Explicit conversion from the Casimir force to Planck's law of radiation

Abstract

The Casimir force has its origin in finite modification of the infinite zero-point energy induced by a specific boundary condition for the spatial configuration. In terms of the imaginary-time formalism at finite temperature, the root of Planck's law of radiation can be traced back to finite modification of the infinite vacuum energy induced by the periodic boundary condition in the temporal direction. We give the explicit conversion from the Casimir force to Planck's law of radiation, which shows the apparent correspondence between the system bounded by parallel conducting plates and the thermodynamic system. The temperature inversion symmetry and the duality relation in the thermodynamics are also discussed. We conclude that the effective temperature characterized by the spatial extension should no longer be regarded as genuine temperature.

Zero modes, entropy bounds and partition functions

“…It is clear from the structure of the Epstein ζ -functions that such a temperature-inversion symmetry will hold, in some form, for cavities of rectangular shape and their periodic counterparts, the tori. A number of calculations have explicitly verified these rather elementary facts [22][23][24][25]. The symmetry applies for the other flat space forms as well [15,[26][27][28].…”

Anomalous Casimir effect in axion electrodynamics

“…The calculation machinery is quite analogous to the imaginary-time formalism of finite-temperature field theory (see Ref. [3] for discussions on temperature inversion symmetry in the Casimir effect). A pioneering experimental test for the Casimir force in the original scenario started out more than a half century ago [4], while the more accurate measurement is established after decades of development [5][6][7][8].…”

Comment on "Quantum critical paraelectrics and the Casimir effect in time"

“…This is a facet of the property known as temperature inversion symmetry discussed in the literature that leads to explicit conversion from Casimir force to Planck's law of radiation. 14,15 Very recently, in Refs. 16 and 17, using the ε expansion and/or the limit N → ∞ in the framework of the classical O(N) symmetric ϕ 4 model with film geometry one obtains results for the amplitude of the correlation length and quantities related to the Casimir effect in a close vicinity of the upper critical dimension that can be conversed to the field of quantum paraelectric-ferroelectric phase transitions in particular and to quantum critical phenomena in general.…”