Editing Copenhagen interpretation (section)

==Background==
{{main|Old quantum theory}}
Starting in 1900, investigations into atomic and subatomic phenomena forced a revision to the basic concepts of [[classical physics]]. However, it was not until a quarter-century had elapsed that the revision reached the status of a coherent theory. During the intervening period, now known as the time of the "[[old quantum theory]]", physicists worked with approximations and heuristic corrections to classical physics. Notable results from this period include [[Max Planck]]'s calculation of the [[blackbody radiation]] spectrum, [[Albert Einstein]]'s explanation of the [[photoelectric effect]], Einstein and [[Peter Debye]]'s work on the [[specific heat]] of solids, [[Niels Bohr]] and [[Hendrika Johanna van Leeuwen]]'s [[Bohr–van Leeuwen theorem|proof]] that classical physics cannot account for [[diamagnetism]], Bohr's model of the [[hydrogen atom]] and [[Arnold Sommerfeld]]'s extension of the [[Bohr model]] to include [[special relativity|relativistic effects]]. From 1922 through 1925, this method of heuristic corrections encountered increasing difficulties; for example, the Bohr–Sommerfeld model could not be extended from hydrogen to the next simplest case, the [[helium atom]].<ref name="chevalley1999">{{cite book|first=Catherine |last=Chevalley |chapter=Why Do We Find Bohr Obscure? |title=Epistemological and Experimental Perspectives on Quantum Physics |editor-first1=Daniel |editor-last1=Greenberger |editor-first2=Wolfgang L. |editor-last2=Reiter |editor-first3=Anton |editor-last3=Zeilinger |editor-link3=Anton Zeilinger |publisher=Springer Science+Business Media |doi=10.1007/978-94-017-1454-9 |isbn=978-9-04815-354-1 |year=1999 |pages=59–74}}</ref>

The transition from the old quantum theory to full-fledged quantum physics began in 1925, when [[Werner Heisenberg]] presented a [[Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen|treatment of electron behavior]] based on discussing only "observable" quantities, meaning to Heisenberg the frequencies of light that atoms absorbed and emitted.<ref name="sources-intro">{{cite encyclopedia |first=B. L. |last=van der Waerden |author-link=Bartel Leendert van der Waerden |title=Introduction, Part II |encyclopedia=Sources of Quantum Mechanics |publisher=Dover |year=1968 |isbn=0-486-61881-1}}</ref> [[Max Born]] then realized that in Heisenberg's theory, the classical variables of position and momentum would instead be represented by [[matrix (mathematics)|matrices]], mathematical objects that can be multiplied together like numbers with the crucial difference that the order of multiplication matters. [[Erwin Schrödinger]] presented an equation that treated the electron as a wave, and Born discovered that the way to successfully interpret the [[wave function]] that appeared in the [[Schrödinger equation]] was as a tool for calculating [[probability|probabilities]].<ref>{{cite journal |last=Bernstein |first=Jeremy |author-link=Jeremy Bernstein |title=Max Born and the Quantum Theory|journal=[[American Journal of Physics]] |volume=73 |issue=11 |pages=999–1008 |year=2005|bibcode = 2005AmJPh..73..999B |doi = 10.1119/1.2060717 |doi-access=free }}</ref>

Quantum mechanics cannot easily be reconciled with everyday language and observation, and has often seemed counter-intuitive to physicists, including its inventors.{{refn|group=note|As Heisenberg wrote in ''Physics and Philosophy'' (1958): "I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?"}} The ideas grouped together as the Copenhagen interpretation suggest a way to think about how the mathematics of quantum theory relates to physical reality.