Non-inertial Frame Research Articles

Generalización de las transformaciones de Lorentz

Within the framework of special relativity, there are numerous models that allow inertial reference frame to be related to another accelerated (non-inertial) reference frame. We are going to provide necessary and sufficient conditions that will determine the optimal transformation in a unique way.

Quantum simulation of the Unruh effect with a Rydberg-dressed Bose-Einstein condensate

We propose a scheme for investigating the Unruh effect, i.e., the thermal radiation observed by uniformly accelerating observers or detectors, with ultracold atoms coupled by an off-resonant laser. We find that periodic modulation of the Rydberg-dressing interaction between atoms plays a significant role in the manipulation of a thermal bath in a uniformly accelerating reference frame. Our calculations show that the resulting Unruh temperature strongly depends on the driving frequency of the modulated Rydberg-dressing potential and the soft-core nature of the dressing interaction, i.e., the soft-core radius and height. These results reveal the potential applications of ultracold atoms with controllable long-range interaction in a wide variety of analog gravity phenomena.

Comment on “Analyses of Mössbauer Experiments in a Rotating System: Proper and Improper Approaches” [Annals of Physics Volume 418, July 2020, 168191

The notion of classical well localized trajectories of a single photon in Minkowski spacetime does not make any rigorous sense by the well-known existence of a proof that single photons cannot be well localized. This leads to principal difficultness when photodetection probability on relativistic non inertial frame of reference is considered. In order to resolve this tension, we extend canonical Minkowski geometry up to relevant point-free Minkowski geometry [Ann. Physics 423 (2020) 168329]. The photodetection probability density on uniformly rotating frame endrowed with point-free Lorentzian geometry is obtained. The result of S. A. Podosenov et al. [Ann. Physics 413 (2020) 168047] is obtained without any reference to unphysical notion of the classical trajectories of photon. The paper again shows the correctness of the remarkable result of Prof. C. Corda concerning the Mossbauer rotor experiment as new proof of general relativity, which has been awarded by the Gravity Research Foundation. In addition, the paper also shows various very elementary mistakes, misunderstandings and flaws by the self-called “YARK group”, which is a group of fringe researchers who attempts to promote wrong science, in particular, against the relativity theory.

Rotating Newtonian Fluids in a Non-Inertial Frame of Reference

Rotating Newtonian Fluids in a Non-Inertial Frame of Reference

Neural Network-Based Intuitive Physics for Non-Inertial Reference Frames

Classical mechanics offers us reliable means to predict various physical quantities, but it is difficult to derive the precise dynamic equations underlying most phenomena and obtain physical quantities in real-world situations. Intuitive physics, the ability to intuitively understand and predict physical phenomena, prevents this complication. However, its applications are confined to the inertial frame of reference. Here, we explored the potentials of neural network-based intuitive physics for solving non-inertial reference frames. We designed three experiments, each of which represents different types of real-world challenges. The task required predicting the speed of an object while the observer accelerates. We demonstrated that multilayer perceptron, invariant methods, and long-term memory networks successfully learn underlying dynamics from observations. This implies that neural network-based intuitive physics provides alternative means to predict various quantities in real-world applications that are unsolvable by classical physics methods.

System Modeling and Motion Control of a Cable-Driven Parallel Platform for Underwater Camera Stabilization

Underwater camera platform’s low image stabilization accuracy and poor waterproofness seriously restrict the quality of photos. In order to better cope with underwater camera work, this paper proposes a cable-driven underwater camera stabilized platform. It is a mobile platform driven in parallel by four flexible cables. To improve image stabilization accuracy and anti-interference performance, the system’s dynamic model is established in a non-inertial reference frame. And the random water wave interference is modeled. Moreover, a novel double-loop integral-type global fast terminal sliding mode control strategy is designed. Lyapunov stability theory is used to analyze the stability of the strategy. Finally, by comparing with the existing global fast terminal sliding mode controller and traditional sliding mode controller, the designed controller is simulated and verified. The results show that the proposed control strategy not only has the advantages of fast response and robustness, but also has the characteristics of rapid convergence in a finite time and high accuracy. This method can provide a valuable reference for the development of underwater camera stabilized platforms.

