Editing Pigeonhole principle (section)

==Quantum mechanics==
[[Yakir Aharonov]] et al. presented arguments that [[quantum mechanics]] may violate the pigeonhole principle, and proposed [[Interferometry|interferometric]] experiments to test the pigeonhole principle in quantum mechanics.<ref>{{Cite journal | doi=10.1073/pnas.1522411112| pmid=26729862| pmc=4725468|title = Quantum violation of the pigeonhole principle and the nature of quantum correlations| journal=Proceedings of the National Academy of Sciences| volume=113| issue=3| pages=532–535|year = 2016|last1 = Aharonov|first1 = Yakir| last2=Colombo| first2=Fabrizio| last3=Popescu| first3=Sandu| last4=Sabadini| first4=Irene|author4-link=Irene Sabadini| last5=Struppa| first5=Daniele C.| last6=Tollaksen| first6=Jeff| bibcode=2016PNAS..113..532A| doi-access=free}}</ref> 

Later research has called this conclusion into question.<ref>{{Cite web | url=https://physicsworld.com/a/quantum-pigeonholes-are-not-paradoxical-after-all-say-physicists/ |title = Quantum pigeonholes are not paradoxical after all, say physicists|date = 8 January 2015}}</ref><ref name="Rae Forgan 2014">{{cite arXiv | last1=Rae | first1=Alastair | last2=Forgan | first2=Ted | title=On the implications of the Quantum-Pigeonhole Effect | date=2014-12-03 | class=quant-ph | eprint=1412.1333 }}</ref> In a January 2015 [[arXiv]] preprint, researchers Alastair Rae and Ted Forgan at the University of Birmingham performed a theoretical [[wave function]] analysis, employing the standard pigeonhole principle, on the flight of electrons at various energies through an [[interferometer]]. If the electrons had no interaction strength at all, they would each produce a single, perfectly circular peak. At high interaction strength, each electron produces four distinct peaks, for a total of 12 peaks on the detector; these peaks are the result of the four possible interactions each electron could experience (alone, together with the first other particle only, together with the second other particle only, or all three together). If the interaction strength was fairly low, as would be the case in many real experiments, the deviation from a zero-interaction pattern would be nearly indiscernible, much smaller than the [[lattice spacing]] of atoms in solids, such as the detectors used for observing these patterns. This would make it very difficult or impossible to distinguish a weak-but-nonzero interaction strength from no interaction whatsoever, and thus give an illusion of three electrons that did not interact despite all three passing through two paths.{{Citation needed|date=February 2025}}