Indeterminism in Classical Physics

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Discussion Overview

The discussion centers on the concept of indeterminism in classical physics, particularly in the context of Newtonian mechanics and elastic collisions. Participants explore the implications of collision scenarios involving multiple bodies and the definitions of determinism in mathematical models.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant references Roger Penrose's argument that while determinism holds in simple collisions, it breaks down in more complex scenarios, such as triple collisions, where the order of interactions affects the outcome.
  • Another participant emphasizes the need for a clear definition of determinism, suggesting it pertains to whether a model's state at one time can predict all future states.
  • It is noted that in perfectly elastic collisions, slight variations in initial conditions can lead to significant changes in motion, indicating potential discontinuities in the model.
  • A further claim is made that the existence of special initial conditions leading to discontinuities implies that the model cannot be fully deterministic.
  • Another participant introduces a different perspective, suggesting that even in idealized scenarios, such as a rigid body on a surface, determinism may not hold in determining constraint reactions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of determinism in classical mechanics, with some supporting Penrose's conclusions about indeterminism in complex collisions, while others challenge the applicability of determinism in various scenarios. The discussion remains unresolved regarding the extent and implications of indeterminism.

Contextual Notes

Participants highlight the importance of definitions and the conditions under which determinism may or may not apply, indicating that assumptions about ideal bodies and collision mechanics are critical to the discussion.

klen
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I was reading the Roger Penrose book Emperor's New Mind and he was explaining the determinism in Newtonian mechanics.
He says that if we consider two solid balls colliding (assuming elastic collision) then outcome depends continuously on initial state of the balls.
But if we consider triple or higher order collisions say three balls A,B,C come together at once it makes a difference if we consider A and B come together and then C to collide with B immediately afterwards or if we consider A and C to come together and then B to collide with A immediately afterwards.
From this he concludes that there is indeterminism in exact triple collisions and the output depends discontinuously on the input state.
I don't quite understand above conclusions. Could anyone please explain it to me??
 
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First important thing is to define determinism. The word is used in various shades of meaning.

The definition I like is this: determinism is a property of mathematical model. The model is deterministic if the state of the model system at one time is sufficient to determine its state at all past and future times.

The motions of perfect balls are rectilinear except when they collide; in collision, they change their velocity.

It is true that slight variation of the initial condition can lead to great variation of the resulting motion. In case of perfectly solid spheres, the collisions are instantaneous. This allows for the possibility that the resulting motions after the collisions are discontinuous functions of the initial conditions.

The initial condition for which there is discontinuity in the motion is special, because due to the discontinuity, the motion for this condition is not determined. It can be anyone from those defining the discontinuity. Hence the model is not entirely deterministic.
 
Jano thanks for your reply it was helpful
 
Well, talking of ideal bodies in Newtonian mechanics, it's not determined even the problem of finding the constraint reactions of a four-feet rigid body resting on the pavement.
 

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