quantum mechanics - Will Determinism be ever possible?

What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?

Answer

Laplace's determinism is not physically correct over long periods of time. That is, it neglects chaos/"sensitive dependence on initial conditions"/exponential growth of microscopic perturbations already in Newtonian dynamics, which was seriously thought about only in the 20th century. Being true, this also will not be overcome. Stochasticity enters some classical dynamical paths with time.

There is subtlety here. In classical mechanics, or the evolution of the wave function, there is a kind of microdeterminism, so that what occurs in the next instant is fully determined by what occurred up until that point. It is in the longer time evolution of a chaotic system that stochasticity creeps in.

By the way, Lapalace said "We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow." This part remains true in chaotic classical mechanics.

However, he then continued "An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence. (Laplace 1820)" This is the part that classical chaos invalidates.

You might also read http://plato.stanford.edu/entries/determinism-causal/

Finally, there are also questions whether, in light of general relativity, black holes, etc, we can even speak of a "state of the universe as a whole" There may not be such a god's eye view altogether. These issues need a philosophy forum, however.