Editing Einstein–Podolsky–Rosen paradox (section)

== Locality ==
''[[Principle of locality|Locality]]'' has several different meanings in physics. EPR describe the principle of locality as asserting that physical processes occurring at one place should have no immediate effect on the elements of reality at another location. At first sight, this appears to be a reasonable assumption to make, as it seems to be a consequence of [[special relativity]], which states that energy can never be transmitted faster than the [[speed of light]] without violating [[Causality (physics)|causality]];<ref name=Griffiths2004/>{{rp|427–428}}<ref name=Blaylock>{{cite journal| last =Blaylock| first = Guy| title = The EPR paradox, Bell's inequality, and the question of locality| journal = American Journal of Physics| volume = 78| issue = 1| pages = 111–120| date=January 2010| arxiv = 0902.3827| bibcode = 2010AmJPh..78..111B| doi = 10.1119/1.3243279| s2cid = 118520639}}</ref> however, it turns out that the usual rules for combining quantum mechanical and classical descriptions violate EPR's principle of locality without violating special relativity or causality.<ref name=Griffiths2004/>{{rp|427–428}}<ref name=Blaylock/> Causality is preserved because there is no way for Alice to transmit messages (i.e., information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining "+" and 50% probability of obtaining "−", completely at [[randomness|random]]; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets. Furthermore, Bob is able to perform his measurement only ''once'': there is a fundamental property of quantum mechanics, the [[no-cloning theorem]], which makes it impossible for him to make an arbitrary number of copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting "+" and 50% of getting "−", regardless of whether or not his axis is aligned with Alice's.

As a summary, the results of the EPR thought experiment do not contradict the predictions of special relativity. Neither the EPR paradox nor any quantum experiment demonstrates that [[Faster-than-light communication|superluminal signaling]] is possible; however, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it. Einstein derided the quantum mechanical predictions as "[[action at a distance (physics)|spooky action at a distance]]".{{efn|"Spukhaften Fernwirkung", in the German original. Used in a letter to [[Max Born]] dated March 3, 1947.<ref>{{cite book |title=Albert Einstein Max Born, Briefwechsel 1916-1955 |publisher=Langen Müller |location=München |edition=3 |year=2005 |pages=254 |language=de}}</ref>}} The conclusion they drew was that quantum mechanics is not a complete theory.<ref name=Bell1981>{{cite journal| last =Bell| first =John| title =Bertlmann's socks and the nature of reality| journal =J. Physique Colloques| volume =C22| pages =41–62| year =1981| url =https://cds.cern.ch/record/142461?ln=en| bibcode =1988nbpw.conf..245B }}</ref>