The -dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity

Matthew J. Lake

doi:10.1140/epjc/s10052-024-13667-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 92
https://doi.org/10.1140/epjc/s10052-024-13667-9

Regular Article - Theoretical Physics

The $(1 + 3)$ -dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity

Matthew J. Lake¹^,2^a

¹ Faculty of Physics, Babeş-Bolyai University, Mihail Kogălniceanu Street 1, 400084, Cluj-Napoca, Romania
² School of Physics, Sun Yat-Sen University, 510275, Guangzhou, People’s Republic of China

^a matthew.lake@ubbcluj.ro

Received: 17 October 2024
Accepted: 27 November 2024
Published online: 27 January 2025

Abstract

We show that the $(1 + 3)$ $$(1+3)$$ -dimensional ‘superboost’ operators, proposed in Dragan and Ekert’s most recent work on superluminal reference frames (Dragan et al. in Class Quantum Gravity 40(2): 025013, 2023), are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their $(1 + 3)$ -dimensional ‘superflip’, which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as ‘time’ and time as ‘space’. We conclude that their extension of the ‘quantum principle of relativity’, proposed in earlier work on $(1 + 1)$ $$(1+1)$$ -dimensional spacetimes (Dragan and Ekert in New J Phys 22(3): 033038, 2020), to ordinary Minkowski space, is simply Einstein’s principle of relativity, proposed in 1905.

© The Author(s) 2025

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