How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Abstract

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here add further support to this conclusion by considering parallel semitransparent plates, that is, δ-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (τ, x, y, ξ). Fixed ξ in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of ξ. In the limit of large Rindler coordinate ξ (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just M g, where g is the gravitational acceleration and M is the total mass of the system, consisting of the mass of the plates renormalized by the Casimir energy of each plate separately, plus the energy of the Casimir interaction between the plates. This reproduces the previous result in the limit as the coupling to the δ-function potential approaches infinity.

Casimir effect of two conducting parallel plates in a general weak gravitational field

“…Furthermore, computation of the energy, i.e. |T 00 | , has also been done for large number of problems in various spacetimes and in some cases [1,2] has helped us to confirm the validity of the principle of correspondence in the context of the Casimir effect. Finding the total gravitational force on a set of two conducting Casimir plates [1,2] is a typical example.…”

“…7 Examples: finding coefficients γ 0 , γ 1 , λ 0 , λ 1 In this section a number of spacetimes are investigated and the parameters appearing in (28), (52), and (53) will be found. To this end, we will try to find their weak field form according to (3), (4), and (7).…”

“…In fact, some non-trivial topologies in curved spacetime do the same job as a boundary does [6,7]. The Casimir energy in curved spacetime has also been analyzed by many authors ( [1,2,6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and references therein). Recently, a Casimir apparatus consisting of two ideal conducting parallel plates in the weak field limit of the Kerr and the Horava-Lifshitz spacetimes has been studied in [8][9][10][11].…”

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

“…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.…”

Archimedes force on Casimir apparatus

“…We analyze weighting the Casimir apparatus in weak gravitational field in this talk. This problem has attracted some attention in recent years [1][2][3][4][5][6][7][8] and there used to be controversy in the literature we will mention below. We argue that the key point is physically correct definition of the weighting procedure, since there is no possibility to weight Casimir energy alone -one always measure the weight of Casimir apparatus as a whole.…”