EQUALITY OF INERTIAL AND GRAVITATIONAL MASS WITHIN THE FRAMEWORK OF GENERALIZED SPECIAL RELATIVITY AND THE SAVICKAS MODEL

Abstract

This study examines the equivalence between inertial and gravitational mass within the frameworks of Generalized Special Relativity (GSR) and the Savickas model, with specific objectives to clarify their relationships and implications concerning the principle of equivalence. Our results indicate that, under GSR, inertial mass as measured by an observer in free fall does not equal gravitational mass when both are influenced by gravitational fields. In contrast, the Savickas model consistently supports their equality. This study also highlights that in scenarios involving an accelerating elevator, both models affirm the equality of inertial and gravitational mass, reinforcing the formal definitions of mass in each context. Thus, our findings contribute to a deeper understanding of the implications of mass equivalence in relativistic frameworks. The primary objective is to explore their implications for the equivalence principle and to determine under what conditions these masses remain equal. Our analysis reveals that, in GSR, inertial and gravitational masses are unequal when influenced by gravitational fields, as measured by an external observer. Conversely, the Savickas model consistently supports their equality under similar conditions. Furthermore, in the context of an accelerating elevator, both models affirm the equality of these masses, aligning with classical interpretations of the equivalence principle. These findings provide a deeper understanding of mass equivalence in relativistic frameworks, offering insights into foundational concepts in modern physics.