The Feigel Process. The Momentum of Quantum Vacuum. Geert Rikken Vojislav Krstic. CNRS-France. Ariadne call A0/1-4532/03/NL/MV 04/1201

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1 The Fegel Pocess The Momenum of Quanum Vacuum a an Tggelen CNRS -Fance Laboaoe e Physque e Moélsaon es Mleux Complexes Unesé Joseph Foue/CNRS, Genoble, Fance Gee Ren Vosla Ksc CNRS Fance CNRS-Fance Laboaoe Naonal es Champs Magnéques Pulsés Unesé Paul Sabae, Toulouse, Fance Aane call A/-5//NL/MV /

2 Wha s clame by A. Fegel? Phys. Re.. Le. 9,, ( elecc homogeneous mea mus obey Loenz naance Ths soles Abaham-Mnows Conoesy Ths pecs a fne momenum ensy fo zeo-pon flucuaons n leco-magnec Mae

3 Vacuum Langangan L [ ] s Gallean naan (een Loenz -naan: (fo << Vacuum sess enso T 8 [ ] [ ] δ s symmec conseaon of momenum P ( S / c conseaon of angula momenum G (

4 omogeneous elecc Langangan L [ ] ε s NOT Gallean naan: elecc sess enso T s NOT NCSSARILY symmec Momenum s consee P ( G ( s 8 [ ] [ ] δ Momenum of wha? P S / c s angula momenum?

5 Fegel s appoach: he wo poblems mus be elae, an mus be solable smulaneously ( ε ε ε L [ ] [ ] s Gallean naan naan : Conseaon of Noehe momenum: G L( xα, α, Aα, β Aα Conseaon of Pseuo-momenum momenum: L ( ε :

6 Fegel conclues: P ε ( G (Mnows Momenum? [ ] ( ( ( ( * P P ω ω δ ω ( ˆ ω ω ω ω h l nl c n c ε ε ω ( h mpy acuum -ansoopc meum n acuum

7 Classcal lecoynamcs of b-ansoopc mea: ε m a a a a a ( ( δ Consue equaons Macoscopc Maxwell equaons ( a a a a q m Newon -Loenz equaon Mcoscopc Mae

8 Maco-Maxwell Newon-Loenz ( ( T δ 8 S G S f T G ( ( M P U δ M P f U P ( ( ( [ ] µ ε f 8 «pseuo momenum» conseaon (Fegel Mnows eson of negy/momenum conseaon ( ( T δ 8 T M foce ensy Rgoous conseaon of oal momenum (mae fel

9 ( ( ( ( L T f f S G S f T G δ (Mnows 8 8 Abahams eson of enegy/momenum conseaon

10 Poblems wh he Fegel pape. Conseaon of momenum an pseuo momenum ensy follow fom onay classcal elecoynamcs apple o b-ansoopc mea, wh acually a sloppy flaw coece Classcal elecoynamcs obeys Gallean Inaance.. The Abaham-Mnows s no sole because s no een aesse A conoesy noles a scusson of he M foce ensy (hus nhomogeneous mea o me-epenen fels an he (symmey of he sess enso. Thee s no unque soluon (on macoscopc leel.. Fom ( P s conclue ha P Ths assumes no moon an no fel a some san me, wheeas aleay no souces (fee chages hae been aope. The fnal esul s also no Gallean naan P The soluon an consan leas o no conacon. Nee o aess he ynamc poblem!

11 ε T. The enso changes une me eesal. The enso changes une pay e( εω p pp ω Φ ω Φ Roaoy powe; ( ω ω g δ ( ω, p εδ g ε p ε Fesnel speson law ( Φ p ε nml pl nm y y ε p p Magneo-eleccal effec ( ( ω ω ( ( ω p εδ S p p S, x x S

12 Suble heoems S So n Abaham s eson: G S u n Mnows s eson: hω G ( ε S c c

13 Fne classcal macoscopc meum: elasc scaeng hω, p hω h ω c ˆ ou c ˆ n h ω, p ε, p( ω ( ˆ ˆ σ ˆ { hω ( ˆ n ou ou, n, S ( n ou PT hω hω ˆ ˆ n n ˆ ˆ ou ou σ ( ˆ Ω Ω σ ( ˆ Ω n n, ˆ, ˆ ou ou, S, S n ( Obec says a es Van Tggelen an Ren, Commen Phys. Re. Le. ( ou ou n

14 Quanum elecoynamcs: Inelasc scaeng fom molecules n a aaon fel an subec o an hω, ' p S hω, A xce sae hω, Goun sae A ( S hω c Magneo-elecc Q Pay : OK Tme-eesal: OK Loenz-naance? Value of?

15 Quanum elecoynamcs: hω, ' p S hω, xce sae hω, p nsen opple fcon ˆ ' h' N ( A ( ' ˆ h hω mc [ ] ( ' ( ω N ( N ( ω [ N ( N ( ] p ω A Goun sae p( S Loenz/Gallean naance?? Vacuum Themal equlbum

16 xpemenal efcaon of Fegel heoy phase-sense oque-measuemens on mco-sze samples se-ew: sac magnec fel example:. Ohmch, Y Osaa, Re. Sc. Ins. 7, ( canlee e aas - an Alphen oscllaons of S RuO oque τ ~ p ~ olage change momenum, (foce p oscllaon esoluon δv ~ δτ ± - Nm AC elecc fel, pepencula o, apple by elecoe-plaes (sample hole/sc

17 some numbes on he Fegel pocess... maeal: amon ε 6, µ,.5 g/cm, m µg : 6 T AC elecc Fel: 7 V/m a canlee egen-fequency (euce o 8.7 z ue o sample mass followng Fegel: acuum flucuaons λ max. nm.7 µm/s alenaes: soopc hgh nensy fel (p ~ nensy lase-fel p 7-5 gm/s yels τ -9 Nm exp. esoluon δτ ± - Nm

18 Possble expemenal appoach: canlee-magneomey: sample pezoesse pah / elemen l - µm w 5 µm - 5 µm f 5 - z small samples possble! foce/oque apple ~ mechancal sess ~ olage / essance change on pezoesse elemen

Field due to a collection of N discrete point charges: r is in the direction from

Field due to a collection of N discrete point charges: r is in the direction from Physcs 46 Fomula Shee Exam Coulomb s Law qq Felec = k ˆ (Fo example, f F s he elecc foce ha q exes on q, hen ˆ s a un veco n he decon fom q o q.) Elecc Feld elaed o he elecc foce by: Felec = qe (elecc