Chapter 9 Bell’s theorem

About quantum correlations, which are stronger than any correlations allowed by classical physics, and about the CHSH inequality which demonstrates this fact, and which is a variant of Bell’s theorem.

Every now and then, it is nice to put down your lecture notes and go and see how things actually work in the real world. What is wonderful (and surprising) about quantum theory is that it turns up in many places that we might not expect it to, such as in the polarisation of light, where we stumble across an intriguing paradox.

If we take two polarising filters, and place them on top of each other with their polarisations oriented at 90^\circ to one another, then basically no light will pass through, since the only light passing through the first filter is orthogonally polarised with respect to the second filter, and is thus blocked. But then, if we take a third filter, and place it in between the other two, at an angle in the middle of both (i.e. at 45^\circ), then somehow more light is let through than if the middle filter weren’t there at all.126

This is intrinsically linked to Bell’s theorem, which proves the technical sounding statement that “any local real hidden variable theory must satisfy certain statistical properties”, which is not satisfied in reality, as many quantum mechanical experiments (such as the above) show!

  1. For the more visually inclined, there is a video on YouTube by minutephysics about this experiment, or you can play with a virtual version at Virtual Lab by Quantum Flytrap.↩︎