Relativistic Quantum Mechanics and Relativistic Entanglement in the Rest-Frame Instant Form of Dynamics
arXiv:0907.1816 · doi:10.1063/1.3591131
Abstract
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived non-canonical predictive coordinates. In it we quantize the frozen Jacobi data of the non-local 4-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space whose existence is implied by Wigner-covariance. The formalism takes care of the properties of both relativistic bound states and scattering ones. There is a natural solution to the \textit{relativistic localization problem}. The non-relativistic limit leads to standard quantum mechanics but with a frozen Hamilton-Jacobi description of the center of mass. Due to the \textit{non-locality} of the Poincaré generators the resulting theory of relativistic entanglement is both \textit{kinematically non-local and spatially non-separable}: these properties, absent in the non-relativistic limit, throw a different light on the interpretation of the non-relativistic quantum non-locality and of its impact on foundational problems.
73 pages, includes revisions
References in corpus (15)
- An Atomic Gravitational Wave Interferometric Sensor (AGIS)
- General Relativistic Effects in Atom Interferometry
- Relativistic entanglement of two massive particles
- Unsharp Localization and Causality in Relativistic Quantum Theory
- Covariant Equilibrium Statistical Mechanics
- Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
- Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames
- The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
- Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: II. Applications: Rotating Frames, Sagnac Effect, Faraday Rotation, Wrap-up Effect
- Entanglement and Relativity
- Towards Relativistic Atomic Physics. I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field
- Basis States for Relativistic, Dynamically-Entangled Particles
- Towards Relativistic Atomic Physics. II. Collective and Relative Relativistic Variables for a System of Charged Particles plus the Electro-Magnetic Field
- New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems
- Massless Particles plus Matter in the Rest-Frame Instant Form of Dynamics
Cited by in corpus (11)
- Obtaining the Non-relativistic Quantum Mechanics from Quantum Field Theory: Issues, Folklores and Facts
- From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect
- The Rest-Frame Instant Form and Dirac Observables for the Open Nambu String
- Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics
- Geometrical Formulation of Relativistic Mechanics
- Manifestly Covariant Canonical Quantization of the Scalar Field and Particle Localization
- Dark Matter as a Relativistic Inertial Effect in Einstein Canonical Gravity?
- On Relativistic Entanglement and Localization of Particles and on their Comparison with the Non-Relativistic Theory
- A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics
- Post-Minkowskian Gravity: Dark Matter as a Relativistic Inertial Effect?
- Relativistic Entanglement from Relativistic Quantum Mechanics in the Rest-Frame Instant Form of Dynamics