6 ms·

After some research I've come to the conclusion that my statement is in fact definitively wrong. What I said was this: We do not know if classical mechanics is

After some research I've come to the conclusion that my statement is in fact definitively wrong. What I said was this: We do not know if classical mechanics is deterministic. I am wrong. The correct statement is: We do know that classical mechanics is not deterministic. So essentially I'm wrong but so is everyone else so I'm paying nobody. Source: https://sites.pitt.edu/~jdnorton/Goodies/Dome/ https://sites.pitt.edu/~jdnorton/Goodies/Dome/ Essentially this is proof by contradiction. Classical mechanics is not deterministic. My answer was, however, better than everyone else's given that my answer was in itself not absolute and encompassed this possibility and the opposing possibility as well.

l-lousy 5y ago
This felt somewhat wrong to me (as I’m sure it did many people that have take a Physics class) and ended up finding a Reddit discussion about this[1]. Seems like it’s not totally correct because the function for the ball becomes discontinuous [1] https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_simple_violation_of_determinism_in/ https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_s...
- deltasixeight 5y ago
  Reddit proves it. Case closed. Just kidding. No seriously that thread is long and there's no singular point, it's a debate. Take a look at this (not the same link above I target a single comment): https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_simple_violation_of_determinism_in/c33in7z/?utm_source=reddit&utm_medium=web2x&context=3 https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_s... I'll have you know you're debating with higher powers here. Some people here are not your typical people who just took a physics class. Either way intuition without the math is enough to break your brain. Imagine the opposite scenario you flick a ball up the dome with just the right amount of force that it comes to rest right at the apex. One property of Newtonian mechanics is that motion is time reversible. Meaning that the opposite motion here should be valid. And the opposite motion of the scenario I described is indeed what occurs. The particle is at rest on the dome and arbitrarily just rolls off randomly. Note that this is caveated on the site with the fact that this intuition doesn't work with hemispheres. Apparently with a hemisphere you can flick the ball with a certain amount of force and it takes infinite time to reach the apex of the dome. So if you time reverse that it means any ball resting on a hemispherical dome can roll off of the apex arbitrarily but it takes an infinite amount of time. The un-determinism only works for the special dome here called "Nortons Dome."
kergonath 5y ago
The dome is not a proof. It has several flaws and the reasoning is invalid. A mass perfectly on the top of it will just stay there. It would need a force being applied to it to move at the time T. It can happen with a time-dependent force, i.e. not Newtonian dynamics. Or if a particle can change its velocity without a force being applied to it, i.e. not Newtonian mechanics. It is more straightforward to see using Lagrangian or Hamiltonian mechanics, which are better suited to this kind of constrained problem, if one is so inclined.
- deltasixeight 5y ago
  >It is more straightforward to see using Lagrangian or Hamiltonian mechanics, which are better suited to this kind of constrained problem, if one is so inclined. Why? He proved it mathematically without needing to Lift the entire system into a Functor. Everything works fine here. >A mass perfectly on the top of it will just stay there. It would need a force being applied to it to move at the time T. You didn't read the site. All of this is addressed and anticipated. This is an unsubstantiated comment where you barely read the article. There is a section where he addresses the First law. Then after that section he addresses how your intuition can be helped to visualize the legitimacy of this paradox with time reversal. If I tell you about it here, maybe it will make you interested enough that you'll actually read the site before formulating an unsubstantiated comment. Imagine that your at the rim of the dome and you flick the ball upwards with the perfect amount of force so that the ball rolls up the dome and rests perfectly at the apex for an indefinite amount of time. Now imagine this scenario time reversed. Boom. Newtons laws are time reversible and so is this scenario. If the time reversed scenario is able can intuitively occur then so can the time reversed scenario which is EXACTLY what norton is describing. What's going on here is that in the mathematics the apex of the dome represents a place where the mathematical functions do not have a property called Lipschitz continuity. When this property is lost, determinism is also lost. Do note that Norton is not describing reality as we know it. He is describing Newtons Model of reality and the consequences that occur within the model itself. What happens to a marble in the real world rolling down an actual dome is not something he addressing, he is just addressing newtons mathematical model itself.
  - 5y ago
Miiko 5y ago
> We do know that classical mechanics is not deterministic. > Source: https://sites.pitt.edu/~jdnorton/Goodies/Dome/ https://sites.pitt.edu/~jdnorton/Goodies/Dome/ Nope, according to this analysis, classical mechanics IS deterministic: https://blog.gruffdavies.com/2017/12/24/newtonian-physics-is-deterministic-sorry-norton/ https://blog.gruffdavies.com/2017/12/24/newtonian-physics-is...
- deltasixeight 5y ago
  Yeah that blog post demolishes Nortons Dome. No seriously here's some other relevant sources that I would consider more legit: http://dsbaero.engin.umich.edu/wp-content/uploads/sites/441/2019/06/BhatIndeterminacy.pdf http://dsbaero.engin.umich.edu/wp-content/uploads/sites/441/... http://jamesowenweatherall.com/SCPPRG/FletcherSam2010Man_Dome.pdf http://jamesowenweatherall.com/SCPPRG/FletcherSam2010Man_Dom... https://www.researchgate.net/publication/271399217_The_Norton_Dome_and_the_Nineteenth_Century_Foundations_of_Determinism https://www.researchgate.net/publication/271399217_The_Norto... and Nortons Original paper: http://philsci-archive.pitt.edu/8833/4/dome_100711.pdf http://philsci-archive.pitt.edu/8833/4/dome_100711.pdf Anyway that analysis you posted actually has most of it's point addressed in the initial two papers. Read it.
  - Miiko 5y ago
    I read them. The first paper you referenced do not address any points (it just gives another example, similar to the Norton's Dome), and the second one actually confirms the major point given by Gruff Davies: > Newton’s laws are deterministic, but they’re not complete. That second paper identifies Lipschitz condition as missing part, and, by the way, it also states in the abstract: > I do not seek to conclude that these examples are necessarily strong evidence that classical mechanics is not deterministic; rather, I want to emphasize the legitimacy of pragmatic considerations in deciding what legitimately counts as a Newtonian system That is, the original Newton's principle of determinacy ("The initial positions and velocities of all the particles of a mechanical system uniquely determine all of its motion.") might be proven wrong, but that does not make "classical" (non-relativistic) mechanics indeterministic, only incomplete. To quote Gruff Davies again: > If we think about particles’ states, and consider higher orders like jounce, snap, crackle and pop. (and all the way to infinity), we can see that the choice of path of unstable particles is fully determined by their values, so this isn’t evidence for indeterminism, it is evidence for incompletion.

