Newton's third law, there must be particles with mass accelerating and affecting each other. Historically, I am just wondering if anyone knows, or has read the Principia to find, if Newton took it as an assumption.

If not, what other method did he use to prove it?

I can understand taking arbitrary points with arbitrarily small mass don't necessarily have to be atomic, but the simple assumption that matter can be divided seems like an awfully large assumption due to the split attitudes of scientists at the time on the nature of mass and its divisibility.

## Answers and Replies

Doug Huffman
Gold Member
I just glanced through my Newton's Principia for the Common Reader by Chandrasekhar on another matter. No, Newton did not address the microscopic. His Universal Law of Gravitation (Book III, Propositions I - XV) was deduced from planetary motions. Coulomb's similar law addressed the microscopic.

I just glanced through my Newton's Principia for the Common Reader by Chandrasekhar on another matter. No, Newton did not address the microscopic. His Universal Law of Gravitation (Book III, Propositions I - XV) was deduced from planetary motions. Coulomb's similar law addressed the microscopic.

That's interesting! It is weird though, because in his proof of the shell theorem, at least as I have seen it, it is again assumed internal forces be neglected and the infinitesimally small spheres brings the same problem I mentioned above: the divisibility of mass; alas, it is different than before because it isn't assumed point particles, but assumed thin shells -- so no real implications on atomic structure there.

Seems like quite a lot of assumptions, but I guess he had no physical reason to question them at the time.

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
Hello all, I was talking to a friend of mine earlier explaining why a force acts as if all the mass is concentrated at the center of mass. I know of no other proof than taking the time derivatives of the center of mass. Seeing as this was long before definitive proof of the atomic structure of matter...

My question is, did Newton assume or imply the system must be divided into atoms?

For one to even be able to consider the internal forces canceling due to Newton's third law, there must be particles with mass accelerating and affecting each other. Historically, I am just wondering if anyone knows, or has read the Principia to find, if Newton took it as an assumption.

If not, what other method did he use to prove it?

I can understand taking arbitrary points with arbitrarily small mass don't necessarily have to be atomic, but the simple assumption that matter can be divided seems like an awfully large assumption due to the split attitudes of scientists at the time on the nature of mass and its divisibility.

Newton did not need to know the microscopic details in order to determine that gravity would act on a body as if all of its mass was concentrated at one point. Indeed, many others had determined the c.o.m. of various figures even before Newton came along:

http://en.wikipedia.org/wiki/Center_of_mass

Newton did not need to know the microscopic details in order to determine that gravity would act on a body as if all of its mass was concentrated at one point. Indeed, many others had determined the c.o.m. of various figures even before Newton came along:

http://en.wikipedia.org/wiki/Center_of_mass

From the wiki,

"[Archimedes] worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point — their center of mass."

I am not speaking explicitly about the c.o.m., but more about the forces assumed to be acting on an object which can then be generalized as if being acted upon by a force on its c.o.m. Seeing as Newton's own laws necessitate a mass and acceleration for force, it seems to me as a pretty big assumption that forces must therefore act on the c.o.m. itself. It seems intuitively obvious, and it had been shown previously that it at least seems as if all forces act on the c.o.m; nevertheless, it is still an assumption.

So what I am seeing is that it was a lasting assumption, not lacking approximate experimental verification, that Newton didn't consider as needing proof.

A quick google search yielded nothing on the proof with which Archimedes showed that forces act on the center of mass; this leads me to wonder what the wiki article means in that he "showed." Seeing as it was prior to analytical geometry, I am assuming it probably wasn't done mathematically.

Quite likely, Newton was atomist.

Doug Huffman
Gold Member
Quite likely, Newton was atomist.
Only in the broadest - sloppiest - sense. Newton was a corpususcularian for his alchemy and corpuscular theory of light.

russ_watters
Mentor
From the wiki,

"[Archimedes] worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point — their center of mass."

I am not speaking explicitly about the c.o.m., but more about the forces assumed to be acting on an object which can then be generalized as if being acted upon by a force on its c.o.m. Seeing as Newton's own laws necessitate a mass and acceleration for force, it seems to me as a pretty big assumption that forces must therefore act on the c.o.m. itself. It seems intuitively obvious, and it had been shown previously that it at least seems as if all forces act on the c.o.m; nevertheless, it is still an assumption.

So what I am seeing is that it was a lasting assumption, not lacking approximate experimental verification, that Newton didn't consider as needing proof.

A quick google search yielded nothing on the proof with which Archimedes showed that forces act on the center of mass; this leads me to wonder what the wiki article means in that he "showed." Seeing as it was prior to analytical geometry, I am assuming it probably wasn't done mathematically.
That's all fine but none of it has anything to do with whether matter is made of atoms or not.

That's all fine but none of it has anything to do with whether matter is made of atoms or not.

I'm not speaking in terms of atoms as we know them today, because of course none of that information could have been known then. I am speaking with the mindset that an atom is just simply divided matter to whatever scale -- seeing as back then they could have no idea.

All I'm saying is that the only proof I know of, mathematically, in the classical Newtonian sense of why an object acts as if all forces acting upon it are as if they are focused on its center of mass. This proof requires taking arbitrarily small segments of matter and assuming the internal forces add to zero due to Newtons third law, and then, using the second time derivative of the c.o.m. to gain its acceleration and therefore its force.

