A New Causal Interpretation of EPR-B Experiment

(1)

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A New Causal Interpretation of EPR-B Experiment

Michel Gondran, Alexandre Gondran

To cite this version:

Michel Gondran, Alexandre Gondran. A New Causal Interpretation of EPR-B Experiment. 2009.

�hal-00290179v2�

(2)

Experiment

MihelGondran Alexandre Gondran

UniversityParisDauphine,Paris,Frane, SeTLab,UTBM,Belfort,Frane,

mihel.gondranpolytehni que. org alexandre.gondranutbm. fr

Marh 3,2009

Abstrat

Inthis paperwe studyatwo-step versionofEPR-B experiment,the

BohmversionoftheEinstein-Podolsky-Rosenexperiment. Itstheoretial

resolutioninspaeandtimeenablesustorefutethelassi"impossibility"

todeomposeapairofentangledatoms intotwodistintstates, onefor

eahatom.WeproposeanewausalinterpretationoftheEPR-Bexper-

imentwhereeahatomhasapositionandaspinwhile thesingletwave

funtionveriesthetwo-bodyPauli equation. Inonlusion we suggest

aphysialexplanationofnon-loalinuenes,ompatiblewithEinstein's

pointofviewonrelativity.

keywords: EPR-B-ausalinterpretation-entangledatoms-two-body

Pauliequation-singletstate

1 Introdution

Thenonseparabilityisoneofthemostpuzzlingaspetsofquantum mehanis.

Foroverthirtyyears,theEPR-B,thespinversionproposedbyBohm[5,6℄ofthe

Einstein-Podolsky-Rosen experiment[1℄,theBelltheorem [2℄ andthe BCHSH

inequalities [2,3, 4℄ have been at the heart of thedebate on hidden variables

andnon-loality;buthithertothepreisenatureofthephysialproessthatlies

behind the"non-loal" orrelationsin thespins of thepartiles has remained

unlear.

ManyexperimentssineBell'spaperhavedemonstratedviolationsofthese

inequalitiesandhavevindiatedquantumtheory[7,8,9,10,11,12,13,14,15,

16, 17℄. The rst one was done with pairs of entangled photons and learly

violate Bell's inequality [10, 11, 12, 13℄. Entangled protons have also been

studied in an early experiment [9℄. The generation of EPR pairs of massive

atoms instead of masslessphotons hasbeen onsidered [14, 15℄; it also shows

experimentalviolationofBell'sinequalitywitheientdetetion[15℄.

In a new experiment, Zeilinger and all [26℄ measure previously untested

orrelationsbetweentwoentangledphotons,theyshowthatthese orrelations

violateaninequalityproposed byLeggettfornon-loal realistitheories[25℄.

(3)

Theusual onlusionofthese experimentsisto rejetthenon-loalrealism

beausetheimpossibilitytodeomposeapairofentangledatomsintotwostates,

oneforeahatom.

Inthispaperweshow,ontheEPR-B experiment,that thisdeomposition

ispossible: aausalinterpretationexistswhereeahatomhasaposition anda

spinwhilethesingletwavefuntionveriesthetwo-bodyPauliequation.

Todemonstrate this; we onsider atwo-stepversionofEPR-B experiment

and we use an analyti expression of the wave funtion and the probability

density. The expliit solution is obtained via a omplete integration of the

two-bodyPauliequationovertimeandspae.

ArstausalinterpretationofEPR-Bexperimentwasproposedin1987by

Dewdney,HollandandKyprianidis[21,22℄. Thisinterpretationhadaaw: the

spinof eah partiledependsdiretly on thesinglet wavefuntion, andso the

spinmodule ofeahpartilevariedduringtheexperimentfrom 0to

~ 2

^.

Theexpliitsolutionintermsoftwo-bodyPaulispinorsandtheprobability

density for the two steps of the EPR-B experiment are presented in setion

2. The solutionin spaeand time showshowit ispossibleto deduetests on

thespatial quantizationofpartiles, similar tothose oftheStern andGerlah

experiment.

Insetion3, weprovidearealistiexplanation ofthe entangled statesand

amethodtodesentanglethewavefuntionofthetwopartiles.

The resolution in spae of the equation Pauli is essential: it enables the

spatialquantizationinsetion2andexplainsdeterminismanddesentanglingin

setion3.

Inonlusionweproposeaphysialexplanationofnon-loalinuenes,om-

patiblewithEinstein'spointofviewonrelativity.

