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Let's start off by removing the restriction of computational resources such that we're not limited by computing power and by finite precisions. Let's also use the word exact to mean absolute certainty (ie. probability is precisely 1) about a quantity. Take a real group of particles at an initial state. We may or may not be able to derive a set of governing ...

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As Emilio pointed out, the uncertainty principle is not a limiting factor. However, as for simulating or calculating future states, this is not really generally possible for classical systems, because of chaotic behaviour.

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The Uncertainty Principle will never, as far as we know, prevent you from simulating any physical system. The reason for this is that quantum mechanics is - except for that little problem with measurements - completely deterministic. To be more precise, say you want to simulate a given system within quantum mechanics. You begin by describing your ...

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I'd agree with Ali that the answer depends on the interpretation. For example, the Bohm interpretation (http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory ) is a striking example of a deterministic interpretation.

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There is a relationship that determines indeterminism :). It is called the Heisenberg Uncertainty Principle. Size can be described by the variable $x$ for the position of a particle/atom/molecule. The principle says that we can only know the value of $x+\Delta x$ and the momentum of the particle $p+\Delta p$ (where $\Delta x,\Delta p$ denote small ...

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The border is fuzzy. The border is roughly determined by the value of Plank constant. If the values of the task is close to it, then quantum mechanics guides the scene. More explicitly, atom parts (like electron orbitals) are mostly in-deterministic, while molecules, including DNA molecules, are mostly deterministic.

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