Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Abstract

A new formulation of relativistic quantum mechanics is proposed in the framework of the restframe instant form of dynamics with its instantaneous Wigner 3-spaces and with its descrption 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 3-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space h1whose 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 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 non-locality of the Poincare' generators the resulting theory of relativistic entanglement is both kinematically non-local and spatially non-separable, properties absent in the non-relativistic limit.

Massless particles plus matter in the rest-frame instant form of dynamics

“…We have also added some comments on how to apply to this isolated system the procedure of quantization based on the recently developed rest-frame form of relativistic quantum mechanics [16]. If a suitable definition for a pseudo-differential operator corresponding to √ κ 2 exists, we have a description of an isolated photon, to be compared with the one-particle approximations used for a photon in Refs.…”

“…The quantization of the bosonic variables z, h, η 1 , κ 1 , and η, κ is done with the new restframe quantization scheme for relativistic quantum mechanics introduced in Ref. [16] 1 in an un-physical Hilbert space H = H com ⊗H η 1 ⊗H η , where H com is the Hilbert space of the frozen Jacobi data of the external decoupled center of mass. The physical states and the associated physical Hilbert space have to be identified by solving the restrictions < Φ phys |ˆ P (int) |Φ phys > = < Φ phys |ˆ K (int) |Φ phys > = 0 (quantization of the rest-frame conditions (3.19) eliminating the internal center of mass inside the Wigner 3-space).…”

“…[16] the quantization of the frozen Jacobi data z, h, is done in the preferred h-basis (definition of the rest frame) in the momentum representation:…”

“…The ACES mission of ESA will make the first precision measurement of the gravitational redshift near Earth (deviation of the null geodesics for light rays from the Minkowski ones at the 1/c 2 order) by putting the Pharao atomic clock on the Space Station [10]. Protocols for teleportation from Earth to the Space Station [11] will require "photon" (eikonal approximation to light rays) propagating along null geodesics and a relativistic formulation of entanglement [12]. Finally this framework will also be needed for the search of gravitational waves by means of atom interferometers [13].…”

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

“…[26,28,29,33], the three collective variables can be expressed as known functions of the Lorentz-scalar rest time τ = c T s = h ·x = h · Y = h · R, of canonically conjugate Jacobi data (frozen Cauchy data) z = M c x N W (0) and h = P /M c 14 , of the invariant mass M c = √ ǫ P 2 of the system and of its rest spinS.…”