2023/06/16 by W.A. Mitaroff, Mitaroff, Winfried A.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Physics Education (physics.ed-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2306.09582
openalex publication_date 2023/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper time, R. Above ratio is useful, e.g. for describing the decay length of an unstable particle in the lab. But essential characteristics of time dilation, missed out in many textbooks, are manifest in the differences (quadratic, absolute and relative) between lab time and proper time. After an introduction to the basics, we regard the movement of a clock over a fixed spatial distance Δx. Explicit formulae are given for R and for the differences, and their behaviour as functions of the velocity is discussed and plotted. Approximate formulae are given for very slow movements. Time synchronization within an inertial system by "slowly" moving a clock over a finite distance Δx, mentioned vaguely in some textbooks, may quantitatively be comprehended by requiring the time difference to be less than the clock's time resolution. We derive explicit formulae for the maximal velocity obeying these constraints (to the best of our knowledge not presented elsewhere).