We investigate the Casimir effect at finite temperature in electromagnetic Rindler space, and find the Casimir energy is proportional to temperature^4/diameter^2 and in the high temperature limit, where Temp is 27C is the temperature and diameter is about 100nm is a small cutoff. The parameters of metamaterials we proposed are quite simple, this experiment would be easily implemented in laboratory.
Previously they computed the quantum Casimir energy of electromagnetic de Sitter space and find it is proportional to the size of horizon, the same order as dark energy. They also suggest to make metamaterials to mimic de Sitter space and measure the predicted Casimir energy. This experiment is of great importance in two aspects. First, it could detect an unusual large Casimir effect. Second, it may provide an alternative of the origin of dark energy for our accelerating universe. However, the experiment they proposed is difficult to be practiced for several reasons.
First, the permittivity and permeability of metamaterials they designed are very complicated. Second, due to the spherical symmetry of de Sitter space, one has to make the corresponding metamaterials one spherical shell by one spherical shell and finally assemble them together, which is, of course, a hard task. Third, they do not consider the temperature effect which is an important factor in an actual experiment. In this letter, we try to overcome those problems. We consider the Rindler space instead, which is much simpler than de Sitter space but shares almost all the important features such as Hawking radiation, area law of entropy, infinite red-shift on horizon and, in particular, the huge Casimir effect.
Rindler space is a flat spacetime experienced by observers with constant acceleration a. Rindler space is related with the Minkowski space by suitable coordinate transformations, however physics in those two spaces are completely different.
Metamaterials can mimic the gravitational metrics up to an arbitrary conformal factor. The metamaterial can be built up layer by layer.
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