An alternative response to the off-shell quantum fluctuations: a step forward in resolution of the Casimir puzzle
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Regular Article - Theoretical Physics
An alternative response to the off-shell quantum fluctuations: a step forward in resolution of the Casimir puzzle G. L. Klimchitskaya1,2 , V. M. Mostepanenko1,2,3,a 1
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, Saint Petersburg 196140, Russia Institute of Physics, Nanotechnology and Telecommunications, Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg 195251, Russia 3 Kazan Federal University, Kazan 420008, Russia
2
Received: 13 August 2020 / Accepted: 10 September 2020 © The Author(s) 2020
Abstract The spatially nonlocal response functions are proposed which nearly coincide with the commonly used local response for electromagnetic fields and fluctuations on the mass shell, but differ significantly for the off-shell fluctuating field. It is shown that the fundamental Lifshitz theory using the suggested response functions comes to an agreement with the measurement data for the Casimir force without neglecting the dissipation of free electrons. We demonstrate that reflectances of the on-shell electromagnetic waves calculated using the nonlocal and commonly employed local responses differ only slightly. The Kramers–Kronig relations for nonlocal response functions possessing the firstand second-order poles at zero frequency are derived, i.e., the proposed response satisfies the principle of causality. An application of these results to resolution of the Casimir puzzle, which lies in the fact that the Lifshitz theory is experimentally consistent only with discarded dissipation, is discussed.
1 Introduction Beginning in 2000, much attention is being given to the Casimir force [1] acting between closely spaced uncharged surfaces. This force is caused by the quantum fluctuations (both zero-point and thermal) of the electromagnetic field. It extends familiar van der Waals force [2] to larger separations where the relativistic effects become essential. The general theory of van der Waals and Casimir forces between two material plates developed by Lifshitz [3,4] is in fact semiclassical. It describes electromagnetic fluctuations in the framework of thermal quantum field theory in the Matsubara formulation, but the response of matter to these fluctuations is treated classically by means of the standard continuity bounda e-mail:
[email protected] (corresponding author)
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ary conditions where the frequency-dependent dielectric permittivity plays the role of a response function. Taking into consideration that the Casimir effect finds numerous multidisciplinary applications in quantum field theory, physics of elementary particles, gravitation and cosmology, atomic physics, condensed matter physics, as well as in nanotechnology (see, e.g., the monographs [5–11]), it is hardly surprising that the Lifshitz theory was used and cited in thousands of papers. Over a protracted period of the last 20 years, the Lifshitz theory has been facing a challenge when calculating the Casimir force between metallic surfaces
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