Relativistic Classical and Quantum Mechanics: Clock Synchronization and Bound States, Center of Mass and Particle Worldlines, Localization Problems and Entanglement

We make a critical comparison of relativistic and nonrelativistic classical and quantum mechanics of particles in inertial frames as well of the open problems in particle localization at both levels. The solution of the problems of the relativistic center-of-mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled nonlocal (nonmeasurable) relativistic center-of-mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial nonseparability not existing in nonrelativistic entanglement. Then, we try to reconcile the two visions showing that also at the nonrelativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. The existing results about the nonrelativistic and relativistic localization of particles and atoms support the view that detectors only identify effective particles following this type of trajectories: these objects are the phenomenological emergent aspect of the notion of particle defined by means of the Fock spaces of quantum field theory.

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QUANTUM MECHANICS IN NONINERTIAL FRAMES WITH A MULTITEMPORAL QUANTIZATION SCHEME II: NONRELATIVISTIC PARTICLES

International Journal of Modern Physics A ◽

10.1142/s0217751x0603254x ◽

2006 ◽

Vol 21 (19n20) ◽

pp. 3917-3945 ◽

Cited By ~ 16

Author(s):

DAVID ALBA

Keyword(s):

Quantum Mechanics ◽

Bound States ◽

Center Of Mass ◽

Quantization Scheme ◽

Unitary Evolution ◽

Classical Level ◽

Noninertial Effects ◽

Special Cases ◽

Relativistic Particles

The nonrelativistic version of the multitemporal quantization scheme of relativistic particles in a family of noninertial frames (see Ref. 1) is defined. At the classical level the description of a family of nonrigid noninertial frames, containing the standard rigidly linear accelerated and rotating ones, is given in the framework of parametrized Galilei theories. Then the multitemporal quantization, in which the gauge variables, describing the noninertial effects, are not quantized but considered as c-number generalized times, is applied to nonrelativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of the center-of-mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid noninertial frames are recovered as special cases.

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