Gravitation of the Casimir Effect and the Cosmological Non-Constant

Whereas the total energy in zero-point fluctuations of the particle physics vacuum gives rise to the cosmological constant problem, differences in the vacuum give rise to real physical phenomena, such as the Casimir effect. Hence we consider the zero-point energy bound between two parallel conducting plates — proxy for a solid slice of cosmological constant — as a convenient laboratory in which to investigate the gravitation and inertia of vacuum energy. We calculate the Casimir effect in a weak gravitational field, obtaining corrections to the vacuum stress-energy and attractive force on the plates due to the curvature of spacetime. These results suggest that if the cosmological constant is due to zero-point energy then it is susceptible to fluctuations induced by gravitational sources. The Casimir effect [1,2] is one of the most remarkable phenomena in the strange and spooky world of quantum mechanics. At the most basic level, the attractive force acting on two parallel conducting plates is a physical manifestation of zero-point energy. Idealized, the plates are cold and uncharged in vacuo, so there are no real particles or fields present, but a virtual quantum electrodynamic field creates a pressure difference across the plates, resulting in this uniquely quantum force. Our attraction to the Casimir effect follows from its potential relationship to the cosmological constant (Λ) [3,4] — perhaps a cosmological manifestation of zero-point energy. In Zeldovich’s landmark 1968 paper [5] he declared that once Einstein has introduced Λ, “the genie has been let out of the bottle and it is no longer easy to force it back in.” In a prescient statement, he observed that “a new field of activity arises, namely the determination of Λ”: What is known about it? What are the limits on it? What experiments can probe Λ? Numerous experiments are currently focusing on these very questions! [6] Furthermore, Zeldovich offered the provocative suggestion that the cosmological constant may be due to the energy density and pressure of the particle physics vacuum. In support of this speculation, he used the energy density and pressure for the vacuum of scalar particles of mass m