SalvorHardin wrote:A truly random system system is one that can only be accurately modelled using quantum mechanics (i.e. atomic and sub-atomic particles). This is because the laws of quantum mechanics are probabilistic not deterministic. ...
Not quite. Our stated laws of quantum mechanics are probabilistic, not deterministic, but that doesn't necessarily prove that the actual underlying way that the universe works isn't deterministic.
SalvorHardin wrote:... Consider two radioactive atoms of the same element (same isotope); we do not know when they will will decay, only the probability that each will have decayed by a particular time. If these atoms behaved according to the laws of classical physics then you would be able to state the exact time when each would decay.
Only if you knew every relevant aspect of the state of those atoms, sufficiently accurately to ensure that the inaccuracies in your predicted outcome were still sufficiently small by the time that the atom is predicted to decay. A key insight of chaos theory is that even if a universe were to work in a completely deterministic way, predicting what will happen in its future from its laws depends on knowing its initial state absolutely and completely accurately and performing your calculations absolutely and completely accurately. Otherwise, it's perfectly possible that the way the laws apply to the state you're considering causes inaccuracies to build up each time you advance your calculations forward in time, and if it does, the inaccuracies will eventually build up to the point where they overwhelm your results - i.e. your results become useless. Working more accurately and with more accurate initial data will mean that the calculations can be taken further ahead in time before that happens and so delay the point at which your results become useless, but it will still happen: only absolute and complete accuracy will delay it indefinitely.
As a thought experiment, imagine each atom had a tiny dice-rolling mechanism behind it, with the sequence of outcomes of its dice rolls determining when the atom decays. That dice-rolling mechanism cannot be seen directly by anything we possess, so only its indirect effects are things we can observe - i.e. when the atoms decay. And the way it operates is completely deterministic, but it does roll the dice in quite a vigorous, bouncing fashion that lets uncertainties build up chaotically (in particular, if a die bounces, quite small differences about exactly how it hits the ground on one bounce can cause differences in how fast it is rotating that lead to much bigger differences in how it hits the ground on the next, a recipe for chaotic effects). So we would see the times that each atom decays as random, even though they were deterministic and could in principle be determined exactly if we knew enough...
Basically, there's a sort of analogue of Clarke's 3rd law ("
Any sufficiently advanced technology is indistinguishable from magic") that applies here, which is "Any sufficiently hidden determinism is indistinguishable from true randomness". (I should possibly add that various scientists have conducted experiments to try to reveal hidden determinism behind quantum effects, and they have had negative results that they have interpreted as saying that there are no "hidden variables" - i.e. that the effects really aren't deterministic. But those I've looked at seem to me only to say that any deterministic mechanism behind quantum effects must involve things that violate generally-accepted scientific principles, such as faster-than-light communication between the deterministic mechanisms underlying quantum effects in different locations. I.e. they certainly raise the "sufficiently hidden" bar that a deterministic explanation of quantum effects has to clear, but they don't make one entirely inconceivable...)
Anyway, what all that means is that as an answer to the question "Is anything truly random?", "Yes, quantum effects are truly random" is an excellent working hypothesis and it looks very unlikely that it will cease to be anytime soon, but it's not absolutely 100% certain. And that's basically as good as we ever get for any "scientific law" - so don't expect an absolutely certain answer to the question!
Gengulphus