Can deterministic world view be denied by anything other than quantum mechanics

Question

If we ignored quantum mechanics and looked at the world with a deterministic Newtonian view. Does not that mean that there is no randomness and that if all the information of the state of the universe during the big bang is accessible one can predict the state of the universe at any period of time and predict that I am writing this question right now.

Of course something like that denies the free will but I am asking if there is any thing other than quantum mechanics that denies the deterministic world view.

Answer 1

From the theory of highly dynamic systems and chaos, perfectly classical and in principle deterministic systems can exhibit a behavior, where minute perturbations of the initial conditions are exponentially enhanced over time, and thus arbitrarily small perturbations can, after a finite time span, lead to a state that bears no resemblance at all to the evolved state of the unperturbed system.

Of course, this system is deterministic if you know all the initial conditions exactly. Not just to high precision, but exactly. But that would generally (since the rational numbers are not a dense set and therefore have zero probability to be occurring exactly in a real-life setting) require an infinite amount of information, which is of course impossible - so your system is really, fundamentally unpredictable, although still in principle deterministic - this is pretty much the definition of "chaos".

According to people more clever than me, quantum mechanics is also deterministic, by the way - see the question that @Greg links to in his comment to your question.

I do not know if that rules out "free will", because I have never seen a consistent and coherent definition of what "free will" is, but it should be clear that it leaves ample room for complexity and unpredictability.

Answer 2

Determinism is not denied by anything (QM included). The so-called no-go theorems against deterministic hidden-variable theories are logically fallacious. They start with the assumption that determinism is false (using fancy names like "free-will assumption" or "no-conspiracy assumption") and conclude, guess-what, that QM is incompatible with classical deterministic realism.

I have yet to see a sound argument against determinism.

Answer 3

Norton's Dome is an example of nondeterminism in Newtonian Mechanics. There is a potential $V(r)=mgCr^{3/2}$ (say from a dome shaped like $h=Cr^{3/2}$) that gives multiple solutions with no way to pick when, if, or in which direction the particle moves.

However, this is not a serious blow against determinism because firstly, that is not a fundamental force, and no real force is going to look like that exactly, and secondly the nondeterminism only happens for a perfect exact amount of energy, any less and it can't be/get to the top, and any more and it has to be moving when at the top so it slides down the side in the direction it is going and it does so right away. And even if you had a perfect potential like that, and a perfect energy, the nondeterministic equilibrium is unstable, you'd have to perfectly isolate the system from arbitrarily small perturbations.

But, since that is all from Newtonian Mechanics and just sliding a body along a hill at that, it does tell you that popular theories aren't as deterministic as people like to pretend.