Invariant Minimum Speed Research Articles

The cosmological constant and energy quantization in hydrogen atom in light of a doubly special relativity with a minimum speed

We show the existence of an invariant minimum speed in space–time as a new fundamental constant of nature by forming the basis of a doubly special relativity so-called Symmetrical Special Relativity (SSR). Such an observer-independent minimum speed emerges from the Dirac’s Large Number Hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure in space–time with two speed limits, i.e., the speed of light c and a minimum speed V. So the symmetry in space–time given by an invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio. We investigate how the minimum speed plays a fundamental role in the quantization of energy in hydrogen atom. The minimum speed V is related to a preferred background frame (ultra-referential SV) represented by the surface of a dark cone forbidden to the world line of any particle. It is related to the vacuum energy that leads to the cosmological constant. An investigation of SSR is done and a hypothetical experiment of Bose–Einstein condensation is proposed to detect the minimum speed as a possible Lorentz violation at very low energies.

Cosmic gravitational background waves in the scenario of a deformed relativity with an invariant minimum speed

Cosmic gravitational background waves in the scenario of a deformed relativity with an invariant minimum speed

Deformed special relativity with an invariant minimum speed as an explanation of the cosmological constant

This paper shows the need of the emergence of a universal minimum speed in the space-time by means of a more thorough investigation of Dirac's large number hypothesis (LNH). We will realize that there should be a minimum speed $V$ with the same status of the invariance of the speed of light $c$, however $V$ has gravitational origin. Hence, such a minimum speed forms a new kinematic basis in the space-time, thus leading to a new Deformed Special Relativity (DSR) for the quantum world so-called Symmetrical Special Relativity (SSR). Furthermore, we will show that such a new structure of space-time (SSR) reveals a connection between $V$ and a preferred reference frame $S_V$ of background field that leads to the cosmological constant $\Lambda$, which can be associated with a cosmological anti-gravity. We will also investigate the effect of the number of baryons $N$ (Eddington number) of the observable universe on the Hydrogen atom. Finally, we will show that SSR-metric plays the role of a de-Sitter (dS)-metric with a positive cosmological constant, which could assume a tiny value.

Lorentz violation with an invariant minimum speed as foundation of the Gravitational Bose Einstein Condensate of a Dark Energy Star

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.

Lorentz violation with an invariant minimum speed as foundation of the uncertainty principle in Minkowski, dS and AdS spaces

This research aims to provide the geometrical foundation of the uncertainty principle within a new causal structure of spacetime so-called Symmetrical Special Relativity (SSR), where there emerges a Lorentz violation due to the presence of an invariant minimum speed [Formula: see text] related to the vacuum energy. SSR predicts that a dS scenario occurs only for a certain regime of speeds [Formula: see text], where [Formula: see text], which represents the negative gravitational potentials ([Formula: see text]) connected to the cosmological parameter [Formula: see text]. For [Formula: see text], Minkowski (pseudo-Euclidean) space is recovered for representing the flat space ([Formula: see text]), and for [Formula: see text] ([Formula: see text]), Anti-de Sitter (AdS) scenario prevails ([Formula: see text]). The fact that the current universe is flat as its average density of matter distribution ([Formula: see text] given for a slightly negative curvature [Formula: see text]) coincides with its vacuum energy density ([Formula: see text] given for a slightly positive curvature [Formula: see text]), i.e. the cosmic coincidence problem, is now addressed by SSR. SSR provides its energy–momentum tensor of perfect fluid, leading to the EOS of vacuum ([Formula: see text]). Einstein equation for vacuum given by such SSR approach allows us to obtain [Formula: see text] associated with a scalar curvature [Formula: see text], whereas the solution of Einstein equation only in the presence of a homogeneous distribution of matter [Formula: see text] for the whole universe presents a scalar curvature [Formula: see text], in such a way that the presence of the background field [Formula: see text] opposes the Riemannian curvature [Formula: see text], thus leading to a current effective curvature [Formula: see text] according to observations. This corrects the notion of gravity as being only of Riemannian origin as the flat space has connection with a background gravity. In view of the current dS scenario with a quasi-zero [Formula: see text] slightly larger than [Formula: see text], we will just obtain a Generalized Uncertainty Principle (GUP) given in the cases of weak gravity and anti-gravity.

Variation of the speed of light and a minimum speed in the scenario of an inflationary universe with accelerated expansion

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.

Lorentz violation with an invariant minimum speed as foundation of the tachyonic inflation within a Machian scenario

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.

Testing Lorentz symmetry violation with an invariant minimum speed

This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g. isotope Na[Formula: see text]) is a thermometer for an ultracold gas like the dipolar gas Na[Formula: see text]K[Formula: see text]. 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 the lab, thus leading to the so-called proper time dilation so that the atomic decay rate of an ultracold radioactive sample (e.g. Na[Formula: see text]) 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 an ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).

Lorentz violation with a universal minimum speed as foundation of de Sitter relativity

We aim to investigate the theory of Lorentz violation with an invariant minimum speed 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 ([Formula: see text]) connected to a set of infinite cosmological constants ([Formula: see text]), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological “constant” varying in 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.

DOUBLE SPECIAL RELATIVITY WITH A MINIMUM SPEED AND THE UNCERTAINTY PRINCIPLE

The present work aims to search for an implementation of a new symmetry in the spacetime by introducing the idea of an invariant minimum speed scale (V). Such a lowest limit V, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the spacetime at the subatomic level for very low energies close to the background frame (v ≈ V), providing a fundamental understanding for the uncertainty principle, i.e. the uncertainty relations should emerge from the spacetime with an invariant minimum speed.

Deformed special relativity with an invariant minimum speed and its cosmological implications

The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by particles, represents a preferred reference frame associated with a universal background field that breaks Lorentz symmetry. Thus the structure of space-time is extended due to the presence of a vacuum energy density, which leads to a negative pressure at cosmological scales. The tiny values of the cosmological constant and the vacuum energy density shall be successfully obtained, being in good agreement with current observational results.