Bell's theorem Adams

Suppose we have two entangled particles in the state that are sent far apart, one to Alice and the other one to Bob.

The probability that Alice measures the spin of her particles to be is and the same is true for Bob. After Alice has measured she immediately knows that Bob’s spin has to be as well because of how the initial state is defined.

In case there was a hidden classical variable, then the Bell’s inequality would be satisfied:

which, considering that

can be rewritten as

For the experiment we will consider , and :

If we consider

we can rewrite the probabilities above as the modulus squared of their coefficients:

which, for is