Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

World Lines in Einstein's Elevator

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. World Lines in Einstein's Elevator. Preprints 2021, 2021030230. Rouaud, M. World Lines in Einstein's Elevator. Preprints 2021, 2021030230.


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. Some experimental consequences are discussed such as trajectory deviation, desynchronization of a falling clock and the Michelson interferometer. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the box where 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.


Einstein, elevator, lift, uniformly accelerated, worldline, circle, Michelson


Physical Sciences, Theoretical Physics

Comments (1)

Comment 1
Received: 19 April 2021
Commenter: Mathieu Rouaud
Commenter's Conflict of Interests: Author
Comment: A third experiment proposal: the Michelson interferometer in the Einstein elevator.
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