Summary
An alternative to the Lorentz equation (governing radiating electrons) is constructed. The equation is a differential-difference equation of retarded type, containing a constant time delay, and appears to be as compatible with basic assumptions of physics and observational data as that of lorentz. Further, and most importantly, this equation does not display pre-acceleration effects, and, with a suitable boundary condition, does not contain runaway solutions. The time delay remains to be specified.
Riassunto
Si costruisce un'equazione alternativa a quella di Lorentz (che governa l'irraggiamento degli elettroni). Si tratta di un'equazione differenziale alle differenze di tipo ritardato, contenente un ritardo costante, che sembra compatibile con le ipotesi fondamentali della fisica e con i dati sperimentali al pari di quella di Lorentz. Inoltre, fatto più importante, non si trovano in questa equazione effetti di preaccelerazione, né, con opportune condizioni ai limiti, soluzioni di fuga. Resta da specificare il ritardo.
Резюме
Конструируется альтернатива уравнению Лорентца (определяющему излучение электронов). Предложенное уравнение представляет дифференциальноразностное уравнение запаздывающего типа, содержащее постоянное время запаздывания. Оказывается, что это уравнение совместимо с основными предположениями физики и наблюдаемыми данными, так же как и уравнение Лорентца. Кроме того, это уравнение не обнаруживает эффектов предварительного ускорения и при соответствующем граничном условии не содержит быстро растущих решений. Время задержки следует конкретизировать.
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References
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See ref. (1,4)H. A. Lorentz:The Theory of Electrons, 2nd edition (New York, N. Y., 1952);J. D. Jackson:Classical Electrodynamics (New York, N. Y., 1962). See the review byT. Erber:Fort. der Phys.,9, 343 (1961), for a rather full account of many of these attempts.
See ref. (2) See, for example: second and third entries.
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In most physical situations it is expected that this can be relaxed to justF ext=0 for −α≤t<0, where α≈λ.
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Cohn, J. Time delay and pre-acceleration. Nuov Cim B 26, 47–56 (1975). https://doi.org/10.1007/BF02755536
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DOI: https://doi.org/10.1007/BF02755536