2 Simulation and tests of EPR-B experiment in

two steps

Fig.1presentstheEinstein-Podolsky-Rosen-Bohmexperiment. Asoure

S

^re-

atedinOpairsofidentialatomsAandB,butwithoppositespins. Theatoms

A and Bsplit following 0y axis in opposite diretions, and head towards two

identialStern-Gerlahapparatus

A

^and

B

^.

Theeletromagnet

A

"measures"theAspininthediretionoftheOz-axis andtheeletromagnet

B

"measures"theBspininthediretionoftheOz'-axis,

(4)

whihisobtainedafter arotationofanangle

δ

^around^the^Oy-axis.

Wefurther onsider that atoms A and Bmay be representedby Gaussian

wavepakets in xand z. Wenote r

= (x, z)

^. ^The ^initial^wave^funtion ^of ^the

entangledstateis thesinglet state:

Ψ 0 (

^r

A ,

^r

B ) = 1

√ 2 f (

^r

A )f (

^r

B )( | + A i|− ^B i − |− ^A i| + B i )

⁽¹⁾

where

f (

^r

) = (2πσ ² ₀ ) ⁻

¹²

e ⁻

x2+z2 4σ2

0 andwhere

|± ^A i

⁽

|± ^B i

⁾^are^theeigenvetorsof the spin operators

b s z

A ⁽

b s z

B⁾ ⁱⁿ ^the ^z-diretion ^pertaining ^to ^partiule ^A ^(B):

b s z

A

|± ^A i = ± ( ^~ ₂ ) |± ^A i

⁽

b s z

B

|± ^B i = ± ( ^~ ₂ ) |± ^B i

^). ^We^treat^lassially^dependene

withy: speed

− v y

^for^A^and

v y

^for^B.

Thewavefuntion

Ψ(

^r

A ,

^r

B , t)

ôf^the^twoîdential^partilesÂ ând^B,êle-

trially neutraland withmagnetimoments

µ 0

^,^subjet^to ^magneti^elds^B

A

and B

B

, admits in the basis

|± A i

^and

|± B i

⁴^omponents

Ψ ^a,b (

^r

A ,

^r

B , t)

^and

veriesthetwo-bodyPauliequation[24℄p. 417:

i ~ ∂Ψ ^a,b

∂t =

− ~ ²

2m ∆ A − ~ ² 2m ∆ B

Ψ â,b + µB Â _j (σ j ) â _c Ψ ^c,b + µB ^B _j (σ j ) ^b _d Ψ â,d

⁽²⁾

withtheinitialonditions:

Ψ ^a,b (

^r

A ,

^r

B , 0) = Ψ ^a,b ₀ (

^r

A ,

^r

B )

⁽³⁾

where the

σ j

^are^the^Pauli^matrixes ^and^where ^the

Ψ ^a,b ₀ (

^r

A ,

^r

B )

^orrespond^to

thesingletstate(1).

We take as numerial values those of the Stern-Gerlah experiment with

silveratoms [18,19℄. Forasilveratom, onehas

m = 1, 8 × 10 ⁻ ²⁵

^kg,

v y = 500

m/s ,

σ 0

⁼¹⁰

− 4

m. For the eletromagneti eld B,

B x = B ₀ ^′ x

^;

B y = 0

^and

B z = B 0 − B ₀ ^′ z

^with

B 0 = 5

^Tesla,

B ₀ ^′ =

^∂B

∂z

= − ^∂B

∂x

= 10 ³

^Tesla/m^over^a

length

∆l = 1 cm

^. ^The^sreen^thatîntereptsâtomsîsâtâ^distane

D = 20 cm

(time

t 1 = _v ^D

_y

= 4 × 10 ⁻ ⁴

^s)^from ^theêxit ôf^the^magnetiêld.

Oneofthediulties oftheinterpretationoftheEPR-Bexperimentisthe

existeneoftwosimultaneousmeasurements. Bydoingthesemeasurementsone

aftertheother,theinterpretationoftheexperimentwillbefailitated. Thatis

thepurposeofthetwo-stepversionoftheexperimentEPR-Bstudiedbelow.

2.1 First step: Measurement of A spin and position of B

Intherststepwemake,onaoupleofpartilesAand Bin asingletstate,a

Sternand Gerlah"measurement"foratom A,and foratomBamereimpat

measurementonasreen.

Itistheexperimentrstproposedin1987byDewdney,HollandandKypri-

anidis[21℄.

