In fact, though, it's a perfectly sensible operation in quantum physics terms, because it's what happens in an interferometer:

Now, that probably still seems pretty weird, starting with this split-and-then-dump-out business, which seems like a completely bizarre thing to do.

Mathematically, it's impossible for particles 1, 2, and 3 to end up together if particles 1 and 2 were in the same box, or if particles 2 and 3 were in the same box, or if particles 1 and 3 were in the same box. In particular, if all three particles end up in one of the eight boxes, that state is incompatible with any two of the particles having been in the same box after the initial split. And for any particular arrangement of three particles in eight boxes, you can show that there's a counterintuitive result regarding the intermediate state. The real idea is both more and less weird.Ī better particles-in-boxes description of the idea is that three quantum particles are split between two boxes, then the contents of the two boxes are dumped out together over a different set of eight boxes. But that's not a completely accurate description of what the paper describes. Most of the descriptions of this paper say things like 'the authors show that you can put three quantum particles into two boxes in such a way that no two particles are in the same box,' which, again, makes my brain hurt. It did, however, get me to finally look into this closely enough to see what it's about. The current burst of interest (which caught my eye on social media yesterday) is just related to the final print publication. And there have been some response papers, one of which got its own Physics World story. The authors claim to have found a situation where quantum-mechanical particles violate the common-sense pigeonhole principle, and that's a pretty brain-twisting thing to contemplate.įirst of all, this isn't actually all that new- a preprint version was posted in mid-2014, and was reported in Physics World at that time. This has been reported in stories with headlines like Can three pigeons be in two pigeonholes with no two pigeons in the same hole?, which pretty effectively captures the 'Wait. Then there are five computers that are used by a total of 20 or more students and there are five computers used by a total of at most 15 students.And yet, there's been a flurry of interest in a just-published paper in the Proceedings of the National Academy of Sciences that seems to violate this. There are 42 students who are to share 12 computers. However, GPP can be used to prove the following statement: If we removed the condition that no computer is used by more than six students, then the conclusion is not necessarily true anymore. Then at least five computers are used by three or more students. Each student uses exactly one computer and no computer is used by more than six students. In Dijkstra's article referenced above, the following statement can be proved using EPP: The GPP allows us to show that out of 367 people not born on a leapday, one can find 2 dates and 4 people whose birthday falls on one of these 2 dates. (GPPb) If nk+ s or fewer objects are placed in n boxes, then for each 0 ≤ m ≤ n there exist m boxes with a total of at most mk + max (0,s+m-n) objects

Pigeonhole principle