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I'm not surprised by this. The Butterfly Effect only applies to nonlinear chaotic systems and at the quantum level everything is linear. Nondeterministic, but l

I'm not surprised by this. The Butterfly Effect only applies to nonlinear chaotic systems and at the quantum level everything is linear. Nondeterministic, but linear. You can easily build macro-scale nonlinear systems from micro-scale linear quantum systems; a double pendulum for example. I rather dislike that the word "chaotic" gets applied to all sorts of things. It has a specific meaning, and it refers to nonlinear systems with sensitive dependence to initial conditions. It does not imply some vague connotation of "random." Chaotic systems are nonlinear and thus theoretically deterministic but practically unpredictable. Quantum systems are not even deterministic in theory, but they're linear and thus they do not exhibit sensitive dependence (the Butterfly Effect).

_0ffh 6y ago
That was my understanding also. Good thing I scanned the page first, that saved me some typing work! =)
tbabb 6y ago
Quantum mechanics is deterministic in most interpretations except Copenhagen, which is losing favor.
- klysm 6y ago
  Is there a term for deterministic but where there is ‘hidden’ state such that it appears random?
  - ithkuil 6y ago
    Hidden variable theories don't satisfy the bell equation. There are other interpretations that don't require hidden variables and yet are fully deterministic. There is no free lunch though, so usually these interpretations require you "lose" something else. As a layperson, the one that I can make most sense of is the Everettian interpretation (often called Many Worlds, although I personally find that a source of confusion). In the Everettian interpretation there is only a quantum state and the observer is part of it. Thus the non-determinism and the wave function collapse is just an illusion due to the fact that the observers themselves are in a superposition state (which they are not aware of) and entangled with what they observe.
    - guerrilla 6y ago
      > Hidden variable theories don't satisfy the bell equation. No, local hidden variable theories don't [1]. De Broglie–Bohm pilot wave theory [2] is a non-local hidden variable theory. [1]. https://en.wikipedia.org/wiki/Quantum_nonlocality https://en.wikipedia.org/wiki/Quantum_nonlocality [2]. https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory [3]. https://www.youtube.com/watch?v=RlXdsyctD50 https://www.youtube.com/watch?v=RlXdsyctD50
      - ithkuil 6y ago
        Oh yes, pardon my sloppiness. I was focusing be contrast between determinism an indeterminism and I was giving locality for granted. The Everettian interpretation is fully local, where any non-locality is just an illusion caused by observers observing correlations they cannot otherwise explain if they insist on the impossibility of themselves being made of matter itself being in superposition. EDIT: it's understandably hard to throw away the first person pooling if view and our innate feeling of self and identity. Fuethermor the mechanisms of consciousness are poorly understood. I'd argue that what's making it hard to make progress on understanding consciousness is entangled with what makes it hard to accept the Everettian interpretation (which is the simplest consequence of basic quantum mechanics, nothing is added )
trhway 6y ago
>Quantum systems are not even deterministic in theory one can say that non-determinism is where the butterfly effect is factored out into - as we don't have enough precision, nor in initial conditions, nor in the model description, to predict the deterministic behavior.
kurlberg 6y ago
The resolution of this "paradox" is at the heart of "Quantum Chaos", the study of the relationship between classical chaos and quantum mechanics. In a chaotic system, minute differences in initial conditions are quickly amplified, making long time predictions impossible. A striking example of this is the potential instability of the solar system; we cannot rule out that a planet (earth!?) shoots off into space long before the sun turns into a red giant. On the other hand, in the wavelike world of quantum mechanics, trajectories are ``smeared out'' because of the uncertainty principle, and this seems to preclude the complicated picture of interlocking, yet divergent trajectories present in chaotic systems. Thus, a fundamental (and somewhat philosophical) question is: how can macroscopic chaos arise in a world governed by quantum mechanics? The answer to this has been the subject of debate, but from the point of view of mathematical physics, a more concrete question is at the center: in what ways does chaos in classical dynamical systems manifest itself quantum mechanically, in particular in terms of spectral properties of "quantized Hamiltonians". There is a fascinating connection between quantum chaos and number theory (the Riemann zeta function): the distribution of (normalized) gaps between zeros of the Riemann zeta function appears to be the "same" as the distribution of gaps between eigenvalues of quantized Hamiltonians associated to classically chaotic systems. There is a fun story of how H. Montgomery had (partially) computed the "pair correlation" ofthe gaps between Riemann zeta zeros, and at tea time at IAS he mentioned this to F. Dyson, who immeditely told him that this is the same as for random matrices, more details can be found in http://www.bourbaphy.fr/keating.pdf http://www.bourbaphy.fr/keating.pdf Some further info about quantum chaos: http://www.ams.org/notices/200801/tx080100032p.pdf http://www.ams.org/notices/200801/tx080100032p.pdf https://en.wikipedia.org/wiki/Quantum_chaos https://en.wikipedia.org/wiki/Quantum_chaos https://www.scientificamerican.com/article/quantum-chaos-subatomic-worlds/ https://www.scientificamerican.com/article/quantum-chaos-sub... http://www.scholarpedia.org/article/Quantum_chaos http://www.scholarpedia.org/article/Quantum_chaos

