Summary
Supposing the wave equation to be invariant when passing from one reference frame to another, we find the conditions of invariance and the connection between the measures of the same phenomenon in the two reference frames. If the transformation is linear and of axial type, we prove that the constant of the wave equation is the same in the two reference frames: if this constant is equal toc, we find that the equations of transformation become those of Lorentz.
Riassunto
Nell’ipotesi che l’equazione delle onde sia invariante passando da un sistema di riferimento ad un altro, si trovano le condizioni d’invarianza e il legame tra le misure di uno stesso fenomeno nei due sistemi di riferimento. Se la trasformazione è lineare e di tipo assiale, si dimostra che la costante dell’equazione delle onde è la stessa nei due sistemi di riferimento: se questa costante è posta uguale ac, si trova che le equazioni di trasformazione diventano quelle di Lorentz.
Резюме
Предполагая, что уравнение волн должно быть инвариантным при переходе от одной системы отсчета к другой, мы получаем условия инвариантности и связь между мерами одного и того же явления в двух системах отсчета. Если преобразование является аксиальным и линейным, мы доказываем, что постоянная уравнения волн является одинаковой в двух системах отсчета. Если эта константа равнаc, то мы получаем уравнения преобразования, которые сводятся к преобразованиям Лорентца.
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References
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M. Di Jorio:Fourier waves, inLectures on Optics at the University of Pisa (1968), p. 126.
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I would like to dedicate this work to the memory of my wife,Pina. Most of the work relating to it was done during her illness.
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di Jorio, M. The theory of restricted relativity, independent of a postulate on the velocity of light. Nuov Cim B 22, 70–78 (1974). https://doi.org/10.1007/BF02737460
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DOI: https://doi.org/10.1007/BF02737460