Considerthat at time

t 0

^the ^partile Â ârrives ât ^the êntrane ôf êletro-

magnet

A

^.

△ t

^is ^the ^rossing^duration ^of eletromagnet

A

^and

t

^is ^the ^time

after the

A

êxit. ^The^wave^funtion ân^beâlulated,^from ^the^wave^funtion

(1), termto terminbasis[

|± A i , |± B i

^℄. Âfter^this êxitôf^the^magnetiêld

A

^,

attime

t 0 + △ t + t

^,^the^wave^funtion⁽¹⁾^beomes^[19℄:

Ψ(

^r

A ,

^r

B , t 0 + △ t + t) = 1

√ 2 f (

^r

B )

⁽⁴⁾

× f ⁺ (

^r

A , t) | + A i|− B i − f ⁻ (

^r

A , t) |− A i| + B i

(5)

f ^± (

^r

, t) ≃ f (x, z ∓ z △ ∓ ut)e ⁱ⁽

^±muz^~

^+ϕ

^±

^(t))

⁽⁵⁾

and

∆t = ∆l v y

= 2 × 10 ⁻ ⁵ s, z ∆ = µ 0 B ^′ ₀ (∆t) ²

2m = 10 ⁻ ⁵ m, u = µ 0 B ₀ ^′ (∆t)

m = 1m/s.

⁽⁶⁾

Theatomidensity

ρ(z A , z B , t 0 + ∆t +t)

^is^found^byintegrating

Ψ ^∗ (

^r

A ,

^r

B , t 0 +

△ t + t)Ψ(

^r

A ,

^r

B , t 0 + △ t + t)

^on

x A

^and

x B

^:

ρ(z A , z B , t 0 + ∆t + t) = (2πσ ² ₀ ) ⁻

¹²

e ⁻

(zB)2 2σ2

0

!

(7)

× (2πσ ² ₀ ) ⁻

¹²

1 2 e ⁻

(zA−z∆−ut)2 2σ2

0

+ e ⁻

(zA+z∆+ut)2 2σ2

0

!!

.

We dedue that the beam of partiles A is divided into two, while the B

beamofpartilestaysone. Thisresultaneasily betestedexperimentally.

Moreover,wenote that thespae quantizationofpartile A is identialto

that of anuntangled partile in a Stern and Gerlah apparatus: the distane

δz = 2(z ∆ + ut)

^between ^the ^two ^spots

N ⁺

^(spin ⁺⁾ ^and

N ⁻

^(spin

−

⁾ ^of ^a

familyofpartileAisthesameasthedistanebetweenthetwospots

N ⁺

^and

N ⁻

ôfâ^partileⁱⁿâ^lassi^Sternând^Gerlahêxperiment^[19℄. ^This^resultân

easilybetestedexperimentally.

Wenally deduefrom (7)that:

•

^the^densityôf Â îs^the ^same, ^whether ^partile Â îs êntangled ^with ^Bôr

not,

•

^the^densityôf^Bîs^notâeted^by^the"measurement"ofA.

These two preditions of quantum mehanis an be tested. Only spins are

involved. We onlude from (4) that the spins of A and B remain opposite

throughouttheexperiment.

2.2 Seond step: "Measurement" of A spin, then of B

spin.

TheseondstepisaontinuationoftherstandresultsinrealizingtheEPR-B

experimentintwosteps.

Ona oupleof partiles A andB in asinglet state,rst wemade aStern

and Gerlah"measurement"ontheA atombetween

t 0

^and

t 0 + △ t + t 1

^, ^then

a Sternand Gerlah "measurement" onthe Batom withan eletromagnet

B

forminganangle

δ

^with

A

^between

t 0 + △ t + t 1

^and

t 0 + 2( △ t + t 1 )

^.

Beyondtheexitofmagnetield

A

^,^at^time

t 0 + △ t +t 1

^,^the^wave^funtion^is

givenby(4). Immediatelyafterthe"measurement"ofA,stillattime

t 0 + △ t+t 1

^,

iftheAmeasurementis

±

^,^theonditionnalwavefuntions ofBare:

Ψ B/ ± A (

^r

B , t 0 + △ t + t 1 ) = f (

^r

B ) |∓ ^B i .

