JournalofModernPhysics,2019,10,1247-1254
https://www.scirp.org/journal/jmp
ISSNOnline:2153-120X
ISSNPrint:2153-1196
DisentanglementofaSingletSpinStateina
CoincidenceStern-GerlachDevice
Per-OlofWestlund
1
,H˚akanWennerstrˆom
2
1
DepartmentofChemistry,TheoreticalChemistry,Ume˚aUniversity,Ume˚a,Sweden
2
DepartmentofPhysicalChemistry,LundUniversity,Lund,Sweden
Howtocitethispaper:Westlund,P.-O.
andWennerstrˆom,H.(2019)Disentanglement
of a SingletSpin State ina Coincidence Stern-
GerlachDevice.JournalofModernPhysics,
10,1247-1254.
https://doi.org/10.4236/jmp.2019.1010083
Received:May8,2019
Accepted:September20,2019
Published:September23,2019
Copyright
c
2019byauthor(s)andScientific
Research PublishingInc.
This work is licensed under the Creative Com-
monsAttributionInternationalLicense(CC
BY4.0).
http://creativecommons.org/licenses/by/4.0/
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sectetuernec,malesuadanec,elit.Aliquam
ornaretelluseuurna.Sednecmetus.Cum
sociisnatoquepenatibusetmagnisdispar-
turientmontes,nasceturridiculusmus.Pel-
lentesquehabitantmorbitristiquesenectuset
netusetmalesuadafamesacturpisegestas.
Phasellusidmagna.Duismalesuadainter-
dumarcu.Integer metus.Morbipulvinarpel-
lentesquemi.Suspendissesedesteumagna
molestieegestas.Quisquemilorem,pulvinar
eget,egestasquis,luctusat,ante.Proinauc-
torvehiculapurus.Fusceacnislaliquamante
hendreritpellentesque.Classaptenttacitiso-
ciosquadlitoratorquentperconubianostra,
perinceptoshymenaeos.Morbiwisi.Etiam
arcumauris,facilisissed,eleifendnon,non-
ummyut,pede.Crasutlacustempormetus
mollisplacerat.Vivamuseutortorvelmetus
interdum malesuada.
Sedeleifend,erossitametfaucibuselemen-
tum,urnasapienconsectetuermauris,quis
egestasleojustononrisus.Morbinonfelisac
liberovulputatefringilla.Maurisliberoeros,
lacinianon,sodalesquis,dapibusporttitor,
pede.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Morbi dapibus mauris condimentum
nulla.Cum sociisnatoque penatibusetmagnis
disparturient montes,nasceturridiculusmus.
Etiamsitameterat.Nullavarius.Etiamt-
inciduntduivitaeturpis.Donecleo.Morbi
vulputateconvallisest.Integeraliquet.Pel-
lentesque aliquetsodalesurna.
Nullameleifendjustoinnisl.Inhachabitasse
plateadictumst.Morbinonummy.Aliquam
utfelis.Invelitleo,dictumvitae,posuereid,
vulputatenec,ante.Maecenasvitaepedenec
dui dignissim suscipit.Morbi magna.Vestibu-
lumidpurusegetvelitlaoreetlaoreet.Prae-
sentsedleovelnibhconvallisblandit.Ut
rutrum.Donecnibh.Donecinterdum.Fusce
sed pede sit amet elitrhoncus ultrices.Nullam
atenimvitaepedevehiculaiaculis.
Classaptenttacitisociosquadlitoratorquen-
tperconubianostra,perinceptoshymenaeos.
Aeneannonummyturpisidodio.Integereu-
ismodimperdietturpis.Utnecleonecdi-
amimperdietlacinia.Etiamegetlacuseget
miultriciesposuere.Inplacerattristiquetor-
tor.Sedportavestibulummetus.Nullaia-
culissollicitudinpede.Fusceluctustellusin
dolor.Curabiturauctorvelitasem.Mor-
bisapien.Classaptenttacitisociosquadl-
itoratorquentperconubianostra,perincep-
toshymenaeos.Donecadipiscingurnavehic-
ulanunc.Sedornareleoinleo.Inrhoncus
leoutdui.Aeneandolorquam,volutpatnec,
fringillaid,consectetuervel,pede.
Nullamalesuadarisusuturna.Aenean
pretiumvelitsitametmetus.Duisiaculis.In
hachabitasseplateadictumst.Nullammo-
lestieturpisegetnisl.Duisamassaidpede
dapibusultricies.Sedeuleo.Inatmaurissit
amettortorbibendumvarius.Phasellusjusto
risus,posuerein,sagittisac,variusvel,tor-
tor.Quisqueidenim.Phasellusconsequat,
liberopretium nonummy fringilla,tortor lacus
vestibulumnunc,utrhoncusligulanequeid
justo.Nullamaccumsaneuismodnunc.Proin
vitae ipsumac metusdictum tempus.Nam ut
wisi.Quisque tortor felis, interdum ac, sodales
a,sempera,sem.Curabiturinvelitsitamet
duitristiquesodales.Vivamusmaurispede,
laciniaeget,pellentesquequis,scelerisqueeu,
est.Aliquamrisus.Quisquebibendumpede
eudolor.
Donec tempusneque vitaeest.Aenean egestas
odio sed risus ullamcorper ullamcorper.Sed in
nullaatortortinciduntegestas.Namsapien
tortor,elementumsitamet,aliquamin,port-
titorfaucibus,enim.Nullamconguesuscipit
nibh.Quisqueconvallis.Praesentarcunibh,
vehicula eget,accumsaneu,tincidunta,nibh.
Suspendissevulputate,tortorquisadipiscing
viverra, lacus nibh dignissim tellus, eu suscipit
risusantefringilladiam.Quisquealiberov-
elpedeimperdietaliquet.Pellentesquenunc
nibh,eleifenda,consequatconsequat,hen-
dreritnec,diam.Sedurna.Maecenaslaoreet
eleifendneque.Vivamuspurusodio,eleifend
non,iaculisa,ultricessitamet,urna.Mau-
risfaucibusodiovitaerisus.Innisl.Praesent
purus.Integeriaculis,semeuegestaslacinia,
lacuspedescelerisqueaugue,inullamcorper
dolorerosaclacus.Nuncinlibero.
Fuscesuscipitcursussem.Vivamusrisusmi,
egestasac,imperdietvarius,faucibusquis,
leo.Aeneantincidunt.Donecsuscipit.Cras
idjustoquisnibhscelerisquedignissim.Ali-
quamsagittiselementumdolor.Aeneancon-
sectetuerjustoinpede.Curabiturullamcorper
ligula nec orci.Aliquam purus turpis, aliquam
id, ornarevitae, porttitornon, wisi.Maecenas
luctusportalorem.Donecvitaeligulaeu ante
pretiumvarius.Prointortormetus,convallis
et,hendreritnon,scelerisquein,urna.Cras
quisliberoeuligulabibendumtempor.Viva-
mustellusquam,malesuadaeu,tempussed,
temporsed,velit.Doneclaciniaauctorlibero.
Praesentsednequeidpedemollisrutrum.
Vestibulumiaculisrisus.Pellentesquelacus.
Ut quisnunc sedodio malesuada egestas.Duis
amagnasitametligulatristiquepretium.Ut
pharetra.Vestibulumimperdietmagnanec
wisi.Maurisconvallis.Sedaccumsansollic-
itudinmassa.Sedidenim.Nuncpedeenim,
laciniaut,pulvinarquis,suscipitsemper,elit.
Crasaccumsaneratvitaeenim.Crassollici-
tudin.Vestibulumrutrumblanditmassa.
Sedgravidalectusutpurus.Morbilaoreet
magna.Pellentesque eu wisi.Proin turpis.In-
tegersollicitudinauguenecdui.Fuscelectus.
Vivamusfaucibusnullaneclacus.Integerdi-
am.Pellentesquesodales,enimfeugiatcursus
volutpat,semmaurisdignissimmauris,quis
consequatsemestfermentumligula.Nullam
justo lectus, condimentum sit amet, posuere a,
fringillamollis, felis.Morbi nullanibh, pellen-
tesqueat,nonummyeu,sollicitudinnec,ip-
sum.Crasneque.Nuncaugue.Nullamvitae
quamidquampulvinar blandit.Nunc sitamet
orci.Aliquameratelit,pharetranec,aliquet
a,gravidain,mi.Quisqueurnaenim,viverra
quis,suscipitquis,tinciduntut,sapien.Cras
placeratconsequatsem.Curabituracdiam.
Curabiturdiamtortor,molliset,viverraac,
tempusvel,metus.
Curabituraclorem.Vivamusnonjustoin
duimattisposuere.Etiamaccumsanligula
idpede.Maecenastinciduntdiamnecvelit.
Praesentconvallissapienacest.Aliquamul-
lamcorpereuismodnulla.Integermollisenim
veltortor.Nullasodalesplaceratnunc.Sed
tempusrutrumwisi.Duisaccumsangravi-
dapurus.Nuncnunc.Etiamfacilisisduieu
sem.Vestibulumsemper.Praesenteueros.
Vestibulumtellusnisl,dapibusid,vestibulum
sit amet,placerat ac,mauris.Maecenas etelit
uteratplaceratdictum.Namfeugiat,turpis
etsodalesvolutpat,wisiquamrhoncusneque,
vitaealiquamipsumsapienvelenim.Maece-
nassuscipitcursusmi.
