Relativity and Cosmology


A Concept for Simultaneity in the STR

Authors: Per Hokstad

Abstract. Simultaneity is a key concept in the special theory of relativity (STR), considering two reference frames moving relative to each other at constant speed, v. We introduce a new approach to simultaneity and its relation to clock readings and position. The two clocks at the origins play a crucial role. We synchronize these at time 0, and refer to this event as the ‘point of initiation’. From symmetry reasons, we conclude that these two clock readings –at least in some sense – represent simultaneity. The second element of our approach is a new version of the Lorentz transformation; where we in a new way combine the four (time, space) variables at a specific position, giving a state variable of two orthogonal components. The resulting description of simultaneity is well suited to analyse and conclude on the travelling twin case. Further, we provide a generalization; specifying a two dimensional time vector. The absolute value of the time vector specifies a measure of distance (in time) from the point of initiation. We utilise this distance to specify simultaneity of events related to the two reference frames; simultaneity corresponding to identical distances; i.e. time vectors having same absolute value (=‘total distance’). We can also give the time vector as a complex number, where the real part equals the clock reading at the relevant position.

Comments: 8 Pages.

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Submission history

[v1] 2017-11-27 16:08:13

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