_0ffh 6y ago

That was my understanding also. Good thing I scanned the page first, that saved me some typing work! =)

tbabb 6y ago

Quantum mechanics is deterministic in most interpretations except Copenhagen, which is losing favor.

klysm 6y ago
Is there a term for deterministic but where there is ‘hidden’ state such that it appears random?
- ithkuil 6y ago
  Hidden variable theories don't satisfy the bell equation. There are other interpretations that don't require hidden variables and yet are fully deterministic. There is no free lunch though, so usually these interpretations require you "lose" something else. As a layperson, the one that I can make most sense of is the Everettian interpretation (often called Many Worlds, although I personally find that a source of confusion). In the Everettian interpretation there is only a quantum state and the observer is part of it. Thus the non-determinism and the wave function collapse is just an illusion due to the fact that the observers themselves are in a superposition state (which they are not aware of) and entangled with what they observe.
  - guerrilla 6y ago
    > Hidden variable theories don't satisfy the bell equation. No, local hidden variable theories don't [1]. De Broglie–Bohm pilot wave theory [2] is a non-local hidden variable theory. [1]. https://en.wikipedia.org/wiki/Quantum_nonlocality https://en.wikipedia.org/wiki/Quantum_nonlocality [2]. https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory [3]. https://www.youtube.com/watch?v=RlXdsyctD50 https://www.youtube.com/watch?v=RlXdsyctD50
    - ithkuil 6y ago
      Oh yes, pardon my sloppiness. I was focusing be contrast between determinism an indeterminism and I was giving locality for granted. The Everettian interpretation is fully local, where any non-locality is just an illusion caused by observers observing correlations they cannot otherwise explain if they insist on the impossibility of themselves being made of matter itself being in superposition. EDIT: it's understandably hard to throw away the first person pooling if view and our innate feeling of self and identity. Fuethermor the mechanisms of consciousness are poorly understood. I'd argue that what's making it hard to make progress on understanding consciousness is entangled with what makes it hard to accept the Everettian interpretation (which is the simplest consequence of basic quantum mechanics, nothing is added )

trhway 6y ago

>Quantum systems are not even deterministic in theory one can say that non-determinism is where the butterfly effect is factored out into - as we don't have enough precision, nor in initial conditions, nor in the model description, to predict the deterministic behavior.

kurlberg 6y ago

The resolution of this "paradox" is at the heart of "Quantum Chaos", the study of the relationship between classical chaos and quantum mechanics. In a chaotic system, minute differences in initial conditions are quickly amplified, making long time predictions impossible. A striking example of this is the potential instability of the solar system; we cannot rule out that a planet (earth!?) shoots off into space long before the sun turns into a red giant. On the other hand, in the wavelike world of quantum mechanics, trajectories are ``smeared out'' because of the uncertainty principle, and this seems to preclude the complicated picture of interlocking, yet divergent trajectories present in chaotic systems. Thus, a fundamental (and somewhat philosophical) question is: how can macroscopic chaos arise in a world governed by quantum mechanics? The answer to this has been the subject of debate, but from the point of view of mathematical physics, a more concrete question is at the center: in what ways does chaos in classical dynamical systems manifest itself quantum mechanically, in particular in terms of spectral properties of "quantized Hamiltonians". There is a fascinating connection between quantum chaos and number theory (the Riemann zeta function): the distribution of (normalized) gaps between zeros of the Riemann zeta function appears to be the "same" as the distribution of gaps between eigenvalues of quantized Hamiltonians associated to classically chaotic systems. There is a fun story of how H. Montgomery had (partially) computed the "pair correlation" ofthe gaps between Riemann zeta zeros, and at tea time at IAS he mentioned this to F. Dyson, who immeditely told him that this is the same as for random matrices, more details can be found in http://www.bourbaphy.fr/keating.pdf http://www.bourbaphy.fr/keating.pdf Some further info about quantum chaos: http://www.ams.org/notices/200801/tx080100032p.pdf http://www.ams.org/notices/200801/tx080100032p.pdf https://en.wikipedia.org/wiki/Quantum_chaos https://en.wikipedia.org/wiki/Quantum_chaos https://www.scientificamerican.com/article/quantum-chaos-subatomic-worlds/ https://www.scientificamerican.com/article/quantum-chaos-sub... http://www.scholarpedia.org/article/Quantum_chaos http://www.scholarpedia.org/article/Quantum_chaos