Quisque consectetuer.In suscipit mauris a do-
lor pellentesque consectetuer.Mauris convallis
nequenonerat.Inlacinia.Pellentesqueleo
eros,sagittisquis,fermentumquis,tincidun-
tut,sapien.Maecenassem.Curabitureros
odio,interdumeu,feugiateu,portaac,nis-
l.Curabiturnunc.Etiamfermentum convallis
velit.Pellentesquelaoreetlacus.Quisquesed
elit.Namquistellus.Aliquamtellusarcu,
adipiscingnon,tincidunteleifend,adipiscing
quis,augue.Vivamuselementumplaceraten-
im.Suspendisseuttortor.Integerfaucibus
adipiscingfelis.Aeneanconsectetuermattis
lectus.Morbimalesuadafaucibusdolor.Nam
lacus.Etiamarcu libero,malesuada vitae,ali-
quamvitae,blandittristique,nisl.
Maecenasaccumsandapibussapien.Duis
pretiumiaculisarcu.Curabiturutlacus.Ali-
quamvulputate.Suspendisseutpurussedsem
tempor rhoncus.Utquam dui, fringillaat, dic-
tum eget,ultricies quis,quam.Etiamsem est,
pharetra non, vulputate in, pretium at, ipsum.
Nunc semper sagittis orci.Sed scelerisquesus-
cipitdiam.Utvolutpat,doloratullamcorp-
ertristique,erospurusmollisquam,sitamet
ornareantenunc etenim.
Phasellusfringilla,metusidfeugiatcon-
sectetuer,lacuswisiultricestellus,quislobor-
tisnibhloremquistortor.Donecegestas
ornarenulla.Maurismitellus,portafau-
cibus,dictumvel,nonummyin,est.Ali-
quameratvolutpat.Intellusmagna,port-
titorlacinia,molestievitae,pellentesqueeu,
justo.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Sedorcinibh,scelerisquesitamet,
suscipitsed,placeratvel,diam.Vestibulum
nonummy vulputate orci.Donec et velit ac ar-
cuinterdumsemper.Morbipedeorci,cursus
ac,elementumnon,vehiculaut,lacus.Cras
volutpat.Namvelwisiquisliberovenenatis
placerat.Aeneansedodio.Quisqueposuere
purusacorci.Vivamusodio.Vivamusvar-
ius,nullasitametsemperviverra,odiomau-
risconsequatlacus,atvestibulumnequearcu
eutortor.Doneciaculistincidunttellus.Ali-
quameratvolutpat.Curabiturmagnalorem,
dignissimvolutpat,viverraet,adipiscingnec,
dolor.Praesentlacusmauris,dapibusvitae,
sollicitudinsitamet,nonummyeget,ligula.
Crasegestasipsumanisl.Vivamus variusdo-
lorutdolor.Fuscevelenim.Pellentesque
accumsanligulaeteros.Crasidlacusnon
tortorfacilisisfacilisis.Etiamnislelit,cur-
sussed,fringillain,conguenec,urna.Cum
sociisnatoquepenatibusetmagnisdispar-
turientmontes,nasceturridiculusmus.In-
tegeratturpis.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes,nascetur
ridiculusmus.Duisfringilla,ligulasedporta
fringilla,ligulawisicommodofelis,utadipisc-
ingfelisduiinenim.Suspendissemalesuada
ultricesante.Pellentesquescelerisqueaugue
sitameturna.Nullavolutpataliquettortor.
Crasaliquam,tellusataliquetpellentesque,
justosapiencommodoleo,idrhoncussapien
quamaterat.Nullacommodo,wisiegetsol-
licitudinpretium,orciorcialiquamorci,ut
cursusturpisjustoetlacus.Nullaveltor-
tor.Quisque eratelit, viverrasit amet, sagittis
eget,portasitamet,lacus.
In hac habitasse platea dictumst.Proin at est.
Curabitur tempusvulputate elit.Pellentesque
sem.Praesent eusapien.Duis elitmagna,ali-
quet at,tempus sed, vehicula non, enim.Mor-
biviverraarcunecpurus.Vivamusfringilla,
enimet commodomalesuada,tortormetusel-
ementumligula,necaliquetestsapienutlec-
tus.Aliquammi.Utnecelit.Fusceeuismod
luctustellus.Curabiturscelerisque.Nullam
purus.Namultriciesaccumsan magna.Morbi
pulvinarloremsitametipsum.Donecutjus-
tovitaenibhmolliscongue.Fuscequisdiam.
Praesent tempuserosutquam.
Donecinnisl.Fuscevitaeest.Vivamusante
ante,mattislaoreet,posuereeget,conguevel,
nunc.Fuscesem.Namvelorcieuerosviver-
raluctus.Pellentesquesitametaugue.Nunc
sitametipsumetlacusvariusnonummy.In-
teger rutrum sem egetwisi.Aenean eu sapien.
Quisqueornaredignissimmi.Duisaurnavel
risus pharetraimperdiet.Suspendissepotenti.
Morbijusto.Aeneannecdolor.Inhac
habitasseplateadictumst.Proinnonummy
porttitorvelit.Sedsitametleonecmetus
rhoncusvarius.Crasante.Vestibulumcom-
modosemtinciduntmassa.Namjusto.Ae-
neanluctus,felisetcondimentumlacinia,lec-
tusenimpulvinarpurus,nonportavelitnisl
sed eros.Suspendisse consequat.Mauris a dui
et tortormattispretium.Sednullametus, vo-
lutpatid, aliquameget, ullamcorperut, ipsum.
Morbieununc.Praesentpretium.Duisali-
quampulvinarligula.Ut blanditegestasjusto.
Quisqueposueremetusviverrapede.
Vivamussodaleselementumneque.Viva-
musdignissimaccumsanneque.Sedatenim.
Vestibulumnonummyinterdumpurus.Mau-
ris ornarevelitid nibh pretiumultricies.Fusce
temporpellentesque odio.Vivamusauguepu-
rus,laoreetin,scelerisquevel,commodoid,
wisi.Duisenim.Nullainterdum,nunceusem-
pereleifend,enimdolorpretiumelit,utcom-
modoligulanislaest.Vivamusante.Nulla
leomassa,posuerenec,volutpatvitae,rhon-
cuseu,magna.
Quisquefacilisisauctorsapien.Pellentesque
gravidahendreritlectus.Maurisrutrumso-
dalessapien.Fuscehendreritsemvellorem.
Integerpellentesquemassavelaugue.Integer
elit tortor, feugiat quis, sagittis et, ornare non,
lacus.Vestibulumposuerepellentesqueeros.
Quisquevenenatisipsumdictumnulla.Ali-
quam quis quam nonmetus eleifend interdum.
Nam eget sapien ac mauris malesuadaadipisc-
ing.Etiameleifendnequesedquam.Nulla
facilisi.Proinaligula.Sedidduieunibh
egestastincidunt.Suspendissearcu.
Maecenasdui.Aliquamvolutpatauctorlorem.
Crasplaceratestvitaelectus.Curabitur
massalectus,rutrumeuismod,dignissimut,
dapibus a, odio.Ut eros erat, vulputate ut, in-
terdumnon,portaeu,erat.Crasfermentum,
felis inportacongue, velit leo facilisisodio,vi-
taeconsectetuerloremquamvitaeorci.Sed
ultrices,pedeeuplaceratauctor,anteligula
rutrum tellus,vel posuere nibh lacusnec nibh.
Maecenaslaoreetdoloratenim.Donecmo-
lestie dolornec metus.Vestibulumlibero.Sed
quiserat.Sedtristique.Duispedeleo,fer-
mentumquis,consectetuereget,vulputatesit
amet,erat.
Donecvitaevelit.Suspendisseportafermen-
tummauris.Utvelnuncnonmaurisphare-
travarius.Duisconsequatliberoquisurna.
Maecenasatante.Vivamusvarius,wisised
egestastristique,odiowisiluctusnulla,lobor-
tisdictumdolorligulainlacus.Vivamusali-
quam, urna sed interdum porttitor,metus orci
interdum odio,sitamet euismodlectus feliset
leo.Praesentacwisi.Namsuscipitvestibu-
lum sem.Praesent eu ipsumvitae pede cursus
venenatis.Duissed odio.Vestibulum eleifend.
Nullautmassa.Proinrutrummattissapien.
Curabiturdictumgravidaante.
Phasellusplaceratvulputatequam.Maece-
nasattellus.Pellentesquenequediam,dig-
nissim ac, venenatisvitae, consequat ut, lacus.
Nam nibh.Vestibulum fringilla arcu mollis ar-
cu.Sedetturpis.Donecsemtellus,volut-
pat et,variuseu, commodo sed,lectus.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Quisqueenimarcu,suscipitnec,tempus
at,imperdietvel,metus.Morbivolutpatpu-
rusaterat.Donecdignissim,semidsemper
tempus, nibh massa eleifendturpis,sed pellen-
tesquewisipurussedlibero.Nullamlobortis
tortorvelrisus.Pellentesqueconsequatnulla
eutellus.Donecvelit.Aliquamfermentum,
wisiacrhoncusiaculis,tellusnuncmalesuada
orci,quisvolutpatduimagnaidmi.Nuncvel
ante.Duisvitaelacus.Crasnecipsum.
