Introduction
The Copenhagen interpretation of quantum mechanics proposes, generally, that the outcome of any measurement cannot be measured with certainty. This leads to the situation where measurements of a property performed on two identical systems can give different answers.
However, can a deeper reality, hidden beneath quantum mechanics, described by a more fundamental theory predict the outcome of measurement with certainty. Einstein, a proponent of a deeper reality (hidden variables) hidden famously insisted that, "I am convinced God does not play dice”.
Quantum mechanics puzzle
Quantum mechanics creates the puzzling situation in which a measurement of one system can "poison" the measurement of the other system, no matter what the distance between them. One could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other.
For example, say, in a neutral-Pion decay, where two photons travel some light years apart – if the spin of one photon is measured, quantum mechanic suggests that that measurement instantaneously forces the second photon into a state of well-defined spin - even though it is light years away from the first.
Einstein, Podolsky, and Rosen (EPR) argued that elements of reality must be added to quantum mechanics and postulated that the existence of unknown properties should account for the discrepancy – that there is a deeper reality.
A conundrum
How do we reconcile the fact that the second photon "knows" that the spin of the first photo has been measured, even though they are separated by light years of space and far too little time has passed for information to have traveled to it according to special relativity?
We can accept the postulates of quantum mechanics its seemingly uncomfortable coexistence with special relativity, or we may believe that quantum mechanics is not complete:
