Treatment of an accelerating observer via the special theory of relativity

TL;DR

This paper derives a new special relativity formula relating an inertial observer's clock time to an accelerating observer's clock time, based solely on the traveler's velocity profile, and applies it to relevant scenarios.

Contribution

It introduces a novel formula for initial observer's time as a function of accelerating observer's proper time, expanding the application of special relativity to accelerating frames.

Findings

Derived a formula t(t') relating clock times for accelerating observers.

Successfully applied the formula to various scenarios involving acceleration.

Demonstrated the formula's reliance on the velocity profile v(t').

Abstract

The clock time t' of an accelerating observer, simultaneous with the measured clock time t of an inertial observer,is easily established in special relativity (as proper time) by the well-known time-dilation formula for t'(t). In this work, a special-relativity formula t(t') for an initial observer's clock time t, simultaneous with a traveler's measured clock time t', is derived and applied successfully to various relevant situations. The equation for t(t') requires knowledge only of the velocity profile v(t') of the traveler.