A traveler-centered intro to kinematics

TL;DR

This paper introduces a traveler-centered approach to kinematics that emphasizes local time and avoids the complexities of extended simultaneity, making the concepts more accessible for beginners and highlighting the local nature of gravitational acceleration.

Contribution

It presents a synchrony-free, traveler-centered framework for teaching kinematics that explicitly excludes global time, enhancing conceptual understanding for students.

Findings

Time as a local quantity depends on the clock used.

Coordinate-acceleration approximates felt acceleration for travelers.

Gravitational acceleration is mass-independent and geometrically derived.

Abstract

Treating time as a local variable permits robust approaches to kinematics that forego questions of extended-simultaneity, which because of their abstract nature might not be addressed explicitly until a first relativity course and even then without considering the dependence of clock-rates on position in a gravitational field. For example we here use synchrony-free ``traveler kinematic" relations to construct a brief story for beginning students about: (a) time as a local quantity like position that depends on ``which clock", (b) coordinate-acceleration as an approximation to the acceleration felt by a moving traveler, and (c) the geometric origin (hence mass-independence) of gravitational acceleration. The goal is to explicitly rule out global-time for all from the start, so that it can be returned as a local approximation, while tantalizing students interested in the subject with more widely-applicable equations in range of their math background.