Wave-Particle PropertiesBasics of Neutron InterferometryDephasing and decoherenceGeometric phaseUnavoidable quantum losses Quantum Contextuality and Kochen-SpeckerLarmor and Compton frequency effectsRésumé

Helmut Rauch

Atominstitut, TU-Wien, Austria, EU

Dephasing

and decoherence

of neutron

matter waves

Dephasing

and decoherence

of neutron

matter waves

CONNECTION

de Broglie

Schrödinger

& boundary conditions

H(

r ,t) i (

r ,t)

t

Wave PropertiesParticle Properties

m = 1.674928 (1) x 10-27 kg

s = 12

= - 9.6491783(18 ) x 10-27 J/T

= 887(2) s

R = 0.7 fm

= 12.0 (2 .5) x10-4 fm3

u - d - d - quark structure

m ... m ass, s ... spin, ... m agnetic m om ent, c ... C om pton w avelength, B ... ... -decay lifetim e, R ... (m agnetic) confine- deBroglie w avelength, c ... m ent radius, ... electric polarizability; all other -B ________________ coherence length, p ... packet m easured quantities like electric charge, m agnetic tw o level system length, d ... decay length, k.… m onopole and electric dipole m om ent are com - m om entum w idth, t ... chopper

patible w ith zero B ________________ opening tim e, v ... group velocity, … … phase.

ch

m.c = 1.319695 (20) x 10-15 m

For thermal neutrons= 1.8 Å, 2200 m/s

Bh

m. v

Bh

m.v = 1.8 x 10-10 m

c1

2 k

10-8 m

p v t . 10-2 m

d v . 1.942(5) x 106 m

0 2 (4)

The NeutronThe Neutron

•

Neutron interferometry•

Neutron interferometry

The New Yorker Collection, Ch. Adams 1940

effeffceff

2II0

I00

DkkDNbkD)n1(sdk

cosBAI

Neutron InterferometryNeutron Interferometry

Quantum skierQuantum skier

Interferometer experiment

Interferometer familyInterferometer family

I0

= c| trr

+ rrt

|2

Interferometer set-up S18

Interferometer set-up S18

Instutut

Laue-Langevin, Grenoble

reactor

16000

14000

12000

10000

8000

6000

4000

2000

0

inte

nsity

(cou

nts/

10s)

-800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600ΔD / µm

D:DATA:Cycle 155:ifm30:adjust:nosample_3_wide.dat H beam O beam

High order interferencesHigh order interferences

0 10 20-10-20-30Δ[Å]

λ

= 1.92(2) Å

Individual eventsIndividual events

H. Rauch, J. Summhammer, M. Zawisky, E. Jericha, Phys.Rev. A42 (1990) 3726

II I iHt I i Bt

I i Bt I i

e e

e e

/ /

/ /

2

angleLarmor...v

B2gBtBt2

Theory: H.J.Bernstein, Phys.Rev.Lett. 18(1967)1102, Y.Aharonov, L.Susskind, Phys.Rev. 158(1967)1237

( )

( )

( )

/

/

e

e

I

I

2 0

20

0

0

( ) ( )( ) ( )2 04 0

2cos1

2)0(I)()0(I 02I

0I00

Experiment: H.Rauch, A.Zeilinger, G.Badurek, A.Wilfing, W.Bauspiess, U.Bonse, Phys.Lett. 54A(1975)425S.A.Werner, R.Colella, A.W.Overhauser, C.F.Eagen, Phys.Rev.Lett. 35(1975)1053A.G.Klein, G.I.Opat, Phys.Rev. D11(1976)523E.Klempt, Phys.Rev. D13(1975)3125M.E.Stoll, E.K.Wolff, M.Mehring, Phys.Rev. A17(1978)1561

B

n

Spinor SymmetrySpinor Symmetry

4π-symmetry

ijjizyx

yxzxzyzx iii

1222

1001

00

0110

zyx ii

),,( zyx

bxaibaba ...

h/sinAm4h/Agmm2

sinqsinq-anglecolatude...

