## Demystifying quantum mechanics VI

When one says that one wants to demystify quantum mechanics, then it may create the false impression that there is nothing strange about quantum mechanics. Well, that would be a misleading notion. Quantum mechanics does have a counterintuitive aspect (perhaps even more than one). However, that does not mean that quantum mechanics need to be mysterious. We can still understand this aspect, and accept its counterintuitive aspect as part of nature, even though we don’t experience it in everyday life.

The counterintuitive aspect of quantum mechanics is perhaps best revealed by the phenomenon of quantum entanglement. But before I discuss quantum entanglement, it may be helpful to discuss some of the historical development of this concept. Therefore, I’ll focus on an apparent paradox that Einstein, Podolski and Rosen (EPR) presented.

They proposed a simple experiment to challenge the idea that one cannot measure position and momentum of a particle with arbitrary accuracy, due to the Heisenberg uncertainty. In the experiment, an unstable particle would be allowed to decay into two particles. Then, one would measure the momentum of one of the particles and the position of the other particle. Due to the conservation momentum, one can then relate the momentum of the one particle to that of the other. The idea is now that one should be able to make the respective measurements as accurately as possible so that the combined information would then give one the position and momentum of one particle more accurately than what Heisenberg uncertainty should allow.

Previously, I explained that the Heisenberg uncertainty principle has a perfectly understandable foundation, which has nothing to do with quantum mechanics apart from the de Broglie relationship, which links momentum to the wave number. However, what the EPR trio revealed in their hypothetical experiment is a concept which, at the time, was quite shocking, even for those people that thought they understood quantum mechanics. This concept eventually led to the notion of quantum entanglement. But, I’m getting ahead of myself.

The next development came from John Bell, who also did not quite buy into all this quantum mechanics. So, to try and understand what would happen in the EPR experiment, he made a derivation of the statistics that one can expect to observe in such an experiment. The result was an inequality, which shows that, under some apparently innocuous assumptions, the measurement results when combine in a particular way must always give a value smaller than a certain maximum value. These “innocuous” assumptions were: (a) that there is a unique reality, (b) that there are no nonlocal interactions (“spooky action at a distance”) .

It took a while before an actual experiment that tested the EPR paradox could be perform. However, eventually such experiments were performed, notably by Alain Aspect in 1982. He used polarization of light instead of position and momentum, but the same principle applies. And guess what? When he combined the measurement result as proposed for the Bell inequality, he found that it *violated* the Bell inequality!

So, what does this imply? It means that at least one of the assumption made by Bell must be wrong. Either, the physical universe does not have a unique reality, or there are nonlocal interactions allowed. The problem with the latter is that it would then also contradict special relativity. So, then we have to conclude that there is no unique reality.

It is this lack of a unique reality that lies at the heart of an understand of the concept of quantum entanglement. More about that later.