⁽⁸⁾

(6)

Tomeasure B,we referto the basis

|± ^′ B i

^where

|± ^′ B i

^are ^the eigenvetorsof the spin operators

b s z

^′_B ⁱⁿ ^the z'-diretion pertaining to partiule B. We note r

′ = (x ^′ , z ^′ )

^. ^So, ^after ^the measurement of B, at time

t 0 + 2( △ t + t 1 )

^the

onditionalwavefuntionsofBare:

Ψ B/+A (

^r

^′ _B , t 0 + 2( △ t + t 1 )) = cos δ

2 f ⁺ (

^r

^′ _B , t 1 ) | + ^′ _B i + sin δ

2 f ⁻ (

^r

^′ _B , t 1 ) |− ^′ B i ,

⁽⁹⁾

Ψ B/ − A (

^r

^′ _B , t 0 + 2( △ t + t 1 )) = − sin δ

2 f ⁺ (

^r

^′ _B , t 1 ) | + ^′ _B i + cos δ

2 f ⁻ (

^r

^′ _B , t 1 ) |− ^′ B i .

⁽¹⁰⁾

Wethereforeobtain,inthistwostepsversionoftheEPR-Bexperiment,the

sameresultsforspatialquantizationandorrelationsofspinsasintheEPR-B

experiment.

3 Causalinterpretationofthe EPR-Bexperiment

Weassume,atmomentofthereationofthetwoentangledpartilesAandB,

thateahofthetwopartilesAandBhasaninitialwavefuntion

Ψ ^A ₀ (

^r

A , θ ^A ₀ , ϕ ^A ₀ )

and

Ψ ^B ₀ (

^r

B , θ ^B ₀ , ϕ ^B ₀ )

^with^spinors^whihâreôpposite^spins;^forêxample

Ψ ^A ₀ (

^r

A , θ ^A ₀ , ϕ ^A ₀ ) = f (

^r

A )

cos ^θ ₂

^A⁰

| + A i + sin ^θ ₂

⁰^A

e ^iϕ

^A⁰

|− A i

and

Ψ ^B ₀ (

^r

B , θ ^B ₀ , ϕ ^B ₀ ) = f (

^r

B )

cos ^θ ₂

⁰^B

| + B i + sin ^θ ₂

^B⁰

e ^iϕ

^B⁰

|− ^B i

with

θ ^B ₀ = π − θ ₀ ^A

^and

ϕ ^B ₀ = ϕ ^A ₀ − π

^.

ThenthePauli prinipletellsusthat thetwo-body wavefuntion mustbe

antisymmetri;after alulationwend:

Ψ 0 (

^r

A , θ ^A , ϕ ^A ,

^r

B , θ ^B , ϕ ^B ) = − e ^iϕ

^A

f (

^r

A )f (

^r

B ) × ( | + A i|− B i − |− A i| + B i )

whihisthesameasthesinglet state,fatorwise(1).

Thus,weanonsiderthatthesingletwavefuntionisthewavefuntionof

afamilyoftwofermions Aand Bwith oppositespins: diretionof initialspin

AandBexist,butisnotknown. Itisaloalhiddenvariablewhihistherefore

neessaryto addintheinitialonditionsof themodel.

ThisisnottheinterpretationfollowedbytheshoolofBohm [21,22,24,23℄

in theinterpretationofthesingletwavefuntion;theysuppose, forexample,a

zerospinforeahofpartilesAandBattheinitialtime.

Itremains to determinethe wavefuntion and thetrajetoriesof partiles

AandB:fromtheentangledwavefuntion,initialspinsandinitialpositionsof

eahpartile.

We assume therefore that the intial position of the partile A is known

(

x Â ₀ , y ₀ Â = 0, z Â ₀ )

^as^well^as ^the^partile^B⁽

x ^B ₀ = x ^A ₀

^,

y ₀ ^B = y ₀ ^A = 0

^,

z ₀ ^B = z ₀ ^A

^).

3.1 Step 1: Measurement of A spin and position of B

Equation(4)showsthatthespinsofAandBremainoppositethroughoutstep

1. Equation (7) shows that the densities of A and Bare independent; for A

equal to the density of a family of free partiles in a lassial Stern Gerlah

apparatus,whoseinitialspinorientationhasbeenrandomlyhosen;forBequal

tothedensityofafamilyoffreepartiles.

(7)

partileinitswaveintoaspin

+

^or

−

^. ^The^spinôf^partile^B^follows^thatôfÂ,

whileremainingopposite.

