In A Philosophical Essay on Probabilities, published in 1814, Pierre-Simon Laplace introduced a notorious hypothetical creature: a “vast intelligence” that knew the complete physical state of the present universe. For such an entity, dubbed “Laplace’s demon” by subsequent commentators, there would be no mystery about what had happened in the past or what would happen at any time in the future. According to the clockwork universe described by Isaac Newton, the past and future are exactly determined by the present. ...I believe that this view is mistaken.
A century later, quantum mechanics changed everything.
I don't just mean that some classical theories use probability, like statistical mechanics. Or that quantum mechanics sometimes predicts a sure result.
I mean that determinism is not a genuine difference between classical and quantum mechanics.
A couple of recent papers by Flavio Del Santo and Nicolas Gisin make this point.
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name "principle of infinite precision").Also:
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name "principle of infinite precision"). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on "finite information quantities" (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem''. We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').Another:
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as "physically real" and classical mechanics, like quantum physics, is indeterministic.The point here is that any deterministic theory involving real numbers becomes indeterministic if you use finitary measurements and representations of those reals. In practice, all those theories are indeterministic.
Also, any indeterministic theory can be made deterministic by including the future observables in the present state. Quantum mechanical states are usually unknowable, and people accept that, so one could add the future (perhaps unknowable) being in the present state.
Thus whether a physical theory is deterministic is just an artifact of how the theory is presented. It has no more meaning than that.