# Indeterminism in Classical Physics

1. May 24, 2013

### klen

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 dont quite understand above conclusions. Could anyone please explain it to me??

2. May 24, 2013

### Jano L.

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 any one from those defining the discontinuity. Hence the model is not entirely deterministic.

3. May 25, 2013