Casimir Momentum in Complex Media? Bart van Tiggelen

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Casimir Momentum in Complex Casimir Momentum in Complex Media? Media? Bart van Tiggelen Bart van Tiggelen Collaborators: Collaborators: Geert Rikken (LNCMI Grenoble/Toulouse) Geert Rikken (LNCMI Grenoble/Toulouse) Sébastien Kawka (Ph.D Grenoble Sébastien Kawka (Ph.D Grenoble ENS Pisa) ENS Pisa) James Babington (postdoc ANR Grenoble) James Babington (postdoc ANR Grenoble) Costas Soukoulis 60 years, June 2011 Costas Soukoulis 60 years, June 2011 Grenoble

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Casimir Momentum in Complex Media? Bart van Tiggelen. Grenoble. Collaborators: Geert Rikken (LNCMI Grenoble/Toulouse) Sébastien Kawka (Ph.D Grenoble  ENS Pisa ) James Babington (postdoc ANR Grenoble). Costas Soukoulis 60 years, June 2011. Momentum from Nothing. B 0. E 0. ε , μ ,g. - PowerPoint PPT Presentation

Transcript of Casimir Momentum in Complex Media? Bart van Tiggelen

Page 1: Casimir Momentum in Complex Media? Bart van Tiggelen

Casimir Momentum in Complex Casimir Momentum in Complex Media?Media?

Bart van TiggelenBart van Tiggelen

Collaborators:Collaborators:

• Geert Rikken (LNCMI Grenoble/Toulouse)Geert Rikken (LNCMI Grenoble/Toulouse)• Sébastien Kawka (Ph.D Grenoble Sébastien Kawka (Ph.D Grenoble ENS Pisa) ENS Pisa)•James Babington (postdoc ANR Grenoble)James Babington (postdoc ANR Grenoble)

Costas Soukoulis 60 years, June 2011Costas Soukoulis 60 years, June 2011

Grenoble

Page 2: Casimir Momentum in Complex Media? Bart van Tiggelen
Page 3: Casimir Momentum in Complex Media? Bart van Tiggelen
Page 4: Casimir Momentum in Complex Media? Bart van Tiggelen

Momentum from NothingMomentum from Nothing

εε,,μμ,g,g

k, k,', kE0

B0

Page 5: Casimir Momentum in Complex Media? Bart van Tiggelen

0

v)1(

cl

ijlij

BEχH

BχED

*

ε

0000jijiij EBBEg

Magneto-electric birefringenceMagneto-electric birefringence

0*det00

220

2

χpεpεχpp

ccp

c

lnmlinmpiΦ p

Fresnel dispersion lawFresnel dispersion law

kx

Bi-anisotropic MediaBi-anisotropic Media

Fizeau effectFizeau effect

ky

vv

ijij gi

EE0 0 x Bx B00

Rotatory powerRotatory power

1010-15-151010-8-8

1010-2-2

Page 6: Casimir Momentum in Complex Media? Bart van Tiggelen

0

3

0

003

0

12

11

2

11

00

cd

c

gdc

k

k

vk

BEk

BE

0040

3

4

3

2BE g

cc

cut-off in X-ray ?cut-off in X-ray ?

phenomenological continuum theoryphenomenological continuum theory

Photonic momentum in dielectric media? Photonic momentum in dielectric media? classical « Abraham » contribution already controversialclassical « Abraham » contribution already controversialUV catastrophe of vacuum energy ?UV catastrophe of vacuum energy ?Lorentz invariance of quantum vacuum?Lorentz invariance of quantum vacuum?Inertia of quantum vacuum? Inertia of quantum vacuum?

jijiijij

t

BBEET

c

4

1

8

1

4

1

220

0

0

BE

TBEv

vcasi

Inertial mass of quantum vacuum?Inertial mass of quantum vacuum?

Page 7: Casimir Momentum in Complex Media? Bart van Tiggelen

)bubble nowater (

2

1)in water bubble(

2

1)bubble( 333

kk kkr dddE

MeV101

130

43

c

a c

Schwinger (1993)Schwinger (1993)

UV catastrophe in sonoluminescence

(> 1934)

cut-off in the UV ?cut-off in the UV ?

eV001.0

1

1536

23)bubble( 0

2

a

cE

Page 8: Casimir Momentum in Complex Media? Bart van Tiggelen

2

2

1)( P

2

23

030

p

casi dc

++

Free electronFree electron

Electric quadruoleElectric quadruole

Rizzo etal, 2003-2009, Babington & BAvT, 2011Rizzo etal, 2003-2009, Babington & BAvT, 2011

03

030

)( BEP 0 gdccasi

ggME ME = 10= 10-17--17-- -

1010-11-11

The UV catastrophe is realThe UV catastrophe is real

magnetic dipolemagnetic dipole

gME(ω)/n

Page 9: Casimir Momentum in Complex Media? Bart van Tiggelen

2222222

22 )(

2)(2)(

2

11),,( BEBEBEv

vBE

ccL

BBB

EEE

0

0

003

40

4

*0 BE

BE

K

004

*0

HE

),()2(

1lim 040

21

3

ddK

c

c

Zero energy flowZero energy flow infinite momentum densityinfinite momentum density

Lorentz Lorentz scalarscalar

Bi-anisotropic Bi-anisotropic Lorentz-invariant vacuumLorentz-invariant vacuum

)'(2),',(Im20)','(),(0 2* rrrr ijji GEE Fluctuation-Fluctuation-DissipationDissipation

