3.3. DOELECTRONSTRAVELALONGTRAJECTORIES? 43
Brogliewavewhichhadexpandedtoseveralcentimetersacrosswasintenseenough
totriggerevenasinglegeigercounter,thenifasetofgeigercounterswerearranged
inaclosearray,theywouldallbetriggeredsimultaneously. Likewise,awaveofsuch
dimensionsshouldleaveadiffuseglowonaphotographicplate,orathickcylindrical
trackthroughacloudchamber. Noneofthisiseverobserved. Nomatterhowbig
thedeBrogliewaveofasingleelectronbecomes(asbigasabaseball, asbigasa
house...),onlyasingle”click”ofageigercounterisheard,onlyasharp”dot”ona
photographicplateisrecorded.Anelectronisnot,literally,awave. Asfarascanbe
determinedfrommeasurementsofelectronposition,electronsarediscrete,point-like
objects.
Ifelectronsarepointlikeobjects,thenonecouldimagine(withthehelpofapow-
erfulmicroscope)actuallyobservingthebarrierastheelectronsreachit,todetermine
iftheygothroughslitA,orslitB,orsomehowthroughboth. Ifonewouldperform
suchanexperiment,^2 theresultisthateachelectronisindeedobservedtopasseither
throughslitAorslitB(neverboth),butthentheinterferencepatterniswipedout!
Instead,onefindstheuniformdistributionofeq. (3.35).Thusifanelectronisforced
(essentiallybyobservation)togothroughoneortheotherofthetwoslits,theinter-
ferenceeffectislost.Interferenceisregainedonlyiftheelectronisnotconstrainedto
atrajectorywhichhaspassed,withcertainty,throughoneortheotherslit.
Weareleftwiththeuncomfortableconclusionthatelectronsarepointlikeobjects
whichdonotfollowdefinitetrajectoriesthroughspace. Thissoundslikeaparadox:
howthencanelectronsgetfromonepointtoanother? Itisactuallynotaparadox,
butitdoesrequireaconsiderablereadjustmentofourconceptofthephysicalstate
ofelectrons(nottomentionatoms,molecules,andeverythingelsethatmakesupthe
physicalUniverse). Thiswillbethesubjectofthenextlecture.
(^2) Thisisusuallypresentedasa”thought”experimentinmosttextbooks,butrecentlyareal
experimentofthissorthasbeencarriedout,withtheresultsdescribedabove.