Chapter 22
The EPR Paradox and Bell’s
Theorem
Nomanisanisland...
JohnDonneSupposewehaveabaseballinPhiladelphia,andafootballinDetroit,andwewant
tospecifythephysicalstateof thecombinedbaseball-footballsystem. Inclassical
physics,thisisdonebyfirstspecifyingthestateofthebaseball(itsmass,composition,
location,velocity...),andthenspecifying,inasimilarway,thestateofthefootball.
Therearenobaseball+footballstatesthatcan’tbedescribedinthisway.Ifwedecide
tochangethephysicalstateofthefootball(bygivingitakick,say)thenofcourse
thiswillnotverymuchaffectthestateofthefarawaybaseball.
Thepointhereisthatthephysicalstatesofcompositesystemsinclassicalphysics
areseparable,inthesensethatthedescriptionofthestateofthewholesystemcan
alwaysbereduced toaspecificationofthe stateoftheparts. Suppose,insteadof
sportsequipment,weconsiderthestateofasystemoftwoequalmassparticles,which
isrepresented byapointin12-dimensionalphasespace{%x 1 ,%x 2 ,%p 1 ,%p 2 }. Obviously,
thisstatecompletelydetermines,andisdeterminedby,thephysicalstate{%x 1 ,%p 1 }of
particle1,andthephysicalstate{%x 2 ,%p 2 }ofparticle2. Moreover,ifparticle 1 isnot
ininteractionwithparticle 2,thenmeasurementofitslocationand/ormomentum
willnotinanywayaffectthepositionormomentumofparticle2.
Physicalstatesofcompositesystems,whichhavethesame”commonsense”prop-
erty of separability, certainly existinquantummechanics. For example, suppose
particle 1 isinstateψAandparticle 2 isinstateψB.Thenthestateofthecombined
1 − 2 systemisdeterminedtobe
ψ(x 1 ,x 2 )=ψA(x 1 )ψB(x 2 ) (22.1)Likewise, ifparticle 1 isinstateψC, andparticle 2 isinstateψD, the combined