Lorentz symmetry breaking effects on relativistic EPR correlations

The European Physical Journal C, Sep 2015

Lorentz symmetry breaking effects on relativistic EPR (Einstein–Podolsky–Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then we obtain the Wigner rotation angle via the Fermi–Walker transport of spinors and consider the WKB (Wentzel–Kramers–Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.

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Lorentz symmetry breaking effects on relativistic EPR correlations

Eur. Phys. J. C Lorentz symmetry breaking effects on relativistic EPR correlations H. Belich 1 C. Furtado 0 K. Bakke 0 0 Departamento de Física, Universidade Federal da Paraíba , Caixa Postal 5008, João Pessoa, PB 58051-970 , Brazil 1 Departamento de Física e Química, Universidade Federal do Espírito Santo , Av. Fernando Ferrari, 514, Goiabeiras, Vitoria, ES 29060-900 , Brazil Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB (Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations. - In special relativity, the Wigner rotation corresponds to the product of two Lorentz boots in different directions which gives rise to a boost preceded or followed by a rotation [1, 2]. Besides, the Wigner rotation is characterized by leaving the 4-momentum of the particle unchanged and making a precession of the spins in the rest frame of the particles. One effect associated with the Wigner rotation is the Thomas precession [3, 4]. Another effect associated with the Wigner rotation is the precession of spins of the relativistic Einstein–Podolsky– Rosen (EPR) correlation [5] with respect to the initial configuration of spins due to the action of Lorentz transformations. This precession of spins yields an apparent deterioration of the initial correlations between the spins and decreases the degree of violation of the Bell inequality. In Refs. [6–10], it is shown that there exists a decrease in the degree of the Bell inequality, yielded by the relativistic motion of the particle in the Minkowski spacetime. On the other hand, in curved spacetime, the decrease in the degree of the Bell inequality is yielded by the relativistic motion of the particles, the a e-mail: b e-mail: c e-mail: gravitational field, and the position of the observers [11–15]. Other interesting studies of quantum entanglement in curved spacetime have been made in Refs. [16–21]. A geometric approach was proposed by Borzeszkowski and Mensky [22] in order to study the relativistic EPR correlations in the presence of a gravitational field by applying the parallel transport along the world lines of the particles. However, Terashima and Ueda [12] showed that by taking into account the accelerated motion of the particle and the gravitational field, thus, the parallel transport cannot yield the perfect direction of the relativistic EPR correlations. From this perspective, a geometric approach based on the Fermi– Walker transport has been proposed in Ref. [14] in order to obtain the Wigner rotation angle and the precession of the spins of a relativistic EPR correlation. In this paper, we discuss the Lorentz symmetry breaking effects on relativistic EPR correlations. We start by introducing the description of fermions in curved spacetime in the presence of Lorentz symmetry breaking effects. The interest in studying the violation of the Lorentz symmetry, for instance, comes from the origin of the electron electric dipole moment, which is not explained by the Standard Model of particle physics. At present days, just experimental upper bounds have been established [23]. From this perspective, the necessity of investigating the physics beyond the Standard Model has arisen. A possible way of dealing with a scenario beyond the Standard Model is the extension of the mechanism for spontaneous symmetry breaking through vector or tensor fields, which implies that the Lorentz symmetry is violated. The seminal work made by Kostelecký and Samuel [24] in string theory, where it is shown that the Lorentz symmetry is violated through a spontaneous symmetry breaking mechanism triggered by the appearance of nonvanishing vacuum expectation values of nontrivial Lorentz tensors, is considered to be the starting point for building several models that deal with the violation of the Lorentz symmetry. Such models are considered to be effective theories whose analysis of the phenomenological aspect at low energies may provide information and impose restrictions on the fundamental theory which they stem from. In particular, a geometrical approach to investigating the effects of the violation of the Lorentz symmetry on photons was proposed in Refs. [25,26], where the Lagrangian of the modified Maxwell theory coupled to gravity is written in terms of an effective metric tensor. Therefore, our first objective in this work is to extend the geometrical approach proposed in Refs. [25,26] to a fermionic field by modifying the Minkowski spacetime. Then, by establishing a possible scenario of the Lorentz symmetry violation, we wish to investigate the effects of the L (...truncated)


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H. Belich, C. Furtado, K. Bakke. Lorentz symmetry breaking effects on relativistic EPR correlations, The European Physical Journal C, 2015, pp. 410, Volume 75, Issue 9, DOI: 10.1140/epjc/s10052-015-3640-1