Newtons laws work by considering objects as point particles. To be able to consider objects as point particles, one must then define the c.o.m. and show that we can treat the system as if all force were being concentrated there. This is the part I am questioning -- and the only proof I know of is mentioned above. If mass were to be continuous and unable of being thought of arbitrarily small particles, why would the assumption that force being applied to an object act as if it were being concentrated at the c.o.m.?

I am not at all saying Newton considered these arbitrarily small particles were charged or even had a defined mass -- just the fact that there are finite particulates, however small, that are acting on one another rather than continuously distributed mass.

russ_watters
Mentor
That's fine, but it is a mathematical model that need not have any connection to reality. It works fine whether atoms exist or not and the size of the chunks is arbitrary and unrelated to atoms.

That's fine, but it is a mathematical model that need not have any connection to reality.

This could be said of absolutely anything in physics! Newton didn't stop at the fact that his law of gravitation described the movement of the planets. This is why he mathematically proved the shell theorem from the question of, "Ok Mr. Newton. It's cool and all that you deduced a cool formula from Kepler's data, but why does gravity act on the planets as if all of the force stems from very near its geometric center."

The shell theorem is the gravitational equivalent to what I am speaking about. Yeah, everybody since Archimedes has known that, but why!

Although no one has been inside a nearly hollow sphere (that I know of) with mass enough for appreciable gravitational effect, I think a lot of people, due to the success of the mathematical model, would believe gravity would act just the same. From Doug's post above, it seems as if Newton took the many times mentioned effect for granted and moved forward, rather than backward like he did with gravity.

Maybe it is because his theory for gravity was new at the time. So, it required further proof; but, as I said before, everyone since Archimedes has known that the aforementioned effect seems to work -- they just didn't require as much rigor!

And no it doesn't have any implications as to the mass of atoms, if those are even thing. It just implies that there is mass acting on each other due to the mathematical model.

anorlunda
Staff Emeritus
This proof requires taking arbitrarily small segments of matter and assuming the internal forces add to zero due to Newtons third law, and then, using the second time derivative of the c.o.m. to gain its acceleration and therefore its force.

You are thinking wrong. The shell theory is a completely static analysis. No motion. No acceleration. No time derivatives of anything.

Use the F=ma relation, and note that since a=0 and therefore the net force on every massive particle must also be zero. That has nothing to do with atomic structure.

You are thinking wrong. The shell theory is a completely static analysis. No motion. No acceleration. No time derivatives of anything.

Use the F=ma relation, and note that since a=0 and therefore the net force on every massive particle must also be zero. That has nothing to do with atomic structure.

I can see how it can be misleading in how I wrote that response, but I wasn't referring to the shell theorem there. I was speaking of a proof that forces acting on an object behave as if all the forces were being concentrated at the center of mass. As you can see, that is quite a lot to type every time I mention it, but I see now I should have been more clear, especially in that post.

anorlunda
Staff Emeritus
But even the C.O.G. problem is static. No motion. No acceleration. No time derivatives. If you are even thinking about acceleration, you are going down the wrong path.

But even the C.O.G. problem is static. No motion. No acceleration. No time derivatives. If you are even thinking about acceleration, you are going down the wrong path.

I don't know where you are coming from or what you think I am trying to say. I only mentioned Newton's use of the shell theorem. Read nearly any one of my posts to see what I am referring to. It is the motion resulting from the introduction of a force and this force acts as if it is concentrated at the center of mass. What I mentioned before was the method used to prove this which I have seen in 3 different classical mechanics texts.

anorlunda
Staff Emeritus
Are you sure you're interpreting the problem correctly? Consider a rod shaped solid object. If I push it at the C.O.M, it will move away with no rotation. But if I push on one end, it starts rotating. I can balance it in a gravitational field with my finger at the C.O.M. but I can not balance it with my finger at other places.

Clearly, not every force acts as if it were applied only on the C.O.M.

Are you sure you're interpreting the problem correctly? Consider a rod shaped solid object. If I push it at the C.O.M, it will move away with no rotation. But if I push on one end, it starts rotating. I can balance it in a gravitational field with my finger at the C.O.M. but I can not balance it with my finger at other places.

Clearly, not every force acts as if it were applied only on the C.O.M.

Yes, but we are getting off topic.

(a) By pushing it at the c.o.m. you are applying a force with no net torque about its natural rotation axis -- its center of mass. The bolded text is the result of what I am talking about. Forces act as if all of the forces were concentrated at the center of mass and all external forces act at that point.
(b) Yes it spins because the force applied isn't along its natural axis of rotation and you are therefore applying a torque with respect to the c.o.m. (<- application of what I am talking about) It is a force relative to the center of mass that causes rotation. If what I were talking about were not true, then there would be no rotation, but there would be translational motion.
(c) your finger is applying a normal force on its center of gravity which has nothing at all to do with what I am talking about

No this doesn't matter at all for static situations because we are talking about the effects of forces -- so I have no idea why you keep mentioning them. There would be no effect to mention if there were no movement!

My question was pretty much answered long ago by Doug -- no reason to continue on unless there is further insight. Thanks all.

sophiecentaur
Science Advisor
Gold Member
2020 Award
Quite likely, Newton was atomist.

As he invented a form of The Calculus, you could say that he at least went along with the idea of splitting things and processes into small steps for the purpose of working things out - even if he didn't believe in it as an absolute truth.