beamscoherent by the enclosed area ...A

Ahm4sin

hAgmm2rdrmrdk

gt31tg

21tvrr

prL

VLgzmm2pL

rMm

Gm2pH

i2

gi

sgrav

i02gi

i

3200

0gi

2g

i

2

GRAVITATION

•

EXPERIMENT:•

Colella, Overhauseer,Werner, 1975

•

Werner, Staudenmann, Collela, Overhauser, 1975, 1978

•

Bonse & Wroblewski

1983

•

Atwood, Shull, Arthur 1984

•

THEORY:•

Page 1975;•

Anandan

1977•

Stodolsky

1979 •

Audretsch

& Lommerzahl

1982

COW-Experiment (Colella, Overhauser, Werner)

Eokom

km

mgH

2 2

2

2 2

2( )

k k kom gH

ko ( ) sin

2

2

cow II I k S

cowm

hgAo 2

2

2 sin

R. Colella, A.W. Overhauser, S.A. Werner, Phys.Rev.Lett. 34 (1974) 1472

E0

= 20 meV; mgH

~ 1.003 neV

Earth Rotation EffectEarth Rotation Effect

J.L.Staudenmann, S.A.Werner, R.Colella, A.W.Overhauser, PR/A21(1980)1419

State presentationsState presentationsSchrödinger Equation:

t)t,r(i)t,r()t,r(V)t,r(

m2

2

Wave Function (Eigenvalue solution in free space):

kde)t,k()2()t,r( 3)trk(i2/3

Spatial distribution: Momentum distribution:2)t,r()t,r(

2)t,k()t,k(g

Coherence Function:

;'rr

'ttStationary situation: :)0(

kde)k(g)2()()0()( 3rki2/3

and others (Wigner function etc.)

Partial waves fill the whole space

SPATIAL VERSUS MOMENTUM MODULATIONSPATIAL VERSUS MOMENTUM MODULATION

Momentum distribution

Spatial distribution

3500

3000

2500

2000

1500

1000

500

inte

nsity

[cou

nts/

360s

]

2.742.722.70wavelength [Å]

1 = 0 Å 1 = 490 Å

1.0

0.8

0.6

0.4

0.2

0.0norm

aliz

ed c

oher

ence

func

tion

80060040020002 [Å]

1 = 0 Å 1 = 490 Å

M.Baron, H.Rauch, M.Suda, J.Opt.B5 (2003) S341

Wave packet structureWave packet structure

Decoherence versus

Dephasing

20

10

0

-10

-20

B [G

]

0.60.50.40.30.20.10.0

T [s]

800

600

400

200

0

Anza

hl p

ro 0

.2G

-20 -10 0 10 20

B [G]

Magnetic noise fieldsMagnetic noise fields

Dephasing at low order

20000

15000

10000

5000

0

Inte

nsity

(cou

nts/

10s)

-100 0 100D (m)

H-Beam + B = 9G O-Beam + B = 9G

20000

15000

10000

5000

0

Inte

nsity

(cou

nts/

10s)

-100 0 100D (m)

H-Beam + B = 9G O-Beam + B = 9G

20000

15000

10000

5000

0

Inte

nsity

(cou

nts/

10s)

-100 0 100D (m)

H-Beam + B = 9G O-Beam + B = 9G

Magnetic noise fields

M.Baron, H.Rauch, M.Suda, J.Opt.B5 (2003) S244

3500

3000

2500

2000

1500

1000

500

inte

nsity

[cou

nts/

360s

]

2.742.722.70wavelength [Å]

1 = 0 Å 1 = 490 Å

1.0

0.8

0.6

0.4

0.2

0.0norm

aliz

ed c

oher

ence

func

tion

80060040020002 [Å]

1 = 0 Å 1 = 490 Å

M.Baron, H.Rauch, M.Suda, J.Opt.B5 (2003) S341

Wave Packet StructureWave Packet Structure

Dephasing

at high order

G.Sulyok

Y. Hasegawa, J. Klepp., H.Lemmel, H.Rauch, Phys.Rev. A81 (2010) 053609

2

22

21

21

21

eeeC vBlBt

Mono- and multi-mode noise

N

iiii tBtB

1)cos()(

),(),(ˆ2

),(),( 22

trtrBmktrH

ttri

zLxxtBBtrB ˆ))()().((),( 0

On-resonance→ single

photon

exchange

lvB n

21

02 Br

H.Weinfurter, G.Badurek, H.Rauch, D.Schwahn, Z.Phys. B72(1988)195

Off-resonance

→ Multi-photon

exchange

tB

BtB

cos0)(

1

0

f jj

j ja z b z

[ ]

