Summary
We discuss the possibility of testing the hypothesis that the proper acceleration of a massive particle cannot exceed a natural limit, determined by its rest mass. To this aim we consider the phenomenological consequences of a geometric scheme in which the space-time, at a microscopic level, is to be regarded as a four-dimensional hypersurface locally embedded in a higher-dimensional phase space. As a first consequence we find that the energy of a uniformly and linearly accelerated particle should be quantized. Moreover, in this context the universality of the gravitational interaction is violated, but no contradiction is found with the upper bounds deduced from the present tests of the equivalence principle.
Riassunto
Discutiamo la possibilità di verificare l’ipotesi che l’accelerazione propria di una particella massiva non possa eccedere un limite naturale, fissato dalla sua massa a riposo. A questo scopo analizziamo le conseguenze fenomenologiche di uno schema geometrico in cui lo spazio-tempo, a livello microscopico, deve essere considerato come un’ipersuperficie quadridimensionale localmente immersa nello spazio delle fasi ottodimensionale. Come prima conseguenza troviamo che l’energia di una particella che si muove di moto rettilineo uniformemente accelerato dovrebbe essere quantizzata. Inoltre, in questo contesto si viola l’universalità dell’interazione gravitazionale, ma non troviamo alcuna contraddizione con i limiti superiori dedotti dai tests noti del principio di equivalenza.
Резюме
Мы обсуждаем возможность проверки гипотезы, что собственное ускорение массивной частицы не может превышать естественного предела, который определяется массой покоя частицы. С этой целью мы рассматриваем феноменологические следствия геометрической схемы, в которой пространствовремя на микроскопическом уровне следует рассматривать как четырехмерное гиперпространство, локально внедренное в фазовое пространство с большим числом измерений. Как первое следствие, мы получаем, что энергия равномерно и линейно ускоренной частицы должна быть квантована. Кроме того, в этом контекцте нарушается универсальность гравитационного взаимодействия, но не обнаружено противоречия с верхними границами, полученными из проверки принципа эквивалентности.
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Research supported by M.P.I., fund 40% art. 65 D.P.R. 382/80.
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Caianiello, E.R., Gasperini, M. & Scarpetta, G. Phenomenological consequences of a geometric model with limited proper acceleration. Nuov Cim B 105, 259–278 (1990). https://doi.org/10.1007/BF02726101
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DOI: https://doi.org/10.1007/BF02726101