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Chapter 8 Casimir Forces: Fundamental Theory, Computation, and Nanodevice Applications

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Abstract

Seventy years after submission to the Physical Review of the crucial quantum electrodynamical treatment of interatomic dispersion forces by Casimir and Polder, our understanding of such interactions in both the unretarded and retarded regimes has undergone a dramatic and intricate evolution. In this contribution, we explore the ultimate physical motivations leading to this fascinating trajectory rich in momentous implications for the goal of both fabrication and operation of highly integrated micro- and nano-structures. The first and most obvious development has been the growing appreciation that, far from only representing a weak, though exotic, effect, Casimir’s “zero point pressure of electromagnetic waves” between two conducting parallel planes is actually a dominant interaction on the nanoscale. This resulted in Feynman’s unforgettable caricature – in “There’s plenty of room at the bottom” – of van der Waals forces between microparts as a “man with his hands full of molasses,” which led to such forces being understood as the leading cause of undesirable stiction for several decades. However, commencing in the 1980s, the realization that such strong dispersion interactions might offer unique technological opportunities surfaced. The second thrust was connected to the discovery that, unlike expected from London’s intermolecular force theory and the naive assumption of additivity, dispersion forces depend quite unpredictably on topology and on the interplay of dielectric properties of the interacting media. This may lead to drastic departures from results obtained through perturbative methods and indeed to the prediction, later verified both in the unretarded and retarded regimes, that dispersion forces may become repulsive. The challenge of computing Casimir forces in more general geometries different from that of two parallel planes has led to substantial progress from the numerical standpoint although open problems remain. Lastly, in one of the earliest and most significant discoveries in the history of the field, it was shown that dispersion forces can be modulated in time, for instance by illumination in semiconductors. This discovery opened the way to consideration of thermodynamical engine cycles enabled by Casimir forces and to a novel, highly effective means for energy transfer on the nanoscale.

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Notes

  1. 1.

    Notice that ‘induction’ here describes what we presently refer to as polarization (Ref. [2], p. 164). This quotation is from the 2nd edition (1881) of the Treatise. However, the entire last paragraph of Art. 27 is identical in both the 1st (1873) and 3rd editions (1892). Both statements closely paraphrase, with somewhat more familiar language, equivalent principles stated by William Thomson (Baron Kelvin) in his On the Mathematical Theory of Electricity in Equilibrium, indeed cited by Maxwell (see the Reprint of Papers on Electrostatics and Magnetism, p. 43, Art. 59) [3]. Also, ‘electricity,’ and related terms, are used where the modern term of charge is meant.

  2. 2.

    Therefore the statement that “neutrons have no charge and are neither attracted nor repelled by charged particles” (Ref. [6], p. 501) is obviously incorrect as neutrons, as all nucleons, are polarizable [7] (see the “Naïve picture” in Sect. 8.2.1 therein) and thus they can be “acted on by an electrified body.” The erroneous statement does not appear in later editions [8].

  3. 3.

    The fact that “repetition of a plausible statement increases a person’s belief in the referential validity or truth of that statement,” popularly referred to as the ‘truth effect,’ was demonstrated decades ago by means of psychology experimentation [21].

  4. 4.

    This calculation was first attempted by S. C. Wang in 1927 [31].

  5. 5.

    The very personal ferocity surrounding Casimir effect controversies is, by itself, a subject worthy of social science study. For details about this particular exchange see, for instance, “A fraction too much friction causes physics fisticuffs” by Chris Lee [73]. For further details, and for the effect of such debates throughout the process of technology transfer, see Ref. [18].

  6. 6.

    This is a translation into English quoted in Ref. [104]; see also Ref. [105] (in German) and Ref. [106] (in Russian).

  7. 7.

    Here “a molecule is the smallest possible portion of a particular substance.” [123] (Vol. II, p. 46).

  8. 8.

    This concept might be a provocative solution of ‘double-starred’ Prob. 10.31, “Mutually induced dipoles” in Electricity and Magnetism by Purcell and Morin [122].

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Acknowledgements

I am grateful to Professor Di Bartolo, Director, for his gracious invitation to participate – as a humble student – in the NATO Advanced Study on “Quantum Nano-photonics,” and for much more. I was particularly touched by the splendid atmosphere created by the Organizers, Maura Cesaria and Luciano Silvestri, and wish to thank many fellow-students for their great interest in Casimir forces and for their inspiring comments to the lectures I presented. I dedicate this contribution to my father, Italo Pinto (1928–2017), who passed away before the Proceedings could appear in print, for a lifetime of steadfast encouragement and support in the pursuit of my dreams to investigate the secrets of the universe and communicate that enthusiasm and curiosity to others.

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  1. Department of Aerospace Engineering, Faculty of Engineering, Izmir University of Economics, Teleferik Mahallesi, Balçova/İzmir, Turkey

    Fabrizio Pinto

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  1. Fabrizio Pinto
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Editors and Affiliations

  1. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Baldassare Di Bartolo

  2. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Luciano Silvestri

  3. IMM-CNR, Lecce, Italy

    Maura Cesaria

  4. Department of Physics and Astronomy, Wheaton College, Norton, MA, USA

    John Collins

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Pinto, F. (2018). Chapter 8 Casimir Forces: Fundamental Theory, Computation, and Nanodevice Applications. In: Di Bartolo, B., Silvestri, L., Cesaria, M., Collins, J. (eds) Quantum Nano-Photonics. NATO 2017. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1544-5_8

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