Summary
In the recently developed asynchronous formulation of the relativistic theory of extended bodies, the inertial mass of a body does not explicitly depend on its pressure or stress. The detailed analysis of the weight of a box filled with a gas and placed in a weak gravitational field shows that this feature of asynchronous relativity implies a breakdown of the equivalence between inertial and passive gravitational mass for stressed systems.
Riassunto
Nella formulazione asincrona della teoria relativistica di corpi estesi, recentemente sviluppata, la massa inerziale di un corpo non dipende esplicitamente dalla sua pressione o dallo sforzo. L’analisi dettagliata del peso di una scatola riempita di gas e posta in un campo gravitazionale debole mostra che questa caratteristica della relatività asincrona implica una rottura dell’equivalenza tra massa gravitazionale inerziale e passiva per sistemi sotto sforzo.
Резюме
В недавно развитой асинхронной формулировке релятивистской теории протяженных тел инерциальная масс тела явно не зависит от давления или напряжения. Подробный анализ веса сосуда, наполненного газом и помещенного в слабое гравитационное поле, показывает, что указанная особенность асинхронной формулировки теории относительности подразумевает нарушение эквивалентности между инерциальной и пассивной гравитационной массой для систем, находящихся в напряженном состоянии.
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It seems that the names «synchronous» and «asynchronous» have been introduced for the first time in the paper byG. Cavalleri andG. Salgarelli:Nuovo Cimento A,62, 722 (1969).
This is the position held in the paper byG. Cavalleri andG. Salgarelli:Nuovo Cimento A,62, 722 (1969) and in several latter papers.
H. Arzeliès:Nuovo Cimento A,50, 287 (1967).
The energy-momentum tensor of general relativity is a generalization of a relation of the synchronous approach, as will be shown below.
The derivation and discussion of the basic equations in both approaches is presented inH. Arzeliès:Fluides relativistes (Paris, 1971).
For a very simple derivation of the synchronous relations for a gas, seeM. G. Calkin andM. H. Jericho:Am. J. Phys.,45, 1224 (1977).
This equation is equivalent to one derived and discussed inR. Adler, M. Bazin andM. Schiffer:Introduction to General Relativity (New York, N. Y., 1965), p. 184.
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This work has been supported by the Brazilian National Council for Scientific and Technological Development (C.N.Pq.).
Traduzione a cura della Redazione.
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de Andrade Martins, R. Violation of the equivalence principle for stressed bodies in asynchronous relativity. Nuov Cim B 78, 187–199 (1983). https://doi.org/10.1007/BF02721096
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DOI: https://doi.org/10.1007/BF02721096