Attractive Forces between Flat Plates

Sparnaay, M.J.

doi:10.1038/180334b0

Cited by 99 publications

(80 citation statements)

References 2 publications

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“…Thermodynamics allows the possibility of zero-point energy and experimental evidence (such as that for van der Waals forces) requires its existence. [10] It is natural to choose the unknown constant for the zero-point energy in (17) so as to fit the experimentally measured van der Waals forces. This corresponds to an oscillator energy…”

Section: Wien Displacement Results and Zero-point Energymentioning

confidence: 99%

Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum

Boyer

2003

American Journal of Physics

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A thermodynamic analysis of the harmonic oscillator is presented. Motivation for the study is provided by the blackbody radiation spectrum; when blackbody radiation is regarded as a system of noninteracting harmonic oscillator modes, the thermodynamics follows from that of the harmonic oscillators. Using the behavior of a harmonic oscillator thermodynamic system under an adiabatic change of oscillator frequency ω, we show that the thermodynamic functions can all be derived from a single function of ω/T , analogous to Wien's displacement theorem. The high-and low-frequency energy limits allow asymptotic energy forms involving T alone or ω alone, corresponding to energy equipartition and zero-point energy. It is suggested that the "smoothest possible" function which behaves as a − bx at small values of x and vanishes at large x is ae −bx/a because it is a monotonic analytic function every derivative of which is a multiple of the function itself. In this sense, it is noted that the Planck spectrum with zero-point radiation corresponds to the function satisfying the Wien displacement result which provides the smoothest possible interpolation between energy equipartition at low frequency and zero-point energy at high frequency.

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Section: Wien Displacement Results and Zero-point Energymentioning

confidence: 99%

Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum

Boyer

2003

American Journal of Physics

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“…[1] What began as an obscure phenomenon in electrodynamics [2] has became of general theoretical interest in quantum field theory [3], has been connected to wave phenomena in acoustics [4] and boating, [5] and is now of technological concern in connection with microelectromechanical devices. [6] In particular, there have been accurate experimental measurements of electromagnetic Casimir forces [7] and suggestions that such forces will create a "stiction" which will bind surfaces together at small separations. In order to overcome such stiction, the repulsive aspects of Casimir forces have recently been reinvestigated.…”

Section: Introductionmentioning

confidence: 99%

Casimir forces and boundary conditions in one dimension: Attraction, repulsion, Planck spectrum, and entropy

Boyer

2003

American Journal of Physics

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Quantities associated with Casimir forces are calculated in a model wave system of one spatial dimension where the physical ideas are transparent and the calculations allow easy numerical evaluation. The calculations show strong dependence upon fixed-or free-end (Dirichlet or Neumann) boundary conditions for waves on a one-dimensional string, analogous to infinitely-conducting or infinitely-permeable materials for electromagnetic waves. 1) Due to zero-point fluctuations, a partition in a one-dimensional box is found to be attracted to the walls if the wave boundary conditions are alike for the partition and the walls, but is repelled if the conditions are different.2) The use of Casimir energies in the presence of zero-point radiation introduces a natural maximum-entropy principle which is satisfied only by the Planck spectrum for both like and unlike boundary conditions between the box and partition.3)The one-dimensional Casimir forces increase or decrease with increasing temperature depending upon like or unlike boundary conditions. The Casimir forces are attractive and increasing with temperature for like boundary conditions, but are repusive and decreasing with temperature for unlike boundary conditions. 4) In the high-temperature limit, there is a temperature-independent Casimir entropy for like boundary conditions, but a vanishing Casimir entropy for unlike boundary conditions. These one-dimensional results have counterparts for electromagnetic Casimir forces in three dimensions.

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“…[4] Thermodynamics allows the possibility of zero-point energy and experimental evidence such as van der Waals forces requires its existence. [5] Casimir forces and energies are those which arise due to the discrete, classical normal modes structure of a system. [6] In total contrast to particles, waves are influenced in the interior of a volume by the presence of boundary conditions at the walls.…”

Section: Introductionmentioning

confidence: 99%

Conjectured derivation of the Planck radiation spectrum from Casimir energies

Boyer¹

2003

J. Phys. A: Math. Gen.

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By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum corresponds to that spectrum of random radiation (having constant energy k B T per normal mode at low frequencies and zero-point energy (1/2)hω per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. Our analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.

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Attractive Forces between Flat Plates

Cited by 99 publications

References 2 publications

Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum

Thermodynamics of the harmonic oscillator: Wien’s displacement law and the Planck spectrum

Casimir forces and boundary conditions in one dimension: Attraction, repulsion, Planck spectrum, and entropy

Conjectured derivation of the Planck radiation spectrum from Casimir energies

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