# Learntofish's Blog

## More on Bell’s Theorem

Posted by Ed on January 6, 2012

In a previous post I shared some links with easy explanations on Bell’s theorem. Here, I want to continue although the explanations are more technical and require more knowledge:

11) Nonlocal correlations between the Canary Islands
This is an excellent blogpost on the blog BackReaction. It discusses the role of nonlocality in Bell’s theorem, in particular the locality loophole and the freedom-of-choice loophole.
Prerequisite: Understanding of light cones. Here are some practice questions on light cones.

12) Is the moon there when nobody looks? Reality and the quantum theory
This is a very intuitive article by David Mermin. He introduces machines that have 3 settings and two lamps (red and green) and shows that assigning 3 “real” properties to particles results in a contradiction.

13) Spooky Actions At A Distance?: Oppenheimer Lecture
A lecture by David Mermin on EPR and Bell’s theorem. Here, he uses three entangled particles (see Greenberger–Horne–Zeilinger state) instead of two. I recommend watching this lecture after you have read 12).

14) Bertlmann’s socks and the nature of reality
by John Stewart Bell
Here, John Bell derives the d’Espagnat inequality by considering socks that may or may not survive one thousand washing cycles at 45°C, 90°C and 90°C.

The d’Espagnat inequality is: N(A,notB)+N(B,notC)≥N(A,notC)
Bell mentions that this is trivial: Each member in N(A,notC) on the right hand side either doesn’t have property B and therefore is in N(A,notB) or has property B and therefore is in N(B,notC). Thus, the left hand side cannot be less than the right hand side, in other words the left hand side is greater or equal than the right hand side.
Note: When you read the document don’t wonder about the figures. They are not missing but shown in the end.
By the way, Reinhold Bertlmann was a colleague of John Bell at CERN. He is a professor now and still seems to wear differently coloured socks.
Bell’s original paper (see DrChinese’s site) becomes much more understandable with this document.

15) Part 1 – From Bell’s Inequalities to Entangled Qubits: A New Quantum Age?
This is a talk by Alain Aspect who conducted some experiments on Bell’s theorem. There are five parts.

16) Hidden variable – Derivation of line
In his talk Alain Aspect shows that one can construct a hidden variable theory that predicts a line for the expectation value. An easy to follow derivation can be found in Quantum theory: concepts and methods by Asher Peres on page 161-162.