ωj

= ω0

+ j ω

a J Bj j ( ) 1

sin( / )2

I z e a z b z eif j j

ij t

j

22

1 (

B t

B B t( )

cos

00

0 1

B1

=62.8G

ω/2π=7534 Hz

)cos(2 tja j

j

jj

Multi-photon exchange: results

(parallel fields)

J.Summhammer, K.A.Hamacher, H.Kaiser, H.Weinfurter, D.L.Jacobson, S.A.Werner, Phys.Rev.Lett.75(1995)3206 et al. PRL 75 (1995) 3206

ν

= 7534 Hz → ΔE= 3.24.10-11eV

<< ΔEbeam

= 10-4eV

Formalism zLxxtBBtrB ˆ))()().((),( 0

N

iiii tBtB

1)cos()(

ti

n

xiknNnnIII

nn

NeeeJJtx

)()........(),( 11

),.........(),........(),........(),.........(2

sin22

22

1111

0

0220

20

NNNN

i

ii

iii

iii

nn

nnnvLT

BTT

nmBmkkn

0

)(2

0 ........Re1).(),(21).(

1

vx

with

eJJetxetxtxI

iii

n

tninn

iIII

iI

i

N

m

m

timm

fexctxI )(),(0

evenn

mnn

niNnnmm

ii

f

NeJJc

;10 cos)().......(

1

mT

im

M

ii dttI

TtI

MI

00

100 )(1)(1

),(),(ˆ2

),(),( 22

trtrBmktrH

ttri

dttT

CmT N

iiii

m

0 1cos1

Multi-frequency

photon

exchange

ω1

= 1 kHz, B1

= 40 G ω1

= 2 kHz; ω2

= 3 kHz;

B1

= 15 G; B2

= 14.2 G

G. Sulyok, H. Lemmel, H. Rauch, Phys.Rev. A85 (2012) 033624

one

frequency two

frequencies

ω 0 h f

0.0

0.4

0.81.0

0.0

0.2

0.40.0

0.2

0.4

0.0

0.2

0.40.0

0.2

0.4

0.0

0.2

0.4

0.0

0.2

0.4

0.0

0.2

0.4

0.0

0.2

0.4

0 5 10 15 0 5 10 15 0 5 10 15

magnetic field amplitude B1 [Gauss]

2 h 4 h

6 h 10 h 14 h

20 h 24 h 34 hFou

rier

co

effic

ien

ts |c

|

ω f

ω f

ω f

ω f

ω f ω f

ω f

ω f

n

f1

= 3kHz, f2

=5kHz, f3

=7kHz, f4

=11kHz, f5

=13kHz

Bi

= 4 G

Bi

= 11 G

G. Sulyok, H. Lemmel, H. Rauch, Phys.Rev. A85 (2012) 033624

Five-mode

caseFive-mode

case

mT

im

M

ii dttI

TtI

MI

00

100 )(1)(1

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

upper frequency f [kHz]

dam

pin

g fa

cto

r k

measured valuessimulation with random phasessimulation with random phasesand random frequencies

up

30

25

20

15

10

5

0

ampl

itude

(a.

u.)

50403020100frequency (kHz)

30

25

20

15

10

5

0

ampl

itude

(a.

u.)

50403020100frequency (kHz)

800

600

400

200

0

Anza

hl p

ro 0

.2G

-20 -10 0 10 20

B [G]

Decoherence dephasing

Decoherence dephasing

dttT

CmT N

iiii

m

0 1cos1

Robustness of the

geometric phase

Berry-topological

phase

1

ttitRH

)(|)(|)(

))(()())(()(ˆ tRntEtRnRH n

))(()( )( tRnet ti

))(( tRn

))0(())(( RTR

)(||)())((

)(||)()(||)(1)0()(arg)(

0

0

RnRnRdidttRE

dttdtdtidtttTT

R

T

n

T

)0(|)0(|)(|

titi

eet

…. eigenstates of the instantaneous

HamiltonianΦ(t) ….. generalized

phase

for a closed

path:

for a constant

magnetic

field:

≐ 4π-symmetry

of spinors

dynamical

phase geometric

phase

2sin2cos

|2

sin|2

cos|

ie

Berry Phase (adiabatic

& cyclic

evolution)

Non-adiabatic

evolution Non-adiabatic

& non-cyclic

evolution

[ Berry; Proc.R.S.Lond. A 392, 45 (1984)]

[Samuel & Bhandari, PRL 60, 2339 (1988)][Aharonov

& Anandan, PRL 58, 1593 (1987)

(for 2-level systems)Ω

Geometric PhasesGeometric Phases

Variance

of geometric

phase

(g) tends

to 0 for increasing

time of evolution

in a magnetic

field.

