3.4c. Critical points in the classical theories (continuation)

        Now let us see something about the theory of electric dipoles. We know that conductors, when submitted to an electromotive force, become headquarters of an electric current; but if the conductor has been isolated from the field source as in Figure 5a the current will soon cease, and this will happen when a certain threshold is established for the separation of charges in the conductor. In his studies on capacitors, Faraday noticed that dielectrics, although they do not conduct electric currents, manifest a qualitatively similar behavior. These materials resist in part to the penetration of the electric field in its interior, a phenomenon that in some aspects reminds Archimedes’s buoyant force, as opposed to the gravitational field.

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Figure 5: Comments in the text

        By the end of the era of electric fluids, there appeared a promising theory in order to explain this phenomenon (electric polarization of dielectrics). This theory admitted the dielectric constituted by small conductive spheres immersed in an insulating environment [27]; the complex phenomenon was reduced to a summational of simple effects, as shown in Figure 5b. The theory is perfect within the proposed limits although, in spite of its representativeness and to use Mario Bunge’s words [28] it can be considered of low risk since it explains what is observed (phenomenological or behaviorist character) through an internal mechanism (representative character) of secondary importance. In other words, the microscopic model (Figure 5b) does not modify at all the model from which it originated (Figure 5a).

        In the beginning of the atomic era the situation was no longer the same the conductive spheres were identified with Thomson’s atoms and the insulating environment to the ether between them. The representative character of the theory increased in importance and transformed it into a high risk theory.

        After the identification of the corpuscular character of the cathodic rays (1897) such corpuscles were later called electrons Thomson suggested that the positive charge of an atom could be uniformly distributed in a sphere with negative corpuscles inside the positive charge [27]. On the other hand, as Tipler says [29], Thomson saw the atom as a positively load fluid, with the electrons plunged in a stable configuration in order to make the group neuter. Due to mutual repulse, as described by Eisberg et al. [op. cit. in 20], the electrons would be uniformly distributed in the positive load sphere whence the so called plum pudding model; and when the vibrates the electrons would vibrate around their equilibrium positions which would explain in terms of quality the emission of electromagnetic radiation.

        The free electrons theory was soon after developed (1900-1909) and it is not hard to recover its logic: if the positive fluids of Thomson’s atoms intercommunicate somehow or constitute a single amorphous mass whose electrons are practically free although attached to the mass as a whole. If such thing happens, the material is a conductor; otherwise it is a dielectric. Although the idea of negative particles still existed, the idea of fluid persisted, and physicists of the time were about to imagine the models presented in Figures 5a and 5b as electric dipoles, since they were very similar to the macroscopic group represented by both Coulomb’s charges with the same intensity and opposite signs.

        The notion of static electric dipole also appeared and germinated an akin concept: the dynamic electric dipole. Hertz’s experiments and Thomson’s model favored this conception. In fact, the radio transmitter and radio receiver used by Hertz are called dipole antennae; and the plum pudding model with electrons vibrating around an equilibrium position reminds these antennae. With this model in mind, in his theory of thermal radiation emission Planck states that the emitting surface contains electrons which are tied to fixed points through forces obeying Hooke’s law [30].

        While Thomson’s model was still accepted, the free electrons theory represented a branch of this tree and the idea of microscopic dipoles stemmed from another of its branches. Nevertheless there were too many experimental restrictions to the model, and Thomson in spite of his elaborated mathematical calculations was unable to achieve general agreement concerning experimentation [op. cit in 29]. Due to Rutherford’s conclusive analysis of the atom nucleus, the tree was cut down, but its branches had already blossomed. Electric polarization in dielectris and radiation emission were again explained by phenomenological theories; although of low risk such theories were endowed with a very intensive abstractionism. The atomic dipoles kept few physical characteristics, but a lot of mathematical ones.

        An atom of hydrogen (Rutheford’s model) possesses a dipole momentum vectors that varies according to time, and according to Goldenberg [31], it should generate a variable electric field in time and, therefore, should emit electromagnetic radiation. Although classically correct, this conclusion presupposes the non-existence of stationary electric fields, a supposition which is not backed by experimentation.

        The absence of this radiation in the normal atom of hydrogen was one of the great paradoxes found in the primitive quantum physics [31], and it was solved only through the acceptance of an undulatory electron: the electronic structure of atoms and molecules can be represented by a single cloud of negative charges [31], an image that reminds an inverse Thomson model: a (fluid) cloud negatively loaded with a punctiform and positive nucleus located inside the negative charge. In other words, the electric dipole as it is conceived today is incompatible with classic electromagnetism; the principles of classic electromagnetism are imperfect to explain the paradox it generated.