New developments in the Casimir effect

Abstract

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

Measurement of the Casimir force between a spherical gold tip and Si(111)-(7 × 7) surfaces

“…We use this equation with the plasma frequency for Si (2.4 × 10 13 rad/s) to evaluate our experimental results. The deviation from an ideal surface geometry or roughness should be considered to predict actual forces, as mentioned by Bordag et al 27) For experimental studies of the Casimir force, atomic force microscopy (AFM) has been widely used to evaluate the subtle force. To minimize capillary force due to water layers 28) on surfaces and improve the sensitivity of force-sensing cantilevers, AFM measurements have been performed in a vacuum, as seen in Table I.…”

Энергия Казимира В Некомпактной Электродинамике На Решетке

“…Из непрерывной теории [1] хорошо известно, что энергия Казимира зависит от R, как C/R 3 , поэтому попытаемся фитировать последовательность точек, полученную из решеточных вычислений, функцией…”

“…Такие задачи часто встречаются в прило-жениях, и современные методы расчета сил Казимира должны быть пригодны для исследования и этого круга задач. К сожалению, существующие на сегодняшний день подходы к расчету сил Казимира, основанные на методе функций Грина, не ЭНЕРГИЯ КАЗИМИРА В НЕКОМПАКТНОЙ ЭЛЕКТРОДИНАМИКЕ НА РЕШЕТКЕ 263 обладают достаточной универсальностью [1]. С их помощью были решены задачи с простой геометрией граничных поверхностей (плоской, сферической, цилиндриче-ской и т.п.…”

“…Ситуация еще более усложняет-ся в случае, когда казимировское взаимодействие происходит при конечных темпе-ратурах, а также под воздействием внешних полей. Существующие приближенные методы, такие, например, как алгоритм PFA (Proximity Force Approximation) [1], [2], часто не позволяют получить достоверный результат в физически интересной обла-сти значений параметров. Точность этих методов также очень трудно оценить, что представляет собой дополнительную проблему при их применении.…”

Evidence for a Causal Relationship between Mach’s Principle and the Quantitative Latency for Universal Entanglement

“…Casimir effects facilitate the transformation of virtual particles into real particles [12] assuming there is a changing boundary condition of the electromagnetic field. The dynamic volume of the human brain can be considered a complex of changing boundary conditions that range from the entwined rostral-caudal waves moving coherently at ~4.5 m·s -1 over the cerebral cortices [13] to the rotating electromagnetic field that moves along the axon barrel of each neuron towards the synapse.…”