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1 Casimir Effect and Short-Range Forces 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 4.
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