Morbinunc.Aliquamconsectetuervariusnul-
la.Phaselluseros.Crasdapibusporttitorris-
us.Maecenasultricesmiseddiam.Praesent
gravida velit at elit vehicula porttitor.Phasel-
lusnislmi,sagittisac,pulvinarid,gravidasit
amet,erat.Vestibulumest.Loremipsumdo-
lorsit amet,consectetueradipiscingelit.Cur-
abitur idsem elementum leo rutrumhendrerit.
Utatmi.Donectinciduntfaucibusmassa.
Sed turpis quam, sollicitudin a, hendrerit eget,
pretiumut,nisl.Duishendreritligula.Nunc
pulvinarcongueurna.
Nuncvelit.Nullamelitsapien,eleifendeu,
commodo nec, semper sit amet, elit.Nulla lec-
tus risus,condimentum ut,laoreeteget, viver-
ra nec, odio.Proin lobortis.Curabitur dictum
arcuvelwisi.Crasidnullavenenatistortor
congueultrices.Pellentesqueegetpede.Sed
eleifendsagittiselit.Namsedtellussitamet
lectusullamcorper tristique.Maurisenim sem,
tristiqueeu,accumsanat,scelerisquevulpu-
tate, neque.Quisquelacus.Donec etipsum sit
amet elitnonummy aliquet.Sed viverranisl at
sem.Namdiam.Maurisutdolor.Curabitur
ornaretortorcursusvelit.
Morbitinciduntposuerearcu.Crasvenenatis
estvitaedolor.Vivamusscelerisquesemper
mi.Donecipsumarcu,consequatscelerisque,
viverraid,dictumat,metus.Loremipsum
dolor sit amet, consectetuer adipiscing elit.Ut
pede sem, tempus ut, porttitor bibendum, mo-
lestieeu,elit.Suspendissepotenti.Sedidlec-
tus sitamet purus faucibusvehicula.Praesen-
tsedsemnonduipharetrainterdum.Nam
viverra ultricesmagna.
Aeneanlaoreetaliquamorci.Nuncinterdum
elementumurna.Quisqueerat.Nullamtem-
porneque.Maecenasvelitnibh,scelerisquea,
consequatut,viverrain,enim.Duismagna.
Donecodioneque,tristiqueet,tincidunteu,
rhoncusac, nunc.Maurismalesuadamalesua-
da elit.Etiam lacus mauris, pretium vel, blan-
ditin, ultriciesid,libero.Phasellusbibendum
eratutdiam.Incongueimperdietlectus.
Aeneanscelerisque.Fuscepretiumporttitor
lorem.Inhachabitasseplatea dictumst.Nulla
sitametnislatsapienegestaspretium.Nunc
nontellus.Vivamusaliquet.Namadipiscing
euismoddolor.Aliquameratvolutpat.Nul-
lautipsum.Quisquetinciduntauctorau-
gue.Nuncimperdietipsumegetelit.Ali-
quamquamleo,consectetuernon,ornaresit
amet,tristiquequis, felis.Vestibulumante ip-
sumprimisinfaucibusorciluctusetultrices
posuerecubiliaCurae;Pellentesqueinterdum
quamsitametmi.Pellentesquemaurisdui,
dictuma,adipiscingac,fermentumsitamet,
lorem.
Utquiswisi.Praesentquismassa.Vivamus
egestasrisusegetlacus.Nunctincidunt,risus
quisbibendumfacilisis,lorempurusrutrum
neque,necportatortorurnaquisorci.Ae-
neanaliquet,liberosempervolutpatluctus,
pedeeratlaciniaaugue,quisrutrumsemip-
sumsitametpede.Vestibulumaliquet,nibh
sediaculissagittis,odiodolorblanditaugue,
egetmollisurnatellusidtellus.Aeneanali-
quetaliquamnunc.Nullaultriciesjustoeget
orci.Phasellustristiquefermentumleo.Sed
massametus,sagittisut,semperut,pharetra
vel,erat.Aliquamquamturpis,egestasvel,
elementumin,egestassitamet,lorem.Duis
convallis,wisisitametmollismolestie,libero
mauris portadui, vitaealiquam arcuturpis ac
sem.Aliquamaliquetdapibusmetus.
Vivamuscommodoeroseleifenddui.Vestibu-
luminleoeuerattristiquemattis.Crasat
elit.Craspellentesque.Nullamidlacussit
ametliberoaliquethendrerit.Proinplacerat,
minonelementumlaoreet,eroselittincidun-
tmagna,arhoncussemarcuidodio.Nul-
laegetleoaleoegestasfacilisis.Curabitur
quisvelit.Phasellus aliquam,tortornecornare
rhoncus,purusurnaposuerevelit,etcommo-
dorisustellusquistellus.Vivamusleoturpis,
tempussitamet,tristiquevitae,laoreetquis,
odio.Proinscelerisquebibendumipsum.Eti-
amnisl.Praesentveldolor.Pellentesquevel
magna.Curabitururna.Vivamuscongueur-
na in velit.Etiam ullamcorper elementum dui.
Praesentnon urna.Sed placeratquam non mi.
Pellentesquediammagna,ultricieseget,ultri-
cesplacerat,adipiscingrutrum,sem.
Morbisem.Nullafacilisi.Vestibulumante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Nullafacilisi.Mor-
bisagittisultriceslibero.Praesenteuligula
sedsapienauctorsagittis.Classaptenttaciti
sociosquadlitoratorquentperconubianos-
tra,perinceptoshymenaeos.Donecvelnunc.
Nuncfermentum,lacusidaliquamporta,dui
tortoreuismoderos,velmolestieipsumpurus
eulacus.Vivamuspedearcu, euismod ac,tem-
pusid,pretiumet,lacus.Curabitursodales
dapibusurna.Nunceusapien.Doneceget
nuncapededictumpretium.Proinmauris.
Vivamusluctusliberovelnibh.
Fuscetristiquerisusidwisi.Integermolestie
massaidsem.Vestibulumveldolor.Pel-
lentesquevelurnavelrisusultricieselemen-
tum.Quisquesapien urna,blandit nec,iaculis
ac,viverrain,odio.Inhachabitasseplatea
dictumst.Morbinequelacus,convallisvitae,
commodoac,fermentumeu,velit.Sedinor-
ci.Infringillaturpisnonarcu.Donec inante.
Phasellustemporfeugiatvelit.Aeneanvar-
iusmassanonturpis.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;
Aliquamtortor.Morbiipsum massa,imperdi-
etnon,consectetuervel,feugiatvel,lorem.
Quisqueeget loremnec elitmalesuadavestibu-
lum.Quisquesollicitudinipsumvelsem.Nul-
laenim.Proinnonummyfelisvitaefelis.Nul-
lampellentesque.Duisrutrumfeugiatfe-
lis.Maurisvelpedesedliberotinciduntmol-
lis.Phasellussedurnarhoncusdiameuismod
bibendum.Phasellussednisl.Integercondi-
mentumjusto id orciiaculis varius.Quisque et
lacus.Phaselluselementum, justoat dignissim
auctor,wisi odiolobortisarcu,sed sollicitudin
felisfeliseuneque.Praesentatlacus.
Vivamussitametpede.Duisinterdum,nunc
egetrutrumdignissim,nisldiamluctusleo,
ettinciduntvelitnislidtellus.Inloremtel-
lus,aliquetvitae,portain,aliquetsed,lectus.
Phasellussodales.Utvariusscelerisqueerat.
Invelnibheuerosimperdietrutrum.Donec
ac odio nec neque vulputatesuscipit.Nam nec
magna.Pellentesquehabitantmorbitristique
senectus et netus et malesuada fames acturpis
egestas.Nullamporta,odioetsagittisiaculis,
wisi neque fringilla sapien, vel commodo lorem
loremidelit.Utsemlectus,scelerisqueeget,
placeratet,tinciduntscelerisque,ligula.Pel-
lentesque nonorci.
Etiamvelipsum.Morbifacilisisvestibulum
nisl.Praesentcursuslaoreetfelis.Integer
adipiscingpretiumorci.Nullafacilisi.Quisque
posuerebibendumpurus.Nullaquammauris,
cursuseget,convallisac,molestienon,enim.
Aliquamcongue.Quisquesagittisnonummy
sapien.Proinmolestiesemvitaeurna.Mae-
cenas lorem.Vivamus viverra consequat enim.
Nuncsedpede.Praesentvitaelectus.Prae-
sentnequejusto,vehiculaeget,interdumid,
facilisiset,nibh.Phasellusatpurusetlibero
laciniadictum.Fuscealiquet.Nullaeuante
placeratleosemperdictum.Maurismetus.
Curabiturlobortis.Curabitursollicitudin hen-
dreritnunc.Donecultriceslacusidipsum.
Donecanibhutelitvestibulumtristique.In-
tegeratpede.Crasvolutpatvariusmagna.
Phaselluseuwisi.Praesentrisusjusto,lobor-
tis eget, scelerisqueac, aliquet in, dolor.Proin
idleo.Nunciaculis,mivitaeaccumsancom-
modo, nequesemlacinianulla,quisvestibulum
justosemineros.Quisquesedmassa.Morbi
lectus ipsum, vulputate a, mollis ut,accumsan
placerat,tellus.Nullaminwisi.Vivamuseu
ligulaanuncaccumsancongue.Suspendisse
aclibero.Aliquameratvolutpat.Donecau-
gue.Nuncvenenatisfringillanibh.Fusceac-
cumsan pulvinar justo.Nullam semper, duiut
dignissim auctor, orcilibero fringilla massa,b-
landitpulvinarpedetortoridmagna.Nunc
adipiscing justo sed velit tincidunt fermentum.
