Casimir Effect and The “vacuum energy catastrophe” Short-Range Forces http://www.lkb.ens.fr „ The mean energy density per unit volume Astrid Lambrecht and Serge Reynaud, of electromagnetical field at thermal equilibrium A. Canaguier-Durand, J. Lussange, R. Guerout, R. Messina, P. Monteiro, I. Cavero-Pelaez, L. Rosa …

Collaborations : M.-T. Jaekel (LPT ENS Paris), ‰ is finite for the first Planck law (1900) P.A. Maia Neto (Rio de Janeiro), V.V. Nesvizhevsky, J. Chevrier (Grenoble), ‰ is infinite when accounting for C. Genet, T. Ebbesen (Strasbourg), zero-point fluctuations (Planck 1912) G. Ingold (Augsburg), D. Dalvit (Los Alamos), ‰ is much too large to be compatible with gravity observations for I. Pirizhenko (Dubna), V. Klimov (Moscow) … any reasonable cutoff frequency (Nernst 1916)

Discussions with a number of other A major problem for fundamental physics people, in particular within the known since 1916, still unsolved today … ESF network “CASIMIR” http://www.casimir-network.com S. Weinberg, Rev. Mod. Phys. 61 1 (1989)

A common “solution” : the denial of vacuum Confining the vacuum in a cavity : energy the Casimir effect Quotation : Pauli 1933 « For fields [in contrast to the material oscillator], it is more

consistent not to introduce the zero-point energy … ¾ Here written for an ideal case For, on the one hand, the latter would give rise ‰ Parallel plane mirrors to an infinitely large energy per unit volume ‰ Perfect reflection ‰ Null temperature due to the infinite number of degrees of freedom ... and, as is evident from experience, it does not produce any ¾ Attractive force (negative pressure) gravitational field ... And, on the other hand, it would be unobservable since it cannot be emitted, absorbed or scattered, and hence, cannot A universal effect from confinement of vacuum fluctuations : be contained within walls. » it depends only on ћ, c, and geometry

W. Pauli, Die Allgemeinen Prinzipien der Wellenmechanik (Springer, 1933) Hendrik Casimir 1948

1 Search for scale dependent modificationsmodifications ofof Constraints at sub-mm scales the gravity force law (“fifth-force experiments”) the gravity force law (“fifth-force experiments”) ‰ Best result to date : Excluded domain Eöt-wash group The exclusion plot for in the plane (λ,α) deviations with a (U. Washington, Seattle) Yukawa form ‰ Cavendish-type experiments

Geophysical with torsion pendulum

Laboratory ‰ At 95% confidence, a Yukawa interaction with Satellites

Windows remain α

10 gravitational strength open for deviations at short ranges log must have a range log10λ (m) LLR Planetary FIG. 6: Constraints on Yukawa violations of the gravitational 1/r2 law. The shaded region is ™ D.J. Kapner et al or long ranges Courtesy : J. Coy, E. Fischbach, R. Hellings, excluded at the 95% confidence level. Heavy PRL 98 (2007) 021101 lines labeled Eöt-Wash 2006, Eöt-Wash 2004, C. Talmadge & E. M. Standish (2003) ; see Irvine, Colorado and Stanford show experimental M.T. Jaekel & S. Reynaud IJMP A20 (2005) ™ E.G. Adelberger et al constraints from this work, Refs. [11], [14], [15] and [16, 17], respectively. Lighter lines show PRL 98 (2007) 131104 various theoretical expectations summarized in The Search for Non-Newtonian Gravity, E. Fischbach & C. Talmadge (1998) Ref. [9].

Constraints at shorter scales Casimir experiments

Excluded domain ‰ Recent precise experiments : ‰ At (~) µm scales, in the plane (λ,α) dynamic measurements of comparison with theory of VdW-nuclear Casimir measurements the resonance frequency of a ‰ Also worth with Van der Casimir microelectromechanical resonator Waals * and nuclear # forces at shorter scales

Cavendish

The hypothetical new α force would be seen as a 10 ‰ Shift of the resonance difference between log determined by the gradient G experiment and theory of the Casimir force ‰ Plane-sphere Casimir effect F new ≡ F exp − F th calculated within the proximity log λ (m) 10 Courtesy R.S. Decca force approximation (see below) * S. Lepoutre et al, EPL 88 (2009) 20002 (Indiana U – Purdue U Indianapolis)

# V. Nesvizhevsky et al, Phys. Rev. D77 (2008) 034020 R.S. Decca, Talk at Sante Fe Workshop (09/2009) @ http://cnls.lanl.gov/casimir/

2 Comparison with theory The description of metals ?

Recent experimental results deviate from theoretical expectations ‰ A problem with the description of metallic mirrors ?

