Non-inertial Frame Research Articles

Comments on the article Harry Lassa Accelerating Frames of Reference and the Clock Paradox

Comments on the article Harry Lassa Accelerating Frames of Reference and the Clock Paradox

Einstein's Rocket Ship, the Deflection of Light and the Precession of the Orbital Perihelion

The nature of the principle of equivalence is explored. The light ray travel path in an accelerated reference frame, a rocket ship, is described and the rocket ship model is used to derive the deflection of light by a massive body. By accounting for the effect of the velocity of the accelerated observer relative to an inertial frame, the additional deflection angle is obtained due to the aberration of the light beam. This model is applied to the deflection of light by a central gravitational field, giving the total deflection angle in agreement with the standard result. Also, a novel approach is given by considering the deflection of light by a massive body to obtain the precession of the perihelion of a planet.

Lattice and quintic nonlinearity induced stripe phase in Bose–Einstein condensate under non-inertial and inertial motion

We consider a parametrically forced Bose–Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that the existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and the lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis of the obtained solution is performed and we found that the solution is stable. In order to gain a better understanding of the underlying physics, we compute the energy, showing nonlinear compression of the condensate in some parameter domain.

Design and development of a UAV Experimental Platform

This paper deals with the design, construction, and instrumentation of a UAV experimental platform. It is formed by a mechanism and a UAV hexacopter. The mechanism allows the movement around of non-inertial frame of the vehicle while restricting the movement around of inertial frame. The UAV hexacopter is fixed to the mechanism and contains an IMU sensor to measure the angular position of the vehicle. The data acquisition, processing and compute of the control signals is developed on board the vehicle through a NI myRIO®. By considering the dynamical behavior of the UAV hexacopter, it can be divided in rotational and translational motion. The stabilization of the rotational dynamics is addressed in this work, where two control loops around the Euler angles roll and pitch are implemented and tested in the experimental platform. The development of the instrumentation and the construction of the experimental platform are presented to explain how the system measures the angular position around the non-inertial frame of the UAV. The main contribution of this work is the design of the experimental platform. The effectiveness and practicality to stabilize a UAV hexacopter are shown through experimental results.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Massive Unruh particles cannot be directly observed

We show that massive particles created in a relativistically accelerated reference frame, as predicted by the Unruh effect, can only be found in a tiny layer above the event horizon, whose thickness corresponds to a single Compton wavelength. This is beyond the reach of any detector and suggests that the Unruh effect may not ever be directly observed for massive fields. The case of massless particles is also examined, for which qualitatively different behaviour is observed in a low-acceleration regime, suggesting that an observation of the Unruh effect for massless particles is more promising.

Quantum coherence behaviors of fermionic system in non-inertial frame

In this paper, we analyze the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also study the quantum coherence tradeoff between particle and antiparticle sector. It is found that there exists quantum coherence transfer between particle and antiparticle sector, but the coherence lost in particle sector is not entirely compensated by the coherence generation of antiparticle sector. Besides, we emphatically discuss the cohering power and decohering power of Unruh channel with respect to the computational basis. It is shown that cohering power is vanishing and decohering power is dependent of the choice of Unruh mode and acceleration. Finally, we compare the behaviors of quantum coherence with geometric quantum discord and entanglement in relativistic setup. Our results show that this quantifiers in two region converge at infinite acceleration limit, which implies that this measures become independent of Unruh modes beyond the single-mode approximations. It is also demonstrated that the robustness of quantum coherence and geometric quantum discord are better than entanglement under the influence of acceleration, since entanglement undergoes sudden death.

Nonlinear Antiswing Control of Offshore Cranes With Unknown Parameters and Persistent Ship-Induced Perturbations: Theoretical Design and Hardware Experiments

In practical applications, offshore cranes are widely utilized on large scale ships to accomplish the tasks of transferring cargos from one ship to another or between ships and harbors. Compared with traditional land-fixed cranes, offshore cranes work in noninertial (ship) frames and their movements are significantly influenced by such complicated disturbances as sea waves, etc. Hence, the control issue of offshore cranes presents much more challenges. At present, existing controllers for offshore cranes are designed based upon linearized dynamics, and they need the accurate values of the plant parameters. However, the values of the parameters, including cargo/jib masses, are usually difficult to measure or even unknown, which makes exact gravitational force compensation difficult and unavoidably results in positioning errors for luffing and hoisting/lowering control. To deal with these practical issues, we suggest a novel model-parameter-free control approach to achieve effective control for underactuated offshore crane systems. By constructing an elaborate storage function, we provide a complete Lyapunov-based stability analysis. As far as we know, this paper provides the first control strategy to asymptotically regulate an offshore crane system subject to parametric uncertainties and ship-induced perturbations, which is developed without simplifying the original nonlinear dynamic equations. At last, a series of experimental results, carried out on a self-built offshore crane hardware platform, are presented to validate the effectiveness and robustness of the presented control scheme.

