Superluminal Transformations and Finite Limits Incompatible, New No-Go Theorem Achieves Proof

Scientists are increasingly questioning the bedrock assumptions linking quantum indeterminism with the limits imposed by relativity. Amrapali Sen from the International Centre for Theory of Quantum Technologies, University of Gdańsk, and Flavio Del Santo from Constructor Knowledge and the University of Geneva, alongside Dragan and Ekert et al., have investigated whether superluminal transformations , formally permitted by Lorentz symmetry , genuinely introduce indeterminacy into physical systems. Their new research establishes a compelling ‘no-go’ theorem demonstrating that finite, bounded superluminal transformations are incompatible with fundamental physical assumptions, suggesting any indeterminism observed within such frameworks is merely a reflection of incomplete knowledge rather than an objective property of nature. This finding is significant because it challenges the notion that extending relativity with superluminal elements necessarily leads to a quantum-like indeterminacy, potentially steering theoretical physics towards deterministic interpretations of reality.

This work challenges the notion that indeterminism observed in SpTs originates from objective probabilities, instead suggesting it arises from epistemic limitations, or subjective ignorance. Experiments employed a deliberate theoretical framework, akin to foundational proposals exploring extreme scenarios, to delineate the Manifest and non-Manifest domains of physical observables.

Researchers distinguished between outcomes directly accessible through measurements and those defined within the non-Manifest domain, utilising a bridging ‘Theory’ to connect these realms and assess whether Quantum theory adequately fulfils this role. The study pioneered a methodology for extracting specific data by carefully separating these domains, enabling a precise examination of indeterminacy’s origins. This contrasts sharply with quantum theory, where probabilities are often considered ontologically fundamental. The team rigorously analysed the implications of SpTs, revealing that maintaining both superluminality and finiteness necessitates unbounded content, thereby precluding objective indeterminacy.
This innovative approach allows for a re-evaluation of tensions surrounding determinism, information, and the arrow of time, offering a novel perspective on foundational physics. Furthermore, the research benefited from funding through the IRA Programme, project no. FENG0.02.01-IP0.05 0006/23, and the FNP, acknowledging the support crucial to its completion. Acknowledgements also extend to Matthias Salzger and Sebastian Horvat for their valuable contributions and insightful suggestions throughout the study, highlighting the collaborative nature of this groundbreaking work. This meticulous methodology provides a powerful lens through which to examine the interplay between symmetry, completeness, finite information, and a determinate past, ultimately advancing our understanding of the universe’s fundamental nature.

Superluminality, Finiteness and Deterministic Universes Revealed

The research demonstrates that any attempt to accommodate faster-than-light phenomena within a framework of limited information density necessitates a deterministic universe, effectively eliminating objective randomness. Experiments weren’t conducted in the traditional sense, but rather a rigorous mathematical derivation was performed, yielding a ‘no-go’ theorem that dictates the coexistence of superluminality and finiteness is impossible. This theorem suggests that any indeterminism seemingly arising from superluminal transformations is merely a reflection of our limited knowledge, not an inherent property of reality. Tests prove that even with unchanged equations of motion, this ontic indeterminacy propagates due to chaotic behaviour, leading to multiple possible future states from the same initial conditions.

Further analysis revealed that standard interpretations of special relativity, which prohibit superluminal motion to avoid paradoxes, may require re-evaluation. Data shows that Lorentz transformations, the mathematical foundation of relativity, formally admit superluminal velocities, prompting a reconsideration of the link between determinism and relativity. The breakthrough delivers a framework where uncertainties are large enough to obscure the detection of superluminal signalling, effectively removing the causal inconsistencies. Measurements confirm that the mathematical derivation of Lorentz transformations yields both subluminal and superluminal velocities, as detailed in the study.

The team derived a general form for transformations between inertial frames, revealing that the symmetry of the transformation function, A(v), dictates whether the velocity is subluminal or superluminal. Specifically, the symmetric case yields the standard subluminal transformation, while the antisymmetric case allows for superluminal velocities. This work establishes a rigorous theoretical foundation for exploring the implications of superluminality and its relationship to the fundamental nature of indeterminacy.

Superluminality, Finite Information, and Deterministic Outcomes

Their research establishes a no-go theorem indicating that any superluminal transformation must allow for unbounded information, effectively leading to a deterministic universe. This finding challenges interpretations suggesting indeterminism arises from extending principles beyond standard relativity. The team acknowledges that their results depend on assumptions regarding the measure of information, though they note the conclusions hold regardless of the specific choice. The significance of this work lies in clarifying the source of indeterminism when considering superluminal possibilities. Future research, as indicated by the authors, could involve relaxing the assumptions made to further explore the interplay between information limits and the nature of indeterminacy.