l-lousy 5y ago

This felt somewhat wrong to me (as I’m sure it did many people that have take a Physics class) and ended up finding a Reddit discussion about this[1]. Seems like it’s not totally correct because the function for the ball becomes discontinuous [1] https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_simple_violation_of_determinism_in/ https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_s...

deltasixeight 5y ago
Reddit proves it. Case closed. Just kidding. No seriously that thread is long and there's no singular point, it's a debate. Take a look at this (not the same link above I target a single comment): https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_simple_violation_of_determinism_in/c33in7z/?utm_source=reddit&utm_medium=web2x&context=3 https://www.reddit.com/r/Physics/comments/mn11r/the_dome_a_s... I'll have you know you're debating with higher powers here. Some people here are not your typical people who just took a physics class. Either way intuition without the math is enough to break your brain. Imagine the opposite scenario you flick a ball up the dome with just the right amount of force that it comes to rest right at the apex. One property of Newtonian mechanics is that motion is time reversible. Meaning that the opposite motion here should be valid. And the opposite motion of the scenario I described is indeed what occurs. The particle is at rest on the dome and arbitrarily just rolls off randomly. Note that this is caveated on the site with the fact that this intuition doesn't work with hemispheres. Apparently with a hemisphere you can flick the ball with a certain amount of force and it takes infinite time to reach the apex of the dome. So if you time reverse that it means any ball resting on a hemispherical dome can roll off of the apex arbitrarily but it takes an infinite amount of time. The un-determinism only works for the special dome here called "Nortons Dome."

