22.4. FORWHOMTHEBELL(’STHEOREM)TOLLS 355
wehavejustseenthattheobserveratdetector 2 cannever,bysimplyobservingone
oftheparticles,concludeanythingaboutthesettingsofdetector1. Non-localityis
notaviolationofrelativityinthesenseofinformationtransfer.
Atthispoint,itisworthnotingisthatnon-localityisnotreallyuniquetoentan-
gledstates; somekindofnon-localeffectoccursinalmostanymeasurement. Con-
sider,forexampleasingleparticle,whosewavepacketψ(x)isdistributeduniformly
inalarge,darkroom,filledwithparticledetectors. Atagiventimet= 0 thedetec-
torsaresuddenlyallswitchedonand,justassuddenly,thepositionoftheparticle
ismeasured. Thismeansthatthewavepacketoftheparticle,whichwasspreadall
overtheroomatt<0,suddenlycollapsestoanarrowgaussianintheregionofone
ofthedetectorsatt=0.Thisisknownasthe”collapseofthewavefunction”,andit
alsoseemstobeaformofnon-localbehavior.Ifwethinkoftheparticlewavepacket
assomesortoffluid,bywhatmechanismdoesitinstantaneouslycollapse?
Now,involume 1 ofthesenotesIhaveurgedyoutoavoidthinkingofthewavefunc-
tionasrepresentingsomesortofmaterialfluid. Therearejusttoomanydifficulties
inherentinthatkindofpicture. Rather,oneshouldthinkofHilbertSpace, rather
thanordinaryspace,asbeingthearenaofdynamics,wherethestate(vector)ofa
systemevolvescontinuously,accordingtotheSchrodingerequation,byrotation.This
changeofarenaalleviatesalotoftheproblemsassociatedwithnon-locality. Onthe
otherhand,Ialsosaidthatameasurementcausesthestateto”jump,”probabilisti-
cally,intooneofanumberofeigenstatesofthequantitybeingmeasured.
Itstimetofaceuptotherealproblem,thehardproblem:Bywhatprocessdoes
ameasurementcauseastatetosuddenlyjumptooneofasetofstates? Canthis
behavioritselfbeexplainedquantummechanically? Thisverypuzzlingissuehasnot
beensettledtothisday.ItisknownastheProblemofMeasurement.