Extension of the electrokinematics theorem to the electromagnetic field and quantum mechanics

Summary A recent electrokinematics theorem leads to a general equation that, through an arbitrary irrotational fieldF, connects the motion of the electric-charge carriers, the internal potential and the dielectric properties of a physical system with its external currents, voltages and powers. It has been proved for quasi-electrostatic fields,i.e. when the vector potential may be disregarded, and on the basis of classical mechanics. Here the theorem is extended to any type of electromagnetic field and to quasi-relativistic quantum mechanics, in the case of many-particle systems for which, moreover, the probability current density is suitably computed. The new equation so obtained, throughF, connects the external currents again with the internal electric permittivity and the scalar potential, in the same way as in the preceding approach, and with the carrier velocity that, however, has to be computed according to quantum mechanics. Moreover, it contains two new contributions, one deriving from the vector potential and the other from a current density arising from the electron spin. By means of proper choices ofF, new expressions of the external currents of the system are determined as functions of the motion of its internal carriers. In particular, the electrokinematics theorem is exploited to compute the output current in two-terminal nanoelectronic devices in which, owing to the small sizes, quantum effects cannot be disregarded. Finally, such results, when they are applied to the double-barrier tunnelling structures, allow us to show the splitting of the electron pulse into two uncorrelated pulses, and as a consequence, to obtain a possible shot noise suppression, up to fifty per cent of the full shot noise.     

On the radiation of the electromagnetic impulse pendulum

Summary In this paper we clarify the sources of radiation in a number of experiments, concerning the electromagnetic impulse pendulum, carried out by various authors. The calculated radiated energy was found to be negligible, in all cases, compared to the energy stored in their systems, in contradiction to their claim. We elucidate the way by which Newton's third law is applicable and how the reaction force of the moving pendulum is transferred to the stationary frame. In the MIT experiment of Graneauet al., average values for quantities like the time constant, resistance etc. are given ignoring their standard deviations. Calculating and taking into account their errors, due to their dependence on the temperature, we found agreement between the theoretical and experimental values of the pendulum momentum.     

The electromagnetic impulse pendulum and momentum conservation

Summary Largely quantitative experiments by Pappas have indicated that the momentum imparted to an electrodynamic impulse pendulum was not balanced by an equal and opposite momentum change of field energy as required by the special theory of relativity. The authors repeated Pappas' experiment using discharge currents from a capacitor bank which contained a known amount of stored energy. It turned out that, for momentum conservation, the magnetic-field energy required would have been 1000 to 2000 times as large as the energy that was actually stored in the capacitors. In the second part of the paper the pendulum experiments are interpreted in terms of Ampère's force law. It is shown that the Ampère force exerted on the pendulum is almost exactly the same as the lorentz force, but it arises in different parts of the pendulum conductor. Furthermore, the Ampère reaction force does not reside in the field but in the stationary part of the circuit which supplies current to the pendulum. Hence in the Ampère electrodynamics the momentum is definitely conserved. The experimental and analytical findings confirm the work by Pappas. A new and important experimental fact emerged from the present investigation. The momentum imparted to the pendulum was found to be significantly smaller than the calculated mechanical impulse given by the Lorentz and Ampère force laws. The Ampère force distribution offers an explanation of this observation in terms of the elastic distortion of the pendulum structure. The Lorentz force distribution could not produce this distortion.

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Riassunto Esperimenti ampiamente quantitativi di Pappas hanno indicato che l'impulso assegnato ad un pendolo ad impulso elettrodinamico non è bilanciato da un cambio d'impulso uguale e opposto dell'energia del campo come richiesto dalla teoria speciale della relatività. Gli autori ahnno ripetuto l'esperimento di Pappas usando correnti di scarico da una riserva di capacitori che contiene una quantità nota di energia immagazzinata. Risulta che, per la conservazione del momento, l'energia del campo magnetico richiesta sarebbe da 1000 a 2000 volte grande come l'energia che è in realtà immagazzinata nei capacitori. Nella seconda parte del lavoro gli esperimenti cel pendolo sono interpretati sulle basi delle leggi di forza di Ampère. Si mostra che la forza di Ampère esercitata sul pendolo è quasi esattamente uguale alla forza di Lorentz, ma essa si verifica in parti differenti del conduttore del pendolo. Inoltre, la forza di reazione di Ampère non sta nel campo, ma nella parte stazionaria del circuito che fornisce corrente al pendolo. Quindi nell'elettrodinamica di Ampère l'impulso è conservato in maniera definita. I risultati sperimentali e dell'analisi confermano il lavoro di Pappas. Da questo studio è emerso un nuovo ed importante fatto sperimentale. Il momento impartito al pendolo appare essere specificativamente piú piccolo dell'impulso meccanico calcolato fornito dalla leggi di forza di Lorentz ed Ampère. La distribuzione di forze di Ampère offre una spiegazione di questa osservazione in termini di distorsione elastica della struttura del pendolo. La distribuzione di forze di Lorentz potrebbe non produrre questa distorsione.

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Резюме Количественные эксперименты Паппаса показывают, что импульс, переданный электромагнитному импульсному маятнику, не компенсируется равным и противоположным изменением импульса поля, как это следует из специальной теории относительности. Авторы повторили эксперимент Паппаса, используя разряд батареи конденсаторов, которая содержит известное количество запасенной энергии. Оказывается, что для охранения импульса требуемая энергия магнитного поля должна в 1000–2000 раз превосходить энергию, фактическн запасенную в конденсаторах. Во второй части статьи эксперименты с маятником интерпретируются в терминах закона для силы Ампера. Показывается, что сипа Ампера, действующая на мятник, оказывается точно такои же, как сила Лоренца, но возникает в разных частях прводника маятника. Кроме того, сила реакции Ампера принадлежит не полю, а стационарной части контура, который подводит ток к маятнику. Следовательно, электродинамический импульс Ампера сохраняется. Экспериментальные и теоретические результаты подтверкдают работу Паппаса. Из проведенных исследований получен новый и важный зкспериментальный результат. Обнаружено, что импульс, переданный маятинку, оказывается знапительно меньше, чем вычесленный механический импульс, определяемый законами для сил Ампера и Лоренца. Распеделение силы Ампера предлагает объяснение этого факта с помощью упругой деформации структуры маятника. Распределение силы Лоренца не может создавать такой деформации.

     

Elementary proof of Zeeman's theorem

We prove that the nonaffine conformal transformations of four-dimensional Minkowski space are necessarily global causality violators, and use this fact to obtain an elementary group-theoretic proof of the theorem that global causality implies the Lorentz group.     

On the Electromagnetic Origin of Inertia and Inertial Mass

We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton’s second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle’s own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle’s vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle’s vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the “4/3 mass paradox” for a spherical charge distribution.