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arXiv:2610.00494

Causal Trade-Offs in Superluminal Extensions of Relativity. A no-go theorem

Amrapali Sen, Matthias Salzger, V. Vilasini

quant-phgr-qcSubmitted Sep 30, 2026• Announced Oct 2, 2026• 0 citations
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Abstract

Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.

Comments
21 pages, 10 figures

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Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.
Quantum theory is widely regarded as fundamentally indeterministic, yet classical frameworks can also exhibit indeterminism once infinite information is abandoned. At the same time, relativity is usually taken to forbid superluminal signalling, although Lorentz symmetry formally admits superluminal transformations (SpTs). Dragan and Ekert have argued that SpTs entail a form of indeterminism analogous to that encountered in quantum theory. Here, we derive a theory-independent no-go theorem from a set of natural assumptions: any framework admitting non-order-preserving SpTs must either abandon finite information, relinquish time-symmetric informational content, deny that the past stores memory, or abandon the notion that time determines a preferred causal ordering. In particular, one possible implication is that any theory accommodating SpTs suggests an ontology with unbounded informational content, akin to deterministic classical theories formulated over the real numbers. Consequently, any ontic indeterminacy associated with superluminal transformations cannot originate from finite information.
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.
Non-classical correlations resulting from entangled quantum systems have sparked debates about the compatibility of quantum theory and relativity, and about the right way to think about causation. Key to a causal theory is that superluminal signalling is forbidden, which holds in quantum theory. In Bell scenarios, relativistic causality principles like no superluminal signalling are often assumed to follow from the standard no-signalling constraints on correlations. We explore the connections between a range of relativistic principles, including no superluminal signalling and no causal loops, and constraints on correlations that can arise with arbitrary interventions, within multi-party Bell scenarios. This includes standard no-signalling conditions and proposed relaxations allowing phenomena like jamming, where it was suggested that superluminal signalling and causal loops remain impossible. Using our recent framework combining relativistic principles with causal modelling, we show that any theory (classical or non-classical) allowing jamming must rely on causal fine-tuning and superluminal causal influences. Additionally, we show that jamming theories can lead to superluminal signalling in certain situations, highlighting limitations for their physicality. However, we identify cases where jamming correlations avoid superluminal signalling under general interventions, demonstrating that standard no-signalling constraints are not necessary for this purpose. We also show that these constraints are insufficient to rule out superluminal signalling and are neither necessary nor sufficient for ensuring no causal loops under general interventions. Finally, we derive necessary and sufficient conditions for ruling out superluminal signalling and operationally detectable causal loops, solidifying our understanding of relativistic causality principles in information processing tasks in space-time.
The principle of relativity claims the invariance of the results for experiments carried out in inertial reference frames if the system under examination is not in interaction with the outside world. In this paper it is analysed a model suggested by J. S. Bell, and later developed by P. H. Eberhard, D. Bohm and B. Hiley on the basis of which the EPR correlations would be due to superluminal exchanges between the various parts of the entangled system under examination. In the model the existence of a privileged reference frame ( PF ) for the propagation of superluminal signals is hypothesized so that these superluminal signals may not give rise to causal paradoxes. According to this model, in an EPR experiment, the entangled system interacts with the outer world since the result of the experiment depends on an entity (the reference frame PF ) that is not prepared by the experimenter. The existence of this privileged reference frame makes the model non invariant for Lorentz transformations. In this paper, in opposition to what claimed by the authors mentioned above, the perfect compatibility of the model with the theory of relativity is strongly maintained since, as already said, the principle of relativity does not require that the results of experiments carried out on systems interacting with the outside world should be invariant.