determinism - Is randomness deterministic?

Is randomness based on lack of knowledge or behavior of universe is true random?

Or in other words,

are the allegation by EPR about hidden variable in the QM theory justifiable? What evidence can disprove/prove EPR?

Answer

This is a very general question, and can be answered from several perspectives. I shall try to give an overview so you can perhaps research the areas that interest you a bit more.

Firstly, the most fundamental interpretation of probability (as considered by most mathematicians) is Bayesian probability. This effectively states that probability measures state of knowledge of an observer.

This view has interesting ties with physics, in particular quantum mechanics. One could consider the random outcome of a QM measurement (wavefunction collapse) from a frequentist approach, but it is often more appealing philosophically to consider it as a state of knowledge. (The famous thought experiment of Schrodinger's cat is a good example - until one opens the box, we can only say it is an "alive-dead" cat!)

Interestingly, Bayesian probability does not explicitly preclude determinism (or non-determinism). Our current understanding of quantum mechanics does however. In other words, even knowing perfectly the state of a system at a given time, we cannot predict the state of the system at a future time. This most famous upset Albert Einstein, who spent many years of his life looking for a more fundamental deterministic theory - a so-called hidden-variables theory. Since then, however, we have learnt of Bell's theorem, which implies the non-existence of local hidden variables, suggesting that there is no more fundamental theory that "explains away" the non-determinism of QM. This is however a very contentious issue, and in any case does not rule out the existence of non-local hidden variable theories - the most famous of which is Bohm's interpretation.

In summary, this issue is far from settled, and creates a lot of contention between different groups of physicists as well as philosophers today.