Theoretical Physics

General Clocks and the Clock Hypothesis

Download PDF (222.1 KB) PP. 188 - 193 Pub. Date: December 1, 2017

DOI: 10.22606/tp.2017.24005

Author(s)

A. Sfarti^*
CS Dept, UC Berkeley, 387 Soda Hall, Berkeley

Abstract

The present paper extends a previous proof of the Clock Hypothesis from the case of light clocks to clocks realized from oscillating massive particles. We also extend the study from the case of clocks undergoing constant proper acceleration to the case of clocks undergoing variable proper acceleration. We transformed the problem into one of general relativity and we applied the Euler- Lagrange formalism, thus providing a straightforward tool in solving this class of problems.

Keywords

Clock Hypothesis, general relativity, Schwarzschild metric, Euler-Lagrange formalism

References

[1] W. Rindler, “Essential Relativity”, (2nd ed.), New York, Springer--‐Verlag (1977).

[2] J. Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature, 268 (July 28, 1977).

[3] J. Bailey et al., “Final report on the CERN muon storage ring including the anomalous magnetic moment and the electric dipole moment of the muon, and a direct test of relativistic time dilation,” Nuclear Physics B ,150 (1979).

[4] S.R. Mainwaring, G.E. Stedman, “Accelerated Clock Principles in Special Relativity,” Phys. Rev., A47 (1993).

[5] R. Anderson, I. Vetharaniam, G.E. Stedman, “Conventionality of Synchronization, Gauge Dependence and Test Theories of Relativity,” Physics Reports, 295 (1998).

[6] A.M. Eisele, “On the Behavior of an Accelerated Clock”, Helvetica Physica Acta 60 (1987).

[7] S. C. Fletcher, “Light Clocks and the Clock Hypothesis,” Found Phys, 43, (2013).

[8] A. Sfarti, “Euler-Lagrange Solution for Calculating Particle Orbits in Gravitational Fields,” Fizika A, 19, 4, (2010).

[9] L .D. Landau, E. M. Lifshitz, “Mechanics - Course of Theoretical Physics,” vol 1, 3th ed, Elsevier edit., (2007).

[10] A. Albrecht, A. Islesias, “The Clock Ambiguity: Implications and New Developments,” The Fundamental Theories of Physics, 172, Springer Verlag, (2012).