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Register a new userTesting Lorentz symmetry violation with an invariant minimum speed
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Added by
Cl\\'audio Nassif Cruz
Publication date
2017
fields
Physics
and research's language is
English
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This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope $Na^{25}$) is a thermometer for a ultracold gas like the dipolar gas $Na^{23}K^{40}$. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed $V$ in the subatomic world, one expects that the proper time of such a clock moving close to $V$ in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called {it proper time dilation} so that the atomic decay rate of a ultracold radioactive sample (e.g: $Na^{25}$) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).
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We show the relationship between the scalar kinematics potential of Symmetrical Special Relativity (SSR) and the ultra-referential of vacuum connected to an invariant minimum speed postulated by SSR. The property of the conformal metric of SSR is showed, from where we deduce a kind of de Sitter metric. The negative curvature of spacetime is calculated from the conformal property of the metric. Einstein equation provides an energy-momentum tensor which is proportional to SSR-metric. We also realize that SSR leads to a deformed kinematics with quantum aspects directly related to the delocalization of the particle and thus being connected to the uncertainty principle. We finish this work by identifying the lagrangian of SSR with the so-called tachyonic models (slow-roll), where the tachyonic potential is a function depending on the conformal factor, thus allowing the SSR-lagrangian to be able to mimic a tachyonic lagrangian related to the so-called Dirac-Born-Infeld lagrangian, where the superluminal effects are interpreted as being a large stretching of spacetime due to new relativistic effects close to the invariant minimum speed as being the foundation of the inflationary vacuum connected to a variable cosmological parameter that recovers the cosmological constant for the current universe.
We aim to search for the connection between the spacetime with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) with Lorentz violation and the Gravitational Bose Einstein Condensate (GBEC) as the central core of a star of gravitational vacuum (gravastar), where one normally introduces a cosmological constant for representing an anti-gravity. This usual model of gravastar with an equation of state (EOS) for vacuum energy inside the core will be generalized for many modes of vacuum (dark energy star) in order to circumvent the embarrassment generated by the horizon singularity as the final stage of a gravitational collapse. In the place of the problem of a singularity of an event horizon, we introduce a phase transition between gravity and anti-gravity before reaching the Schwarzschild (divergent) radius $R_S$ for a given coexistence radius $R_{coexistence}$ slightly larger than $R_S$ and slightly smaller than the core radius $R_{core}$ of GBEC, where the metric of the repulsive sector (core of GBEC) would diverge for $r=R_{core}$, so that for such a given radius of phase coexistence $R_S<R_{coexistence} <R_{core}$, both divergences at $R_S$ of Schwarzschild metric and at $R_{core}$ of the repulsive core are eliminated, thus preventing the formation of the event horizon. So the causal structure of SSR helps us to elucidate such puzzle of singularity of event horizon by also providing a quantum interpretation for GBEC and thus by explaining the origin of a strong anisotropy due to the minimum speed that leads to the phase transition gravity/anti-gravity during the collapse of the star. Furthermore, due to the absence of an event horizon of black hole (BH) where any signal cannot propagate, the new collapsed structure presents a signal propagation in its region of coexistence of phases where the coexistence metric does not diverge.
We aim to investigate the theory of Lorentz violation with an invariant minimum speed so-called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So we are able to realize that there is a similarity between SSR and a new space with variable negative curvature ($-infty<mathcal R<0$) connected to a set of infinite cosmological constants ($0<Lambda<infty$), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological constant varying in the time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.
This article reports on the Fifth Meeting on CPT and Lorentz Symmetry, CPT10, held at the end of June 2010 in Bloomington, Indiana, USA. The focus is on recent tests of Lorentz symmetry using atomic and optical physics.
In this paper we aim to investigate a deformed relativistic dynamics well-known as Symmetrical Special Relativity (SSR) related to a cosmic background field that plays the role of a variable vacuum energy density associated to the temperature of the expanding universe with a cosmic inflation in its early time and an accelerated expansion for its very far future time. In this scenario, we show that the speed of light and an invariant minimum speed present an explicit dependence on the background temperature of the expanding universe. Although finding the speed of light in the early universe with very high temperature and also in the very old one with very low temperature, being respectively much larger and much smaller than its current value, our approach does not violate the postulate of Special Relativity (SR), which claims the speed of light is invariant in a kinematics point of view. Moreover, it is shown that the high value of the speed of light in the early universe was drastically decreased and increased respectively before the beginning of the inflationary period. So we are led to conclude that the theory of Varying Speed of Light (VSL) should be questioned as a possible solution of the horizon problem for the hot universe.
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