Bell Theorem

Bell Non-locality:- It has been shown mathematically and to some extent experimentally that quantum mechanics is Bell non-local. What does that even mean? We will start with two basic principles which we believe to be true from our daily experiences!

The story of hidden variables:- Take an unbiased coin and toss it! Can you guess the outcomes with 100% certainty before tossing the coin? The answer is no!  We cannot predict the results because the outcomes are probabilistic in nature. But we can make it deterministic and predict the final outcome with 100% certainty even before tossing the coin simply by classical mechanics if one could provide the initial condition of the coin, force, torque applied on the coin and the gravitational, frictional forces experienced by the coin! 

     Probabilistic outcomes arise because of lack of knowledge in such quantities or variables—now known as ‘Hidden Variables’. EPR (Einstein, Podolsky and Rozen) argued that any probabilistic outcome can be turned into a deterministic outcome if one could supply similar hidden variables!
     This is known as the principle of determinism or realism (there is a very small difference between the idea of realism and determinism but let us ignore that for simplicity!). 

Locality:- Now consider a scenario that two friends Alice and Bob tossing two coins in some two distant (space-like separated) locations with time information such that these results can be correlated event by event. Do you think, Alice’s outcomes will depend on that of Bob? From our day-today experiences, we can tell that the results should be completely uncorrelated and one’s outcomes should not depend on the other. This is known as locality principle.

      Can we explain the statistical results produced by the subatomic particles using local hidden variables?     

     Theoretical as well as (to some extent) experimental evidences show that even quantum mechanical results violate the local hidden variable theory! Isn’t it amazing? It means what we experience in our daily life, like either the principle of locality or the principle of determinism/realism or both must be wrong!