The Principle of Equivalence: Periastron Precession, Light Deflection, Binary Star Decay, Graviton Temperature, Dark Matter, Dark Energy and Galaxy Rotation Curves

The nature of the principle of equivalence is explored. The path of gravitons is analyzed in an accelerating system equivalent to a gravitating system. The finite speed of the graviton results in a delay of the gravitational interaction with a particle mass. From the aberration found in the path of the graviton we derive the standard expression for the advancement of the periastron of the orbit of the mass around a star. In a similar way, by analysing the aberrations of the graviton and light paths in an accelerating reference frame, the expression for the deflection of light by a massive body is obtained identically to the standard result. We also examine the binary star system and calculate the decay in its orbital period. The decay is attributed to the redshift of the graviton frequency relative to the accelerating system. Here too, we obtain good agreement with experimental measurements. Also, hypothesizing that gravitons behave like photons, we determine the temperature of the gravitons in a binary star system and form the Bose-Einstein distribution. Finally, we show how the redshift of gravitons may be the source of dark matter, dark energy and flat line spiral galaxy rotation curves.

The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

A Path Integral Generalization of Bell Local Hidden Variable Models for Unstable Particles

We discuss the problem of the generalization of Bell local hidden variable models for unstable particles as nucleons or decaying quantum bound states. We propose to extend the formalism of real deterministic hidden variables in the complex domain, in analogy with the quantum Gamow ket formalism, and we introduce a time dependent classical probability density distribution by which we implement hidden time dependence in the quantum expectation values. We suggest therefore a classical framework which may recover by asymptotic temporal limits the standard Bell stationary quantum statistical averages. Endly we discuss the possible relevance of our proposal for general non-isolated quantum systems in noninertial frames and the consequent dynamic effects of vacuum instabilities on E.P.R tests and Q.M. ensemble statistical averages.

ПОСТРОЕНИЕ ГРАНИЦ ОБЛАСТЕЙ УСТОЙЧИВОСТИ РЕЖИМА СТАЦИОНАРНОГО ВРАЩЕНИЯ РОТОРНОЙ СИСТЕМЫ С ЖИДКОСТЬЮ, ОСЬ КОТОРОЙ РАСПОЛОЖЕНА В АНИЗОТРОПНЫХ ЗАКРЕПЛЕНИЯХ

Earlier, the authors generalized the original method for studying the stability of stationary rotation of rotor systems containing a viscous incompressible fluid, the axis of which is located in isotropic anchors, in the case when the viscoelastic anchors of the axis of the rotor system are anisotropic. The generalization is based on two theorems that say that finding the stability conditions of such systems is associated with the possibility of elliptical precession-type motion, and with such motion there is a special non-inertial reference frame in which the hydrodynamic elements of the system periodically change in time. The study of such movements allows us to construct the boundaries of regions with different degrees of instability, in particular, the boundaries of the stability regions of the stationary rotation regime in the parameter space of the problem. The boundaries of the stability regions are constructed for cases when the anchoring of the rotor axis is anisotropic. In the space of the anchorage parameters, a parametrically defined D-curve is obtained as a function of the dimensionless frequency of the rotor precession. The two most interesting cases are considered – anisotropic stiffness of anchors (damping is isotropic in this case) and the opposite situation: isotropic stiffness of anchors with anisotropic damping. The obtained results are compared with the known results for the case of isotropic anchoring of the rotor axis. It is shown that the anisotropy of anchors, which is always present in real rotary systems due to the imperfection of technologies for the production of anchors, does not lead to negative effects. Moreover, using the obtained D-curves, it is possible to obtain technological tolerances for the production of fasteners, using what is known as the permissible deviation of the stiffness or damping value along the axes.

ИССЛЕДОВАНИЕ УСТОЙЧИВОСТИ СТАЦИОНАРНОГО ВРАЩЕНИЯ РОТОРНОЙ СИСТЕМЫ С ЖИДКОСТЬЮ, ОСЬ КОТОРОЙ РАСПОЛОЖЕНА В АНИЗОТРОПНЫХ ЗАКРЕПЛЕНИЯХ

