Summary
The study of wave equations in accelerated reference frames allows, in principle, a selection among theories of inertia based on the transformation properties of the corresponding potentials. It is shown, in particular, that invariance of the classical equations of motion and of the Schrödinger equation under the same set of transformations leads to Sciama’s theory of inertia in the limitGM/c 2 R∼1. Tests which allow to distinguishing between this vector theory and general relativity are proposed and briefly discussed.
Riassunto
Lo studio delle equazioni d’onda in sistemi di riferimento accelerati permette, in linea di principio, di operare una scelta tra teorie inerziali basata sulle proprietà di trasformazione dei potenziali corrispondenti. Si dimostra, in particolare, che l’invarianza delle equazioni classiche del moto e dell’equazione di Schrödinger rispetto allo stesso gruppo di trasformazioni conduce alla teoria inerziale di Sciama nel limiteGM/c 2 R∼1. Esperimenti capaci di distinguere tra questa teoria vettoriale e quella della relatività generale sono proposti e brevemente discussi.
Реэюме
Исследование волновых уравнений в ускоренных системах отсчета поэволяет, в принципе, сделать выбор между теориями инерции, основанными на трансформационных свойствах соответствуюших потенциалов. В частности, покаэывается, что инвариантность классических уравнений движения и уравнения Щре-дингера относительно той же системы преобраэований приводит к теории инерции Щиама в пределеG M/c 2 R ∼ 1. Предлагается и вкратце обсуждается проверка, которая поэволяет отличить зту векторную теорию от обшей теории относительности.
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Work supported by the National Research Council of Canada.
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Papini, G. Inertial potentials in classical and quantum mechanics. Nuovo Cimento B (1965-1970) 68, 1–10 (1970). https://doi.org/10.1007/BF02710354
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DOI: https://doi.org/10.1007/BF02710354