Search Results (34)

We analyse different configurations of four emitters in a Relativistic Positioning System (RPS) with: (i) one inertial and three static emitters, (ii) one hyperbolic and three static emitters, and (iii) three rotating and one static emitter. For every configuration, we analyse the emission/reception conditions, represent the emission configuration regions and write the user’s location solution. We follow the notions and terminology of previous works on this topic. Full article

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article

We extend the representation frame formalism, previously introduced to account for key cosmological observations in the Einstein static universe, to non-relativistic quantum mechanics. In this framework, each inertial observer is associated with a flat representation referential $R_{obs}$, defined as the tangent space to the spatial manifold at the observer’s position, in which all measurements are represented. The Euclidean structure of $R_{obs}$ allows quantum systems to be described using the standard Schrödinger formalism, avoiding the technical ambiguities that arise when quantising directly on curved manifolds. We derive the relation between the Hamiltonian governing quantum dynamics in $R_{obs}$ and its counterpart defined on the physical manifold U, and show that curvature effects enter as observer-dependent modifications of effective potentials. Although the resulting quantum description depends on the observer’s representation frame, we show that this does not lead to contradictions between observers: consistency of measurement outcomes follows from the standard structure of quantum correlations established by physical interactions. We illustrate the formalism with explicit applications, including the hydrogen atom in an Einstein static universe and quantum systems in the vicinity of a black hole, highlighting how spacetime curvature manifests itself in the observer’s quantum description. Full article

In this paper, we mainly investigate the radial symmetry and monotonicity of positive solutions for a nonlinear system involving pseudo-relativistic operators and fractional derivatives of order $(0,1)$. First, we prove a more general Narrow Region Principle and a Decay at Infinity Principle, which are essential for nonlocal pseudo-relativistic operators. Then, by using the direct method of moving planes, we prove the radial symmetry and radial monotonicity of positive solutions for the nonlinear system in the bounded domain $B_1\left(0\right)$ and the whole space, respectively. Finally, we show that the positive solutions of the system are strictly monotonically increasing in a Lipschitz coercive epigraph. Full article

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness—the view that the quantum state is operationally incomplete until the measurement context is specified—provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov’s to Gleason’s framework for quantum probabilities. Full article

State-of-the-art atomic clocks, in combination with high-precision time-frequency transfer techniques, have established a novel relativistic geodetic approach for determining the Earth’s geopotential. By exploiting ultra-stable atomic clocks and GNSS Precise Point Positioning (PPP) time-frequency transfer, this study investigates the cross-sea Orthometric Height (OH) determination between two remote stations separated by over 8000 km, corresponding to an OH difference of approximately 2260 m. Simulation results indicate that, when employing clocks with a frequency stability of 1 × 10⁻¹⁸, the remote OH determination could achieve a limiting accuracy of approximately 20 cm. This limitation is primarily attributed to the finite precision of the PPP time-frequency transfer, which constrains the ultimate performance of the OH determination. Furthermore, aggregating multiple observation periods could further enhance the accuracy to approximately 6 cm. These findings demonstrate that the PPP time-frequency transfer facilitates high-precision OH determination over intercontinental distances and thereby provides a feasible pathway toward the realization of a centimeter-level International Height Reference System (IHRS). Full article

We investigate the effect of general relativity on the Sitnikov problem. The Sitnikov problem is one of the simplest three-body problems, in which the two primary bodies (a binary system) have equal mass m and orbit their barycenter, while the third body is treated as a test particle under Newtonian gravity. The trajectory of the test particle is perpendicular to the orbital plane of the binary (along z-axis) and passes through the barycenter of the two primaries. To study the general relativistic contributions, we first derive the equations of motion for both the binary and the test particle based on the first post-Newtonian Einstein–Infeld–Hoffmann equation, and integrate these equations numerically. We examine the behavior of the test particle (third body) as a function of the orbital eccentricity of the central binary e, the dimensionless gravitational radius $\lambda$, which characterizes the strength of general relativistic effect, and the initial position of the test particle ${\overline{z}}_0$. Our numerical calculations reveal the following; as general relativistic effects $\lambda$ increase and the eccentricity e of the binary orbit grows, the distance $\overline{r}$ between the test particle and the primary star undergoes complicated oscillations over time. Consequently, the gravitational force acting on the test particle also varies in a complex manner. This leads to a resonance state between the position $\overline{z}$ of the test particle and the distance $\overline{r}$, causing the energy E of the test particle to become $E\ge 0$. This triggers the effective ejection of the test particle due to the gravitational slingshot effect. In this paper, we shall refer to this ejection mechanism of test particle as the “Sitnikov mechanism.” As a concrete phenomenon that becomes noticeable, the increase in general relativistic effects and the eccentricity of the binary orbit leads to the following: (a) ejection of test particles from the system in a shorter time, and (b) increasing escape velocity of the test particle from the system. As an astrophysical application, we point out that the high-velocity ejection of test particles induced by the Sitnikov mechanism could contribute to elucidating the formation processes of astrophysical jets and hyper-velocity stars. Full article

We investigate the non-relativistic scattering of a plane wave by a vertical segment formulating the problem in terms of the Lippmann–Schwinger equation in two spatial dimensions. Adjusting the coupling strength function we show how to implement the scattering by a system of multiple slits and by a Cantor set. We present detailed calculations of the scattered wave function for the line segment, as well as for the single, double, and multiple slits. We define reflection and transmission functions that are position-dependent in a defined region. From these results, we obtain the probability densities and differential and total cross-sections for these problems. Full article

