Abstract
In this chapter we pursue our investigations on the behaviour of simple SED systems and compare the results with the quantum description in similar circumstances. Four problems are treated, namely, the free particle, the properties of atoms immersed in a magnetic field, the nature of the electron spin and the specific heat of solids. The free particle does not present in itself any particular problem, at least in the nonrelativistic, long-wavelength approximation used here; anyway, the fluctuation of its energy offers the opportunity to take a fresh glance at a complex phenomenon which in QED is described in terms of absorptions and emissions of virtual photons. On the other hand, diamagnetism is considered a purely quantum phenomenon because it does not occur in a classical context; similarly, Debye’s law for the specific heat of solids is conventionally derived within a quantum framework. So, the issue of whether or not SED can correctly describe these phenomena becomes most fundamental for the assessment of its potentialities. We will find out that in both cases SED discloses the quantum properties of matter as originating in its interaction with the zeropoint field, as opposed to the primitive character conferred on them by conventional quantum theory.
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References
For the present exposition we draw from de la Pefia and Jéuregui (1983); further details can be found there. The problem of the free particle in SED is analyzed with the path-integral technique in Pesquera and Santos (1977, 1979); in Cavalleri (1981) the propagator of the free particle is studied. Other papers on the subject are Santos (1974a), de la Peha (1981) and Rueda (1984).
See de la Peña and Jéuregui (1983). The point of view used in this paper differs somewhat from the present one, since here we are distinguishing the quantum-mechanical description from the one provided by QED, which includes the radiative corrections. In the QED literature the radiative corrections to the free particle are normally considered part of the corrections to the mass, as stated above.
A full discussion of the action-angle variables can be seen in Born (1960). For the specific details of the present calculation see Boyer (1980a).
A detailed comparison between the results of SED and quantum theory is made by Boyer (1975b). A model of simple molecules considered as composite particles has recently been studied by Barranco et al. (1989) within SED, using previous work by Boyer (1984c) on the behaviour of spinning magnetic moments; with the adjustment of a single parameter, this model gives results for the magnetic moments which are in excellent agreement with experiment for a large range of values of B 0/T.
Recently Kracklauer (1992) has reached the same conclusion.
Such construction of the spin can be applied to the theory proposed by Sokolov and Tumanov (1956), discussed in section 2.4. The original particle there is classical, but its interaction with the quantized vacuum field transforms its dynamical variables into operators. The spin can be identified following a procedure similar to the present one; of course, the factor 3/4 appears also here (the unpublished calculations are due to A. Jéuregui). As discussed in section 2.4, Schiller and Tesser (1971) show that a magnetic dipoie gives rise to operators satisfying the correct angular momentum commutation relations, which applies also to the spin constructed as just described. Concerning the comment on the high frequencies, we have in mind the possibility that the spin could be more closely linked to the zitterbewegung than here suggested, and then it would be more dependent on the very high frequencies, which are poorly taken into account in a nonrelativistic treatment as the present one. A model of this kind would be close to the one suggested in Hestenes (1985).
Apparently the first suggestion that SED predicts an anomalous magnetic moment for the electron not merely associated with the mass renormalization, is due to Braffort and Taroni (1967).
In Sachidanandam (1983) it is asserted that the gyromagnetic ratio predicted for the electron by SED is 2, if the total canonical angular momentum is used. However, he is referring to orbital motions and the calculations (when corrected for an undue factor 1/2) do not confirm such a conclusion.
A much simpler example of two coupled oscillators was partially discussed in § 6.2.1.
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© 1996 Springer Science+Business Media Dordrecht
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de la Peña, L., Cetto, A.M. (1996). Quantum Properties of Other Simple Systems. In: The Quantum Dice. Fundamental Theories of Physics, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8723-5_8
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DOI: https://doi.org/10.1007/978-94-015-8723-5_8
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