G. De Chiara and G.M. Palma, PRL 91, 090404 (2003)R.S. Whitney, Y. Gefer, Phys.Rev.Lett. 90(2003)190402

Dephasing

-

DecoherenceDephasing

-

Decoherence

Ultra-cold neutronsUltra-cold neutrons

Ultra-cold neutrons at ILLUltra-cold neutrons at ILL

S. Filipp, J. Klepp, Y. Hasegawa, Ch. Plonka, P. Geltenbort, U. Schmidt, H. Rauch, Phys.Rev.Lett.102 (2009) 030404

Experimental set-upExperimental set-up

Compensation of the dynamical phaseCompensation of the dynamical phase

Spin echo to cancel dynamical phase

constant B‐field strenght, but reverse path direction

+dynamic ‐dynamic +geometric +geometric

= 2x geometric phase

Ramsey experiment measures both geometric + dynamical phase

= dynamic + geometric phase

Compensation in the case of noise fieldsCompensation in the case of noise fields

F. Filipp, J. Klepp, Y. Hasegawa, Ch. Plonka, P. Geltenbort, U. Schmidt, H. Rauch, Phys.Rev.Lett.102 (2009) 030404

Rubustness

of the geometric phaseRubustness

of the geometric phase

F. Filipp, J. Klepp, Y. Hasegawa, Ch. Plonka, P. Geltenbort, U. Schmidt, H. Rauch, Phys.Rev.Lett.102 (2009) 030404

Rubustness

of the geometric phaseRubustness

of the geometric phase

→ strength

ΔVΔτ → strength

ΔVΔτ

Visualisation of the robustness of geometric phases

Visualisation of the robustness of geometric phases

Dynamical

Phase ( ): dt

dGeometric

Phase ( ):

Stability calculations

Unavoidable Quantum Losses

Clothier

R., Kaiser H., Werner S.A., Rauch H., Woelwitsch

H., Phys.Rev.A44 (1991)5357

Phase echoPhase echo

Source) (Detector

0

ie0

ie0

ji

rrkiij

i jijeae,

)(0

1,

)(0

ji

rrkiij

i jijebe

REVERSIBILITY-IRREVERSIBILITY

0

1r

2r

3r

1t

2t

3t

0

0

and many

other

combinations…

Barrier Reflectivity

δE T < 1

T + R = 1

RMin

= (V/2E)2δk2L2

> 0

Overall phase

shift

(overall

thickness, potential height)

Exact

dimensions, varios

potentials,

beam

parameters

Parasitic (unavoidable) reflectionsParasitic (unavoidable) reflections

• Quantum Contextuality

and

Kochen-Specker

phenomenon

• Quantum Contextuality

and

Kochen-Specker

phenomenon

Yuji Hasegawa

EPR -

ExperimentEPR -

Experiment

sI II +1

-1

+1

-1

a b

Entanglement of two photon polarizations

= 12

I II + I II

Entanglement between Two-Particles

A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 4747

(1935) 777.(1935) 777.

Two-particle versus

two-path entanglementTwo-particle versus

two-path entanglement

2-Particle Bell-State = 1

2 I II + I II

I, II represent 2-Particles

Measurement on each particle AI a = +1 P a;+1

I + –1 P a;–1I

BII b = +1 P b;+1II + –1 P b;–1

II

where P ;1 = 12 ei e–i

Then, AI, BII = 0

2-Space Bell-State = 1

2 s I p + s II p

s, p represent 2-Spaces, e.g., spin &

Measurement on each property As

= +1 Ps + –1 P+

s

Bp = +1 P

p + –1 P+p

where P = 12 + ei + e–i

Then, As, Bp = 0

==>> (Non-)Contextuality(In)Dependent Results for commuting Observables

-2 < S < 2

S = E(α1

,χ1

) -

E(α1

,χ2

) + E(α2

,χ1

) + E(α2

,χ2

)