kergonath 5y ago

The dome is not a proof. It has several flaws and the reasoning is invalid. A mass perfectly on the top of it will just stay there. It would need a force being applied to it to move at the time T. It can happen with a time-dependent force, i.e. not Newtonian dynamics. Or if a particle can change its velocity without a force being applied to it, i.e. not Newtonian mechanics. It is more straightforward to see using Lagrangian or Hamiltonian mechanics, which are better suited to this kind of constrained problem, if one is so inclined.

deltasixeight 5y ago
>It is more straightforward to see using Lagrangian or Hamiltonian mechanics, which are better suited to this kind of constrained problem, if one is so inclined. Why? He proved it mathematically without needing to Lift the entire system into a Functor. Everything works fine here. >A mass perfectly on the top of it will just stay there. It would need a force being applied to it to move at the time T. You didn't read the site. All of this is addressed and anticipated. This is an unsubstantiated comment where you barely read the article. There is a section where he addresses the First law. Then after that section he addresses how your intuition can be helped to visualize the legitimacy of this paradox with time reversal. If I tell you about it here, maybe it will make you interested enough that you'll actually read the site before formulating an unsubstantiated comment. Imagine that your at the rim of the dome and you flick the ball upwards with the perfect amount of force so that the ball rolls up the dome and rests perfectly at the apex for an indefinite amount of time. Now imagine this scenario time reversed. Boom. Newtons laws are time reversible and so is this scenario. If the time reversed scenario is able can intuitively occur then so can the time reversed scenario which is EXACTLY what norton is describing. What's going on here is that in the mathematics the apex of the dome represents a place where the mathematical functions do not have a property called Lipschitz continuity. When this property is lost, determinism is also lost. Do note that Norton is not describing reality as we know it. He is describing Newtons Model of reality and the consequences that occur within the model itself. What happens to a marble in the real world rolling down an actual dome is not something he addressing, he is just addressing newtons mathematical model itself.
- 5y ago

Miiko 5y ago

> We do know that classical mechanics is not deterministic. > Source: https://sites.pitt.edu/~jdnorton/Goodies/Dome/ https://sites.pitt.edu/~jdnorton/Goodies/Dome/ Nope, according to this analysis, classical mechanics IS deterministic: https://blog.gruffdavies.com/2017/12/24/newtonian-physics-is-deterministic-sorry-norton/ https://blog.gruffdavies.com/2017/12/24/newtonian-physics-is...

deltasixeight 5y ago
Yeah that blog post demolishes Nortons Dome. No seriously here's some other relevant sources that I would consider more legit: http://dsbaero.engin.umich.edu/wp-content/uploads/sites/441/2019/06/BhatIndeterminacy.pdf http://dsbaero.engin.umich.edu/wp-content/uploads/sites/441/... http://jamesowenweatherall.com/SCPPRG/FletcherSam2010Man_Dome.pdf http://jamesowenweatherall.com/SCPPRG/FletcherSam2010Man_Dom... https://www.researchgate.net/publication/271399217_The_Norton_Dome_and_the_Nineteenth_Century_Foundations_of_Determinism https://www.researchgate.net/publication/271399217_The_Norto... and Nortons Original paper: http://philsci-archive.pitt.edu/8833/4/dome_100711.pdf http://philsci-archive.pitt.edu/8833/4/dome_100711.pdf Anyway that analysis you posted actually has most of it's point addressed in the initial two papers. Read it.
- Miiko 5y ago
  I read them. The first paper you referenced do not address any points (it just gives another example, similar to the Norton's Dome), and the second one actually confirms the major point given by Gruff Davies: > Newton’s laws are deterministic, but they’re not complete. That second paper identifies Lipschitz condition as missing part, and, by the way, it also states in the abstract: > I do not seek to conclude that these examples are necessarily strong evidence that classical mechanics is not deterministic; rather, I want to emphasize the legitimacy of pragmatic considerations in deciding what legitimately counts as a Newtonian system That is, the original Newton's principle of determinacy ("The initial positions and velocities of all the particles of a mechanical system uniquely determine all of its motion.") might be proven wrong, but that does not make "classical" (non-relativistic) mechanics indeterministic, only incomplete. To quote Gruff Davies again: > If we think about particles’ states, and consider higher orders like jounce, snap, crackle and pop. (and all the way to infinity), we can see that the choice of path of unstable particles is fully determined by their values, so this isn’t evidence for indeterminism, it is evidence for incompletion.