Chapter 9 Bell’s theorem

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

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 particularly wonderful (and maybe surprising) about quantum theory is that it turns up in many places where we might not expect it to. One such example is in the polarisation of light, where we stumble across an intriguing paradox.

The (much-simplified) one sentence introduction to light polarisation is this: light is made of transverse waves, and transverse waves have a “direction”, which we call polarisation; a polarising filter only allows waves of a certain polarisation to pass through. 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 that can pass through the first filter is orthogonally polarised with respect to the second filter, and is thus blocked from passing through. 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.152

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 on the Quantum Flytrap Virtual Lab.↩︎