One of the deepest results in all of quantum mechanics is Bell’s inequality. While it is remarkably profound, it is also an irksome, ever-present, unswattable fly. Nature’s violation of this inequality implies that nature is intrinsically non-local. Until the day Bell published his theorem, it was thought that everything in nature could be understood under the locality assumption.
While I continue with my research life day-to-day without thinking too much about it, every once in a while that pesky fly reappears, seemingly out of thin air. In this particular instance, it emerged while I was re-reading the excellent piece by N. David Mermin in Physics Today entitled Is the moon there when nobody looks? (pdf!) Alright, so not exactly thin air, perhaps this was self-inflicted.
Regardless, this article by Mermin is particularly pedagogical and explains Bell’s theorem in the simplest manner that I have found. It describes how in a sea of seemingly random data, there are correlations that cannot be explained without considering the existence of an entangled state. Any “local hidden variable” theories cannot explain the data.
What is so bothersome about Bell’s theorem
At some point in the article, Mermin challenges the reader to try to come up with scheme to explain all the observed results using a purely local and deterministic picture. This appears, at first sight, not to be an impossibly difficult task. However (at least for me), one’s schemes are quickly exhausted (very frustratingly!), and one has to face the reality that this may not be possible. In fact, Bell unequivocally showed that this was not possible.
However, there seems to me to be a (rather pathological) way out of Bell’s constraints. It is possible that embedded in Bell’s theorem is an assumption that perhaps we unaware that we are making. This would be analogous to the implicit assumption in Newton’s formulation of gravity of the infinite speed of light — an assumption that when just looking at Newton’s equations, we would not know that we were making. If we are making such an assumption in the Bell experiments, it may be possible to salvage locality in some extremely contrived manner. While this situation seems unlikely even to me, I sincerely hope that there is such an assumption lurking somewhere rather than face up to the more probable idea that nature is intrinsically non-local.
One of the most unfortunate historical circumstances surrounding the publication of Bell’s inequality was that Einstein was not alive to see its formulation. One wonders what his reaction would have been and whether he would have taken The Unswattable to his grave.