Geometric Event-Based Relativistic Quantum Mechanics

TL;DR

This paper introduces a relativistic quantum mechanics framework based on a Hilbert space of events, treating events as primitive and deriving quantum systems as joint probabilities of event positions and times, maintaining full Poincare' symmetry.

Contribution

It presents a novel relativistic quantum mechanics model using event Hilbert spaces, unifying relativity and quantum concepts with geometric symmetry.

Findings

Framework recovers standard relativistic quantum mechanics and quantum field theory

Maintains full Poincare' symmetry as a geometric unitary transformation

Defines observables for event location and timing

Abstract

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Poincare' symmetry as a `geometric' unitary transformation, and possesses observables for space (location of an event) and time (position in time of an event).