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Chaos theory is orthogonal to quantum theory. Neither depends on the existence (or nonexistence) of the other. Chaos is unpredictable but for a different reaso

Chaos theory is orthogonal to quantum theory. Neither depends on the existence (or nonexistence) of the other. Chaos is unpredictable but for a different reason than quantum systems: Chaotic systems are unpredictable because we can never measure the real world perfectly (even ignoring quantum weirdness) and that lack of precision in measurement coupled with nonlinearity means our measurement errors amplify quickly. Nevertheless, chaos is theoretically deterministic. It's just not practically deterministic (except in the coarse-grained statistical sense of saying "the system's position in phase space is somewhere on a strange attractor path bounded by X.") Quantum systems are not even deterministic in theory, let alone practice. And ironically quantum systems are fundamentally linear. So the spookier theory in a sense is based on more tractable math.

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mjburgess 4y ago
Chaos is only deterministic with infinite precision. Since the universe isnt the kinds of place where position-momentum etc. have infinite precision, chaos isnt deterministic. Chaotic orbits of whole moons are non-deterministic on quite short time horizons.
tsimionescu 4y ago
> Quantum systems are not even deterministic in theory, let alone practice. And ironically quantum systems are fundamentally linear. It's important to note that the parts of quantum mechanics that are linear are also fully deterministic - the Schrodinger equation predicts the evolution of the wave function of a system with exact precision (as do the more complex equations of QFT). The part that introduces non-determinism is the non-linear adjustment of the Schrodinger equation that you have to perform after a measurement - the Born rule, also called wave-function collapse. Here the complex-valued wave function of a system randomly takes a single real value at the moment of measurement. It does go back to its deterministic linear evolution afterwards though, but you have to perform this non-linear adjustment. This non-linear adjustment can be interpreted in many ways, but without it QM doesn't agree with even the most basic experiments, so one way or another it is a vital part of the theory, rendering it non-linear overall.
- dreamcompiler 4y ago
  Well-said. I was a bit sloppy in my terminology because the math of quantum computing is mostly linear (albeit complex) but I was thinking of the Schrodinger part. When qbits have to be read, we convert them from complex to real and that step is both nonlinear and nondeterministic.

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mjburgess 4y ago

Chaos is only deterministic with infinite precision. Since the universe isnt the kinds of place where position-momentum etc. have infinite precision, chaos isnt deterministic. Chaotic orbits of whole moons are non-deterministic on quite short time horizons.

tsimionescu 4y ago

> Quantum systems are not even deterministic in theory, let alone practice. And ironically quantum systems are fundamentally linear. It's important to note that the parts of quantum mechanics that are linear are also fully deterministic - the Schrodinger equation predicts the evolution of the wave function of a system with exact precision (as do the more complex equations of QFT). The part that introduces non-determinism is the non-linear adjustment of the Schrodinger equation that you have to perform after a measurement - the Born rule, also called wave-function collapse. Here the complex-valued wave function of a system randomly takes a single real value at the moment of measurement. It does go back to its deterministic linear evolution afterwards though, but you have to perform this non-linear adjustment. This non-linear adjustment can be interpreted in many ways, but without it QM doesn't agree with even the most basic experiments, so one way or another it is a vital part of the theory, rendering it non-linear overall.

dreamcompiler 4y ago
Well-said. I was a bit sloppy in my terminology because the math of quantum computing is mostly linear (albeit complex) but I was thinking of the Schrodinger part. When qbits have to be read, we convert them from complex to real and that step is both nonlinear and nondeterministic.