Proposal: S.M. Roy, V. Singh, Phys.Rev. A48 (1993) 3379

S. Basu, S.Bandyopadhyay, G. Kar, D. Home, Phys.Lett. A279 (2001) 281

Spin-observables

+z

-z

xs

ys

s

Path-observables

I

II

xp

yp

zp

p

Basis : +z

–z , Azimuthal angle : , Polar angle : s

Basis : I

II , Phase shift : , Relative intensity : p

zs

Spin-path (momentum) entanglementSpin-path (momentum) entanglement

Contextuality ExperimentContextuality Experiment

.Y.Hasegawa, R.Loidl, G.Badurek, M.Baron, H.Rauch, Nature 425 (2003) 45 and Phys.Rev.Lett.97 (2006) 230401

Manipulation of twoManipulation of two--subspacessubspaces

(a) Path(a) Path (b) Spin(b) Spin

Violation of a BellViolation of a Bell--like inequalitylike inequality

E' , =

N'+ + , + N'+ + +,+ – N'+ + ,+ – N'+ + +,N'+ + , + N'+ + +,+ + N'+ + ,+ + N'+ + +,

where N'+ + , = P

sP

p

E' 1,1 = 0.542 0.007E' 1,2 = 0.488 0.012E' 2,1 = – 0.538 0.006E' 2,2 = 0.483 0.012

where

1 = 02 = 0.501 = 0.792 = 1.29

===>>> S' E' 1,1 + E' 1,2 – E' 2,1 + E' 2,2

= 2.051 0.019 > 2

Cf. Max. violaion: SCf. Max. violaion: S’’=2.81>2=2.81>2

More

recent

result:

S = 2.291±0.008

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Phys.Rev.Lett. 103 (2009) 040403

Y.Hasegawa, R.Loidl, G.Badurek, M.Baron, H.Rauch,

Nature 425 (2003) 45 and Phys.Rev.Lett.97 (2006) 230401

measurement,s p s px x y y

measurements p s px y y x

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Phys.Rev.Lett. 103 (2009) 040403

Results of the Cabello ExperimentResults of the Cabello ExperimentResults of the Cabello Experiment

Set-up for Peres-Mermin proofSet-up for Peres-Mermin proof

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Phys. Rev. Lett. 103 (2009) 040403

S=2.291±0.008.

1]..[ px

sy

py

sx

py

sy

px

sx

Triple entangled states (GHZ-states)

Triple entangled states (GHZ-states)

H =H

spin

H path

H energy

Kochen-SpeckerKochen-Specker

S. Kochen, E. Specker, J.Math.Mech. 17 (1967) 59

I 0

II 0

Neutron ( )

( )

:where :

:

i i ir

c

L

r

E

e e e E

N b D phase shiftert spin rotator

t zero field precession

Triply

entangled

statesTriply

entangled

states

Mermin's inequality for GHZ-state2 according to

where

In contrast quantum theory predicts4

NC

p s e p s ex x x x y y

p s e p s ey x y y y x

Quantum GHZ

M non contextual theory

M E E

E E

M for

I 0

II 0

I 0

II 0

Neutron's GHZ-state

( )

( )

Relative phases are manipulated:

( )

( )

:where :

:

GHZ

r

Neutron

i i ir

c

L

r

E

E

E

e e e E

N b D phase shiftert spin rotator

t zero field precession

Phase shifter ( )

Spin rotator ( )

Zero field precession ( )

Mermin`s

Inequality

for GHZ-like

StatesMermin`s

Inequality

for GHZ-like

StatesD. Mermin, Phys.Rev.Lett. 65 (1990) 1838

Phase shifter ( )

Spin rotator ( )

Zero field precession ( )

I 0

II 0

Neutron ( )

( )i i ir

E

e e e E

:where :

:

c

L

r

N b D phase shiftert spinrotator

t zero field precession

Mermin`s

Inequality: MeasurementsMermin`s

Inequality: Measurements

Y. Hasegawa, R. Loidl, G. Badurek S. Sponar, H. Rauch, Phys.Rev.Lett. 103 (2009) 040403

Mermin's inequality for tri-GHZ-state2 according to

where

In contrast quantum theory predicts4

NC

p s e p s ex x x x y y

p s e p s ey x y y y x

Quantum GHZ

M non contextual theory

M E E

E E

M for

We obtained the values:

0.659

0.603

0.632

0.664

Finally, 2.558 0.004 2

p s ex x x

p s ex y y

p s ey x y

p s ey y x

Measured

E

E

E

E

M

Phase shifter ( )

Spin rotator ( )

Zero field precession ( )

