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arXiv:0810.5241 · International Journal of Modern Physics A

RELATIVISTIC ATOMIC PHYSICS: FROM ATOMIC CLOCK SYNCHRONIZATION TOWARDS RELATIVISTIC ENTANGLEMENT

Luca Lusanna

Published Apr 9, 2009• 0 citations
arXivHTMLPDF

Abstract

A review is given of the implications of the absence of an intrinsic notion of instantaneous 3-space, so that a clock synchronization convention has to be introduced, for relativistic theories.
DOI
10.1142/s0217751x09044929

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After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators imply a kinematical non-locality and non-separability influencing the theory of relativistic entanglement and not connected with the standard quantum non-locality.
In this paper we argue that the notion of time, whatever complicated and dicult to define as the philosophical category, from physicist’s point of view is nothing else but the sum of ’lapses of time’ measured by a proper clock. As far as Quantum Mechanics is concerned, we distinguish a special class of clocks, the ’atomic clocks’. It is because at atomic and subatomic level there is no other possibility to construct a ’unit of time’ or ’instant of time’ as to use the quantum transitions between chosen quantum states of a quantum object such as atoms, atomic nuclei and so on, to imitate the periodic circular motion of a clock hand over the dial. The clock synchronization problem is also discussed in the paper. We study the problem of defining a time dierence observable for two-mode oscillator system. We assume that the time difference obsevable is the dierence of two single-mode covariant
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.