I think Newtons seconds law would be discarded if we consistently saw the following:
There was no relation between how hard I push things and how fast they move.
Pushing a faster moving object as a hard as I push a slower moving object, for the same amount of time, speeds it up less than the slower object.
When you take two objects, each of which moves the same speed after 5 seconds of pushing as hard as you can, and stick them together, the resulting object moves 4 times as fast after 5 seconds.
The first would get rid of the law completely, the second would make you refine your concept of acceleration, and the third your concept of how acceleration relates to mass.
Now you’re right you could always add epicycles to fix this, but the correct response would be discarding the theory outright.
We could just as easily say that physically pushing on things is not a force. My intuitive explanation would no longer make any sense, but that’s a problem with humans, not the law.
We live in this universe. We could solve this issue by saying that there is “etheric drag” or something which provides a resistive force against fast-moving objects, but I’m glad we invented special relativity instead.
This is a problem with the theory of mass as I presented it in the intuitive section, but you could solve it by saying that the composite object has a quarter of the mass of each of the two objects you stuck together. Maybe you live in a universe where n objects with mass m have total mass m/n2. This is a better universe than one where you have to measure the mass of any object including composite objects each time. Newton’s second law can be used to retroactively define masses based off of experiment, but it’s nicer to live in a universe where masses are more predictable than that.
I’m pointing out that Newton’s second law is tautologically correct as a formal theory. It’s true that it aligns particularly well with human conceptions of manipulating objects in space. It’s true that it works particularly well in our universe. (We only had to define one omnipresent force with a simple inverse-square form that only depends on one free-but-set-by-experiment parameter G to make momentum be conserved for most objects that don’t look like they’re interacting with anything.)
I agree it’s tautologically true, but I’m saying that we only use it because it maps nicely to reality. When it doesn’t map cleanly to reality we replace it with something else (special relativity in your example) instead of continuously adding epicycles.
There’s an infinite number of laws I could generate that would be equally tautologically true (e.g. f = mvdv/dt), but we don’t use them because they require more epicycles to work correctly.
I agree that there are counterfactual frameworks which require more complication to describe reality than Newton’s second law does. There are also counterfactual realities for which Newton’s second law would require more complications to work than other frameworks would. Are you trying to say anything else?
One way to restate my point is that Newton’s second law working well rules out many fundamental rules which might have described our reality, but it doesn’t directly map to any fundamental rules of reality. The larger point which I am trying to communicate is that physical models have a lot of structure which metaphorically defines terms which you can use to describe reality without actually mapping to anything in reality[1]. The theory as a whole doesn’t describe reality without those parts, but those parts don’t necessarily directly correspond to something in reality. A map describes reality, but latitude and longitude lines do not directly correspond to anything in reality even if you can stand at a place in reality and unambiguously use latitude and longitude lines to describe your location using the map. I can use an English sentence to describe the fundamental rules of reality, but the linguistic syntax of that sentence doesn’t correspond to anything fundamental in reality even if it is fundamental to mapping the sentence as a whole to fundamental rules of reality. My physics education presented physical models as package deals with every component corresponding to some intuition about reality, and that led me to confuse map and territory in ways that I wish I had been warned about. I am trying to warn others.
Ok, I think that makes a lot of sense. Newton’s 2nd law is the first step of constructing a model which is (ideally) isomorphic to reality once you’ve filled in all the details.
But you could equally well start off constructing your model with a different first step, and if you do it might be that some nice neat packaged concepts in modelA do not map cleanly onto anything in modelB. The fundamental concepts in physics are fundamental to the model, not to reality.
I think Newtons seconds law would be discarded if we consistently saw the following:
There was no relation between how hard I push things and how fast they move.
Pushing a faster moving object as a hard as I push a slower moving object, for the same amount of time, speeds it up less than the slower object.
When you take two objects, each of which moves the same speed after 5 seconds of pushing as hard as you can, and stick them together, the resulting object moves 4 times as fast after 5 seconds.
The first would get rid of the law completely, the second would make you refine your concept of acceleration, and the third your concept of how acceleration relates to mass.
Now you’re right you could always add epicycles to fix this, but the correct response would be discarding the theory outright.
We could just as easily say that physically pushing on things is not a force. My intuitive explanation would no longer make any sense, but that’s a problem with humans, not the law.
We live in this universe. We could solve this issue by saying that there is “etheric drag” or something which provides a resistive force against fast-moving objects, but I’m glad we invented special relativity instead.
This is a problem with the theory of mass as I presented it in the intuitive section, but you could solve it by saying that the composite object has a quarter of the mass of each of the two objects you stuck together. Maybe you live in a universe where n objects with mass m have total mass m/n2. This is a better universe than one where you have to measure the mass of any object including composite objects each time. Newton’s second law can be used to retroactively define masses based off of experiment, but it’s nicer to live in a universe where masses are more predictable than that.
I’m pointing out that Newton’s second law is tautologically correct as a formal theory. It’s true that it aligns particularly well with human conceptions of manipulating objects in space. It’s true that it works particularly well in our universe. (We only had to define one omnipresent force with a simple inverse-square form that only depends on one free-but-set-by-experiment parameter G to make momentum be conserved for most objects that don’t look like they’re interacting with anything.)
I agree it’s tautologically true, but I’m saying that we only use it because it maps nicely to reality. When it doesn’t map cleanly to reality we replace it with something else (special relativity in your example) instead of continuously adding epicycles.
There’s an infinite number of laws I could generate that would be equally tautologically true (e.g. f = mvdv/dt), but we don’t use them because they require more epicycles to work correctly.
I agree that there are counterfactual frameworks which require more complication to describe reality than Newton’s second law does. There are also counterfactual realities for which Newton’s second law would require more complications to work than other frameworks would. Are you trying to say anything else?
One way to restate my point is that Newton’s second law working well rules out many fundamental rules which might have described our reality, but it doesn’t directly map to any fundamental rules of reality. The larger point which I am trying to communicate is that physical models have a lot of structure which metaphorically defines terms which you can use to describe reality without actually mapping to anything in reality[1]. The theory as a whole doesn’t describe reality without those parts, but those parts don’t necessarily directly correspond to something in reality. A map describes reality, but latitude and longitude lines do not directly correspond to anything in reality even if you can stand at a place in reality and unambiguously use latitude and longitude lines to describe your location using the map. I can use an English sentence to describe the fundamental rules of reality, but the linguistic syntax of that sentence doesn’t correspond to anything fundamental in reality even if it is fundamental to mapping the sentence as a whole to fundamental rules of reality. My physics education presented physical models as package deals with every component corresponding to some intuition about reality, and that led me to confuse map and territory in ways that I wish I had been warned about. I am trying to warn others.
I don’t know whether I am successfully communicating the thing which I am trying to communicate, and I am open to being told that I am wrong.
Ok, I think that makes a lot of sense. Newton’s 2nd law is the first step of constructing a model which is (ideally) isomorphic to reality once you’ve filled in all the details.
But you could equally well start off constructing your model with a different first step, and if you do it might be that some nice neat packaged concepts in modelA do not map cleanly onto anything in modelB. The fundamental concepts in physics are fundamental to the model, not to reality.