Learntofish's Blog

A blog about math, physics and computer science

Bell’s theorem easy explained

Posted by Ed on December 21, 2011

Bell’s theorem states that quantum mechanics is not compatible with a theory of local hidden variables. In other words quantum mechanics can not both be (i) local and (ii) realistic (see also the wiki entry on principle of local causality) where with realistic I mean Counterfactual definiteness. Here are a few sites with an easy to understand explanation of Bell’s theorem.

1) Spooky Action at a Distance – An Explanation of Bell’s Theorem
by Gary Felder
This article is easy to understand and only basic mathematics is used.

2) Does Bell’s Inequality rule out local theories of quantum mechanics?
Updated May 1996 by PEG (thanks to Colin Naturman).
Updated August 1993 by SIC.
Original by John Blanton.
This article is more compact than the one before. It introduces a notation often used in discussions, e.g. N(x+, y−).

3) Einstein-Podolsky-Rosen paradox and Bell’s inequalities
by Jan Schütz
A seminar report introducing the CHSH inequality that is used for experiments.

4) Bell’s Theorem explained
A post on the blog Skeptic’s Play that uses set theory to explain Bell’s theorem.

5) Bell’s theorem analogy
David M. Harrison uses a classroom analogy to derive Bell’s inequality.

6) Violation of Bell’s theorem
Lecture notes by Leonard Susskind also using a Venn diagram.

7) Lecture 17 – Einstein-Podolski-Rosen Experiment and Bell’s Inequality
An excellent lecture by Prof. James Binney. You can download the lecture notes here. This lecture assumes that you know some quantum mechanics, e.g. how to calculate probabilities using Dirac’s bra-ket notation.
Note: If you have wondered too (like me) about the probability density function \rho(\lambda) read this wiki article on local hidden variables. It explains that \rho(\lambda) describes the probability that the source emits entangled particles with the hidden variable \lambda .

8) Paradigms in Physics: Quantum Mechanics
This is an online textbook made available by the Department of Physics, Oregon State University. Have a look at chapter 4 (quantum spookiness). Although they don’t use the term probability density (see note above in 7) it becomes clear now what is meant with \rho(\lambda). The authors use populations instead.

9) Bell’s Theorem with Easy Math and Bell’s Theorem and Negative Probabilities
Two articles by David R. Schneider also known as DrChinese.

10) John Bell himself presenting his theorem
This is a talk given by John Bell at CERN.


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