Abstract
Most of this chapter is devoted to the study of retarded long-range forces and other similar effects on matter which arise as a direct consequence of the existence of the fluctuating electromagnetic zeropoint field. As will become clear, the properties of the vacuum that are used in the derivation of these effects can easily be framed in a classical language, and there is in principle no need to resort to the quantum formalism. In addition to providing at all times during the calculations a physically transparent image, the SED approach has the virtue of confirming that at least for the family of problems considered here, what is essential is the existence of the electromagnetic vacuum; not the quantization of it. Thus, phenomena that have been regarded as some of the “least intuitive consequences of QED” [Schwinger et al. 1978] appear here as some of the most intuitive consequences of SED.
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References
Marshall (1965b) studies the balance between the average energy lost through radiative reaction and the average energy gained from the background field for an oscillator in the space between two parallel conducting plates. A treatment based on the evaluation of the transverse component of the Maxwell stress tensor of the field at one of the plates reproduces the quantum result for the Casimir effect, including a (small) thermal contribution when T > 0. In a similar spirit, Boyer (1968a) reproduces Casimir’s result for the energy change by proposing that the force between the plates arises from the zeropoint field subject to boundary conditions. Further, following the work by Lifshitz (1955) on dispersion forces between dielectric bodies, Boyer calculates the force between the plates by evaluating the electromagnetic stress tensor, thus explicitly showing that there is a clearcut connection
Further discussion on the role of the cutoff in the evaluation of Casimir forces can be found in Candelas (1982).
This is because for isothermal processes the change in the energy content of the field equals the change in the free energy. On the contrary, for adiabatic processes the former equals the change of the total energy of the system. See, e.g., Abraham and Becker (1933), §33.
A slightly different approach to the subject, which also accepts a reformulation in the SED language, is given in González (1985).
We recall that Poincaré postulated a covariant stress tensor that should be added to the electromagnetic stress tensor of the charged particle, in order to provide mechanical stability [see, e.g., Jackson 1975, chapter 17].
A variety of examples are discussed, e.g., in Ambj0rn and Wolfram (1983), where it is shown that the energy modification of the vacuum depends on the number of dimensions of space and the specific shape of the conductors. Although these authors refer to ‘quantized’ vacuum fields, their results are not at all dependent on the quantization of the fields and can equally well be phrased in the language of SED.
We refer the reader to chapter 7 of Milonni (1994) for a more recent derivation of this result, based on the calculation of the zeropoint energy via the mode-summation method. Although the calculation is made there within QED, it can be reproduced step by step using the nonquantized zeropoint field.
See §7.2.1 for a brief discussion on the use of the Drude-Lorentz model for the atom both in SED and in quantum mechanics.
Incidentally, a particularly interesting application of Lifshitz’ technique is to the case of liquid helium [Dzyaloshinskii et al. 1961]. Owing to the small dielectric constant of this material (e ≃ 1.057), the Casimir force across an adsorbed liquid helium film turns out to be repulsive and thus gives rise to its remarkable climbing and wetting properties. Lifshitz’s theory has also been applied successfully to a detailed study of the dispersion forces across the phospholipid layers that build up the biological membranes [Parsegian and Ninham 1970].
Before the integration over the solid angle in k-space is carried out, however, the correlations still depend on the angle between k and a, which means that there is an anisotropy in the distribution of the radiation as seen by the accelerated detector, although it does of course not show up in the formula for the energy density; see Hinton et al. (1983). It is thanks to this anisotropy that the accelerated particle can be expected to meet a resistive force, as mentioned at the end of §6.4.2.
The fluctuation-dissipation theorem is touched upon in sections 7.2 and 11.2. For a general discussion of it we refer the reader to Reichl (1980).
Since the frictional force of the background field on a (nonaccelerated) dipole of frequency ω vanishes only if ρ ~ ω 3, a dipole which is accelerated through the zeropoint field is expected to meet a resistance due to the distorted spectrum of equation (6.92). Haisch et al. (1994a, b) have recently applied this idea in an appealing attempt to explain the origin of the inertia of particles, under the hypothesis that matter is ultimately constituted by primary charged entities or ‘partons’ bound in the manner of oscillators. According to their assumptions, the resistive Lorentz force comes out precisely proportional to the acceleration, and they interpret the factor of proportionality as the inertial mass m of the particle, which turns out to be inversely proportional to the partons’ bare mass. Their frequency of oscillation, however, must be extremely high (of the order of the Planck frequency ω P = (c5 /ħG) 1/2, where G is the Newtonian gravitational constant) for m to acquire the correct value. For some informal comments on this attempt see Powell (1994).
Sonoluminescence is a non-equilibrium phenomenon in which the energy of a sound wave becomes highly concentrated so as to produce the emission of light by collapsing bubbles of gas trapped in a liquid. The light bursts can carry an energy corresponding to over 105 photons in less than 100 ps, representing an amplification of energy by 11–12 orders of magnitude [see Barber and Putterman 1992 and references therein].
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© 1996 Springer Science+Business Media Dordrecht
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de la Peña, L., Cetto, A.M. (1996). Environmental Effects Through the Zeropoint Field. In: The Quantum Dice. Fundamental Theories of Physics, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8723-5_6
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DOI: https://doi.org/10.1007/978-94-015-8723-5_6
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