Bell’s Theorem, or why the universe is even stranger than we might imagine

The Einstein-Podolsky-Rosen “paradox” was at first presented as an argument against some of the basic tenets of quantum mechanics.

One of these basic tenets is that there is genuine randomness in the characteristics of particles. For instance, when one measures the spin of an electron, it is only at the instant the measure is taken that the actual value of the spin is defined. Until then, its value was defined by a probability function, that collapses when the measurement is taken.

The EPR paradox uses the concept of entangled particles. Two particles are “entangled” if they were generated in such a way that they exhibit a totally correlated particular characteristic. For instance, two photons generated by a specific phenomenon (such as an electron-positron annihilation, under some circumstances) will have opposite polarizations. Once generated, these particles can travel vast distances, still entangled.

If some particular characteristic of one of these particles is measured (e.g., the polarization of a photon) in one location, this measurement will, probabilistically, result in a given value. That particular value will determine, instantaneously, the value of that same characteristic on the other particle, no matter how far the particles are. It is this “spooky action at a distance” that Einstein, Podolsky and Rosen believed to be impossible. It seems that the information about the state of one of the particles travels, faster than light, to the place where the other particle is.

Now, we can imagine that that particular characteristic of the particles was defined the very instant they were generated. Imagine you have one bag with one white ball and one black ball, and you separate the balls, without looking at them,  and put them into separate boxes. If one of the boxes is opened in Australia, say, and it is white, we will know instantaneously the color of the other ball. There is nothing magic or strange about this. Hidden inside the boxes, was all along the true color of the boxes, a hidden variable.

Maybe this is exactly what happens with the entangled photons. When they are generated, each one already carries with it the actual value of the polarization.

It is here that Bell’s Theorem comes to show that the universe is even stranger than we might conceive. Bell’s result, beautifully explained in this video, shows that the particles cannot carry with them any hidden variable that tells them what to do when they face a measurement. Each particle has to decide, probabilistically, at the time of the measurement, the value that should be reported. And, once this decision is made, the measurement for the other entangled particle is also defined, even if the other particle is on the other side of the universe. It seems that information travels faster than light.

The fact is that hidden variables cannot be used to explain this phenomenon. As Bell concluded “In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, …

A very easy and practical demonstration of Bell’s theorem can be done with polarized filters, like the ones used in cameras or some 3D glasses. If you take two filters and put them at an angle, only a fraction of the photons that go through the first one make it through the second one. The actual fraction is given by the cosine squared of the angle between the filters(so, if the angle is 90º, no photons go through the two filters). So far, so good. Now, if you have the two filters at an angle (say 45º, so that half the photons that pass the first go through the second filter) and put an additional filter between them, at an angle of 22.5º, it happens that roughly 85% of the photons go through the (now) second filter. Of these, roughly 85% go through the third filter (which used to be the second). That means that, with the three filters in place, roughly 72% of the photons go through, way more than if you had just the two first filters, which were not changed in any way. This, obviously, cannot happen if the decision of the photons was determined from the start.

Do look at the video, and do the experience yourself.