# Another proof that local realism does not work

1. Mar 27, 2014

### jk22

I fell upon another discord between realism and quantum mechanics while studying Bell's theorem :

If we consider measurement of 2 spin 1/2 particles, with operators A, A', B and B' which are set respectively at 0, 45, 90 and 135 degrees (like in Bell experiment), we have $$A=\left(\begin{array}{cc} 1 & 0\\0 & -1\end{array}\right)$$, and so on, and call the products

$$C_1=A\otimes B,C_2=A\otimes B', C_3=A'\otimes B, C_4=A'\otimes B'$$

then local realism implies $$C_4=C_1 C_2 C_3$$

whereas quantum mechanics predicts $$C_4=-C_1 C_2 C_3$$

it's not because the operator has a minus sign in quantum mechanics that the result also has a minus sign, since QM gives only the probabilities, so that in fact QM could give the same result as local realism but not all the time.

Hence this does not prove that QM is not explainable in term of local realism ?

2. Mar 27, 2014

### euquila

What you are saying is that if the numbers line up then QM explainable by LR. That is like saying if I create a strategy for the stock market and it works one day, that it will continue to work for all other days. This is simply false.

The problem with local realism is that considers space as always being attached to the problem. It's always there. It is obvious that we humans like space (we live in it), but trying to think about all physics in the x, y, z is doomed to fail.

I'm interested in what you and others have to say about this (whether you agree/disagree or have other comments).

3. Mar 27, 2014

### Staff: Mentor

I have zero idea what you mean by that.

The problem with local realism is Bells Theorem and its experimental support.

Thanks
Bill

4. Mar 27, 2014

### euquila

Hmmm one of the more unintelligible things I've said. Thank you for clarifying.