Superluminal Quantum Reference Frames

The theory of relativity is generally assumed to provide us with a speed limit for all interactions. Particles cannot travel faster than the speed of light, nor can information. A standard argument for the impossibility of superluminal particles, also known as tachyons, and superluminal observers says that they would allow for backwards-in-time signalling, thus causing causality paradoxes.

Nevertheless, over the years, this assumption has been frequently questioned and the idea of breaking this speed limit has popped up from time to time in an attempt to explain various phenomena. Most recently, Andrzej Dragan and Artur Ekert have argued 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. In this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations and ensure consistency with a few fundamental laws of Physics. We examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within this framework that draws inspiration from previous studies. We consider a number of proposals for how thermodynamic quantities evolve under (subluminal) Lorentz boost and argue that their extensions to superluminal transformations is consistent with the second law of thermodynamics. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, where we find that probabilities are (still) conserved. These insights not only challenge conventional assumptions about superluminal theories but also represent the first work to integrate superluminal transformations within the framework of quantum reference frames. This approach opens new avenues for rethinking the interplay between quantum theory and relativity.