Multibody simulation of railway vehicles with contact lookup tables

The use of contact lookup tables is widely used in multibody railway simulations to increase the computational efficiency. However, due to simplifying assumptions the use of contact lookup tables decreases the accuracy of the simulation results. This paper analyses the increase of computational efficiency and loss of accuracy for a particular multibody simulation. To this end the results based on contact lookup tables are compared with the results of the online solution of the wheel-rail contact constraints. The formulation used to compute the equations of motion of railway vehicles has the following features: (1) the equations of motion are obtained using a systematic procedure based on multibody dynamics, (2) generalized forces included in the equations of motion are obtained using symbolic computations when possible, (3) generalized coordinates are referred to a non-inertial track frame, (4) the equations of motion are obtained using a velocity transformation of the Newton–Euler equations of the vehicle bodies, which are assumed to be rigid and (5) wheel-rail tread contact and flange contact are treated with pre-calculated lookup tables which can take into account the track irregularities. The comparative study presented in this paper shows that this formulation can be used to simulate the dynamics of a railway vehicle in real-time.

Quantum dynamics characteristic and the flow of information for an open quantum system under relativistic motion

In this letter, the dynamics characteristics of quantum entanglement (negativity) and distinguishability (trace distance), and the flow of information for an open quantum system under relativistic motion are investigated. Explicitly, we propose a scenario that a particle A held by Alice suffers from an amplitude damping (AD) noise in a flat space-time and another particle B by Bob entangled with A travels with a fixed acceleration under a non-inertial frame. The results show that quantum distinguishability and entanglement are very vulnerable and fragile under the collective influence of AD noise and Unruh effect. Both of them will decrease with the growing intensity of the Unruh effect and the AD thermal bath. It means that the abilities of quantum distinguishability and entanglement to suppress the collective decoherence (AD noise and Unruh effect) are very weak. Furthermore, it turns out that the reduced quantum distinguishability of Alice’s system and Bob in the physically accessible region is distributed to another quantum distinguishability for Alice’s environment and Bob in the physically inaccessible region. That is, the information regarding the scenario is that the lost quantum distinguishability, as a fixed information, flows from the systems to the collective decoherence environment.

Retrieving the lost fermionic entanglement by partial measurement in noninertial frames

The initial entanglement shared between inertial and accelerated observers degrades due to the influence of the Unruh effect. Here, we show that the Unruh effect can be completely eliminated by the technique of partial measurement. The lost entanglement could be entirely retrieved or even amplified, which is dependent on whether the optimal strength of reversed measurement is state-independent or state-dependent. Our work provides a novel and unexpected method to recover the lost entanglement under Unruh decoherence and exhibits the ability of partial measurement as an important technique in relativistic quantum information.

Equivalence principle and quantum mechanics: quantum simulation with entangled photons.

Einstein's equivalence principle (EP) states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the EP remains valid in non-relativistic quantum mechanics is a controversial issue. To avoid violation of the EP, Bargmann's superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on the propagation of polarization-entangled photon pairs in curved and birefringent optical waveguides and Hong-Ou-Mandel quantum interference measurement. The photonic simulator can emulate superposition of mass states, which would lead to violation of the EP.

Vision sensor and dual MEMS gyroscope integrated system for attitude determination on moving base.

To determine the relative attitude between the objects on a moving base and the base reference system by a MEMS (Micro-Electro-Mechanical Systems) gyroscope, the motion information of the base is redundant, which must be removed from the gyroscope. Our strategy is to add an auxiliary gyroscope attached to the reference system. The master gyroscope is to sense the total motion, and the auxiliary gyroscope is to sense the motion of the moving base. By a generalized difference method, relative attitude in a non-inertial frame can be determined by dual gyroscopes. With the vision sensor suppressing accumulative drift of the MEMS gyroscope, the vision and dual MEMS gyroscope integration system is formed. Coordinate system definitions and spatial transform are executed in order to fuse inertial and visual data from different coordinate systems together. And a nonlinear filter algorithm, Cubature Kalman filter, is used to fuse slow visual data and fast inertial data together. A practical experimental setup is built up and used to validate feasibility and effectiveness of our proposed attitude determination system in the non-inertial frame on the moving base.

