From Kinematics to Interference: Operational Requirements for the Quantum Principle of Relativity

TL;DR

This paper clarifies the operational and kinematic requirements for extending special relativity with superluminal maps, aiming to understand the structure of quantum theory and its potential relation to relativity.

Contribution

It provides a structured organizational framework separating kinematics, operational content, and dynamics to guide the development of a relativistic quantum theory with superluminal features.

Findings

Distinguishes between coordinate maps and physical theories.

Highlights the importance of interference in defining quantum superposition.

Proposes a layered approach to connect kinematics, operations, and dynamics.

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.