Integerplacerat.Pellentesquehabitantmorbi
tristique senectuset netus etmalesuada fames
acturpisegestas.Sedinmassa.Classaptent
tacitisociosquadlitoratorquentperconubi-
anostra,perinceptoshymenaeos.Phasellus
tempusaliquamrisus.Aliquamrutrumpurus
atmetus.Donecposuereodioaterat.Nam
nonnibh.Phasellusligula.Quisquevene-
natislectusinaugue.Sedvestibulumdapibus
neque.
Mauris tempus eros at nulla.Sed quisdui dig-
nissimmaurispretiumtincidunt.Maurisac
purus.Phasellusaclibero.Etiamdapibusia-
culisnunc.Inlectus wisi,elementumeu, sollic-
itudinnec,imperdietquis,dui.Nullaviverra
nequeaclibero.Maurisurnaleo,adipiscing
eu,ultricesnon,blanditeu,dui.Maecenas
duineque,suscipitsitamet,rutruma,laoreet
in,eros.Uteunibh.Fuscenecerattempus
urnafringillatempus.Curabituridenim.Sed
ante.Crassodalesenimsitametwisi.Nunc
fermentum consequatquam.
Utauctor,augueportadignissimvestibulum,
arcudiamlobortisvelit,velscelerisqueris-
usauguesagittisrisus.Maecenaseujusto.
Pellentesquehabitant morbitristique senectus
etnetusetmalesuadafamesacturpiseges-
tas.Mauriscongueligulaegettortor.Nul-
lam laoreeturnasedenim.Doneceget erosut
erosvolutpatconvallis.Praesentturpis.Inte-
germaurisdiam,elementumquis,egestasac,
rutrumvel,orci.Nullafacilisi.Quisqueadip-
iscing,nullavitaeelementumporta,semurna
volutpatleo,sedportaenimrisussedmassa.
Integeracenimquisdiamsodalesluctus.Ut
eget eros a ligula commodo ultricies.Donec eu
urnaviverradolorhendreritfeugiat.Aliquam
acorcivelerosconguepharetra.Quisque
rhoncus,justoeuvolutpatfaucibus,augueleo
posuerelacus,arhoncuspuruspedevelest.
Proinultricesenim.
Aenean tincidunt laoreet dui.Vestibulum ante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Integeripsumlec-
tus,fermentumac,malesuadain,eleifendut,
lorem.Vivamusipsumturpis,elementumvel,
hendrerit ut,semper at,metus.Vivamus sapi-
entortor,eleifendid,dapibusin,egestaset,
pede.Pellentesquefaucibus.Praesentlorem
neque, dignissim in,facilisis nec, hendrerit vel,
odio.Namatdiamacnequealiquetviver-
ra.Morbidapibusligulasagittismagna.In
lobortis.Donecaliquetultricieslibero.Nunc
dictumvulputate purus.Morbivarius.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Intempor.Phaselluscommodoporttitor
magna.Curabiturvehiculaodioveldolor.
Praesentfacilisis,augueaadipiscingvene-
natis,liberorisusmolestieodio,pulvinarcon-
sectetuerfeliseratacmauris.Namvestibu-
lumrhoncusquam.Sedveliturna,pharetra
eu,eleifendeu,viverraat,wisi.Maecenasul-
tricesnibhatturpis.Aeneanquam.Nulla
ipsum.Aliquamposuereluctuserat.Cur-
abiturmagnafelis,laciniaet,tristiqueid,ul-
tricesut,mauris.Suspendissefeugiat.Cras
eleifendwisivitaetortor.Phasellusleopurus,
mattissitamet,auctorin,rutrumin,magna.
Inhachabitasseplateadictumst.Phasellus
imperdietmetusinsem.Vestibulumacenim
nonsemultriciessagittis.Sedveldiam.
Integervelenimsedturpisadipiscingbiben-
dum.Vestibulumpededolor,laoreetnec,po-
suerein,nonummyin,sem.Donecimperdiet
sapienplaceraterat.Donecviverra.Aliquam
eros.Nunc consequat massaid leo.Sed ullam-
corper,loreminsodalesdapibus,risusmetus
sagittislorem,nonporttitorpurusodioneco-
dio.Sedtinciduntposuereelit.Quisqueeu
enim.Donecliberorisus,feugiatac,dapibus
eget, posuere a,felis.Quisque vellectusutme-
tustincidunteleifend.Duis utpede.Duis velit
erat,venenatis vitae,vulputatea,pharetra sit
amet,est.Etiamfringillafaucibusaugue.
Aeneanvelitsem,viverraeu,tempusid,
rutrumid, mi.Nullamnec nibh.Proin ullam-
corper,dolorincursustristique,erosaugue
tempornibh,atgravidadiamwisiatpurus.
Donec mattis ullamcorper tellus.Phasellus vel
nulla.Praesentinterdum,erosinsodalessol-
licitudin,nunc nulla pulvinarjusto, aeuismod
erossemnecnibh.Nullamsagittisdapibus
lectus.Nullamegetipsumeutortorlobortis
sodales.Etiampurusleo,pretiumnec,feu-
giatnon,ullamcorpervel,nibh.Sedvelelit
etquamaccumsanfacilisis.Nuncleo.Sus-
pendissefaucibuslacus.
Pellentesqueinterdumsapiensednulla.Proin
tincidunt.Aliquamvolutpatestvelmassa.
Seddolorlacus,imperdietnon,ornarenon,
commodoeu,neque.Integerpretiumsem-
perjusto.Proinrisus.Nullamidquam.
Namneque.Duisvitaewisiullamcorperdi-
amcongueultricies.Quisqueligula.Mauris
vehicula.
Curabiturnuncmagna,posuereeget,vene-
natiseu,vehiculaac,velit.Aeneanornare,
massaaaccumsanpulvinar,quamlorem
laoreetpurus, eusodalesmagna risusmolestie
lorem.Nunceratvelit,hendreritquis,male-
suadaut,aliquamvitae,wisi.Sedposuere.
Suspendisseipsumarcu,scelerisquenec,ali-
quameu,molestietincidunt,justo.Phasellus
iaculis.Sedposuereloremnonipsum.Pel-
lentesquedapibus.Suspendissequamlibero,
laoreeta,tincidunteget,consequatat,est.
Nullamutlectusnonenimconsequatfacili-
sis.Maurisleo.Quisquepedeligula,auctor
vel,pellentesquevel,posuereid,turpis.Cras
ipsumsem,cursuset,facilisisut,tempuseu-
ismod,quam.Suspendissetristiquedoloreu
orci.Maurismattis.Aeneansemper.Viva-
mustortormagna,facilisisid,variusmattis,
hendreritin,justo.Integerpurus.
Vivamusadipiscing.Curabitur imperdiet tem-
pusturpis.Vivamussapiendolor,congueve-
nenatis,euismodeget,portarhoncus,magna.
Proincondimentumpretiumenim.Fusce
fringilla,liberoetvenenatisfacilisis,erosen-
imcursusarcu,vitaefacilisisodioauguevitae
orci.Aliquamvariusnibhutodio.Sedcondi-
mentumcondimentumnunc.Pellentesque
egetmassa.Pellentesquequismauris.Donec
utligulaacpedepulvinarlobortis.Pellen-
tesqueeuismod.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentelit.Utlaoreet
ornareest.Phasellusgravidavulputatenulla.
Donecsitametarcuutsemtempormalesua-
da.Praesenthendreritaugueinurna.Proin
enimante,ornarevel,consequatut,blandit
in,justo.Donecfeliselit,dignissimsed,sagit-
tisut,ullamcorpera,nulla.Aeneanpharetra
vulputateodio.
Quisqueenim.Proinvelitneque,tristiqueeu,
eleifendeget,vestibulumnec,lacus.Vivamus
odio.Duisodiourna,vehiculain,elementum
aliquam,aliquetlaoreet,tellus.Sedvelit.Sed
velmiacelitaliquetinterdum.Etiamsapi-
enneque,convalliset,aliquetvel,auctornon,
arcu.Aliquamsuscipitaliquamlectus.Proin
tinciduntmagnasedwisi.Integerblanditla-
cusutlorem.Sedluctusjustosedenim.
Morbimalesuadahendreritdui.Nuncmauris
leo, dapibus sitamet, vestibulum et, commodo
id,est.Pellentesquepurus.Pellentesquetris-
tique,nuncacpulvinaradipiscing,justoeros
consequatlectus, sitamet posuerelectusneque
velaugue.Cras consectetuerlibero aceros.Ut
egetmassa.Fuscesitametenimeleifendsem
dictum auctor.In eget risusluctus wisi conva-
llis pulvinar.Vivamus sapien risus,temporin,
viverra in, aliquetpellentesque, eros.Aliquam
euismodliberoasem.
