5 ms·

And as soon as you have a rigid 3-body collision, indeterminism comes back. If A hits B before C, you generally get a different result than if A hits C before B

by btilly 3y ago

And as soon as you have a rigid 3-body collision, indeterminism comes back. If A hits B before C, you generally get a different result than if A hits C before B. If A hits B and C at the same time, a range of solutions are possible, including both limiting solutions of the previous two variations. The extreme example of this is the indeterminism of a break shot in billiards.

tsimionescu 3y ago
Sure, but perfectly rigid bodies are also not compatible with an atomic model of matter, they are just an abstraction used in the maths. If you wanted to model an actual physical experiment, you would model any physical object as two or more rigid bodies connected by springs of an arbitrary small length*. So, anyone using classical mechanics for experimental purposes rather than explorations of the maths would model the collision of three balls in a way where simultaneity is impossible. * This is just like when modeling actual circuits, you model a physical wire as an ideal wire plus a resistor. But we don't say that "classical wire diagrams predict that the current through a wire can be infinite" just because you can draw a circuit with 0 resistance - that circuit modal is simply non-physical.
- btilly 3y ago
  But perfectly rigid atoms are compatible with an atomic model of matter. And in such a model, the indeterminism comes right back. Yes, the idea of perfectly rigid atoms is incompatible with experiment. But so is classical mechanics on the scale where that fact becomes obvious. And so it isn't classical mechanics that is deterministic. You are right that n-body classical mechanics combined with the assumption of a continuous response does become deterministic by the standard existence and uniqueness theorems of ordinary differential equations. But the point still remains, classical mechanics winds up not being deterministic without that extra assumption. And that extra assumption is often omitted in real models of things like elastic collisions.

by btilly 3y ago

tsimionescu 3y ago

Sure, but perfectly rigid bodies are also not compatible with an atomic model of matter, they are just an abstraction used in the maths. If you wanted to model an actual physical experiment, you would model any physical object as two or more rigid bodies connected by springs of an arbitrary small length*. So, anyone using classical mechanics for experimental purposes rather than explorations of the maths would model the collision of three balls in a way where simultaneity is impossible. * This is just like when modeling actual circuits, you model a physical wire as an ideal wire plus a resistor. But we don't say that "classical wire diagrams predict that the current through a wire can be infinite" just because you can draw a circuit with 0 resistance - that circuit modal is simply non-physical.

btilly 3y ago
But perfectly rigid atoms are compatible with an atomic model of matter. And in such a model, the indeterminism comes right back. Yes, the idea of perfectly rigid atoms is incompatible with experiment. But so is classical mechanics on the scale where that fact becomes obvious. And so it isn't classical mechanics that is deterministic. You are right that n-body classical mechanics combined with the assumption of a continuous response does become deterministic by the standard existence and uniqueness theorems of ordinary differential equations. But the point still remains, classical mechanics winds up not being deterministic without that extra assumption. And that extra assumption is often omitted in real models of things like elastic collisions.