Inthe equation(4) partile A anbeonsiderdindependent ofB. Wean

thereforegiveitthewavefuntion

Ψ ^A (

^r

A , t 0 + △ t + t) = cos θ ₀ ^A

2 f ⁺ (

^r

A , t) | + A i + sin θ ^A ₀

2 e ^iϕ

^A⁰

f ⁻ (

^r

A , t) |− A i

⁽¹¹⁾

whihis that ofafree partilein aSternGerlahapparatusand whose initial

spinisgivenby(

θ ₀ ^A , ϕ ^A ₀

^).

IndeBroglieinterpretation[23℄,partileveloityisproportionaltothegradi-

entofthewavefuntionphase. SeeomputeexemplesforYoungexperiment[20℄

and Stern-Gerlah experiment [19℄. So, the equation of itstrajetory is given

bythefollowingdierentialequations: in theinterval

[t 0 , t 0 + ∆t]

^:

dz A

dt = µ 0 B ₀ ^′ t

m cosθ(z A , t)

with

tan θ(z A , t)

2 = tan θ 0

2 e ⁻

µ0B′ 0t2zA 2mσ2

0 (12)

withtheinitialondition

z A (t 0 ) = z ₀ ^A

^;^and ⁱⁿ^the^interval

t 0 + ∆t + t

⁽

t ≥ 0

^):

dz A

dt = u tanh( ^(z

^∆

^+ut)z _σ

2 ^A

0

) + cos θ 0

1 + tanh( ^(z

^∆

^+ut)z _σ

2 ^A 0

) cos θ 0

et

tan θ(z A (t), t)

2 = tan θ 0

2 e ⁻

(z∆ +ut)zA σ2

0

.

⁽¹³⁾

θ(z A (t), t)

^desribes^the^evolution^of^theorientationofspinA.

The aseof partile B is dierent. B follows a retilinear trajetory with

y B (t) = v y t

^,

z B (t) = z ₀ ^B

^and

x B (t) = x ^B ₀

^. ^By^ontrast, ^the orientation of its spinmovesanditwas

θ ^B (t) = π − θ(z A (t), t)

^and

ϕ ^B (t) = ϕ(z A (t), t) − π

^.

Weanthenassoiatethewavefuntion:

Ψ ^B (

^r

B , t 0 + △ t + t) = f (

^r

B )

cos θ ^B (t)

2 | + B i + sin θ ^B (t)

2 e ^iϕ

^B

^(t) |− B i

.

⁽¹⁴⁾

Thiswavefuntionisspei,beauseitdependsuponinitialonditionsofA

(positionsandspins). TheorientationofspinofthepartileBisdrivenbythe

partileAthrough the singletwave funtion. Thus,thesingletwavefuntion is

theatualnon-loalhiddenvariable.

Figure2presentsaplotinthe

(z, y)

^plane^thetrajetoriesofasetof5pairs of entangledatoms whose initial harateristis

(θ ₀ ^A = π − θ ^B ₀ , z ₀ ^A = z ₀ ^B )

^have

beenrandomlyhosen. Thetrajetorieswillthereforedependonboththeinitial

position

z 0

^and^the^initial ^spinorientation

θ 0

^. ^Sine^the^spin^initialorientation aredierent,trajetoriesoftheApartilesmayinterset.

3.2 Step 2: "Measurement" of A spin, and then B spin

Until time

t 0 + △ t + t 1

^, ^we âre ⁱⁿ ^the âse ôf ^step ^1. Immediately after the

"measurement" ofA at thetime

t 0 + ∆t + t 1

^, ^if^the^A measurementis

±

^, ^the

onditionalwavefuntionofBisgivenby(8).

(8)

−0.3

−0.2

−0.1 0

0.1 0.2

−60.3

−4

−2 0 2 4 6x 10⁻⁴

y (meter)

z (meter)

A

Figure2: Fivepairsoftrajetoriesofentangledpartiles. Arrowsrepresentthe

spinorientation(

θ

^).

ThenpartileBisin position

(x ^B ₀ , z ₀ ^B )

^.

Weare exatly in the ase of apartile in aStern and Gerlah magnet

B

whihisanangle

δ

^with

A

^.

TomeasurethespinofB,werefertothebasis

|± ^′ B i

^. ^So,^after^the^measure-

mentofB,attime

t 0 + 2( △ t + t 1 )

^,^theônditional^wave^funtionsôf^Bâre^given

by(9)and(10),andwendagainthequantumorrelations.

4 Conlusion

Fromthewavefuntion of twoentangled partiles, wehavedetermined spins,

trajetoriesandalsoawavefuntionforeahofthetwopartiles.

