Variations of Casimir energy from a superconducting transition

Bimonte, Giuseppe; Calloni, E.; Esposito, Giampiero; Rosa, Luigi

doi:10.1016/j.nuclphysb.2005.08.010

Cited by 74 publications

(65 citation statements)

References 41 publications

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“…Contrary to statements in Ref. [19], it is generally accepted in quantum field theory in curved space-time that the renormalized total T µν must be conserved. …”

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confidence: 57%

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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“…Contrary to statements in Ref. [19], it is generally accepted in quantum field theory in curved space-time that the renormalized total T µν must be conserved. …”

contrasting

confidence: 57%

How does Casimir energy fall?

et al. 2007

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“…In our opinion, this important experiment could bring the final verification of the results obtained from the thermal quantum field theory approach (see also Refs. [75,76] where two short-separation experiments are proposed with the same aim).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Thermal quantum field theory and the Casimir interaction between dielectrics

Geyer¹,

Klimchitskaya²,

2005

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“…The variation of the Casimir free energy during this transition is very small (Mostepanenko, Trunov, 1997). Nevertheless, the magnitude of this variation can be comparable to the condensation energy of a semiconducting film and causes a measurable increase in the value of the critical magnetic field (Bimonte et al, 2005a(Bimonte et al, , 2005b.…”

Section: The Dielectric-metal Transitionmentioning

confidence: 99%