Earlier, one of the authors proposed and developed (together with coworkers) an original method to study the stability of stationary rotation of rotary systems containing a viscous liquid and having a drive that maintains the angular velocity of rotation constant. It was assumed that the rotor has axial symmetry, the anchors of its axis are isotropic. The method is based on two theorems, according to which a change in the degree of instability is associated with the possibility of a perturbed motion of the circular precession type. This motion has a remarkable property: the velocity field and the shape of the liquid surface do not depend on time in a specially selected non-inertial reference frame associated with the line of centers. Finding the conditions for the feasibility of circular precession makes it possible to effectively construct the boundaries of the stability regions of the stationary rotation regime in the space of problem parameters. In addition, the study of the occurrence of circular precession allows us to find the conditions under which a subcritical (supercritical) Andronov-Hopf bifurcation takes place in the rotor system and to identify "dangerous" (“safe”) sections of the boundaries of the stability regions. In this paper, the previously proposed method of stability research applies to systems in which the rotor axis is located in anisotropic Laval type anchors. In the study of rotary systems of this type, it is possible to link the change in the degree of instability with the feasibility of perturbed movements of the elliptical precession type. It can be shown that the imaginary characteristic numbers of the equations in deviations from the stationary rotation mode are possible only in the case when there is a perturbed motion in the form of an elliptical precession. An example of a study of the stability of stationary rotation of a typical rotary system is given. Mechanical effects caused by the fact that gyroscopic stabilization becomes impossible with anisotropic fixing of the rotor axis are noted.

ОБ ОДНОЙ ЗАДАЧЕ УПРАВЛЕНИЯ ДВИЖУЩЕЙСЯ ТЕЛЕЖКОЙ С НАХОДЯЩИМСЯ НА НЕЙ УПРУГИМ СТЕРЖНЕМ

This article discusses the problem of controlling the process of longitudinal oscillations of an elastic homogeneous rod of uniform cross section. A rod is understood as a body, the length of which significantly exceeds its cross dimensions. The rod is on a moving cart, the right end of which is rigidly fixed, and the left end is not fixed. There is no friction between the rod and the cart surface in the problem under consideration. When the cart moves, the rod performs constrained longitudinal oscillations in a noninertial frame of reference associated with the cart. The control is the acceleration of the cart, the magnitude of which is limited. The boundaries of its accepted values are set. The value of the combined external forces acting on the rod is not known exactly, but only its limits of variation are given. The purpose of the control process is to ensure that at a given moment in time, the average value of the stretch of the rod is within a given interval. This average is calculated using the specified function. In order to solve the problem, the method of optimizing a guaranteed result is applied. A transition to a new one-dimensional variable is made, with the help of which the considered problem of control of the longitudinal oscillations of a rod is reduced to a similar control problem in the presence of noise. The necessary and sufficient conditions are found, under which it is possible to accomplish the set goal for any admissible external forces, the total value of which satisfies the given constraints. A corresponding algorithm for constructing the law of variation of the cart acceleration is proposed. An example that clearly shows how to build the cart control, which will guarantee the achievement of the set goal, has been analyzed.

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

Foucault pendulum revisited, the determination of precession angular velocity using Cartesian coordinates

A review on the Foucault pendulum motion is presented using Cartesian coordinates for the ideal case and for small amplitude of oscillations. The choice of referential frames, the formulation and solution of Newton’s differential equation for the non-inertial frame of the Earth and the validity of the approximations used to simplify the determination of the solution are given. Using the angular position of the trajectory cusps, a new method to determine the precession angular velocity of the Foucault pendulum is shown. The pendulum bob trajectories and velocities for the referential frame in rotation with the Earth as well as for the inertial frame are given and the Chevilliet theorem was demonstrated. In addition, the pendulum bob trajectories are shown when an initial velocity is impinged in the direction perpendicular to the pendulum oscillation plane.

The effect of acceleration parameter on thermal entanglement and teleportation of a two-qubit Heisenberg XXX model with Dzyaloshinski-Moriya interaction in non-inertial frames

Thermal entanglement and teleportation properties in non-inertial frames are investigated when a two-qubit Heisenberg XXX model with Dzyaloshinski-Moriya (DM) interaction is used as the quantum channel. We find that thermal entanglement and teleportation fidelity decrease with the acceleration parameter or temperature, in other words, the entanglement teleportation of a teleported state will degenerate in non-inertial frames. Furthermore, our results also show that the average fidelity may be promoted by DM interaction for the ferromagnetic case, which is opposite to the antiferromagnetic case in non-inertial frames, although diminished by acceleration parameter, and their influence can be counteracted.

