Editing Indeterminism (section)

===Quantum mechanics===
{{main|Quantum indeterminacy}}
At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up").

However, the advent of [[quantum mechanics]] removed the underpinning from that approach, with the claim that (at least according to the [[Copenhagen interpretation]]) the most basic constituents of matter at times behave [[quantum indeterminism|indeterministically]]. This comes from the [[wave function collapse|collapse of the wave function]], in which the state of a system upon [[measurement problem|measurement]] cannot in general be predicted.  Quantum mechanics only predicts the probabilities of possible outcomes, which are given by the [[Born rule]]. Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its [[observer (quantum mechanics)|observer]]-dependence, but also of [[objective collapse theories|objective collapse]] and [[Interpretations of quantum mechanics#Comparisons|other theories]].

Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called [[hidden variable (physics)|hidden variables]],<ref>[https://web.archive.org/web/20110319153807/http://www.cosmosmagazine.com/features/online/4137/how-much-free-will-do-we-have Cosmos Magazine: ''How Much Free Will Do We Have'']</ref> would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled ''"[[EPR paradox|Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?]]"'' arguing that such a theory was in fact necessary to preserve the [[principle of locality]].
In 1964, [[John S. Bell]] was able to define [[Bell's theorem|a theoretical test]] for these local hidden variable theories, which was reformulated as a workable experimental test through the work of [[CHSH inequality|Clauser, Horne, Shimony and Holt]]. The negative result of the 1980s [[Aspect experiment|tests]] by [[Alain Aspect]] ruled such theories out, provided certain [[Loopholes in Bell test experiments|assumptions]] about the experiment hold. Thus any [[interpretation of quantum mechanics]], including deterministic reformulations, must either reject [[Principle of locality|locality]] or reject [[counterfactual definiteness]] altogether. [[David Bohm]]'s [[Bohmian quantum mechanics|theory]] is the main example of a non-local deterministic quantum theory.

The [[many-worlds interpretation]] is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in. Technically, [[counterfactual definiteness]] is lacking.

A notable consequence of quantum indeterminism is the [[Heisenberg uncertainty principle]], which prevents the simultaneous accurate measurement of all a particle's properties.