Simulation of multi-particle systems, randomness and chaos

Question

The answer https://physics.stackexchange.com/a/10441/50677 for #2 (chaotic randomness) claims that the absolute knowledge (whatever that would be) of starting conditions were sufficient for a perfect prediction of outcome. I think this is wrong. After all the interactions between particles happens in quantum dimensions and therefore is fundamentally random in the sense that one cannot predict e.g. the amount and direction of impulse that is exchanged in a "collision" interaction between two molecules - we can only trace probability clouds which even after a short time and few particles lead to what we perceive as chaotic behaviour: it is as good as not knowing exactly the starting conditions. This randomness affects systems like a gas atmosphere (thus making weather forecast impossible even if we knew each and every particles initial parameters) as well as the orbits of planets, therefore I think the answer in this point is wrong. Or am I?

Answer 1

The person who asked the question purposefully separated quantum randomness, in the third point, from the second point you mention. They wanted to know about a classic chaotic system (which is, in fact, deterministic).

The flux of a turbulent fluid is chaotic, but not unpredictable in principle, as is (according to most QM interpretations) the outcome of a quantum measurement. This might not be true for a real fluid, which is, as you say, made of atoms, which are subjected to quantum laws. However, the classical theory of fluids, at the scale of the fluid (ignoring atoms), is deterministic and chaotic, and does not need quantum mechanics to function.

In other words, sure, everything is made of quantum fields, so everything is quantum. But this is not a useful picture of reality at other scales, such as that of a human body. Here, we are talking about the usual theory of probability of coin flips, the usual theory of turbulent fluids, and only at the end we work with quantum mechanics.

The answer is not wrong, in the same sense as it is not wrong to use Newton's law of gravitation, even if it is actually invalid in the conditions where a more powerful theory, general relativity, is needed.

Answer 2

You are missing the point. Yes the real world obeys the laws of quantum mechanics and the interplay between this and classically chaotic systems is an interesting subject in its own right, however one of the key insights with chaos theory is that even in a completely classical world where the laws of physics were completely deterministic there would still be systems that were, for all practical purposes, unpredictable. When the answer talks about having absolute knowledge in this completely classical context. Yes this model is wrong, however, to use the common cliche,

all models are wrong, some models are useful.

It is also worth noting that in almost all cases where we encounter chaotic behaviour the uncertainty in our measurements is far greater than any quantum corrections.

So in short, you are, in a sense, technically correct but by being so you are missing the interesting physics in the answer.

Answer 3

It is impossible for us to decide whether reality is deterministic or stochastic. Stochasticity may happen on such small scales that we need to precisely know the state of the entire universe to distinguish it from chaos. Deterministicity may be so complex that we need to precisely measure the entire universe to make a prediction.

Quantum mechanics is a model of reality which is stochastic as this is the best way to explain observations. However, whether there is an underlying deterministic process (hidden variables) that governs this apparent stochasticity is something we can never know. At best we can make statements of the limits of this determinism and argue with Occam’s razor. Just consider that we can simulate quantum randomness on a deterministic computer.

So, to come back to your question, if the universe happens to be deterministic and we could somehow completely isolate and measure a part of it, we could precisely predict the future. Our insights from quantum mechanics and in particular regarding local hidden-variable theories put strong restrictions on what we can actually measure, how much we would have to measure, and whether such a thing as perfect isolation even makes sense, but nothing more.