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QUANTUM SPLITTING

byRobert Nemiroff

Michigan Technological University

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Physics X: About This Course

Officially "Extraordinary Concepts in Physics" Being taught for credit at Michigan Tech

o Light on math, heavy on conceptso Anyone anywhere is welcome

No textbook requiredo Wikipedia, web links, and lectures onlyo Find all the lectures with Google at:

"Starship Asterisk" then "Physics X"o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

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QUANTUM MECHANICS:BEAM SPLITTER

A beamsplittertakesaphotonandreflectsitoffofahalf-silveredmirror. Thebeamsplittercanbetunedsothatthereisa 50% chancethatthephotonwillgorightthroughunaffected,and 50% thatthephotonwillbereflectedatarightangle. Oddly,thesetwopathscaninterfere!

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BEAM SPLITTER PATH CONFUSIONSINGLE BEAM SPLITTER

Supposealightisdirectedtowardabeamsplittersothatlightcantakeeitheroftwopathsaroundarectangle. Twoimagescreensareplacedattheoppositecorneroftherectanglefromthebeamsplitter,onefacing

horizontally,onefacingvertically. Whatappearsontheimagescreens?

1. Interferencepatterns.2. Nointerferencepatterns.3. Blacklightthatonlybeseeninthedark.

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BEAM SPLITTER PATH CONFUSIONSINGLE BEAM SPLITTER

2. Nointerferencepatterns.

Thepathofeachphoton-- "whichpath"information,canbefoundfor

eachphoton justbynotingwhichdirectionitwasgoingasitlefttherectangularapparatus. Thereforenointerferencepatternswillappear.

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BEAM SPLITTER PATH CONFUSIONTWO BEAM SPLITTERS

Onceagain,supposethatalightisdirectedtowardabeamsplittersothatlightcantakeeitheroftwopathsaroundarectangle. A secondbeamsplitterisnowplacedatthe oppositecorneroftherectanglefrom

thebeamsplitter,allowinghalfthelighttoproceedhorizontally,halfvertically. Thetwoimagescreensstillremain.

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BEAM SPLITTER PATH CONFUSIONTWO BEAM SPLITTERS

Whatappearsontheimagescreens?

1. Interferencepatterns.

2. Nointerferencepatterns.3. Onescreenshowsabrightspot,theother-- nothing.4. Thephotonsgetconfusedandaskdirections.

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BEAM SPLITTER PATH CONFUSIONTWO BEAM SPLITTERS

1. Interferencepatterns &3. Onescreenshowsabrightspot,theother-- nothing.

Thesecondbeamsplittermakesitsothat"which-path"informationis

erased. Eachphotonthatstrikeseitherimagescreencouldhavearrivedtheretakingeitherpath. Therefore,thepathsinterfere. Itcouldbeconsideredthateachphotontook"bothpaths"simultaneously,andinterferencepatternsremain. Strangelyenough,onepathcanshowtotalconstructiveinterferenceandhenceabrightspot,whiletheotherpathtotaldestructiveinterference,andhencenothing.

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QUANTUM MECHANICS:MACH-ZEHNDER INTERFEROMETER

Thesetupcanbeusedtoprobeasampleplacedinalightpath.

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QUANTUM MECHANICS:MACH-ZEHNDER INTERFEROMETER

Withnosample,onlydetector1detectslight.o Detector1seesonlyconstructiveinterference.o Detector2seeonlydestructiveinterference.

Withasample,eachdetectorhasa 50% chanceofdetectingthephoton.o Thesampleaffectsthephoton-- allows"which-path"informationo Assumessampleisotherwisetransparent.o Example:horizontalpolarizer.

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

A bombisplacedina Mach-Zehnder Interferometer. Thebombisdesignedtobelightsensitive-- ifilluminateditwillexplode. Thebombmightbeadud,though,andifsowill justletthelightpass. A photonis

releasedby A.

Whathappensifthebombisadud?

1. Lighttakesbothpaths,interferes,andadetectorlightsup.2. Lighttakesthetoppathanddetector D lightsup.3. Lighttakesthebottompathanddetector C lightsup.4. MachandZehnderarearrestedforillicitactivities.

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

1. Lighttakesbothpaths,interferes,andadetectorlightsup.

Sincethebombisadud,itdoesnotaffectthelight (apreconditionoftheexperiment) andtheinterferometeractsasifthereisnoobstruction

atall. Therefore,photonstakeboththetopandbottompaths,evenifsomebodyisstandinginsidetheinterferometer, and C orD detectsthephoton.

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

A bombisplacedina Mach-Zehnder Interferometer. Thebombissupposedtobelightsensitive-- ifilluminateditwillexplode. Thebombmightbeadud,though,andifsowill justletthelightpass. A photonis

releasedby A.

Whathappensifthebombisrealandprimed?

1. Lighttakesbothpaths,interferes,andadetectorlightsup.2. Lighttakesthebottompathandthebombexplodes.3. Lighttakesthetoppath,detector D lightsup,andthebombdoesnotexplode.4. Hilarityensueswhenthebutlerthrowsthewholethinginthetrash.

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

2. Lighttakesthebottompathandthebombexplodes. OR3. Lighttakesthetoppath,detector D lightsup,andthebombdoesnotexplode.

Sohalfthetimethebombexplodes,buthalfthetimeitdoesnot. Therefore,ifdetector C lightsup,thebombisadud. Ifdetector Dlightsup,eitherthebombisadudorthebombislive. SoifD lightsup,youonlyknowwith 50% certaintythatthebombisalive. Still,thatisbetterthandetonatingit!

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QUANTUM MECHANICS:ELITZUR-VAIDMAN BOMB-TESTER

Thereisnoclassicalwayoftestingthebombwithoutexplodingit.

This 50/50 quantumwayisthereforeaclearimprovement.

Thisisanotherexampleofcounterfactualdefiniteness -- determiningsomethingdefinitewith QM byactuallymeasuringit.