Inthisinterpretation,thequantum partilehasaloalpositionlikealas-

sial partile,but ithasalsoanonloalbehaviourthroughthewavefuntion.

Indeedthewavefuntionisnotseparableandnon-loal.BeauseintheBroglie-

Bohminterpretationthewavefuntionpilotsthepartile,italsoreatesthenon

separabilityoftwoentangledpartiles.

Aswesawinstep1,thenon-loalinueneintheEPR-Bexperiment

onlyonernsthespinorientation,andnotthemotionofthepartiles

themselves. Thisisakeypointinthesearhofaphysialexplanationofnon-

loalinuene.

Thesimplest explanation (Okham's razor) ofthis nonloal inuene isto

reintrodue the existene of a spae having ertain properties related to the

ation atadistane, that is akindofether, but anewform of ethergivenby

Lorentz-PoinaréandthenbyEinsteinin 1920. Einstein said[27℄:

"Butontheotherhandthereisaweightyargumenttobeadduedinfavourof

theetherhypothesis. Todenytheetherisultimatelytoassumethatemptyspae

has no physial qualities whatever. Thefundamental fatsof mehanis do not

harmonize with this view. For the mehanial behaviour of a orporeal system

(9)

and relative veloities, but also on its state of rotation, whih physially

may be taken as a harateristi not appertaining to the system in itself. In

order to be able to look upon the rotation of the system, at least formally, as

something real, Newton objetivises spae. Sine he lasses his absolute spae

together with real things, for him rotation relative to an absolute spae is also

somethingreal. Newtonmightnolesswellhavealledhisabsolutespae"Ether";

what is essential is merely that besides observable objets, another

thing, whih isnot pereptible, inustbelooked uponas real, toenable

aeleration or rotation to be looked uponas somethingreal.[...℄

Reapitulating, wemay saythataording tothe general theory of rel-

ativity spae is endowed with physial qualities; in this sense, there-

fore, there exists an ether. Aording to the general theory of relativity

spae without ether is unthinkable;for insuhspaethere notonly would

be no propagation of light, but also no possibility of existene for standardsof

spaeandtime(measuring-rodsandloks), northereforeanyspae-timeinter-

valsinthephysialsense. Butthisethermaynotbethoughtofasendowedwith

the qualityharateristiofponderableinedia, asonsistingofpartswhih may

be trakedthroughtime. The idea of motion may not be applied toit."

Taking into aountthenew experiments,espeially Aspet's experiments,

Popper[28℄(p. XVIII)defendsasimilarviewin1982:

"Ifeelnotquiteonvinedthattheexperimentsareorretlyinterpreted;but

iftheyare,wejusthavetoaeptationatadistane. Ithink(withJ.P.Vigier)

that this would of ourse be very important, but I do not for a moment think

that itwould shake, or even touh, realism. Newton andLorentz were realists

and aepted ation at a distane; andAspet'sexperiments would bethe rst

ruialexperimentbetweenLorentz'sandEinstein'sinterpretationoftheLorentz

transformations."

Lastly, let us notiethe great dierene betweenEPR and EPR-B experi-

ments. Thespinonnetedtotherotationofspae-timeseemstobetheauseof

theinstantaneousationatadistaneinexperimentEPR-B.Itisthuspossible

thatthereisnotinstantaneousationatadistaneinoriginalexperieneEPR.

And in thisase, Einstein wasright. It is theproposalof Popper[28℄ p.25: "

Imays perhaps mentionheresome ofthe dierenes betweenthe original EPR

argumentandBohm'version ofit. These dierenes relate tothe distintionof

twokindsofquantummehanial statepreparations."[...℄ "Indeed,itispossible

that the Bohm-Bell experiment deidesfor ation atadistane, andtherefore

againstspeialrelativitytheory,whereasthe originalEPRargumentsdoesnot."

The new experiments of non-loality have therefore a great im-

portane, notto eliminaterealism and determinism, but asPoppersaid, to

rehabilitate theexistene ofa ertaintypeofether,likeLorentz'sether

andlikeEinstein'setherin 1920.

Referenes

[1℄ Einstein,A.,Podolsky,B.,Rosen,N.: Canquantummehanialdesription

ofrealitybeonsideredomplete?.Phys.Rev.47,777-780(1935).

[2℄ Bell,J.S.:OntheEinsteinPodolskyRosenParadox.Physis1,195(1964).

A New Causal Interpretation of EPR-B Experiment

HAL Id: hal-00290179

https://hal.archives-ouvertes.fr/hal-00290179v2

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