K. V. Shajesh

How Does Casimir Energy Fall

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

PT-symmetric quantum electrodynamics

{E}_{c}

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

are both

Noncontact gears. II. Casimir torque between concentric corrugated cylinders for the scalar case

{E}_{c}/{c}^{2}

How does Casimir energy fall? III. Inertial forces on vacuum energy

. This simple result disproves recent claims in the literature. We clarify some pitfalls in the calculation that can lead to spurious dependences on the coordinate system.

Gravitational and inertial mass of Casimir energy

Abstract The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge e is taken to be imaginary. However, if one also specifies that the potential A μ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field φ has a cubic self-interaction of the form i φ 3 . The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C , which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this Letter the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.

How does Casimir energy fall? IV. Gravitational interaction of regularized quantum vacuum energy

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, ?-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (?, x, y, ?). Fixed ? in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of ?. In the limit of a large Rindler coordinate ? (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just Mg, 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 ?-function potential approaches infinity.

Many-body Contributions to Green's Functions and Casimir Energies

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for noncontact gears. To this end, we calculate the Casimir torque between two such cylinders, described by {delta}-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.

Repulsive long-range forces between anisotropic atoms and dielectrics

We have recently demonstrated that Casimir energy due to parallel plates, including its divergent parts, falls like conventional mass in a weak gravitational field. The divergent parts were suitably interpreted as renormalizing the bare masses of the plates. Here, we corroborate our result regarding the inertial nature of Casimir energy by calculating the centripetal force on a Casimir apparatus rotating with constant angular speed. We show that the centripetal force is independent of the orientation of the Casimir apparatus in a frame whose origin is at the center of inertia of the apparatus.

Electromagnetic δ -function sphere

It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This conclusion holds independently of the orientation of the plates. We review these arguments and 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. We calculate the force on systems consisting of one or two such plates undergoing acceleration perpendicular to the plates. In the limit of small acceleration we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just Mg, 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. Extension of this latter work to arbitrary orientation of the plates, and to general compact quantum vacuum energy configurations, is under development.