Editing Paul Dirac (section)

===Quantum theory===
Dirac's first step into a new quantum theory was taken late in September 1925. [[Ralph Fowler]], his research supervisor, had received a proof copy of an [[Über quantentheoretischer Umdeutung|exploratory paper]] by [[Werner Heisenberg]] in the framework of the old quantum theory of Bohr and [[Arnold Sommerfeld|Sommerfeld]]. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the [[matrix mechanics|matrix formulation]] of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.<ref name="Farmelo 2009 83–88">{{harvnb|Farmelo|2009|pp=83–88}}</ref>

Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had established. Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the [[Poisson bracket]]s that occur in the [[classical mechanics|classical dynamics]] of particle motion.<ref name="Farmelo 2009 83–88"/> At the time, his memory of Poisson brackets was rather vague, but he found [[E. T. Whittaker]]'s ''[[Analytical Dynamics of Particles and Rigid Bodies]]'' illuminating.<ref name="Coutinho12">{{Cite journal|last=Coutinho|first=S. C.|date=1 May 2014|title=Whittaker's analytical dynamics: a biography|url=https://doi.org/10.1007/s00407-013-0133-1|journal=Archive for History of Exact Sciences|language=en|volume=68|issue=3|pages=355–407|doi=10.1007/s00407-013-0133-1|issn=1432-0657|s2cid=122266762}}</ref> From his new understanding, he developed a quantum theory based on [[Commutative property|non-commuting]] dynamical variables. This led him to the most profound and significant general formulation of quantum mechanics to date.<ref>{{cite news|title=Paul Dirac: a genius in the history of physics|url=http://cerncourier.com/cws/article/cern/28693|work=Cern Courier|access-date=13 May 2013|date=15 August 2002}}</ref> His novel formulation using [[Dirac bracket]]s allowed him to obtain the [[quantization (physics)|quantisation]] rules in a [[Canonical quantization|novel and more illuminating manner]]. For this work,<ref name="Dirac1926">{{cite journal| title=On the Theory of Quantum Mechanics| journal=Proceedings of the Royal Society A| year=1926| first=Paul A. M.| last=Dirac| author-link=Paul Dirac| volume=112| issue=762| pages=661–77| jstor=94692| doi=10.1098/rspa.1926.0133 |bibcode = 1926RSPSA.112..661D | doi-access=free}}</ref> published in 1926, Dirac received a PhD from Cambridge.