Nunc velit augue,scelerisquedignissim,lobor-
tiset,aliquamin,risus.Ineueros.Vestibu-
lumanteipsumprimisinfaucibusorciluctus
etultricesposuerecubiliaCurae;Curabitur
vulputateelitviverraaugue.Maurisfringilla,
tortorsitametmalesuadamollis,sapienmi
dapibusodio,acimperdietligulaenimeget
nisl.Quisquevitaepedeapedealiquetsus-
cipit.Phasellustelluspede,viverravestibu-
lum,gravidaid,laoreetin,justo.Cumsoci-
isnatoquepenatibusetmagnisdisparturient
montes,nasceturridiculusmus.Integercom-
modoluctuslectus.Maurisjusto.Duisvar-
iuseros.Sedquam.Craslacuseros,rutrum
eget,variusquis,convallisiaculis,velit.Mau-
ris imperdiet, metus at tristique venenatis, pu-
rusnequepellentesquemauris,aultriceselit
lacusnectortor.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentmalesuada.Nam
lacuslectus,auctorsitamet,malesuadavel,
elementumeget,metus.Duisnequepede,fa-
cilisiseget,egestaselementum,nonummyid,
neque.
Proinnonsem.Donecnecerat.Proinlibero.
Aliquamviverraarcu.Donecvitaepurus.
Donecfelismi,semperid,scelerisqueporta,
sollicitudinsed,turpis.Nullainurna.Integer
variuswisinonelit.Etiamnecsem.Mau-
risconsequat,risusnecconguecondimentum,
ligulaligulasuscipit urna,vitaeportaodioer-
at quissapien.Proinluctus leoiderat.Etiam
massametus,accumsanpellentesque,sagittis
sitamet,venenatisnec,mauris.Praesentur-
na eros, ornarenec, vulputate eget, cursussed,
justo.Phasellus nec lorem.Nullam ligula ligu-
la,mollissitamet,faucibusvel,eleifendac,
dui.Aliquameratvolutpat.
Fusce vehicula,tortor etgravidaporttitor, me-
tusnibhconguelorem,uttempuspurusmau-
risapede.Integertinciduntorcisitamet
turpis.Aeneanametus.Aliquamvestibulum
lobortisfelis.Donecgravida.Sedsedurna.
Maurisetorci.Integerultricesfeugiatligu-
la.Seddignissimnibhamassa.Donecorci
dui,temporsed,tinciduntnonummy,viverra
sit amet, turpis.Quisque lobortis.Proin vene-
natistortornecwisi.Vestibulumplacerat.In
hachabitasseplateadictumst.Aliquampor-
tamiquisrisus.Donecsagittisluctusdiam.
Nam ipsumelit, imperdietvitae, faucibusnec,
fringillaeget,leo.Etiamquisdolorinsapien
porttitorimperdiet.
Craspretium.Nullamalesuadaipsumut
libero.Suspendissegravidahendrerittellus.
Maecenas quislacus.Morbi fringilla.Vestibu-
lumodioturpis,temporvitae,scelerisquea,
dictumnon,massa.Praesenteratfelis,por-
tasitamet,condimentumsitamet,placer-
atet,turpis.Praesentplaceratlacusaen-
im.Vestibulumnoneros.Utcongue.Donec
tristiquevariustortor.Pellentesquehabitant
morbi tristique senectus et netus et malesuada
famesacturpisegestas.Namdictumdictum
urna.
Phasellusvestibulumorcivelmauris.Fusce
quamleo,adipiscingac,pulvinareget,mo-
lestiesitamet,erat.Seddiam.Suspendisse
erosleo,tempuseget,dapibussitamet,tem-
puseu,arcu.Vestibulumwisimetus,dapibus
vel,luctussitamet,condimentumquis,leo.
Suspendissemolestie.Duisinante.Utso-
dales sem sit amet mauris.Suspendisse ornare
pretiumorci.Fuscetristiqueenimegetmi.
Vestibulumeroselit,gravida ac,pharetrased,
lobortisin,massa.Proinatdolor.Duisac-
cumsanaccumsanpede.Nullamblanditelit
inmagnalaciniahendrerit.Utnonummyluc-
tuseros.Fusceegettortor.
Utsitametmagna.Crasaligulaeuurna
dignissimviverra.Nullamtemporleoporta
ipsum.Praesentpurus.Nullamconsequat.
Maurisdictumsagittisdui.Vestibulumsol-
licitudinconsectetuerwisi.Insitametdiam.
Nullammalesuadapharetrarisus.Proinlacus
arcu, eleifendsed, vehiculaat, conguesit amet,
sem.Sedsagittispedeanisl.Sedtincidunto-
dioapede.Seddui.Nameuenim.Aliquam
sagittislacusegetlibero.Pellentesquediam
sem,sagittismolestie,tristiqueet,fermentum
ornare,nibh.Nullaet tellusnon felis imperdi-
etmattis.Aliquameratvolutpat.
Vestibulumsodalesipsumidaugue.Integer
ipsumpede,convallissitamet,tristiquevi-
tae,temporut,nunc.Namnonligulanon
lorem convallis hendrerit.Maecenas hendrerit.
Sedmagnaodio,aliquamimperdiet,portaac,
aliqueteget,mi.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes,nascetur
ridiculusmus.Vestibulumnislsem,dignissim
vel,euismodquis,egestasut,orci.Nuncvi-
taerisusvelmetuseuismodlaoreet.Crassit
ametnequeaturpislobortisauctor.Sedali-
quamsemacelit.Crasvelitlectus,facilisis
id,dictumsed,portarutrum,nisl.Namhen-
dreritipsumsedaugue.Nullamscelerisque
hendreritwisi.Vivamusegestasarcusedpu-
rus.Utornarelectussederos.Suspendisse
potenti.Maurissollicitudinpedevelvelit.In
hachabitasseplateadictumst.
Suspendisseeratmauris,nonummyeget,
pretiumeget,consequatvel,justo.Pellen-
tesqueconsectetuereratsedlacus.Nullam
egestasnullaacdui.Doneccursusrhoncus
ipsum.Nuncetsemeumagnaegestasmale-
suada.Vivamusdictummassaatdolor.Mor-
biestnulla,faucibusac,posuerein,interdum
ut,sapien.Proinconsectetuerpretiumurna.
Donecsit ametnibhnecpurusdignissimmat-
tis.Phasellusvehiculaelitatlacus.Nullafa-
cilisi.Crasutarcu.Sedconsectetuer.Integer
tristiqueelitquisfelisconsectetuereleifend.
Crasetlectus.
Utcongue malesuadajusto.Curabiturcongue,
felisathendreritfaucibus,maurislacusport-
titor pede, nec aliquam turpis diamfeugiat ar-
cu.Nullamrhoncusipsumatrisus.Vestibu-
lumadolorseddolorfermentumvulputate.
Sednecipsumdapibusurnabibendumlobor-
tis.Vestibulum elit.Namligula arcu, volutpat
eget,laciniaeu,lobortisac,urna.Nammol-
lisultricesnulla.Crasvulputate.Suspendisse
atrisus atmetuspulvinarmalesuada.Nullam
lacus.Aliquamtempusmagna.Aliquamut
purus.Prointellus.
Vestibulumanteipsum primisinfaucibusorci
luctus et ultrices posuere cubilia Curae; Donec
scelerisquemetus.Maecenasnonmiutmetus
portahendrerit.Nuncsemper.Crasquiswisi
utloremposueretristique.Nuncvestibulum
scelerisquenulla.Suspendissepharetrasollic-
itudinante.Praesentatauguesitametante
interdum porta.Nunc bibendum augueluctus
diam.Etiam nec sem.Sed eros turpis, facilisis
nec,vehiculavitae,aliquamsed,nulla.Cur-
abiturjustoleo,vestibulumeget,tristiqueut,
tempusat,nisl.
Nullavenenatisloremidarcu.Morbicur-
susurnaaipsum.Donecporttitor.Integer
eleifend,estnonmattismalesuada,minulla
convallismi,etauctorlectussapienutpu-
rus.Aliquamnullaaugue,pharetrasitamet,
faucibussemper,molestievel,nibh.Pellen-
tesquevestibulummagnaetmi.Sedfringilla
dolorveltellus.Nuncliberonunc,venenatis
eget,convallishendrerit,iaculiselementum,
mi.Nullamaliquam,felisetaccumsanvehic-
ula,magnajustovehicula diam,eu condimen-
tumnislfelisetnunc.Quisquevolutpatmauris
avelit.Pellentesquemassa.Integeratlorem.
Nammetuserat,laciniaid,convallisut,pul-
vinarnon,wisi.Crasiaculismaurisutneque.
Crassodales,semvitaeimperdietconsequat,
pede purussollicitudin urna,ac aliquammetus
orciinleo.Utmolestieultricesmauris.Viva-
musvitaesem.Aliquameratvolutpat.Prae-
sentcommodo,nislacdapibusaliquet,tortor
orci sodales lorem, non ornare nulla lorem quis
nisl.
Sedatsemvitaepurusultricesvestibulum.
Vestibulumtinciduntlacusetligula.Pel-
lentesquevitaeelit.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;Duisornare,erateget
laoreetvulputate,lacusipsumsuscipitturpis,
etbibendumnislorcinonlectus.Vestibu-
lumnecrisusnecliberofermentumfringilla.
Morbinonvelitinmagnagravidahendrerit.
Pellentesquequislectus.Vestibulumeleifend
lobortisleo.Vestibulumnonaugue.Vivamus
dictumtempordui.Maecenasatligulaidfe-
liscongueporttitor.Nullaleomagna,egestas
quis,vulputatesitamet,viverraid,velit.
