Differential aging from acceleration, an explicit formula

Abstract

We consider a clock 'paradox' framework where an observer leaves an inertial frame, is accelerated and after an arbitrary trip comes back. We discuss a simple equation that gives, in the 1+1 dimensional case, an explicit relation between the time elapsed on the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. Using this observation we define the differential aging as a function of proper time and show that it is non-decreasing. The reconstruction problem of special relativity is also discussed showing that its, at least numerical, solution would allow the construction of an 'inertial clock'.

Revtex4, 5 pages, 1 fugure

References in corpus (4)

• The twin paradox in compact spaces
• On Radar Time and the Twin `Paradox'
• Twin paradox and space topology
• The role of acceleration and locality in the twin paradox

Cited by in corpus (8)

• Classical aspects of lightlike dimensional reduction
• The twin paradox and Mach's principle
• The twin paradox: the role of acceleration
• The task of the relativistic oscillator in a non-inertial frame of reference
• Relativity principles in 1+1 dimensions and differential aging reversal
• The Computational Power of Minkowski Spacetime
• Towards a closed differential aging formula in special relativity
• Counterintuitive properties of relativistic relative motion for accelerated observers