From Kinematics to Interference: Operational Requirements for the Quantum Principle of Relativity
Mikołaj Sienicki, Krzysztof Sienicki
TL;DR
The paper investigates whether extending special relativity with a formally superluminal Lorentz-type structure (QPR) can yield insights into the structure of quantum theory. It argues that coordinate relabelings alone cannot generate the operational predictions of quantum phenomena and therefore outlines three layers—$K$ (kinematics), $O$ (operational content), and $D/B$ (dynamics/bridges)—to separate form from physical predictions and to specify what a viable QPR+ program must add. By analyzing $1{+}1$ kinematics, it identifies an interval-sign flip and a signAmbiguity in the superluminal branch, and stresses that in $1{+}3$ such maps should be treated as auxiliary redescriptions rather than physical frame changes. Operationally, it shows that closed-loop interference (e.g., Mach–Zehnder-type setups) demands a phase-sensitive amplitude calculus and cannot be captured by classical mixtures alone, thus requiring a nontrivial dynamics/bridge; it discusses a minimal amplitude framework (A1–A4) that naturally leads to complex amplitudes. The paper concludes that, while a coherent QPR+ programme is possible, a concrete dynamical bridge—such as a twin-Hilbert-space tachyon QFT—must be explicitly constructed and demonstrated to satisfy loop-interference requirements and frame-invariance before broader claims about deriving quantum structure from QPR can be substantiated.
Abstract
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory has the structure it does [1]. The discussion that followed has emphasized a basic point: writing down coordinate maps is not the same thing as providing a physical theory. In particular, quantum superposition is not operationally defined by drawing multiple paths on paper: it is defined by what happens when alternatives recombine in an interference loop [2, 3]. In parallel, careful 1+1 analyses have clarified how sign conventions and time-orientation choices enter the superluminal formulas [4]. Finally, tachyonic QFT proposals suggest a possible mathematical bridge via an enlarged (twin) Hilbert space [5], although this proposal remains contested (e.g., on commutator covariance and microcausality grounds) [6]. The aim of this short note is organizational. We keep three layers separate: (K) kinematics (which maps exist and what they preserve), (O) operational content (what an experiment must actually reproduce, especially closed-loop interference), and (D/B) dynamics and bridges (how amplitudes and probabilities are generated, and how subluminal and superluminal sectors might be linked). The goal is not relativity derives quantum theory, but a clear checklist of what must be added for that ambition to become a well-posed programme.