Utlectuslectus,ultriciessitamet,semper
eget,laoreetnon,ante.Proinatmassaquis
nuncrhoncusmattis.Aliquamlorem.Cur-
abiturpharetraduiatneque.Aliquameutel-
lus.Aeneantempus,felisvitaevulputateia-
culis,estdolorfaucibusurna,inviverrawisi
nequenonrisus.Fusceveldolornecsapien
pretiumnonummy.Integerfaucibusmassaac
nulla ornarevenenatis.Nullaquissapien.Sed
tortor.Phasellusegetmi.Crasnunc.Crasa
enim.
Quisque nisl.In dignissim dapibus massa.Ae-
neansemmagna,scelerisquenec,ullamcorper
quis,porttitorut,lectus.Fuscedignissimfa-
cilisistortor.Vivamusgravidafelissitamet
nunc.Nampulvinarodiovelenim.Pellen-
tesquesitametest.Vivamuspulvinarleonon
sapien.Aliquameratvolutpat.Ut elementum
auctormetus.Maurisvestibulumnequevitae
eros.Pellentesquealiquamquam.Donecve-
nenatistristiquepurus.Innisl.Nullavelit
libero,fermentumat,portaa,feugiatvitae,
urna.Etiamaliquetornareipsum.Proinnon
dolor.Aeneannuncligula,venenatissuscipit,
porttitorsit amet, mattissuscipit, magna.Vi-
vamusegestasviverraest.Morbiatrisussed
sapiensodalespretium.
Morbicongueconguemetus.Aeneansedpu-
rus.Nampedemagna,tristiquenec,porta
id,sollicitudinquis,sapien.Vestibulumblan-
dit.Suspendisse ut augue ac nibh ullamcorper
posuere.Integereuismod,nequeateleifend
fringilla,augueelitornaredolor,veltincidunt
purusest idlacus.Vivamusloremdui, commo-
doquis,scelerisqueeu,tinciduntnon,magna.
Cras sodales.Quisque vestibulum pulvinar di-
am.Phasellustincidunt, leovitaetristiquefa-
cilisis,ipsum wisiinterdum sem,dapibus sem-
pernulla velit vel lectus.Cras dapibusmauris
etaugue.Quisquecursusnullainlibero.Sus-
pendisseetloremsitametmaurismalesuada
mollis.Nullamidjusto.Maecenasvenenatis.
Doneclacusarcu,egestasac,fermentumcon-
sectetuer,tempuseu,metus.Proinsodales,
seminpretiumfermentum,arcusapiencom-
modomauris,venenatisconsequataugueur-
nainwisi.Quisquesapiennunc,variuseget,
condimentumquis,laciniain,est.Fuscefacil-
isis.Praesentnecipsum.
Suspendisseadolor.Namerateros,congue
eget,sagittisa,laciniain,pede.Maecenas
inelit.Proinmolestievariusnibh.Vivamus
tristiquepurussedaugue.Proinegestassem-
pertortor.Vestibulumanteipsumprimisin
faucibusorciluctusetultricesposuerecubil-
iaCurae;Classaptenttacitisociosquadl-
itoratorquentperconubianostra,perincep-
toshymenaeos.Vestibulumorcienim,sagittis
ornare,eleifendut,mattisat,ligula.Nulla
molestieconvallisarcu.Uterostellus,condi-
mentum at,sodalesin,ultricesvel,nulla.
Duismagnaante,bibendumeget,eleifend
eget,suscipitsed,neque.Vestibuluminmi
sedmassacursuscursus.Pellentesquepulv-
inarmollisneque.Fusceutenimvitaemauris
malesuadatincidunt.Vivamusaneque.Mau-
rispulvinar,sapienidcondimentumdictum,
quamarcurhoncusdui,idtemporlacusjusto
etjusto.Proinsitametorcieudiameleifend
blandit.Nunceratmassa,luctusac,fermen-
tumlacinia,tinciduntultrices,sapien.Prae-
sentsed orci vitae dolorsollicitudin adipiscing.
Crasaneque.Utrisus dui,interdumat,plac-
eratid,tristiqueeu,enim.Vestibulumante
ipsum primisin faucibusorci luctuset ultrices
posuerecubiliaCurae;Etiamadipiscingeros
vestibulumdolor.Pellentesquealiquam,diam
eget eleifendposuere,augue erosporttitorlec-
tus,acdignissimduimetusnecfelis.Quisque
lacinia.Vestibulumtellus.Suspendissenec
wisi.Aeneanacfelis.Aliquamultricesmetus
etnulla.
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ametneque.Sedcommodomalesuadalectus.
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wisigravidavehicula.Pellentesqueamassa
aleopretiumrhoncus.Suspendisseultrices.
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ttacitisociosquadlitoratorquentperconu-
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pretiumornaremauris.Phasellusauctorer-
ategetenim.Integerscelerisque,feliseucon-
sequatfringilla,loremwisiultriciesvelit,id
vehiculapurusnullaegetodio.Nullammat-
tis,diamarutrumfermentum,odiosapien
tristiquequam,idmollistellusquaminodi-
o.Mauriseusapien.Donecaliquamloremsit
ametlorempharetralobortis.
Donecacvelit.Sedconvallisvestibulumsapi-
en.Vivamustemporlacussedlacus.Nunc
utlorem.Utettortor.Nullamvariuswisiat
diam.Etiamultricies,dolorsitametfermen-
tumvulputate,nequeliberovestibulumorci,
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ipsumdolorsitamet,consectetueradipiscing
elit.Quisquevenenatislobortisaugue.Sed
tempor,tellusiaculispellentesquepharetra,
pededuimalesuadamauris,velultricesurna
maurisacnibh.Etiamnibhodio,ultriciesve-
hicula,vestibulumvitae,feugiateleifend,fe-
lis.Vivamus pulvinar.Aliquameratvolutpat.
Nullaegestasvenenatismetus.Namfeugiat
nuncquiselitegestassagittis.Sedvitaefe-
lis.Inliberoarcu,rhoncusin,commodoeget,
auctorin,enim.Vivamussuscipitest.Nul-
ladapibus,magnavelaliquetegestas,massa
massahendreritlacus,acrutrumtellustellus
sitametfelis.Crasviverra.
Suspendisseeununc.Aliquamdignissimurna
sit ametmauris.Cras commodo, urna ut port-
titor venenatis, arcu metussodalesrisus, vitae
gravidasapienligulainest.Donecvulputate
sollicitudinwisi.Donecvehicula,estidinter-
dumornare,nibhtellusconsectetuerjusto,a
ultrices felis erat at lectus.In est massa, male-
suadanon,suscipitat,ullamcorpereu,elit.
Namnullalacus,bibendumsitamet,sagit-
tissed,temporeget,libero.Praesentligula.
Suspendissenulla.Etiamdiam.Nullaante
diam,vestibulumet,aliquetac,imperdietvi-
tae,urna.Fuscetinciduntlacusvelelit.Mae-
cenasdictum,tortornoneuismodbibendum,
pedenibhpretium tellus,atdignissimleo eros
egetpede.Nullavenenatiseleifenderos.Ae-
nean ut odio dignissim augue rutrum faucibus.
Fusceposuere,tellusegetviverramattis,er-
attellusportami,atfacilisissemnibhnon
urna.Phasellusquisturpisquismaurissus-
cipitvulputate.Sedinterdumlacusnonvelit.
Vestibulumanteipsum primisinfaucibusorci
luctusetultricesposuerecubiliaCurae;
Vivamus vehicula leoajusto.Quisquenec au-
gue.Morbimauriswisi,aliquetvitae,dignis-
simeget,sollicitudinmolestie,ligula.Indic-
tumenim sitametrisus.Curabitur vitaevelit
eudiamrhoncushendrerit.Vivamusutelit.
Praesentmattisipsumquisturpis.Curabitur
rhoncusnequeeudui.Etiamvitaemagna.
Namullamcorper.Praesentinterdumbiben-
dummagna.Quisqueauctoraliquamdolor.
Morbieuloremetestporttitorfermentum.
Nuncegestasarcuattortorvariusviverra.
Fusceeunulla utnulla interdum consectetuer.
Vestibulumgravida.Morbimattisliberosed
est.
Abstract
WeanalyzethespincoincidenceexperimentconsideredbyBellin
the derivation of Bellstheorem.We solve the equationof motion for
thespinsystemwithaspinHamiltonian,H
z
,wherethemagnetic
fieldisonlyinthez-direction.Forthespecificcaseofthecoinci-
dence experiment where the two magnetshave the sameorientation
theHamiltonianH
z
commuteswiththetotalspinI
z
,whichthus
emergesasaconstantofthemotion.Bellsargumentisthenthat
anobservationofspinupatonemagnetAnecessarilyimpliesspin
downattheotherB.ForanisolatedspinsystemA-Bwithclassi-
caltranslationaldegreesoffreedomandaninitialspinsingletstate
thereisnoforceonthespinparticlesAandB.Thespinsarefully
entangledbut noneofthe spinparticlesA orBare deflectedby the
Stern-Gerlachmagnets.ThisresultisnotcompatiblewithBells
assumptionthatspin1/2particlesaredeflectedinaStern-Gerlach
device.AssumingamorerealisticHamiltonianH
z
+H
x
includ-
ingagradientinxdirectionthetotalI
z
isnotconservedandfully
entanglementisnotexpectedinthiscase.Theconclusionisthat
Bellstheoremisnotapplicabletospincoincidencemeasurement
originallydiscussedbyBell.
