[kevyk]

Here's the thought experiment that Bohm proposed:

Two entangled electrons (spin adds to zero) set off in opposite directions. At distance d to the right, electron 1 passes through a Stern-Gerlach magnet which is oriented to measure the spin as "up" or "down." It measures the spin of electron 1 to be "up." At distance 2*d to the left, electron 2 passes through another Stern-Gerlach magnet, which is oriented to measure a "right" or "left" spin. It measures the spin to be "right."

A "realist" looking at the first measurement would conclude that electron 2's "actual" spin was "down." The same experimenter looking at the second measurement would conclude that electron 1's "actual" spin was "left."

The point is that if each electron has an acutal, but unknowable spin, this result should not be possible. Yet, it is what actually happens when the experiment is conducted, and is the result predicted by the classical quantum theory. An electron's spin choice with repect to a given axis seems to be genuinely indeterminate before a measurement is made.

Of course, I will make the disclaimer that there are non-local hidden-variable theories which have not been ruled out--but the smart money seems to be on genuine randomness.