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I am curious about the how Newton discovered his laws of motion and his law of universal gravitation. It seems in modern education, the laws are introduced to students somewhat 'magically', and then the students then do various practical experiments and calculations to verify them.

If we step back into Newtons shoes, ignoring all the things we know about the world today, what was his actual chain of reasoning he used to discover his mechanical laws?

In the second law, Newton introduced the idea of something we call 'force' and that when we apply such a force to a body, it will accelerate in inverse proportion to its mass. Yet wouldnt 'force' and 'mass' have been quite mysterious quantities to Newton.

Assuming a completely blank knowledge about the world, an experimental approach to the second law would seem to require :

(a) a consistent source of 'force', one that could be relied upon to produce the same mysterious amount of push or pull over and over again.

(b) a scalable source of force, one that you can double/triple in size reliably. This requires defining the original 'force' as a 'base unit' of 'force'.

(c) a scalable object to accelerate, one that you can double/triple reliably. Note that there is no notion of 'mass' available to us yet, so all objects would need made of the same material and we would be typically measuring the volume/length of the object.

The experiment proceeds by applying the same 'force' to objects of various volumes, and comparing the accelerations. We deduce that the acceleration is inversely proportional to the volume of the object.

We then scale the force, (i.e. double it), and apply it to our objects again and compare the accelerations. From this we can deduce that the 'force' is proportional to both the volume and the acceleration and we need to introduce a coefficient of inertia in the equation. i.e. F = kVa

At this point we can calculate k for a given material. But at the moment k is only valid for the material of the object we have been accelerating (i.e. lead). We dont know that k is the same for other materials or not (i.e. iron), and we dont even know if other materials obey the same proportionality law. So we repeat our experiments and work out that k depends on the material that we accelerate.

So we now have a concept of the inertia of a material (i.e. its resistance to acceleration), but crucially we still know nothing of its mass. We could then take objects of two materials which produce the same acceleration under the same force and compare them on a set of weighing scales and measure their 'weights' and notice that they balance.

We now have two objects that appear to be 'equivalent' in some way. They accelerate the same, under the same 'force' and they balance on a set of scales. We dont really know if the thing that is pushing or pulling them to the floor (i.e. 'gravity' which we have no clue about yet) depends on the material of the objects, so we dont really know if the two objects contain the same 'mass' or 'stuff'. We simply know that they appear to act the same under the same force.

I look back at my physics education (which was a long time ago) and I wonder if it would have benefited from a proper process of fundamental deduction rather than this reverse engineering approach. In particular, I have this common-sense notion on my head that 'mass' really is the quantity of 'stuff' that is there, and that it was Newton who discovered it. But it would seem that in truth Newton really introduced the notion of 'inertia' didnt he?, which is just a magical constant of proportionality. Indeed, we cant really talk about 'mass' actually being real 'stuff' until we know about the fundamental particles of the world which is not until the 20th century, then we can compare 1g of lead and 1g of iron contain the same number of protons/neutrons (neglecting small differences).

How did Newton really approach this experimentation or did he deduce things from mathematics and his calculus? What did he choose for (a), (b), and (c) above. Did he dangle weights on bits of string as the source of his force and if so isnt there a built in assumption that local gravity is mg, which is like putting the cart before the horse.

Also, did Newton discover his universal law of gravitation before his laws of motion or the other way around?

Hope this makes sense. I know it is not advanced physics but it is interesting to approach things in such a fundamental way sometimes I think.

If we step back into Newtons shoes, ignoring all the things we know about the world today, what was his actual chain of reasoning he used to discover his mechanical laws?

In the second law, Newton introduced the idea of something we call 'force' and that when we apply such a force to a body, it will accelerate in inverse proportion to its mass. Yet wouldnt 'force' and 'mass' have been quite mysterious quantities to Newton.

Assuming a completely blank knowledge about the world, an experimental approach to the second law would seem to require :

(a) a consistent source of 'force', one that could be relied upon to produce the same mysterious amount of push or pull over and over again.

(b) a scalable source of force, one that you can double/triple in size reliably. This requires defining the original 'force' as a 'base unit' of 'force'.

(c) a scalable object to accelerate, one that you can double/triple reliably. Note that there is no notion of 'mass' available to us yet, so all objects would need made of the same material and we would be typically measuring the volume/length of the object.

The experiment proceeds by applying the same 'force' to objects of various volumes, and comparing the accelerations. We deduce that the acceleration is inversely proportional to the volume of the object.

We then scale the force, (i.e. double it), and apply it to our objects again and compare the accelerations. From this we can deduce that the 'force' is proportional to both the volume and the acceleration and we need to introduce a coefficient of inertia in the equation. i.e. F = kVa

At this point we can calculate k for a given material. But at the moment k is only valid for the material of the object we have been accelerating (i.e. lead). We dont know that k is the same for other materials or not (i.e. iron), and we dont even know if other materials obey the same proportionality law. So we repeat our experiments and work out that k depends on the material that we accelerate.

So we now have a concept of the inertia of a material (i.e. its resistance to acceleration), but crucially we still know nothing of its mass. We could then take objects of two materials which produce the same acceleration under the same force and compare them on a set of weighing scales and measure their 'weights' and notice that they balance.

We now have two objects that appear to be 'equivalent' in some way. They accelerate the same, under the same 'force' and they balance on a set of scales. We dont really know if the thing that is pushing or pulling them to the floor (i.e. 'gravity' which we have no clue about yet) depends on the material of the objects, so we dont really know if the two objects contain the same 'mass' or 'stuff'. We simply know that they appear to act the same under the same force.

I look back at my physics education (which was a long time ago) and I wonder if it would have benefited from a proper process of fundamental deduction rather than this reverse engineering approach. In particular, I have this common-sense notion on my head that 'mass' really is the quantity of 'stuff' that is there, and that it was Newton who discovered it. But it would seem that in truth Newton really introduced the notion of 'inertia' didnt he?, which is just a magical constant of proportionality. Indeed, we cant really talk about 'mass' actually being real 'stuff' until we know about the fundamental particles of the world which is not until the 20th century, then we can compare 1g of lead and 1g of iron contain the same number of protons/neutrons (neglecting small differences).

How did Newton really approach this experimentation or did he deduce things from mathematics and his calculus? What did he choose for (a), (b), and (c) above. Did he dangle weights on bits of string as the source of his force and if so isnt there a built in assumption that local gravity is mg, which is like putting the cart before the horse.

Also, did Newton discover his universal law of gravitation before his laws of motion or the other way around?

Hope this makes sense. I know it is not advanced physics but it is interesting to approach things in such a fundamental way sometimes I think.

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