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.
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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
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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)