- #36
Pythagorean
Gold Member
- 4,409
- 321
Q_Goest,
Don't you see the equations I presented? They are differential equations: completely deterministic.
I'm not suggesting the physical states are unknowable (in principle). My discussion was completely classical and deterministic. The physical systems are unknowable in practice because they are chaotic; you will never see two systems exhibit the same exact dynamics: too many variables.
I'm not sure what you mean by "the phsical states at any point in time are fixed" and then justify that from classical. Even classical problems require dynamical starting conditions for a unique solution.
A pendulum occupies the same position twice in one cycle, but you have to include the velocity for a unique solution. The velocity (in general) depends on how the position is changing with time. That requires looking back in time at more than one position.
You're used to seeing linear problems, which are a very special case, but the real world is nonlinear, so superposition fails and with it our intuition.
Don't you see the equations I presented? They are differential equations: completely deterministic.
I'm not suggesting the physical states are unknowable (in principle). My discussion was completely classical and deterministic. The physical systems are unknowable in practice because they are chaotic; you will never see two systems exhibit the same exact dynamics: too many variables.
I'm not sure what you mean by "the phsical states at any point in time are fixed" and then justify that from classical. Even classical problems require dynamical starting conditions for a unique solution.
A pendulum occupies the same position twice in one cycle, but you have to include the velocity for a unique solution. The velocity (in general) depends on how the position is changing with time. That requires looking back in time at more than one position.
You're used to seeing linear problems, which are a very special case, but the real world is nonlinear, so superposition fails and with it our intuition.