Are chaotic systems really determinitistic?

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SUMMARY

Chaotic systems exhibit extreme sensitivity to initial conditions, where minor variations can lead to significant differences in outcomes. This discussion emphasizes that while chaotic systems are mathematically deterministic, the practical ability to predict their behavior is limited due to measurement uncertainties. The maximum Lyapunov exponent (MLE) plays a crucial role in understanding the boundaries of trajectories in chaotic systems. The conversation also highlights the distinction between mathematical models and the complexities of real-world applications, particularly in fields like meteorology.

PREREQUISITES
  • Understanding of Chaos Theory and its principles
  • Familiarity with Maximum Lyapunov Exponent (MLE)
  • Basic knowledge of quantum mechanics and the Heisenberg Uncertainty Principle
  • Concept of deterministic systems versus chaotic systems
NEXT STEPS
  • Research the implications of Maximum Lyapunov Exponents in chaotic systems
  • Explore the application of Chaos Theory in meteorology and atmospheric dynamics
  • Study the Heisenberg Uncertainty Principle and its relevance to measurement in chaotic systems
  • Investigate the philosophical implications of determinism in physical systems
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Students and professionals in physics, mathematicians, meteorologists, and anyone interested in the implications of chaos theory and determinism in real-world 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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