362 CHAPTER23. THEPROBLEMOFMEASUREMENT
THISISAPURESTATE,NOTAMIXTURE!Amixture,fortheparticle-detector
systemwouldbe
M=
{
eitherinstate |up>|red>, withprobability |A|^2
orelseinstate |down>|green>, withprobability |B|^2(23.26)
Wehaveseenthatpurestatescanalwaysbedistinguished,inprinciple,frommix-
tures.Thenweareforcedtoconclude,afterthemeasurementprocesshassupposedly
takenplace,thatthelightonthedetector isneitherflashingred,norgreen, butis
somehowinasuperpositionofthetwopossiblestates!
Whenweaddahumanobservertothesystem,thequantum-mechanicalassault
oncommon-senseonlygetsworse. Denotetheinitialstateoftheobserverbytheket
”|waiting>.”Whentheobserversees aredlightflash,herstatechangestoanew
state,denoted|Isawred>;likewise,ifthegreenlightflashes,theobserverisleft
inthestate|I sawgreen>. TheHamiltoniandescribingthe interactionbetween
particle,detector,andobserverisassumedtoleadto
|up>|ready>|waiting>−→|up>|red>|Isawred> (23.27)Similarly,iftheparticlestartsinaspin-downstate,
|down>|ready>|waiting>−→|down>|green>|Isawgreen> (23.28)Then,iftheinsteadtheparticlestartsoffinthesuperpositionofspinstates|ψ>of
eq. (23.23),sotheinitialstateofthecombinedsystemis
|Ψ 0 > = |ψ>|ready>|waiting>
= A|up>|ready>|waiting>+B|down>|ready>|waiting>(23.29)Then,bythelinearityoftheSchrodingerequation,weareforcedtoconcludethat
theparticle-detector-observersystemendsupintheentangledfinalstate
|Ψf>=A|up>|red>|Isawred>+B|down>|green>|Isawgreen> (23.30)Theobserverhasalsoendedupinaquantumsuperposition,inwhichsheisneitherin
the|Isawred>state,norinthe|Isawdown>state.Andthisstrangeconclusion
isdeduced simply fromthe assumptionthat aparticle inaspinup (down) state
alwaysleadstheobservertoan”Isawred(green)”state,andfromthelinearityof
theSchrodingerequation.
Itstimetostandbackandreconsider.Asimplelineofreasoning,foundedonthe
well-establishedprinciplesofquantummechanics,hasledustoanonsensicalresult.
Itisnotjustthattheconclusioniscounter-intuitive;bynowyoushouldbeusedto
that. Rather, theproblemisthat theapparentconclusion isjustwrong: Human
beingsneverfindthemselvesinsuperpositionsofthiskind. Theremust,somewhere,
beanerrorinourreasoning. Butwhere?