On the quantum mechanics of finite-mass observers

TL;DR

This paper extends quantum mechanics to include finite-mass observers with quantum properties, leading to a fully relative formulation with observer-dependent features and testable predictions.

Contribution

It introduces a new framework for quantum mechanics that accounts for finite-mass observers, incorporating observer-dependent Hilbert spaces and quantization rules.

Findings

Observer-dependent Hilbert spaces established

Novel uncertainty relations derived

Testable experimental signatures proposed

Abstract

The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility for an observer to access its own quantum state of motion. This results in a fully relative formulation of quantum mechanics with observer-dependent Hilbert spaces, relative quantization rules, and novel uncertainty relations, while also elucidating some interpretational issues present in the current formulation of quantum mechanics and giving experimentally testable signatures.