Randomness is relative to the knowledge of an observer. If you can not work out what a system is going to do in advance, it's random to you. If nobody in the universe can work out what a system is going to do in advance, even in principle (which can be established by complexity arguments and such), then it's as good as random, even if the universe is fully deterministic.
"Absolute" randomness isn't a useful concept, it tends to come apart in your hand when examined. Even if the universe is deterministic, you aren't smart enough to make it not random for you, nor can you be.
Randomness is random, if it is somehow entangled with another system then it there are hidden variables that haven't been discovered yet. Quantum physics is "absolutely" random ( see http://en.wikipedia.org/wiki/Hidden_variable_theory for the story).
Hidden variables have not been disproved. What has been proved by Bell's inequalities is that any hidden variables that exist must themselves be irreducibly "quantum", so interest in the theory faded because for those of us on the inside of the universe the existence of fundamentally indeterminate hidden variables is just an unnecessary useless complication. But hidden variables may still exist. For instance, a computer simulating our universe may be using a deterministic PRNG (with strong statistical properties) to resolve quantum mechanics, which makes it deterministic on the outside for those who know and control the PRNG, while appearing fully random on the inside.
There is no such thing as "absolutely random". I'm not kidding, if you try to really seriously define it with math it comes apart in your hands. Both randomness and probability are intrinsically relative.
Comments
Randomness is relative to the knowledge of an observer. If you can not work out what a system is going to do in advance, it's random to you. If nobody in the universe can work out what a system is going to do in advance, even in principle (which can be established by complexity arguments and such), then it's as good as random, even if the universe is fully deterministic.
"Absolute" randomness isn't a useful concept, it tends to come apart in your hand when examined. Even if the universe is deterministic, you aren't smart enough to make it not random for you, nor can you be.
Randomness is random, if it is somehow entangled with another system then it there are hidden variables that haven't been discovered yet. Quantum physics is "absolutely" random ( see http://en.wikipedia.org/wiki/Hidden_variable_theory for the story).
Hidden variables have not been disproved. What has been proved by Bell's inequalities is that any hidden variables that exist must themselves be irreducibly "quantum", so interest in the theory faded because for those of us on the inside of the universe the existence of fundamentally indeterminate hidden variables is just an unnecessary useless complication. But hidden variables may still exist. For instance, a computer simulating our universe may be using a deterministic PRNG (with strong statistical properties) to resolve quantum mechanics, which makes it deterministic on the outside for those who know and control the PRNG, while appearing fully random on the inside.
There is no such thing as "absolutely random". I'm not kidding, if you try to really seriously define it with math it comes apart in your hands. Both randomness and probability are intrinsically relative.