Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed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 semi-ellipses with the center on the event horizon. 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 the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.


uniformly accelerating; worldline; circle; synchronization; Michelson; interferometer; paradox


Physical Sciences, Theoretical Physics

Comments (1)

Comment 1
Received: 19 October 2021
Commenter: Mathieu Rouaud
Commenter's Conflict of Interests: Author
Comment: A discussion about the inertial point of view is added.
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