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Incompleteness implies indeterminacy. Davies point is sort of pedantic but the math from Nortons paper is nondeterministic BECAUSE of incompleteness. We know a

Incompleteness implies indeterminacy. Davies point is sort of pedantic but the math from Nortons paper is nondeterministic BECAUSE of incompleteness. We know at the singularity newtons laws are incomplete so in that region you are correct. Prior to the particle entering a singularity newtons laws describe it deterministically so you are still correct. At some unknown time when the particle exits the singularity Newtons laws still apply but are no longer deterministic, because we do not know what happened in the singularity. We do know the possible states of the particle are still bounded and controlled by newtons laws but within this boundary we are unable to fully determine its unique path if one should exist.

Miiko 5y ago
Well, if you formulate the statement as: > We do know that Newtonian mechanics is not deterministic at singularity points then I fully agree with that. However, that may be fixed by either adding additional requirement (e.g. Lipschitz continuity) or just by not considering Newtonian mechanics applicable to those cases - it is known already that Newton's laws do not fully describe the real word (because quantum uncertainty does exist) and the Lebesgue measure of singularity cases is zero anyway. In case of three-body problem, the singularities are the case of bodies collisions and yes, those cases are not deterministic, but the configuration without collision is known to be fully deterministic.