¾ Lifshitz formulation of the Casimir force

• interaction between two plane mirrors

¾ Dielectric functions modelled

• conduction electrons in the metals with relaxation accounted for (Drude model)

¾ Gold has a finite conductivity

¾ γ≠0 is certainly a better description than γ=0

Experiments agree better with γ=0 than with the expected γ≠0 ! ¾ Artifact in the experiments ? ¾ Problem in the theoretical evaluations ? ¾ Difference between the situation studied The difference does not have a Yukawa form ! in theory and the experiments ? R.S. Decca, D. Lopez, E. Fischbach et al, Phys. Rev. D75 (2007) 077101 S. Reynaud et al, Proceedings of QFEXT'09, arXiv:1001.3375 (2010)

The role of geometry ? Detailed theory of Casimir forces

¾ The geometry of the precise experiments is ‰ Casimir physics : mechanical effects of the coupling between mirrors not the geometry of the precise calculations ! and vacuum fluctuations

¾ Mirrors described by their scattering properties, which are ¾ Calculations in the plane-sphere geometry determined by optics and condensed matter physics usually performed by using the proximity ¾ Confining vacuum fluctuations in a cavity affects the radiation force approximation (PFA) which amounts to pressure and produces the Casimir effect a mere averaging of the plane-plane result over the distances ‰ The “scattering approach” ¾ Used for years for evaluating the Casimir force between ¾ PFA expected to be accurate at the limit R>>L “real” mirrors (non perfect mirrors)

¾ Today the best solution for calculating the Casimir force ¾ But what is the accuracy for given values of R and L ? in non trivial geometries ¾ How does this accuracy depend on the properties of the mirror, M.-T. Jaekel, S. Reynaud, J. Physique I-1 (1991) 1395 arXiv:quant-ph/0101067 on the distance, on the temperature ? A. Lambrecht, S. Reynaud EPJD 8 (2000) 309 arXiv:quant-ph/9907105

S. Reynaud et al, Proceedings of QFEXT'09, arXiv:1001.3375 (2010) A. Lambrecht, P. Maia Neto & S. Reynaud, New J. Physics 8 (2006) 243

3 Temperature and dissipation for plane Temperature in the plane-sphere geometry

mirrors Casimir force calculated between plane mirrors Force between plane and spherical perfect Expressed as a ratio to ideal Casimir formula reflectors at room or zero temperature Drawn as the ratio 1.1 ¾ Strong correlation 20 of force at T≠0 R = 0.1 μm between dissipation R = 0.2 μm 10 to force at T=0 1.08 R = 0.5 μm μ perfect and thermal effects 5 R = 1 m 1.06 μ plasma ¾ Contribution of thermal R = 2 m R = 5 μm ¾ Variation by a F 2 photons repulsive at 1.04 PFA analytic

F perf factor 2 at the highCas 1 some distances ! ϑ 1.02 temperature limit 0.5 ¾ Casimir entropy also (large distances) found negative at some 1 0.2 perfect distances 0.98 plasma 0.1 ¾ ¾ Current precise Features never seen for 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 50 100 0.96 experiments perfect plane mirrors 0.5 1 2 5 LL[[μµm]m] L [μm] A. Canaguier-Durand, P.A. Maia Neto, A. Lambrecht, S. Reynaud G. Ingold, A. Lambrecht, S. Reynaud, Phys. Rev. E80 (2009) 041113 PRL 104 (2010) 040403

Temperature and dissipation in the plane- sphere geometry Force between metallic plane and sphere at room temperature 2 R = 0.1 μm Drawn as the ratio R = 0.2 μm μ 1.8 R = 0.5 m of force at γ = 0 (plasma) R = 1 μm to force at γ ≠ 0 (Drude) R = 2 μm μ Drude 1.6 R = 5 m R = 10 μm ¾ Plasma and Drude / F PFA always closer than 1.4 plasma

expected from PFA F 1.2 ¾ Ratio at large L never approaches the 1 factor 2 given by PFA 0.5 1 2 5 10 L [μm]

A. Canaguier-Durand, P.A. Maia Neto, A. Lambrecht, S. Reynaud PRL 104 (2010) 040403

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