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Under classical mechanics you can in theory predict the state of any self-contained system, even the entire universe, if you know its state perfectly now.

Clearly quantum mechanics breaks that with the famous uncertainty principle. But in real life is there a good example where we can see divergent behaviour at the macro level e.g. can we see examples of a "quantum butterfly effect?"

I know the uncertainty principle is actually saying you can't measure the state absolutely in the first place but that's getting a bit deep for demonstrating an example of how the universe cannot be deterministic.

I'm after a layman's answer here, not a deep description of theory or wave-functions...

Mr. Boy
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    Possible duplicate of Does Quantum Mechanics Allow Macroscopic Anomalies? or Can actual quantum effects occur on a macro scale? – AccidentalFourierTransform Feb 14 '17 at 14:20
  • @AccidentalFourierTransform those are talking about general macro quantum observables, I'm specifically asking about determinism and quantum effects being magnified via chaos theory – Mr. Boy Feb 14 '17 at 14:26
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    I'm not sure whether this counts as a macroscopic phenomenon, but the results are certainly visible at the macro level. Are you familiar with the Stern-Gerlach experiment? – Paraquat Feb 14 '17 at 14:27
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    "Determinism" is a subtle concept, see e.g. Is the universe fundamentally deterministic – ACuriousMind Feb 14 '17 at 14:41
  • I would include cancers initiated by radioactive decays in this category. Ingestion of a radioactive element may be harmless if is eliminated prior to decay. Since the time of decay is not deterministic, the chance of disease for an individual is not deterministic. – Lewis Miller Feb 14 '17 at 15:26
  • You can never "prove a negative" by direct observation. For example if you put a Geiger counter near a radioactive source and claim the clicks are non-deterministic, I can always claim that they really are deterministic, but nobody knows how to determine them yet, or that even if we do know how to do it in theory, we can't measure the initial conditions accurately enough to do it in practice. I don't see that "quantum" or "classical" affects that basic philosophical problem. – alephzero Feb 14 '17 at 16:44
  • @Mr.Boy You can find your example even in classical mechanics, where determinism is challenged by chaos in terms of initial conditions: as soon as initial conditions cannot be known with 100% accuracy and precision, the future state of even a simple system may become indeterminate. Look up "double-jointed pendulum" for a simple example. And this kind of chaos also appears in quantum dynamics, on top of inherent quantum statistics. See kicked rotor https://en.wikipedia.org/wiki/Kicked_rotator, and for instance http://www.lptms.u-psud.fr/membres/ullmo/Articles/eolss-ullmo-tomsovic.pdf – udrv Feb 14 '17 at 20:47

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