Chapter 23
The Problem of Measurement
Iwaspleasedtobeabletoanswerimmediately,andIdid. IsaidIdidn’tknow.
MarkTwainMorethanseventyyearshavepassedsincetheinventionofquantummechanics.
Itisalittledisquietingthatinallthattime,despiteitstriumphantapplicationto
atomic,nuclear,sub-nuclear,andcondensedmatterphysics, nogeneralagreement
hasbeenreached onwhat quantumtheoryreally means. Thiscould indicateone
oftwothings. First,itmaybethatquantumtheoryiswronginsomeunexpected
way,andthisfactwillsomedaybediscoveredbyexperiment. Theotherpossibility
isthattheproblemtobediscussedinthisLectureisnotreallyascientificquestion,
whichcan ultimatelybesettledbyeithercalculationor experiment,butismorea
philosophicalissue,inwhichargumentsfororagainstvariousviewsaredestinedto
beendlesslyrefined,butnogeneral consensuswilleverbereached. Ineithercase,
theinterpretationofquantummechanicsisadeepandfascinatingsubject. Inthis
LectureI willtrytogiveabriefoutlineof themaincontending views,althoughI
cannothope,inthisshortspace,todojusticetoanyoneofthem.
23.1 Mixtures and Pure States
Whatdoesameasurementdo?
Wehaveaskedthat questionbefore,back inLecture 7. Theansweris: Ifthe
detectorisdesignedtomeasuresomeobservableO,itwillleavethemeasuredobject,
atleastforaninstant,inazero-uncertaintystate∆O= 0 ofthatobservable,i.e.,in
aneigenstateoftheoperatorO,andrecordtheeigenvaluefound.
Suppose,onceagain,thattheobjectisanelectron,andthedetectorisaStern-
Gerlachapparatuswhichmeasurestheelectronspininthez-direction. Aredlight
goesoniftheelectronisspin-up,agreenlightgoesonifitisspindown.Theelectron