by the uncertainty principle. Uncertainty is why information is limited.
Uncertainty is the only reason (currently provided by physics) why we cannot propose the existence of an advanced species on another planet capable of mapping the positions and momenta of all particles in the universe.
If such a species existed then they would be able to correlate all outputs and nothing would be truly random.
Yes its determinism, but I don't see how it is a conundrum. Its all fairly straightforward. If there is determinism, and if there are no limits on information that can be gained about a system, then there are no "physical secrets" and no true randomness.
My only point in bringing all this up was to correct wolfgang's false statements concerning the determinism of classical mechanics, the non-determinism of QM, and the supposed relationship between randomness and this non-determinism.
a) Classical Mechanics has no limits on information, but contrary to what many seem to believe it is not deterministic.
If Classical Mechanics were a true theory for the universe we could still define "truly random" values, by say counting the number of space invaders passing through a detector over a fixed time interval. This would be randomness deriving from the non-determinism of the universe.
Classical Mechanics is a provably false theory, and thankfully no space invaders have ever been seen.
b) QM has limits on information, and that alone is enough to define some notion of randomness. Contrary to what many seem to believe, QM is not non-deterministic. The Copenhagen interpretation is non-deterministic and very popular, but it is not the only interpretation. The Bohm interpretation is deterministic.
c) Your subtle differences are not lost on me. YOUR definition of random (random := next number cannot be guessed by anyone) is a definition based on the limits of information. It is crucial what "anyone" can do. Those limits are derived from the limits on what can be learned about other systems in the universe. It has absolutely nothing to do with determinism.
This definition is only correct if the uncertainty principle is not violated, which is why I say that "QM defines random" and not "QM is random". A Bohmian sees no randomness in the outcome of the quantum process, it is all predetermined. A Bohmian defines random as outcomes which are unpredictable due to the limits on information, which is again your definition.
Final remark. You state:
> If the next number cannot be guessed by anyone (i.e. is not correlated to previous values), it is truly random. The difference is subtle but essential.
I'm going to pick on your parenthetical remark. The definition proposed by the parenthetical "anything not correlated to previous values is truly random" is either false, or a bad definition (depending on exactly how it is read).
Bohmian QM is a system where outcomes can be unpredictable, but they are not in a philosophical sense "uncorrelated" because everything is mediated through hidden variables and is fully deterministic. This is nonsense to a Bohmian.
Or maybe this is a practical definition for a Copenhagenist (who believes in intrinsic randomness). Take the outputs and run them through an auto-correlation test. If they fail they are non-random, if they pass they are random. The problem here is that any auto-correlation test has a confidence interval, and has a false positive and false negative rate. Just because a RNG passes the auto-correlation test doesn't mean it isn't just psuedo-random with a long period so you got a false-negative, and just because an over-volted transistor fails a test doesn't mean it wasn't obeying QM, its just a false-positive.