Worldlines in the Einstein's Elevator

Mathieu Rouaud

doi:10.20944/preprints202103.0230.v1

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preprints.org > physical sciences > theoretical physics > doi: 10.20944/preprints202103.0230.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Worldlines in the Einstein's Elevator

Mathieu Rouaud

Version 1 : Received: 3 March 2021 / Approved: 8 March 2021 / Online: 8 March 2021 (15:29:18 CET)
Version 2 : Received: 17 April 2021 / Approved: 19 April 2021 / Online: 19 April 2021 (22:29:31 CEST)
Version 3 : Received: 1 June 2021 / Approved: 1 June 2021 / Online: 1 June 2021 (16:20:13 CEST)
Version 4 : Received: 17 October 2021 / Approved: 19 October 2021 / Online: 19 October 2021 (09:54:49 CEST)
Version 5 : Received: 3 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (15:40:38 CET)

How to cite: Rouaud, M. Worldlines in the Einstein's Elevator. Preprints 2021, 2021030230. https://doi.org/10.20944/preprints202103.0230.v1 Rouaud, M. Worldlines in the Einstein's Elevator. Preprints 2021, 2021030230. https://doi.org/10.20944/preprints202103.0230.v1

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MDPI and ACS Style

Rouaud, M. Worldlines in the Einstein's Elevator. Preprints 2021, 2021030230. https://doi.org/10.20944/preprints202103.0230.v1

APA Style

Rouaud, M. (2021). Worldlines in the Einstein's Elevator. Preprints. https://doi.org/10.20944/preprints202103.0230.v1

Chicago/Turabian Style

Rouaud, M. 2021 "Worldlines in the Einstein's Elevator" Preprints. https://doi.org/10.20944/preprints202103.0230.v1

Abstract

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. The deviation, compared to the classical case, is important close to the horizon, but small in the box, and the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

Keywords

special relativity, Einstein, elevator, lift, horizon, accelerated, ellipse, circle

Subject

Physical Sciences, Theoretical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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