Casimir momentum, if infinite, is Lorentz invariantCasimir momentum, if infinite, is Lorentz invariant

Page 10: Casimir Momentum in Complex Media? Bart van Tiggelen

BB00

εεEE00(t)(t) vv

003 )(

3

41)( BEv tatm 0constant BPv

++ --

EE00(t)(t)

BB00vv

)()(

)()(

1222

1211

rqtqm

rqtqm

fBrEr

fBrEr

02)(2

0constant220

xBREx

BxR

mqtqm

qm

0020

2

)(/

2 BER tmq

m

)(2

12,1 xaRr

Classical Abraham momentum in crossed EM fieldsClassical Abraham momentum in crossed EM fields

(Walker Nature, 1976)(Walker Nature, 1976)

Page 11: Casimir Momentum in Complex Media? Bart van Tiggelen

sec/nm32

)0(vabr

pm

EB

sec/nm02.04

v4Feigel gEB

h

c

sec/nm0.0

10158.0v 20

gEBa

cregula

sec/nm08.0log3

4vv abr

e

atQED m

m

Classical abraham Classical abraham forceforce

Feigel QED with cut-off Feigel QED with cut-off 0.1 nm0.1 nm

Regularization of Regularization of vacuum energy in a=10 cmvacuum energy in a=10 cm

(Milton, 2000)(Milton, 2000)

QED harmonic oscillatorQED harmonic oscillator(Kawka, 2010)(Kawka, 2010)

E=450 V/mm; B=1 T

m/VT10017.0

)T(roomkg/m17.0

)6.16(/VCm1022.00

22

3

30

240

g

a

Ex: HeliumEx: Helium

Page 12: Casimir Momentum in Complex Media? Bart van Tiggelen

BEp )0( LntBEPP cos)0(0

AcousticAcousticpressurepressure

dp/dt=Abraham forcedp/dt=Abraham force

Experiment: Geert RikkenExperiment: Geert Rikken αα(0)(0)

p/(EB) p/(EB)

E=450 V/mm;E=450 V/mm; B=1 T; B=1 T; f= 7.6 kHz f= 7.6 kHz

V= 8 nm/sec+- 0.8V= 8 nm/sec+- 0.8Feigel : 2 nm/secFeigel : 2 nm/sec

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rErBA 000 2

1

221

20210

22202

2

21101

1

2

1

)()(2

1)()(

2

1

rrE

rArAprArAp

e

eem

eem

H

Casimir momentum: Casimir momentum: 1/41/4

QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields

EE00

BB00

+e+e -e-e

21* iii

i

aa

Page 14: Casimir Momentum in Complex Media? Bart van Tiggelen

)(

)(

20212

10111

rAvp

rAvp

em

em

Casimir momentum: Casimir momentum: 2/42/4

QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields

0],[ HK

rBPrBppK 021021 2

1ˆ ee kin

Pseudo-Pseudo- momentum is conservedmomentum is conserved

Conjugate momentaConjugate momenta ≠ ≠ kinetic momentumkinetic momentum

EE00

BB00

+e+e -e-e

Page 15: Casimir Momentum in Complex Media? Bart van Tiggelen

pcmp

pdpm

mm

mmmmM

ii

2/3

4)(

2021

2121

Casimir momentum: Casimir momentum: 3/43/4

QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields

EE00

BB00

21*)()(ˆ

210212211 iiii

aaeeemm krBrArAvvK

210020

2

0020

2

00

1KKBEBEvv

eeMMK

+e+e -e-e

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220

002 )0( c

BEK

Casimir momentum: Casimir momentum: 4/44/4

QED of harmonic oscillator in crossed fieldsQED of harmonic oscillator in crossed fields

2

1

12

1200

12

22

012

12001

log3

4)0(

/2//2/6

4)0(

m

m

mm

mm

cmpp

p

cmpp

pdp

mm

mm

BE

BEK

KK1 1 : 2 % QED correction to Abraham force: 2 % QED correction to Abraham forceKK22: 0.01 % QED correction : 0.01 % QED correction

Kawka & Van Tiggelen, EPL 2010Kawka & Van Tiggelen, EPL 2010

EE00

BB00

+e+e -e-e

Page 17: Casimir Momentum in Complex Media? Bart van Tiggelen

BB00

Faraday RotationFaraday Rotation

A quantum vacuum force F= g dB/dt ?A quantum vacuum force F= g dB/dt ?

0

20

220

204

,

iVBi

c

Chiral geometry with electric polarizabilitiesChiral geometry with electric polarizabilities

00000 HErBErHB dd

εε

εεεε

εε

Page 18: Casimir Momentum in Complex Media? Bart van Tiggelen

BB00

Faraday RotationFaraday Rotation

A quantum vacuum force F= g dB/dt ?A quantum vacuum force F= g dB/dt ?

iVBi

20

2

200,

000 HErd

Chiral geometry with magnetic polarizabilitiesChiral geometry with magnetic polarizabilities

000 BBEr gd Na Na TetraederTetraeder L=10 nm L=10 nm g/m = 1 nm/sec/T g/m = 1 nm/sec/T

µµµµµµ

µµ

Page 19: Casimir Momentum in Complex Media? Bart van Tiggelen

momentum of quantum vacuum tomomentum of quantum vacuum toshed new light on the controversial shed new light on the controversial

nature of zero-point energynature of zero-point energy

Corsica,Corsica,20062006

Congratulations Costas! Congratulations Costas!