Mach Principle and Post-Einsteinian Relativity Theory

Inertia is one of the most mysterious forces of nature. Its physical nature is unknown. Accordingly, attempts are made to avoid this “dark force” in one way or another. In Newton’s mechanics and in the special relativity theory, this is done by postulating inertial reference frame, in the general relativity theory by postulating the equivalence principle. Postulates cannot change the laws of nature. One needs to know the latter. Given that the forces of inertia result in non-inertial reference frames only, a hypothesis of the induction nature of inertia has been made. According to this hypothesis, the forces of inertia result as the reaction of a body to external influence. A system of equations explaining the physical nature of inertia and its connection to gravity has been drafted. A group of coordinate conversion has been suggested, which without violating the general covariance of the laws of nature, enables to distinguish one reference frame associated with one body from another system associated with another body, to determine the privileged ones, and to take into consideration their influence on the readings of measurement instruments. A modified mechanics had been created. It takes into consideration the Mach’s principle and enables to cover all systems with the relativity principle. All of the relativistic effects arise from it. The reasons for emergence of new particles, dark matter, dark energy etc. are explained. New effects are predicted.

Numerical investigation of the flow past an oscillating cylinder in a non-inertial reference frame

Numerical investigation of the flow past an oscillating cylinder in a non-inertial reference frame

Experiments on the CMB Spectrum, Big Jets Model and Their Implications for the Missing Half of the Universe

Based on the limiting continuation of Lorentz-Poincaré invariance, we propose an alternative formulation of the generalized Planck distribution for inertial and noninertial frames. The Lorentz invariant Planck distribution law leads to a new physical interpretation of the dipole anisotropy of the Cosmic Microwave Background. The Big Jets model predicts a distant ‘antimatter blackbody,’ whose radiations could make 50% of the sky very slightly warmer than the isotropic CMB temperature TCMB with a cosine function. The other 50% of the sky has the same isotropic temperature TCMB. Thus, we could have a pseudo-dipole anisotropy because the microwaves emitted from the antimatter blackbody are totally absorbed by our matter blackbody. We suggest that accurate data of satellite experiments might be used to search for the pseudo-dipole anisotropy and the missing half of the antimatter universe.

New theory of stellar convection without the mixing-length parameter: new stellar atmosphere model

Stellar convection is usually described by the mixing-length theory, which makes use of the mixing-length scale factor to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is proportional to the local pressure scale height of the star, and the proportionality factor (i.e. mixing-length parameter) is determined by comparing the stellar models to some calibrator, i.e. the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases and because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper [1] we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behavior of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations expressed in a non-inertial reference frame co-moving with the convective elements. The motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

Protecting quantum coherence in an open system under non-inertial frames

In this paper, we explore the dynamics and protection of quantum coherence in an open system under non-inertial frames by weak measurement and reversal, and design four strategies to protect the quantum coherence of an initial two-qubit entangled state, when the systems suffer from amplitude damping (AD) channel and one subsystem is under non-inertial frames. In practice, there is no strict inertial frames, decoherence and degradation of the quantum coherence caused by the Unruh effect form acceleration will have a significant interaction, therefore it is important to find some means to protect quantum coherence under non-inertial frames.

Formation of freely floating sub-stellar objects via close encounters

We numerically studied close encounters between a young stellar system hosting a massive, gravitationally fragmenting disk and an intruder diskless star with the purpose to determine the evolution of fragments that have formed in the disk prior to the encounter. Numerical hydrodynamics simulations in the non-inertial frame of reference of the host star were employed to simulate the prograde and retrograde co-planar encounters. The initial configuration of the target system (star plus disk) was obtained via a separate numerical simulation featuring the gravitational collapse of a solar-mass pre-stellar core. We found that close encounters can lead to the ejection of fragments that have formed in the disk of the target prior to collision. In particular, prograde encounters are more efficient in ejecting the fragments than the retrograde encounters. The masses of ejected fragments are in the brown-dwarf mass regime. They also carry away an appreciable amount of gas in their gravitational radius of influence, implying that these objects may possess extended disks or envelopes, as also suggested by Thies et al. (2015). Close encounters can also lead to the ejection of entire spiral arms, followed by fragmentation and formation of freely-floating objects straddling the planetary mass limit. However, numerical simulations with a higher resolution are needed to confirm this finding.

Strong-field approximation in a rotating frame: High-order harmonic emission from p states in bicircular fields

High-order harmonic generation with bicircular fields - the combination of counter-rotating circularly polarized pulses at different frequencies - results in a series of short-wavelength XUV harmonics with alternating circular polarizations, and experiments show that there is an asymmetry in the emission between the two helicities: a slight one in helium, and a larger one in neon and argon, where the emission is carried out by p-shell electrons. Here we analyze this asymmetry by switching to a rotating frame in which the field is linearly polarized; this induces an effective magnetic field which lowers the ionization potential of the $p_+$ orbital that co-rotates with the lower-frequency driver, enhancing its harmonic emission and the overall helicity of the generated harmonics, while also introducing nontrivial effects from the transformation to a non-inertial frame in complex time. In addition, this analysis directly relates the small asymmetry produced by s-shell emission to the imaginary part of the recollision velocity in the standard strong-field-approximation formalism.