Abstract:
The Casimir effect results from the optomechanical coupling between field fluctuations and mirrors in quantum vacuum. This contribution to the 20th International Conference on Laser Spectroscopy (ICOLS 2011) discusses the current status in the comparison between theory and experiments.

Abstract:
Comparison with theory of Casimir force measurements are used to test the gravity force law at ranges from 0.1 to 10 micrometers. The interest of such tests depends crucially on the theoretical evaluation of the Casimir force in realistic experimental configurations. We present the scattering approach which is nowadays the best tool for such an evaluation. We then describe the current status of the comparisons between theory and experiments.

Abstract:
We study the influence of finite conductivity of metals on the Casimir effect. We put the emphasis on explicit theoretical evaluations which can help comparing experimental results with theory. The reduction of the Casimir force is evaluated for plane metallic plates. The reduction of the Casimir energy in the same configuration is also calculated. It can be used to infer the reduction of the force in the plane-sphere geometry through the `proximity theorem'. Frequency dependent dielectric response functions of the metals are represented either by the simple plasma model or, more accurately, by using the optical data known for the metals used in recent experiments, that is Al, Au and Cu. In the two latter cases, the results obtained here differ significantly from those published recently.

Abstract:
The Casimir effect is a crucial prediction of Quantum Field Theory which has fascinating connections with open questions in fundamental physics. The ideal formula written by Casimir does not describe real experiments and it has to be generalized by taking into account the effects of imperfect reflection, thermal fluctuations, geometry as well as the corrections coming from surface physics. We discuss these developments in Casimir physics and give the current status in the comparison between theory and experiment after years of improvements in measurements as well as theory.

Abstract:
A field state containing photons propagating in different directions has a non vanishing mass which is a quantum observable. We interpret the shift of this mass under transformations to accelerated frames as defining space-time observables canonically conjugated to energy-momentum observables. Shifts of quantum observables differ from the predictions of classical relativity theory in the presence of a non vanishing spin. In particular, quantum redshift of energy-momentum is affected by spin. Shifts of position and energy-momentum observables however obey simple universal rules derived from invariance of canonical commutators.

Abstract:
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields is used first to build the definition of these observables and then to describe their relativistic properties under frame transformations. The transformations to accelerated frames of the space-time observables depart from the laws of classical relativity. The Einstein laws for the shifts of clock rates and frequencies are recovered in the quantum description, and their formulation provides a conformal metric factor behaving as a quantum observable.

Abstract:
The Casimir effect is a force arising in the macroscopic world as a result of radiation pressure of vacuum fluctuations. It thus plays a key role in the emerging domain of nano-electro-mechanical systems (NEMS). This role is reviewed in the present paper, with discussions of the influence of the material properties of the mirrors, as well as the geometry dependence of the Casimir effect between corrugated mirrors. In particular, the lateral component of the Casimir force and restoring torque between metal plates with misaligned corrugations are evaluated.

Abstract:
Quantum fluctuations impose fundamental limits on measurement and space-time probing. Although using optimised probe fields can allow to push sensitivity in a position measurement beyond the "standard quantum limit", quantum fluctuations of the probe field still result in limitations which are determined by irreducible dissipation mechanisms. Fluctuation-dissipation relations in vacuum characterise the mechanical effects of radiation pressure vacuum fluctuations, which lead to an ultimate quantum noise for positions. For macroscopic reflectors, the quantum noise on positions is dominated by gravitational vacuum fluctuations, and takes a universal form deduced from quantum fluctuations of space-time curvatures in vacuum. These can be considered as ultimate space-time fluctuations, fixing ultimate quantum limits in space-time measurements.

Abstract:
Vacuum field fluctuations exert a radiation pressure which induces mechanical effects on scatterers. The question naturally arises whether the energy of vacuum fluctuations gives rise to inertia and gravitation in agreement with the general principles of mechanics. As a new approach to this question, we discuss the mechanical effects of quantum field fluctuations on two mirrors building a Fabry-Perot cavity. We first put into evidence that the energy related to Casimir forces is an energy stored on field fluctuations as a result of scattering time delays. We then discuss the forces felt by the mirrors when they move within vacuum field fluctuations, and show that energy stored on vacuum fluctuations contributes to inertia in conformity with the law of inertia of energy. As a further consequence, inertial masses exhibit quantum fluctuations with characteristic spectra in vacuum.