We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. Our approach improves upon the proximity force approximation. It can be generalized easily to arbitrary geometries, different boundary conditions, to the computation of Casimir energy densities and to many oth...

The recent discovery that silicon nitride membranes can be used as extremely high Q mechanical resonators makes possible a number of novel experiments, which include improved long range vacuum Casimir force measurements, and measurments of the properties of liquid helium below the lambda point. It is noted that in the thermal correction to the Casimir force, the phase velocity of the excitation...

In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square (m2 < 0). We consider here only the case of the one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of the Abel...

The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force has a significant role in nanomechanics and object manipulation at the nanoscale, leadi...

We consider detailed roughness and conductivity corrections to the Casimir force in the recent Casimir force measurement employing an atomic force microscope. The roughness of the test bodies — a metal plate and a sphere — was investigated with the AFM and the SEM respectively. It consists of separate crystals of different heights and a stochastic background. The amplitude of roughness relative...

We show that the Casimir force between mirrors with arbitrary frequency dependent reflectivities obeys bounds due to causality and passivity properties. The force is always smaller than the Casimir force between two perfectly reflecting mirrors. For narrow-band mirrors in particular, the force is found to decrease with the mirrors bandwidth. PACS: 03.65; 12.20; 42.50