Nature is able to produce correlations that can’t be described by any theory using only local variables. Since the early intuitions of EPR and Schrödinger in 1935, and the first quantitative predictions by John Bell in 1964 followed by their experimental confirmation by Clauser, Aspect and co-workers in the1970’s and 1980’s, this absolutely astonishing fact has become routine in many labs around the world. Moreover, during the last 20 years it has been discovered that this sort of nonlocality is a useful cryptographic resource that has also been mastered outside the lab, over standard optical fiber telecom networks. Hence, one could think that quantum nonlocality has become banal.

But a clear understanding of how these nonlocal correlations happen remains a huge open problem. There is of course no question of a mechanical explanation of the type: one localized physical system “pushes” (interacts with) its direct neighbours, as we have in classical (Newtonian mechanics and general relatively). The impossibility of such a mechanical explanation is precisely the message of Bell’s inequalities.

But then: How come the correlations? How does Nature manage to produce random events that somehow manifest themselves at several locations? In brief: How does Nature perform the trick?

More or less everyone who tries to go beyond Hilbert space calculus uses pictures like: a first event influences a second one (e.g. Einstein’s famous spooky action at a distance). We present experiments that cast serious doubts on the viability of such pictures. Moreover, taking such pictures seriously raises deep concerns about the alleged “peaceful co-existence of quantum nonlocality and relativity”.

What are the alternatives to the picture sketches above? Some vague paths will be presented. I am afraid I have nothing better to offer. Importantly, if someone tells you he has a straightforward solution, beware! The problem is a serious one, central to today’s physics.