Keywords
BellsTheorem,Disentanglement,Stern-GerlachCoincident
Measurement,SingletSpinState
1.Introduction
In1966,Bell[1]presentedananalysisofathoughtexperimentbased
onindependentmeasurementsofthespinstateoftwoinitiallycorrelat-
edparticles.UsinganexampleadvocatedbyBohmandAharonov[2]
hedescribedtheexperimentasfollows:
Considerapairofspin-one-halfparticlesformedsomehow
inthesingletspinstateandmovingfreelyinoppositedirec-
DOI: 10.4236/jmp.2019.1010083Sep.23,20191247JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
tions.Measurementscanbemade,saybyStern-Gerlach
magnets,onselectedcomponentsofthespinsσ
A
andσ
B
.
Ifmeasurementofcomponentσ
A
·~awhere~aissomeu-
nitvector,yieldthevalue+1then,accordingtoquantum
mechanics,measurementsofσ
B
·~amustyieldthevalue
-1andviceversa.Nowwemakethehypothesis,andit
seemsoneatleastworthconsidering,thatifthetwomea-
surements are made at places remote from one another the
orientation ofthemagnet doesnot influencetheresult ob-
tainedwiththeother.Sincewecanpredictinadvance
theresultofmeasuringanychosencomponentofσ
B
,by
previously measuringthe same component of σ
A
it follows
thattheresultofanysuchameasurementmustactually
bepredetermined[1].
Inthepresentpaper,weaimatscrutinizingtheargumentsused
byBellusingrecentadvances[3]intheformaldescriptionofthe
Stern-Gerlachexperiment[4].Acrucialquestionfromourperspec-
tive,concernstheanticipatedcorrelationbetweentheobservationsin
thetwomagnets.Bell’sanalysisisbasedontheassumptionthatthe
initialspinsingletstateispreservedduringthepassagethroughthe
twoStern-Gerlachdevises.Wearguebelowthatthereisacoupling
between the spin andtranslational degrees of freedom causedby inho-
mogeneities inthemagnet field.Thiscoupling leadstochanges inthe
spinstateandapartialdisentanglementoftheinitialsingletstate.
2.TheStern-GerlachSetupandIts
ApplicationtoCoincidence
Measurements
Theessential ingredientsinaStern-Gerlachexperimentisi)asource of
spin particles, for simplicity we consider I= 1/2 particles.The source
shouldgiveparticlesofaswell-definedspeedaspossible.Througha
slitsystemparticlesareselectedtopropagateinanarrowsolidan-
gle,chosenheretobeinthey-direction.Theparticlesthenenter
thegapofamagnetwherethemaincomponent,B
z
ofthefieldB
isperpendiculartothedirectionofpropagation.ThefieldBisin-
homogeneouswithagradient
dB
z
dz
inthez-direction.Itfollowsfrom
Maxwellslawsthatthereisalsoamatchinggradientinsomeother
direction;intheSGcasethex-direction.UsingsuchasetupStern
andGerlachobserved [4]thatsilveratoms,laterrealizedtohavespin
1/2,weredeflectedanamount±zinthegradient.Onlytheset-
woalternativeswereobservedandthedegreeofdeflectionwaslater
foundtobeconsistentwithestimatesofthemagneticmomentasso-
ciatedwiththespinofanelectron.The,empirical,conclusionwas
thatthesilveratomspassedthroughthemagnetasiftheywereei-
therintheI
z
=+1/2orI
z
=1/2state,withequalprobability.In
the conventional, textbookanalysis ofthe experiment the translation-
almotionisdescribedclassicallyandoneleavesthequestionopenof
howaspinofinitiallyunspecifiedpolarizationappearsaspolarized
alongthedirectionofthemagneticfield[5].Byanalyzinghowthe
predictedoutcomeoftheexperimentdependedontherelativeorien-
tation ofthe twomagnets Bell foundthat theexpectedobservation at
one magnet depended on the orientation of the second magnet in spite
ofthefactthattherewasnodirectphysicalinteractionbetweenthe
DOI: 10.4236/jmp.2019.10100831248JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
particlesoncetheyhadleftthesource.Thisobservation,latercoined
Bellstheorem,hasgivenrisetoalargediscussionconcerningnon-
localityeffectsinquantumsystems.[6]Inlateryearsthediscussion
ofthiseffecthasmainlybeenconcentratedonphotonsystems.The
presentpaperissolelyconcernedwiththediscussionoftheoriginal
coincidencespinmeasurementargument.
Considerthespecialcasewhenthetwomagnetshavethesame
orientationinthexz-planechosentobethezdirection.According
totheoriginalSGobservationthespinparticlereachesthedetector
ofmagnetAatsayposition+∆zindicatingthatI
zA
= +1/2.What
istheexpectedobservationfortheotherparticleofthepairatthe
secondmagnet?FollowingBohmsreasoningBellconcludedthatby
necessityI
zB
= 1/2forthisparticleanditthenshouldbeobserved
atzinthesecondmagnet.Toseethebasisforthisconclusion
consideredfirstthespinHamiltionian
H
z
H
zA
+H
zB
= [γ~[B
z
+
dB
z
dz
z(t)]I
z
+[γ~[B
z
+
dB
z
dz
z(t)]I
z
.(1)
whereγand~havetheirusualmeaning.Equation(1)istypically
usedtoanalyzetheSGexperimentinelementarytexts.Itfollows
thatthetotalspininthez-directionI
z
=I
zA
+I
zB
commuteswith
theHamiltonianandI
z
isaconstantofthemotion.Forasinglet
state,|S
0
i,ithasavalueI
z
=0soI
zA
=1/2impliesI
zB
=1/2,
orviceversa.Bynecessitythereis,withinthemagnet,alsoafieldin
thex-directionandthustwoterms
H
x
H
xA
+H
xB
= [γ~
dB
z
dx
x(t)I
x
]
A
+γ~
dB
z
dx
x(t)I
x
]
B
(2)
inthespinHamiltonian.Bohmarguedthatthegradientinthex-
directionwasofnegligibleconsequence[7,8]sothatitisagoodapprox-
imationtoanalyzetheexperiment onthebasisofafurthersimplified
HamiltonianH
z
.StillI
z
isstrictlynotaconstantofthemotion.
TheanalysisofthecoincidenceexperimentbyBellisbasedontwo
basicarguments.ThefirstistheempiricalfindingoftheSGexperi-
ment thata spin 1/2particle isdeflected anamount±z.The second
isthatforparallelorientationsofthe twomagnetsthetotal spinI
z
is
conservedwhichfollowstheoreticallyusingtheHamiltonianH
z
.The
dependence of the outcome on the relative orientation of the two mag-
nets then follows in a straightforward way.We note that the two basic
argumentshavedifferentorigins;oneempiricalandonetheoretical.
3.DescribingtheStern-Gerlach
ExperimentthroughtheHamiltonianH
z
ItisimplicitintheHamiltoinanH
z
thatthetranslationaldegreesof
freedomaredescribedclassically.Wenow investigatetowhichextent
thisHamiltoniandescribesthedynamicsofspinparticlesintheSG
magnet.Incontrasttotheoriginal SGexperimenttheinitialspinstate
isknownandrepresentedbyanentangledsingletinthecoincidence
setup.Theequationofmotionforthespin“densityoperator”,σ(t),
DOI: 10.4236/jmp.2019.10100831249JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
is
d
dt
σ(t) =
i
~
[H
z
(t)](3)
Toillustrateourpointitissufficienttoconsiderthespecialcase
withonlyoneStern-Gerlachdevice.Then
H
z
= H
zA
(4)
Fortwo I=1/2 particlesthereare 16spindensity operatorcompo-
nents.Forthecasewithamagneticfieldsolelyalongthez-direction
onlyfourcomponentscouple;|S
0
><S
0
|,|S
0
><T
0
|,|T
0
><
S
0
|,|T
0
><T
0
|.Here|S
0
idenotesthesingletstateand|T
0
ithe
tripletstatewithS
z
= 0.Theequationofmotion,
d
dt
σ
AB
(t)
|S
0
><S
0
|
σ
AB
(t)
|S
0
><T
0
|
σ
AB
(t)
|T
0
><S
0
|
σ
AB
(t)
|T
0
><T
0
|
=(5)
1
2
0
A
(z)
A
(z)0
A
(z)00
A
(z)
A
(z)00
A
(z)
0
A
(z)
A
(z)0
σ
AB
(t)
|S
0
><S
0
|
σ
AB
(t)
|S
0
><T
0
|
σ
AB
(t)
|T
0
><S
0
|
σ
AB
(t)
|T
0
><T
0
|
whereω
A
(z)≡−γ
A
[B
A
z
+
dB
A
z
dz
A
z
A
].Withtheinitialcondition
ρ(0)
|S
0
><S
0
|
= 1,thesolutionis(seeSI)
σ
AB
(t)
|S
0
><S
0
|
=
1
2
(1+cos(ω
A
(z)t)
σ
AB
(t)
|S
0
><T
0
|
=
1
2
(isin(ω
A
(z)t)
σ
AB
(t)
|T
0
><S
0
|
=
1
2
(isin(ω
A
(z)t)
σ
AB
(t)
|T
0
><T
0
|
=
1
2
(1cos(ω
A
(z)t)
Theforce,F
A
,ontheparticleAis
F
A
=
dB
z
dz
A
hI
z,A
i(t) = 0(7)
since
hI
z,A
i(t) =
1
2
[tr
B
{σ
AB
(t)
|S
0
><T
0
|
}+tr
B
{σ
AB
(t)
|T
0
><S
0
|
}] = 0(8)
It follows that thereisno netforce ontheparticles andtheHamilto-
nianH
zA
(H
z
)isthusinadequateforpredictingtheempiricallybased
anticipatedoutcomeoftheexperiment.Ontheotherhandthecal-
culationshowthatthetwoseparatedspinsAandBarecompletely
entangled.Thisindicatesthatthereisaninternalinconsistencyin
Bell’soriginalargument.TheHamiltonianusedtomotivatethatI
z
isaconstantofmotionisinadequatetoexplainwhyoneobservea
spindependentdeflectionofparticlesemergingfromanon-magnetic
singletspinstate.