Mermin`s

Inequality: ResultsMermin`s

Inequality: Results

Y. Hasegawa, R. Loidl, G. Badurek, K. Durstberger-Rennhofer, S. Sponar, H. Rauch, Phys.Rev.A…. (2010) 002100

Uni. Innsbruck and IQO Innsbruck

Compton frequency

as an internal clock ?initiated

by: H. Müller, A. Peters, S. Chu, Nature 463 (2010) 926

hmcc

cc

2

static: time dependent:

F. Mezei, Z. Physik 255 (1972) 146R. Gähler, Golub, J.Phys. France 49 (1988) 1195

MHzB

L 12 0

Larmor

interferometryLarmor

interferometry

COW-Experiment (Colella, Overhauser, Werner)

Eokom

km

mgH

2 2

2

2 2

2( )

k k kom gH

ko ( ) sin

2

2

cow II I k S

cowm

hgAo 2

2

2 sin

R. Colella, A.W. Overhauser, S.A. Werner, Phys.Rev.Lett. 34 (1974) 1472

E0

= 20 meV; mgH

~ 1.003 neV

mchC

Peters A., Chung

K.Y., Chu

S. Nature 400 (1999) 849

Müller H., Peters A., Chu

S. Nature 463 (2010) 926

Collela

R., Overhauser

A.W., Werner S.A. Phys.Rev.Lett. 34 (1975) 1053

HzmcC

252

10

Use of Compton FrequencyUse of Compton Frequency

Gravity

phase

shift

sin2 02

2

02

2

gAhm

vLmgH

mcUmc

)/1( 20 mcU

ddmc C 21

)( mgHU

zrrandrGMg

czmmgz

rGMmmcLgr

2

222

/

121

Schwarzschild metric

for motion

zrrandrGMg

zmmgzr

GMmLcl

2

2

/

21

classical

motion

Müller H., Peters A., Chu

S. Nature 463 (2010) 926

debate

with: Wolf P., Blanchhet

L., Borde C.J., Raynaud

S., Salomon C., Cohen-Tannoudji, Class.Quantum

Grav. 28 (2011) 145017

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From our experiments we can conclude or at least we can strongly believe:

• There is no well defined natural limit between quantum and classical world.

• Non-locality (in ordinary space) and contextuality are fundamental properties of nature.

• Quantum mechanics gives a correct description of all results but boundary conditions are as important as the basic equation itself.

• Quantum losses are unavoidable and occure in any kind of interaction.

From our experiments we can conclude or at least we can strongly believe:

• There is no well defined natural limit between quantum and classical world.

• Non-locality (in ordinary space) and contextuality are fundamental properties of nature.

• Quantum mechanics gives a correct description of all results but boundary conditions are as important as the basic equation itself.

• Quantum losses are unavoidable and occure in any kind of interaction.

RésuméRésumé

• For the interpretation one should keep in mind that the initial or boundary conditions are also based on statistical measurements of an equally prepared ensemble and, therefore, it does not seem so surprising that only statistical predictions about the outcome of an experiment can be made.

• Thus, we do not know everything at the beginning so we also do not know everything at the end (e.g. every event).

(S. Stenholm 2009).

• For the interpretation one should keep in mind that the initial or boundary conditions are also based on statistical measurements of an equally prepared ensemble and, therefore, it does not seem so surprising that only statistical predictions about the outcome of an experiment can be made.

• Thus, we do not know everything at the beginning so we also do not know everything at the end (e.g. every event).

(S. Stenholm 2009).

Résumé addRésumé add

• Entanglement, quantum contextuality and Kochen- Specker phenomena tell us that quantum physics involves stronger correlations than classical physics does. The quantum world seems not to be chaotic but provides the basis for the stability of atoms, molecules and – last but not least- for the existence of conscious beings.

(G. Eder 2000)

• Entanglement, quantum contextuality and Kochen- Specker phenomena tell us that quantum physics involves stronger correlations than classical physics does. The quantum world seems not to be chaotic but provides the basis for the stability of atoms, molecules and – last but not least- for the existence of conscious beings.

(G. Eder 2000)

Résumé addRésumé add

Neutron interferometry generations

Stefan Filipp

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Baron

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UlrichBonse

Hartmut Lemmel

DietmarPetraschek

KatharinaDurstberger

MichaelZawisky

Wolfgang Treimer

Sam Werner

Jürgen Klepp

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