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Problems in the theory of the Casimir effect. V. M. Mostepanenko. Noncommercial Partnership “Scientific Instruments”, Moscow, Russia. 15 th Lomonosov Conference, Moscow, 2011. CONTENT. Introduction 2. Two parallel ideal metal plates at zero temperature
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Problems in the theory of the Casimir effect V. M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Moscow, Russia 15th Lomonosov Conference, Moscow, 2011
CONTENT • Introduction • 2. Two parallel ideal metal plates at zero temperature • 3. Two parallel ideal metal plates at nonzero temperature • 4. The Lifshitz theory • 5. Comparison of the Lifshitz theory with experimental data • 6. Conclusions and discussion 15th Lomonosov Conference, Moscow, 2011
1. INTRODUCTION The Casimir force arises due to the change of the spectrum of zero-point oscillations of the electromagnetic field by material boundaries. Casimir, 1948 15th Lomonosov Conference, Moscow, 2011
2. TWO PARALLEL IDEAL METAL PLATES AT ZERO TEMPERATURE 15th Lomonosov Conference, Moscow, 2011
The vacuum energy is 15th Lomonosov Conference, Moscow, 2011
After renormalization 15th Lomonosov Conference, Moscow, 2011
3. TWO PARALLEL IDEAL METAL PLATES AT NONZERO TEMPERATURE 15th Lomonosov Conference, Moscow, 2011
After renormalization 15th Lomonosov Conference, Moscow, 2011
The limit of low temperature 15th Lomonosov Conference, Moscow, 2011
The limit of high temperature 15th Lomonosov Conference, Moscow, 2011
4. THE LIFSHITZ THEORY Maxwell equations Continuity boundary conditions 15th Lomonosov Conference, Moscow, 2011
The frequency-dependent dielectric permittivity 15th Lomonosov Conference, Moscow, 2011
are the Matsubara frequencies. Lifshitz, 1956 15th Lomonosov Conference, Moscow, 2011
Reflection coefficients for two independent polarizations: 15th Lomonosov Conference, Moscow, 2011
Models of the frequency-dependent dielectric permittivity Permittivity of dielectric plates as determined by core electrons Permittivity of dielectric plates with dc conductivity included The Drude model permittivity for metallic plates The plasma model permittivity for metallic plates The Lifshitz theory with or violates the Nernst theorem Klimchitskaya, Mohideen, Mostepanenko, Rev. Mod. Phys. 2009 15th Lomonosov Conference, Moscow, 2011
5.COMPARISON OF THE LIFSHITS THEORY WITH THE EXPERIMENTAL DATA 5.1 Indirect measurement of the Casimir pressure using a micromachined oscillator Decca, Lopez, Fischbach, Klimchitskaya, Krause, Mostepanenko, PRD (2003); Ann. Phys. (2005); PRD (2007); EPJC (2007); Decca, Lopez, Osquiguil, IJMPA (2010). 15th Lomonosov Conference, Moscow, 2011
Shematic setup Schematic setup with a micromachined oscillator 15th Lomonosov Conference, Moscow, 2011
Comparison between experiment and theory (first method) The relative experimental error (at a 95% confidence level) varies from 0.19% at 162 nm to 0.9% at 400 nm and 9% at 746 nm. The Drude model is excluded by the data at a 95% confidence level. 15th Lomonosov Conference, Moscow, 2011
Comparison between experiment and theory (second method) The Drude model is excluded by the data at a 95% confidence level. 15th Lomonosov Conference, Moscow, 2011
5.2 Optical modulation of the Casimir force Vacuum chamber Optical filter 640 nm laser beam Photo- diodes Silicon membrane Cantilever Au Sphere z 514nm Ar laser AOM Force difference Function generator 100Hz Lock-in amplifier Chen, Klimchitskaya, Mostepanenko, Mohideen, Optics Express (2007); PRB (2007). 15th Lomonosov Conference, Moscow, 2011
Comparison of experiment with theory using different models of permittivity Within error bars one cannot discriminate between Drude and plasma model for high-conductivity silicon Inclusion of DC conductivity for high-resistivity Si (in dark phase) does not agree with experimental results 15th Lomonosov Conference, Moscow, 2011
5.3 The Casimir force between Au sphere and ITO plate Chang, Banishev, Klimchitskaya, Mostepanenko, Mohideen, Phys. Rev. Lett., to appear. 15th Lomonosov Conference, Moscow, 2011
6. CONCLUSIONS AND DISCUSSION 1. Thermal Casimir effect is the topical subject for both quantum field theory and nanotechnology 2. There are contradictions between some results of thermal quantum field theory and basic principles of thermodynamics 3. The same results of thermal quantum field theory are also in contradiction with several experiments 4. After 11 years of active discussions the opinion becomes popular that the problem cannot be solved without serious changes of the basic concepts concerning the interaction of quantum fluctuations with matter 15th Lomonosov Conference, Moscow, 2011