A conceptual essay on the nature of spacetime

A conceptual essay on the nature of spacetime

A geometrically-exact momentum-based nonlinear theory for pipes conveying fluid

A geometrically-exact nonlinear theory is developed for pipes conveying fluid based on the total momentum of the fluid and pipe. The proposed model accounts for geometric and kinematic nonlinearities of the pipe and inertial coupling between the pipe and internal flow. The fully nonlinear differential governing equations are derived based on the momentum balance of pipe and fluid in floating non-inertial frames, allowing for large displacements and overall rigid-body motions. The internal fluid pressures along a pipe are considered; the fluid is viscous but assumed to be incompressible and homogeneous. A separation of displacements technique combined with an assumption of small incremental displacements is used to derive an updated Lagrangian formulation, which allows a large-displacement nonlinear model to be converted into a series of piecewise-linear models. The resulting time-stepping method is numerically implemented using the finite-volume discretization. The effectiveness of the proposed developments is demonstrated in a series of numerical examples, including a cantilever pipe discharging fluid, a semi-circular curved pipe, and a marine riser subject to top tension and forced motion. The new model is shown to predict an unstable flutter at a relatively low flow velocity for a cantilever discharging pipe, and to predict a transition behavior before the onset of the observed flutter instability.

Eliminating the Unruh effect of relativistic Dirac fields by partial measurements

The retrieval of lost entanglement for relatively accelerated fermionic observers of a tripartite system by a partial measurement technique has been investigated. From the prospective of the negativities of one-tangles and the π-tangle, we show that the degraded entanglement in noninertial frames with single-mode approximation is completely retrieved by an optimal strength of the partial measurement or the partial measurement reversal. In addition, we find that the optimal one-tangle with respect to inertial and noninertial observers turns out to be the same for an optimal strength of partial measurements at q 0 = 0 when two accelerated observers move with infinite acceleration.

Local and global theories of relativity in flat and curved spacetimes

Special and general theories of relativity consist in describing both local and global phenomena - the first in flat, and the second in curved spacetime. In the paper it is shown that each of these two classes of relativistic effects, local and global, is universal and is the subject of a separate theory. First, descriptions in local frames of reference, related by the local Lorentz transformations, form the local theory of relativity, or local relativity (LR). The locality principle allows to apply LR to non-inertial local frames, and the equivalence principle to the local frames in gravitational field. Secondly, descriptions in global frames of reference, constructed from local frames coexisting on a common hypersurface of simultaneity, form the global theory of relativity, or global relativity (GlR). LR and GlR are based on physical coordinates and complement each other, the special and general theories of relativity were hybrids of these two theories. LR and GlR describe the local and global properties of gravity, separating the field effects from the effects of motion by different methods, such as bimetric formalism, where one metric describes geometry of the global frames, and other describes spacetime geometry. It is shown that GlR leads to a picture of collapse with formation of frozars, and also leads to a cutoff of the loop integrals of quantum fields at the Planck length. In GlR, cosmological models are built on hypersurfaces of simultaneity, where both stretching and the Doppler effect contribute to redshifts, and aberration is also taken into account. Predicted an initial violetshift removing the double redshift paradox, and this leads to the slowing time cosmology consistent with observational data.

Upscaled DEM-CFD model for vibrated fluidized bed based on particle-scale similarities

Simulation based on discrete element method (DEM) coupled with computational fluid dynamics (CFD), coupled DEM-CFD, is a powerful tool for investigating the details of dense particle–fluid interaction problems such as in fluidized beds and pneumatic conveyers. The addition of a mechanical vibration to a system can drastically alter the particle and fluid flows; however, their detailed mechanisms are not well understood. In this study, a DEM-CFD model based on a non-inertial frame of reference is developed to achieve a better understanding of the influence of vibration in a vibrated fluidized bed. Because the high computational cost of DEM-CFD calculations is still a major problem, an upscaled coarse-graining model is also employed. To realize similar behaviors with enlarged model particles, non-dimensional parameters at the particle scale were deduced from the governing equations. The suitability and limitations of the proposed model were examined for a density segregation problem of a binary system. To reduce the computational costs, we show that the ratio between the bed width and model particle size can be reduced to a minimum value of 100; to obtain similar segregation behaviors, the ratio between the bed height and model particle size is considered unchanged.