Initial Conditions in Classical Physics

[Phrak]

According to the usual way of applying determinism in physics:-

If we know all the intitial conditions of a closed system at time t₀, we can fully specify the the system at a time t₁>t₀.

This seems natural and obvious within classical physics, but is it really true? I have never heard of a formal theory about this. It just seems to have come about empirically without theoretical support and passed along to the next generations without formal argument. Are there some sources of formal theory/argument I don't know about (theory/argument sans the philosophical trappings of wordplay, or course) ?

 

[gmax137]

Are you asking, 'is it true within classical physics?' or are you asking, 'is it really true?'

 

[Phrak]

Are you asking, 'is it true within classical physics?' or are you asking, 'is it really true?'

Let me rephrase:-


Do current conditions determine future conditions?

 

[KingNothing]

IMO, Yes. But I don't quite get what you are saying. If anything determinism is a theory that cannot be proven empirically because of being unable to measure all conditions.

 

[Vanadium 50]

This is a very confusing thread - the title doesn't seem to match the clarification in #3.

An ansatz of classical physics is that initial conditions completely determine the final conditions. We know we don't live in a classical world.

 

[zoobyshoe]

According to the usual way of applying determinism in physics:-

If we know all the intitial conditions of a closed system at time t₀, we can fully specify the the system at a time t₁>t₀.

This seems natural and obvious within classical physics, but is it really true? I have never heard of a formal theory about this. It just seems to have come about empirically without theoretical support and passed along to the next generations without formal argument. Are there some sources of formal theory/argument I don't know about (theory/argument sans the philosophical trappings of wordplay, or course) ?

To the extent Newton's three Laws assume determinism, they constitute a formal statement that determinism governs all phenomena. And, to the extent they work as predictors of future states of a system, they support that statement. If you wanted, you could regard them as theory rather than axiom, and try to disprove them, which, if you succeeded, would disprove determinism. However, proving or disproving anything is, automatically, a deterministic enterprise, so it would be pretty ridiculous to deterministically embark on trying to disprove determinism: if you disproved it you'd automatically render your proof unreliable.

 

[Phrak]

To the extent Newton's three Laws assume determinism, they constitute a formal statement that determinism governs all phenomena. And, to the extent they work as predictors of future states of a system, they support that statement. If you wanted, you could regard them as theory rather than axiom, and try to disprove them, which, if you succeeded, would disprove determinism. However, proving or disproving anything is, automatically, a deterministic enterprise, so it would be pretty ridiculous to deterministically embark on trying to disprove determinism: if you disproved it you'd automatically render your proof unreliable.

I like how you think. I think I can get around it.

 

[epenguin]

Without going into the philosophy of this I have always found most formulations of 'Newtonian determinism' a slightly false statement of anything it could practically be. The bit about knowing the initial conditions at one time t₀. But as an essential part of the 'initial conditions' is velocities, this can only operationally mean knowing where everything in the system is at at least two different times.

 

[chrisbaird]

To rephrase what others have said, classical physics is deterministic by construction, quantum physics is not deterministic on the quantum level by construction, but is deterministic macroscopically. Quantum physics matches experiment better than classical physics. According to our current understanding therefore, the world is not purely deterministic, but is highly predictable. In my opinion, a perfectly deterministic world would become boring to watch because it would become predictable, but a perfectly non-deterministic world would also be no fun because there would just be chaos. A microscopically non-deterministic/macroscopically deterministic world is the most interesting: there is order and predictability, yet enough uncertainty to keep things interesting. I could wax philosophical about microscopic non-determinism giving space for consciousness and free will to flourish, but that would be running afoul of PF ground rules.