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> but Newtonian mechanics AFAIK says nothing to forbid this In the Wikipedia article on Newton's laws of motion, the first law is stated as "A body remains at

> but Newtonian mechanics AFAIK says nothing to forbid this In the Wikipedia article on Newton's laws of motion, the first law is stated as "A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.". Here it would seem that we leave the state of rest not due to a force, but due to some other cause, which the first law would forbid. So I think that the particular interpretation of Newtonian mechanics used by the author is a bit of a strawman.

sobellian 3y ago
We must ask ourselves what "at rest" means since there are multiple trajectories that give x(0) = 0, x'(0) = 0 and it seems that some posters believe this cannot fully constrain the particle to be either at rest or in motion at t=0. There are multiple ways to resolve this dissonance. We could demand that the higher derivatives are also zero. We could derive some elaborate rule excluding non-zero x''(t) in the neighborhood of t=0. Or something else altogether. The issue IMO with these resolutions is that they're quite complicated and Newton almost certainly did not have any of them in mind. It's much simpler to just content ourselves that NFL is a special case of F=ma (where F=0). I'm not sure why we should contort ourselves to preserve determinism since we know that gets thrown out the window with QM anyway.
- sudosysgen 3y ago
  Newton didn't need to have an understanding of these solutions to foresee the problem. If you don't specifically state that force is a cause for leaving the state of rest, it's relatively straightforward to foresee issues where someone would assume the trajectory first and then imply a scheme for force that leads to unprompted movement, which is something that he definitely wanted to avoid. I also don't think he would have kept the first law if he understood it to be completely redundant and useless as it's entirely contained by the second law. I think it was very deliberately there to introduce force as causative to acceleration and not the opposite.
  - sobellian 3y ago
    Who says that just because it's nondeterministic, it's acausal? Gravity clearly causes it to leave its state of rest. At literally every moment that it has a non-zero acceleration, it has a non-zero net force due to gravity (and the normal force). There is no instant at all where we can say Newton's laws were violated. At t=T the particle has zero net force and is at rest. For every e greater than 0, at t=T+e the particle has net force and is accelerating. NFL isn't quite redundant since many people understand it to define an inertial frame. So if you observe F = 0 but x'' != 0 then you know you're not in an inertial frame.
    - sudosysgen 3y ago
      > Who says that just because it's nondeterministic, it's acausal? No one - I'm saying that it's the opposite. It is acausal, and that is why its nondeterministic. > t literally every moment that it has a non-zero acceleration, it has a non-zero net force due to gravity (and the normal force). There is no instant at all where we can say Newton's laws were violated. At t=T the particle has zero net force and is at rest. For every e greater than 0, at t=T+e the particle has net force and is accelerating. Yes, and you only find this because you assume a trajectory first, and then find force as a result of the trajectory. The force isn't causing the movement, you first assume on your trajectory that the ball stops being at rest immediately after T. Newton's first law is literally that an object stays at rest in its inertial reference frame unless a force causes it to leave its state of rest, yet you have to assume that immediately after T it leaves rest without any valid physical reason. > NFL isn't quite redundant since many people understand it to define an inertial frame. So if you observe F = 0 but x'' != 0 then you know you're not in an inertial frame. The existence of inertial reference frames is a consequence of the first law saying that force is necessary to exit the state of rest. It's not equivalent to the definition of inertial reference frames. Here is Wikipedia's translation of the first law: > Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. This obviously does imply the definition of inertial reference frames, but it doesn't just do that, it also clearly requires force to cause a body to leave uniform motion. In the trajectories suggested by the article, the body leaves the state of rest, but that isn't because a force compels it, it's just by assertion that it must do so after T, and the force is then a result of it no longer being in the same position. I don't see how that is in accordance with the first law. It's clearly leaving rest immediately after the moment T by pure assertion, which makes it an unphysical trajectory. Then the article gets around this by providing a new NFL which has no causative language and is simply a statement about the second derivative of position, and that isn't what it is.

sobellian 3y ago

We must ask ourselves what "at rest" means since there are multiple trajectories that give x(0) = 0, x'(0) = 0 and it seems that some posters believe this cannot fully constrain the particle to be either at rest or in motion at t=0. There are multiple ways to resolve this dissonance. We could demand that the higher derivatives are also zero. We could derive some elaborate rule excluding non-zero x''(t) in the neighborhood of t=0. Or something else altogether. The issue IMO with these resolutions is that they're quite complicated and Newton almost certainly did not have any of them in mind. It's much simpler to just content ourselves that NFL is a special case of F=ma (where F=0). I'm not sure why we should contort ourselves to preserve determinism since we know that gets thrown out the window with QM anyway.

sudosysgen 3y ago
Newton didn't need to have an understanding of these solutions to foresee the problem. If you don't specifically state that force is a cause for leaving the state of rest, it's relatively straightforward to foresee issues where someone would assume the trajectory first and then imply a scheme for force that leads to unprompted movement, which is something that he definitely wanted to avoid. I also don't think he would have kept the first law if he understood it to be completely redundant and useless as it's entirely contained by the second law. I think it was very deliberately there to introduce force as causative to acceleration and not the opposite.
- sobellian 3y ago
  Who says that just because it's nondeterministic, it's acausal? Gravity clearly causes it to leave its state of rest. At literally every moment that it has a non-zero acceleration, it has a non-zero net force due to gravity (and the normal force). There is no instant at all where we can say Newton's laws were violated. At t=T the particle has zero net force and is at rest. For every e greater than 0, at t=T+e the particle has net force and is accelerating. NFL isn't quite redundant since many people understand it to define an inertial frame. So if you observe F = 0 but x'' != 0 then you know you're not in an inertial frame.
  - sudosysgen 3y ago
    > Who says that just because it's nondeterministic, it's acausal? No one - I'm saying that it's the opposite. It is acausal, and that is why its nondeterministic. > t literally every moment that it has a non-zero acceleration, it has a non-zero net force due to gravity (and the normal force). There is no instant at all where we can say Newton's laws were violated. At t=T the particle has zero net force and is at rest. For every e greater than 0, at t=T+e the particle has net force and is accelerating. Yes, and you only find this because you assume a trajectory first, and then find force as a result of the trajectory. The force isn't causing the movement, you first assume on your trajectory that the ball stops being at rest immediately after T. Newton's first law is literally that an object stays at rest in its inertial reference frame unless a force causes it to leave its state of rest, yet you have to assume that immediately after T it leaves rest without any valid physical reason. > NFL isn't quite redundant since many people understand it to define an inertial frame. So if you observe F = 0 but x'' != 0 then you know you're not in an inertial frame. The existence of inertial reference frames is a consequence of the first law saying that force is necessary to exit the state of rest. It's not equivalent to the definition of inertial reference frames. Here is Wikipedia's translation of the first law: > Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. This obviously does imply the definition of inertial reference frames, but it doesn't just do that, it also clearly requires force to cause a body to leave uniform motion. In the trajectories suggested by the article, the body leaves the state of rest, but that isn't because a force compels it, it's just by assertion that it must do so after T, and the force is then a result of it no longer being in the same position. I don't see how that is in accordance with the first law. It's clearly leaving rest immediately after the moment T by pure assertion, which makes it an unphysical trajectory. Then the article gets around this by providing a new NFL which has no causative language and is simply a statement about the second derivative of position, and that isn't what it is.