the paper doesn't prove anything we didn't already know, but rather confirms QM yet again
the Economist article is as completely awful as the average piece of quantum journalism
Wikipedia mentions Hardy but doesn't discuss his version of the paradox
there isn't a negative number of photons present, but there would be if photons had individual trajectories, which this experiment therefore proves is not the case, but we already knew that
Edited for extreme title length. Also corrected the incorrect summary of the research (e.g. article was about photons, summary stated it was about protons).
A real life paradox observed by quantum physicists: when not being observed, there can be a negative number of photons present.
The Economist summarizes the research. The scientific paper is available freely. Wikipedia discusses the paradox at length.