Casimir effect in a weak gravitational field

Sorge, Francesco

doi:10.1088/0264-9381/22/23/012

Cited by 69 publications

(156 citation statements)

References 23 publications

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“…This result for the energy contained in the force equation (3.7) is an immediate consequence of the general formula for the Casimir energy [29] 8) in terms of the frequency transform of the Green's function,…”

Section: Gravitational Acceleration Of Casimir Apparatusmentioning

confidence: 76%

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

Milton¹,

Parashar²,

Shajesh³

et al. 2007

J. Phys. A: Math. Theor.

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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.

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Section: Gravitational Acceleration Of Casimir Apparatusmentioning

confidence: 76%

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

Milton¹,

Parashar²,

Shajesh³

et al. 2007

J. Phys. A: Math. Theor.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

2008

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This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration g, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gravity acceleration g. The general structure of the calculation is therefore elucidated, and the components of the Maxwell energy-momentum tensor are evaluated up to second order in g, improving a previous analysis by the authors and correcting their old first-order formula for the Casimir energy.

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“…The question turns out to be surprisingly less straightforward than one might suspect! Previous authors [8,9,10,11,12] have given disparate answers, including gravitational forces, or gravitationally modified Casimir forces, that depend on the orientation of the Casimir apparatus with respect to the gravitational field of the earth. We will here resolve some of this confusion with a convincingly calculated result consistent with the equivalence principle.…”

mentioning

confidence: 99%

How does Casimir energy fall?

et al. 2007

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Doubt continues to linger over the reality of quantum vacuum energy. There is some question whether fluctuating fields gravitate at all, or do so anomalously. Here we show that for the simple case of parallel conducting plates, the associated Casimir energy gravitates just as required by the equivalence principle, and that therefore the inertial and gravitational masses of a system possessing Casimir energy Ec are both Ec/c 2 . This simple result disproves recent claims in the literature. We clarify some pitfalls in the calculation that can lead to spurious dependences on coordinate system. PACS numbers: 03.70.+k, 04.20.Cv, 04.25.Nx, 03.65.Sq The subject of quantum vacuum energy (the Casimir effect) dates from the same year as the discovery of renormalized quantum electrodynamics, 1948 [1]. It puts the lie to the naive presumption that zero-point energy is not observable. On the other hand, it continues to be surrounded by controversy, in large part because sharp boundaries give rise to divergences in the local energy density near the surface (see Refs. [2,3,4]). The most troubling aspect of these divergences is in the coupling to gravity. Gravity has its source in the local energymomentum tensor, and such surface divergences promise serious difficulties. The gravitational implications of zero-point energy are an outstanding problem in view of our inability to understand the origin of the cosmological constant or dark energy [5,6,7].As a prolegomenon to studying such issues, we here address a simpler question: How does the completely finite Casimir energy of a pair of parallel conducting plates couple to gravity? The question turns out to be surprisingly less straightforward than one might suspect! Previous authors [8,9,10,11,12] have given disparate answers, including gravitational forces, or gravitationally modified Casimir forces, that depend on the orientation of the Casimir apparatus with respect to the gravitational field of the earth. We will here resolve some of this confusion with a convincingly calculated result consistent with the equivalence principle. That is, the renormalized Casimir energy couples to gravity just like any other energy. In our opinion, this fact is evidence that vacuum energy must be taken seriously in gravitational theory and that the problem of boundary divergences must be resolved by a better understanding of the modeling and renormalization processes.We start by recalling the electromagnetic Casimir stress tensor between a pair of parallel perfectly conducting plates separated by a distance a, with transverse dimensions L ≫ a, as given by Brown and Maclay [13]:where the third spatial direction is the direction normal to the plates. This is given in terms of the Casimir energy per unit area, E c = −π 2 c/(720a 3 ). Outside the plates, T µν = 0. Omitted here is a constant divergent term that is present both between and outside the plates, and also in the absence of plates, which cannot have any physical significance. Because the electromagnetic field respects conformal symmetr...

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Casimir effect in a weak gravitational field

Cited by 69 publications

References 23 publications

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

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

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

How does Casimir energy fall?

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