4.ImplicationsofRecentDescriptionof
theSGExperiment
Therehasin recentyears appearedseveral theoreticalaccounts ofthe
SGexperiment[9]-[14].Althoughclearlydifferentintheapproaches
DOI: 10.4236/jmp.2019.10100831250JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
theysharethecommonfeaturethatitisnecessarytoincludeaquan-
tumdescriptionof thetranslationalmotionorother degreesoffreedom
toaccountfortheobservationoftwodistinctpositions±4zatthe
detectorforaspin1/2particle.Thisfurthercorroboratesthecon-
clusionoftheprevioussectionthattheHamiltonianH
z
ofEquation
(1)isinadequatefordescribingtheSG-experiment.Amoreadequate
Hamiltoinan[13,14]fordescribingtheexperimentcanbewritten
H= ~p/2m+γ
~
S·
~
Br)(9)
whereBr)isthemagneticfieldandthehat(ˆr)istodenotethat
thespatialcoordinateisanoperatorintheHamiltonian.Inmost
discussionsoftheSGexperimentthefocusisonthemagneticfield
insidethemagnet,neglectingthegradientinthex-directionsothat
B= B
z
+
dB
z
dz
ˆz(10)
Based onthisexpressionforthe magneticfieldtheoutcomeof theS-
G experiment is adequately predicted.Using aperturbationapproach
we [3] could also show that the effect of thegradient in the x-direction
isto reducethedeviationforspinparticleswith initialpositions slight-
lyoffcenter.ThiscalculationcorroboratesBohmsoriginalassertion
thatthex-gradienthasonlyasmallinfluence.However,itiscausing
the mouth-like shape found at the detector inthe original experiment.
WhenappliedtothecoincidencemeasurementtheHamiltonian(9)
withthe expressionforthemagneticfield (10),fortherespectivepar-
ticles,givesasystemwherethetotalspinI
z
isconserved.However,
thereisanimportantfactormissingintheexpressionforthemag-
neticfieldinEquation(10),whichreferstotheconditionsinsidethe
magnet.Thereisnecessarilyazoneclosetotheentranceofthegap
ofwidthDinthemagnetwherethez-componentofthefieldgrows
fromzerotoB
z
.FromMaxwellsequationsitfollowsthatthereare
alsoagradientofcorrespondingmagnitudeinthey-direction,aswell
asasmallcontributionfromtheasymmetryinthex-direction.In[3]
wehavepresentedanapproximateanalyticalexpressionforthefield
outsidethemagnet,y0.
B
z
(y,z)
B
0
π
{arctan(
z+D
y
)arctan(
zD
y
),
B
y
(y,z) ≈−
B
0
2π
ln{
y
2
+(z+D)
2
y
2
+(zD)
2
,}
B
x
0.
(11)
Usingtheexpression(11)forthefieldintheHamiltonian(9)it
followsthatthecommutatorbecomes
[H,I
z
] = γ(I
xA
B
y A
y,ˆz)+I
xB
B
y B
y,ˆz)).(12)
This shows that I
z
is not a constant of the motion since the commu-
tator ofEquation(12) isnotzero.Tofurtheremphasize theexistence
ofacouplingbetweenspinandtranslationwenotethatthereisan
effectonthemomentum inthey-directionintheentrance zone.This
isevidentfromthenonzerovalueofthecommutator[H,p
y
],caused
bythey-dependenceofbothB
z
andB
y
inEquation(11).Intheen-
trance phasethere isthus, ingeneral, anenergy transferbetween spin
andtranslationdegreesoffreedom.
DOI: 10.4236/jmp.2019.10100831251JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
Itisaconsiderablechallengetosolvetheequationofmotionfor
thecombinedspin-translationdegreesoffreedom.Lackingsuchaso-
lutionweconsiderpossibleimplicationsofthecouplingbetweenspin
andtranslationbyanalyzinghowthespinenergylevelsvaryasthe
initiallystronglycoupledspinsseparateandmovetowardstheirre-
spectivemagnets.Forthesakeofillustrationletthetwomagnets
bepositionedassymmetricallyaspossible.Asthetwospinparticles
moveaparttheystillinteractthroughadipolarcoupling,whilethe
strongerJ-couplingisvarylocal.Thedipolarcouplingresultsintwo
non-degeneratestates,|S
0
iand|T
0
i,bothwithI
z
=0,butwithdif-
ferentpermutationsymmetry.Inadditionthereisadegeneratelevel
withstates|T
1
iand|T
1
i.Astheparticlesseparatethedipolarcou-
plingbecomesnegligiblewhilethereisagrowingZeemantermfrom
themagneticfield.Inthislimit,andassumingthez-componentof
thefieldtobethelargestone,the|T
1
iand|T
1
ilevelsareseparated
byafrequency2ω(y),whilethe|S
0
iand|T
0
istatesaredegenerate
with an energy half way between the other levels (See Figure 1).With
aperfectsymmetrybetweenthetwomagnetsaninitialsingletstate
willremaininthatstatethroughoutthepassage.However,itisnot
feasibletohavemicroscopicallyidenticalfieldsinthetwomagnets.A
differenceinthez-componentsofthemagneticfieldswillresultina
mixing ofthe|S
0
iand |T
0
istates, whilethe I
z
componentis conserved
atavaluezero.AdifferenceintheB
x
orB
y
componentsresultina
breakingofthesymmetrywithrespecttobothparityandI
z
.InFig-
ure1itisseenthattheenergylevelforthesingletstatebynecessity
crosseseitherthelevelforthe|T
1
istate,asinthefigure,orforthe
|T
1
istate,foradifferentchoiceofthesignofthegyromagneticratio.
One approach to handletheproblem oftreating thequantum effects
ofthetranslationaldegreeoffreedomistouseadiabaticapproxima-
tion.In thespecific exampleof Figure1 theadiabatic reasoningwould
predictthattheinitial|S
0
istatewillexperienceanavoidedcrossing
inthepresenceofacouplingtermandcontinueinthe|T
1
istateas
the particles enter the magnet.As expected neither theparity nor the
I
z
valueisconservedduringthecrossover.Thisargumentshows,by
example,arealisticmechanismforhowtheI
z
valueoftheinitialsin-
gletstatecanchangeduringtheentranceofthemagnet,byreferring
tothecommonphenomenonofavoidedlevelcrossing.
5.Conclusion
WehaveanalyzedtheargumentsleadingtotheformulationofBells
theoremforspincoincidencemeasurements.Theproofofthetheo-
rem has twocentralingredients.The rule, based onthe original Stern-
Gerlachobservation, thaton exitfrom theSG-setup aspin 1/2particle
iseitherintheI
z
=+1/2orI
z
=1/2state.Thesecondessential
featureisthatthetotalspininthez-directionI
z
isconserved.This
conservationrulefollowsfromtheHamiltonianEquation(1)usually
usedinsimplifieddiscussionsoftheSGexperiment.However,using
theHamiltonianofEquation(1)andtheknowninitialspinstatethe
equationofmotionforthespincanbesolvedandwefindthatthere
isnonetforceactingontheparticlepassingthroughthemagnet,as
expectedforanon-magneticstate.Thisindicatesthatthereisan
internalinconsistencyoftheoriginalproofofBellstheorem.Recent
work [3], [10]- [12] has shown that it is necessary to include a quantum
descriptionofthetranslationalmotionorotherdegreesoffreedomin
ordertoaccountfortheobservedSGeffect.Theempiricalruleused
DOI: 10.4236/jmp.2019.10100831252JournalofModernPhysics
P.-O.Westlund,H.Wennerstrˆom
Figure1.Theenergylevelatzeromagneticfieldwiththeeigenstates
|S
0
0
i,|T
1
0
i,|T
1
1
iand|T
1
1
iwiththedipole-dipoleenergyω
dd
.Increasing
Zeeman energyω
Z
to theright,indicatinghow theenergy leves change for
thestateswhenω
Z
ω
dd
.
byBellcan thusbetheoreticallyderived, butusingadifferentHamil-
tonianthanBellusedtoconcludethatI
z
ofthecombinedsystemis
conserved.Thecouplingbetweenspinandtranslationemergesfrom
thespatialdependenceofthemagneticfield,whichhascomponents
inmorethanonedirection.ItfollowsthattheI
z
ofthecombined
systemisnotaconstantofthemotion.Wefurtherarguethatthe
mostsignificantdeviationofthefieldfromthemainz-directionoc-
cursonenteringthemagnet.TheproofofBellstheoremthusrests
onanapproximationofunknownvalidity.Wehavegivenoneillus-
tration of thesituation where usingconventional argument, where the
approximationisspecificallygivingamisleadingresult.
Acknowledgements
ThisworkwassupportedbySwedishResearchCouncil(VR).
ConflictsofInterest
Theauthorsdeclarenoconflictofinterest.
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