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Can there exist an argument that could be used for proving that the universe is indeterministic?

If this one seems to be too strict (rigorous), I would also be interested to know a 1-sentence argument from either QEM or statistical mechanics that conjectures the indeterminism of the universe?

Sources:

  1. I already received an answer, "QM wave function is interpreted as a probability density and statistical mechanics postulates equates the ensemble average with the time average of a given physical quantity." (http://www.quora.com/Is-there-an-argument-that-could-be-used-for-proving-that-the-universe-is-indeterministic), but I still fail to see the actual argument.

  2. http://www.wired.com/2014/04/quantum-theory-flow-time/

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    $\begingroup$ Possible duplicate: physics.stackexchange.com/q/63811/50583 $\endgroup$ – ACuriousMind Nov 2 '14 at 22:04
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    $\begingroup$ ACuriousMind, I read this answer already. My question here is about finding whether there can exist such an argument for indeterminism. $\endgroup$ – tesgoe Nov 2 '14 at 22:06
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    $\begingroup$ I do not think you will find a 1-sentence argument, it is a little more complex than that. See for instance en.wikipedia.org/wiki/Bell's_theorem $\endgroup$ – Wolphram jonny Nov 3 '14 at 2:25
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    $\begingroup$ Mr Fernandez, I know Bell's theorem, but I cannot see how it can provide an argument that world must be indeterministic. I have many times heard that we know it for sure that it is such at microscopic level. How can we know that investigation at nano- or higher-resolution level cannot change our mind? Namely, what is this argument, that you have in mind, based on? $\endgroup$ – tesgoe Nov 3 '14 at 6:40
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    $\begingroup$ I would put in the Heisenberg Uncertainty Principle as a corner stone to indeterminancy. ( or the commutator maths in quantum mechanics). In physics there are no proofs. There are only conjectures and falsifications of conjectures. If the HUP is experimentally falsified, then we can talk again. At the moment it holds for all observations. The rest is mathematics, not physics, imo $\endgroup$ – anna v Nov 3 '14 at 7:44
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one-liner

coin flip, there you have it

another one:

The time of radioactive decay of an atom

Explanation:

For a coin flip, there is no (consistent) method to predict the outcome, of course one can approximate in some cases, but no method consistently gives the outcome.

Similarly in 2nd example, although quantum mechanics can predict cross-sections and mean values there is no consistent method to predict the time at which the next radio-active decay will happen. This can also be made more explicit via the time-energy uncertainty relation $\Delta E \Delta \tau$ (note that time is also related to some parts of causality)

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    $\begingroup$ For the coin flip, proving that the long-run average does not exist is a rather nice exercise in probability theory. $\endgroup$ – Kyle Kanos Nov 3 '14 at 16:13
  • $\begingroup$ @KyleKanos, what result do you refer exactly? sounds good $\endgroup$ – Nikos M. Nov 3 '14 at 16:14
  • $\begingroup$ @KyleKanos, ahh i think i get it, you mean the sum of the random variables (either $0$ or $1$ or $-1$, $1$), correct? $\endgroup$ – Nikos M. Nov 3 '14 at 16:16
  • $\begingroup$ Looking back, I slightly confused myself here by misstating the issue. The long-run proportion of coin-flipping reveals the 50-50 deal (e.g., flipping 10, 100, 1000, ... coins will result in # of Heads $\simeq$ # of Tails). The existence of one preferred choice does not exist, as repeated use of Bayes' theorem returns $\mathbb{P}(H)=\mathbb{P}(T)$ for any particular throw. $\endgroup$ – Kyle Kanos Nov 3 '14 at 16:24
  • $\begingroup$ @KyleKanos, ohh ok, i though you were referring to a divergent sum of random variables (if seen as an ordinary sum), i was confused too :) $\endgroup$ – Nikos M. Nov 3 '14 at 16:29

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