Are chaotic systems really determinitistic?

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Discussion Overview

The discussion revolves around the nature of chaotic systems and their classification as deterministic. Participants explore the implications of initial conditions, the behavior of chaotic versus non-chaotic systems, and the philosophical underpinnings of determinism in both classical and quantum contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that chaotic systems are defined by their extreme sensitivity to initial conditions, questioning how such systems can be considered deterministic if initial conditions cannot be known exactly.
  • Others propose that chaos is characterized by the divergence of nearby trajectories over time, suggesting that qualitative behavior can still be determined without precise initial conditions.
  • A participant mentions the maximum Lyapunov exponent as a measure that determines the boundaries of possible trajectories, asserting that identical initial states lead to coinciding trajectories, supporting the idea of determinism.
  • Some contributions emphasize that a system is deterministic if its future state can be predicted from its current state, regardless of practical measurement limitations.
  • Another viewpoint suggests that chaotic behavior leads to rapid divergence of trajectories, making it practically impossible to trace back to the initial conditions, thus challenging the notion of determinism.
  • Participants discuss the implications of measurement uncertainty in quantum mechanics, with some asserting that quantum mechanics remains deterministic despite the uncertainty principle, while others argue that this does not apply to macroscopic chaotic systems.
  • One participant uses the analogy of leaves being scattered by the wind to illustrate the unpredictability of chaotic systems, questioning whether such behavior can be deemed strictly determined.
  • There is a discussion about the distinction between mathematical models of classical and quantum systems and their relationship to reality, with some participants arguing that both models should be deterministic.

Areas of Agreement / Disagreement

Participants express a range of views on the determinism of chaotic systems, with no consensus reached. Some agree on the definitions and implications of chaos, while others challenge the applicability of determinism in practical scenarios.

Contextual Notes

Limitations include the dependence on definitions of chaos and determinism, as well as the unresolved nature of how measurement uncertainty affects the classification of chaotic systems.

  • #61
xshell said:
Thus, chaos is only defined by the property of equation of motion generically i.e its a dynamical property; the end observation might vary acc' to other external constraints imposed on the phase space of the system !

Exactly. Science works with deterministic models which can be very accurate with certain limits. But the models are based on the assumption that the systems are isolated. In practical terms this usually works well, but no system is really isolated.

Now consider the pattern of ripples and waves on the surface of water you described. Take a (hypothetical) Planck time exposure picture of that surface with Planck length resolution. If you read through the posts on this thread, its clear that complete determinism says that the exact contours of that surface are in principle fully determined (from the time of the Big Bang?) The posters make no bones about preferring complete determinism as opposed to allowing even a little bit of randomness into the world. Randomness is imposed on us by quantum measurement. It is a defect which must be dealt with. It's even called the Quantum Measurement PROBLEM.

I think I made the case for a very narrow exception to complete determinism at classical scales, but it depends on the nature of the measurement problem. If the determinist can find a sub-quantum stratum of "hidden" variables, they win.

According to complete determinism, no one can be held responsible for their actions. Adolf Hitler wasn't a bad man. He was just following the inevitable course nature set for him.
 
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