Relativistic mechanics of Casimir apparatuses in a weak gravitational field

Abstract

This paper derives a set of general relativistic Cardinal Equations for the equilibrium of an extended body in a uniform gravitational field. These equations are essential for a proper understanding of the mechanics of suspended relativistic systems. As an example, the prototypical case of a suspended vessel filled with radiation is discussed. The mechanics of Casimir apparatuses at rest in the gravitational field of the Earth is then considered. Starting from an expression for the Casimir energy-momentum tensor in a weak gravitational field recently derived by the authors, it is here shown that, in the case of a rigid cavity supported by a stiff mount, the weight of the Casimir energy EC stored in the cavity corresponds to a gravitational mass M = EC /c 2 , in agreement with the covariant conservation law of the regularized energy-momentum tensor. The case of a cavity consisting of two disconnected plates supported by separate mounts, where the two measured forces cannot be obtained by straightforward arguments, is also discussed.

Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: Scalar case

“…The equations II were rather general, whereas now we consider, following the introduction and our previous work [9,10], Fermi-Walker coordinates for a system of two parallel plates in a weak gravitational field. To first order in the ε parameter of Secs.…”

“…Ever since Casimir discovered that suitable differences of zero-point energies of the quantized electromagnetic field can be made finite and produce measurable effects [1], several efforts have been produced to understand the physical implications and applications of this property [2,3,4,5,6] In particular, we are here concerned with the recent theoretical discovery that Casimir energy gravitates [7,8,9,10]. In Ref.…”

From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field

“…While all approaches now agree about the push and the magnitude of the effect [12], the work in Ref. [10], despite its explicit analytic formulas for T µν , led to legitimate puzzlements, being accompanied by a theoretical prediction of nonvanishing trace anomaly.…”

“…In particular, we are here concerned with a problem actively investigated over the last few years, i.e. the behavior of rigid Casimir cavities in a weak gravitational field [6], [7], [8], [9], [10], [11], [12], [13]. An intriguing theoretical prediction is then found to emerge, according to which Casimir energy obeys exactly the equivalence principle [11], [12], [13], and the Casimir apparatus should experience a tiny push (rather than being attracted) in the upwards direction.…”

Thermally excited quasiparticles in metals, dispersion forces, and the thermal anomaly

“…In particular the works by Kats and Bimonte made it clear that the r σ are indeed reflection amplitudes for electromagnetic waves in the p (TM) and s (TE) polarisation. 16,17 The same expression applies for zero-point and thermal fluctuations, apart from the different frequency ranges that dominate the two contributions. Expanding in powers of r 1σ r 2σ , we get a multiple reflection sum, the basis for the scattering approach to the Casimir pressure.…”