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arXiv:2410.07017 · The European Physical Journal C

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

Matthew J. Lake

Published Jan 27, 2025• 1 citation
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Abstract

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 $$(1+3)$$ ( 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.

DOI
10.1140/epjc/s10052-024-13667-9

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The (1+3)(1+3)(1+3)-dimensional ‘quantum principle of relativity’ is Einstein’s principle of relativity
Abstract We show that the (1+3)(1+3)(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)(1+3)(1+3) ( 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)(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.
Abstract Dragan and Ekert in the paper (2020 New. J. Phys. 22 033038) presented ‘quantum principle of relativity’ (QPR) based on Galilean principle of relativity, which involves both superluminal GS and subluminal Gs families of observers and argue that then they are considered on the same footing it ‘implies the emergence of non-deterministic dynamics, together with complex probability amplitudes and multiple trajectories.’ Here we discuss QPR in the context of Heisenberg’s classification of the fundamental physical theoretical models under the role universal constants of nature: Planck’s constant h and speed of light c. We point out that both the superluminal and subluminal branches are separable in the sense that there is no mathematical coherent formalism that connect both branches. This, in particular, implies that the QPR is incomplete.
Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincar\'e invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference frames in Minkowski spacetime. It is a basic condition imposed on quantum theory in order to construct quantum field theories, hence, it plays a fundamental role in the standard model of particle physics too. As is well known, Minkowski spacetime follows from clear physical principles, like the relativity principle and the invariance of the speed of light. Here we reproduce such a derivation but leave the number of spatial dimensions nnn as a free variable. Then, assuming that spacetime is Minkowski in 1+n1+n1+n dimensions and within the framework of general probabilistic theories, we reconstruct the qubit Bloch ball and finite dimensional quantum theory, and obtain that the number of spatial dimensions must be n=3n=3n=3, from Poincar\'e invariance and other physical postulates. Our results suggest a fundamental physical connection between spacetime and quantum theory.
Abstract Particles cannot travel faster than the speed of light, nor can information. Nonetheless, this assumption has been frequently questioned over the years. This includes radical proposals like tachyons that can be observed in particle accelerators to more subtle ideas like studying superluminal causation to find classical explanations for quantum correlations. Most recently, it has been argued (Dragan and Ekert 2020 New J. Phys. 22 033038) that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. A consequence of this resolution is that different observers no longer agree whether a particle is incoming or outgoing or in a superposition of the two. We further find a similar apparent paradox for the entropy and/or temperature under superluminal Lorentz boosts and resolve it in an analogous fashion. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, showing that the involved probabilities still remain conserved. By applying the toolbox of quantum reference frames, we start charting an unexplored territory of superpositions between sub-and-superluminal quantum observers which gives rise to new conceptual questions.
While particles cannot travel faster than the speed of light, nor can information, this assumption has over the years been frequently questioned. Most recently, it has been argued [New J. Phys. 22, 033038 (2020)] that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. We also discuss Bell experiments under superluminal quantum reference frame transformations, showing that involved probabilities remain conserved.