The relativistic jets of gamma-ray bursts (GRBs) might be powered by a black-hole (BH) hyperaccretion system. The inherent asymmetry in these jets generates recoil forces, inducing oscillations and positional deviations of the BH from equilibrium. In this study, we explore the influence of different initial BH mass, spin, and mass accretion rate, as well as their evolutions on the dynamical properties of BH under the effect of asymmetric jets. Our results reveal that the initial mass and accretion rate significantly impact the BH’s acceleration, velocity, and displacement, while the different initial spin plays a negligible role in shaping the overall dynamical evolution. Additionally, we calculate the gravitational wave (GW) strains associated with the asymmetric jets, finding that the resulting GW signals are too weak to be detected, even for nearby GRBs. These findings provide critical insights into the dynamical response of BHs to asymmetric jets and the associated GW radiation, advancing our understanding of BH physics in GRBs. Full article

For the relativistic navigation system where the position and velocity of the spacecraft are determined through the observation of the relativistic perturbations including stellar aberration and starlight gravitational deflection, a novel parallel Q-learning extended Kalman filter (PQEKF) is presented to implement the measurement bias calibration. The relativistic perturbations are extracted from the inter-star angle measurement achieved with a group of high-accuracy star sensors on the spacecraft. Inter-star angle measurement bias caused by the misalignment of the star sensors is one of the main error sources in the relativistic navigation system. In order to suppress the unfavorable effect of measurement bias on navigation performance, the PQEKF is developed to estimate the position and velocity, together with the calibration parameters, where the Q-learning approach is adopted to fine tune the process noise covariance matrix of the filter automatically. The high performance of the presented method is illustrated via numerical simulations in the scenario of medium Earth orbit (MEO) satellite navigation. The simulation results show that, for the considered MEO satellite and the presented PQEKF algorithm, in the case that the inter-star angle measurement accuracy is about 1 mas, after calibration, the positioning accuracy of the relativistic navigation system is less than 300 m. Full article

We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a leading order of the form $\hslash \left(c\right)\sim \mathsf{\Lambda }/c^p$ for a constant $\mathsf{\Lambda }>0,$ and $p>1.$ We show how the limit $c\to \infty$ implies classicality in quantum mechanics and explain why p has to be larger than $1$. As the limit $c\to \infty$ breaks down both relativity theory and quantum mechanics, as followed by the proposed model, it can then be understood through similar conceptual physical laws. We further show how the position-dependent speed of light gives rise to an effective curved space in quantum systems and show that a stronger gravitational field implies higher quantum uncertainties, followed by the varied $c.$ We then discuss possible ways to find experimental evidence of the proposed model using set-ups to test the varying speed of light models and examine analogies of the model based on electrons in semiconductor heterostructures. Full article

Following Einstein’s prediction that “Physics constitutes a logical system of thought” and “Nature is the realization of the simplest conceivable mathematical ideas”, this topical review outlines a formal extension of local realism limited by the speed of light to global realism with bipolar strings (GRBS) that unifies the principle of locality with quantum nonlocality. The related literature is critically reviewed to justify GRBS which is shown as a necessary and inevitable consequence of the Bell test and an equilibrium-based axiomatization of physics and quantum information science for brain–universe similarity and human-level intelligence. With definable causality in regularity and mind–light–matter unity for quantum superposition/entanglement, bipolar universal modus ponens (BUMP) in GRBS makes quantum emergence and submergence of spacetime logically ubiquitous in both the physical and mental worlds—an unexpected but long-sought simplification of quantum gravity with complete background independence. It is shown that GRBS forms a basis for quantum intelligence (QI)—a spacetime transcendent, quantum–digital compatible, analytical quantum computing paradigm where bipolar strings lead to bipolar entropy as a nonlinear bipolar dynamic and set–theoretic unification of order and disorder as well as linearity and nonlinearity for energy/information conservation, regeneration, and degeneration toward quantum cognition and quantum biology (QCQB) as well as information-conservational blackhole keypad compression and big bang data recovery. Subsequently, GRBS is justified as a real-world quantum gravity (RWQG) theory—a bipolar relativistic causal–logical reconceptualization and unification of string theory, loop quantum gravity, and M-theory—the three roads to quantum gravity. Based on GRBS, the following is posited: (1) life is a living bipolar superstring regulated by bipolar entropy; (2) thinking with consciousness and memory growth as a prerequisite for human-level intelligence is fundamentally mind–light–matter unitary QI logically equivalent to quantum emergence (entanglement) and submergence (collapse) of spacetime. These two posits lead to a positive answer to the question “If AI machine cannot think, can QI machine think?”. Causal–logical brain modeling (CLBM) for entangled machine thinking and imagination (EMTI) is proposed and graphically illustrated. The testability and falsifiability of GRBS are discussed. Full article

A relativistic positioning system is a set of four emitters broadcasting their proper times by means of light signals. The four emitter times received at an event constitute the emission coordinates of the event. The covariant quantities associated with relativistic positioning systems are analysed relative to an observer in Minkowski space-time by splitting them in their relative space-like and time-like components. The location of a user in inertial coordinates from a standard set of emission data (emitted times and satellite trajectories) is solved in the underlying 3+1 formalism. The analytical location solution obtained by Kleusberg for the GPS system is recovered and interpreted in a Minkowskian context. Full article

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered, and the subjacent elements are geometrically interpreted. The case of four static beacons is analysed as a clarifying situation. Full article

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants. Full article