Equivalence Principle Research Articles

Mass and angular momentum for the Kerr black hole in TEGR and STEGR

We study the energy–momentum characteristics of the rotating black hole–Kerr solution of general relativity in the teleparallel equivalent of general relativity (TEGR) and the symmetric teleparallel equivalent of general relativity (STEGR). The previously constructed spacetime-covariant and Lorentz-invariant expressions for conserved Noether currents, superpotentials, and charges are used. The Noether charges describe the total energy, momentum, or angular momentum of a gravitational system depending on the choice of displacement vector ξ. To define the covariant and invariant conserved quantities in both TEGR and STEGR, one needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR, we use the unified “turning-off” gravity principle. In addition, to analyze the Noether conserved quantities in these theories, we use the concept of “gauges.” Changes in the gauge can affect the Noether conserved quantities. We highlight two ways to turn off gravity—by M→0 and by M→0,a→0—which give us different gauges in TEGR and STEGR. In both kinds of gauges, we obtain the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein’s equivalence principle for the Kerr solution were unsuccessful in both TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novel finding.

On the first test of the Weak Equivalence Principle in low Earth orbit

On the first test of the Weak Equivalence Principle in low Earth orbit

Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle

Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle

Kaluza–Klein bubble with massive scalar field

A well-known soliton (bubble) solution of five-dimensional Kaluza–Klein General Relativity is modified by imposing mass on the scalar field. By forcing the scalar field to be short-range, the failure of the original bubble solution to satisfy the equivalence principle is remedied, and the bubble acquires gravitational mass. Most importantly, the mass is quantized, even in this classical setting, and has a value mP/(4α), where mP is the Planck mass, and α is the fine-structure constant. This result applies for any choice of scalar-field mass, as it is an attractor for the field equations.

The Proof of the Fermar's Last Theorem, Mersenne's Prime Conjecture and Poincare Conjecture in Euclidean Geometry

In order to strictly prove from the point of view of pure mathematics Goldbach's 1742 Goldbach conjecture and Hilbert's twinned prime conjecture in question 8 of his report to the International Congress of Mathematicians in 1900, and the French scholar Alfond de Polignac's 1849 Polignac conjecture, By using Euclid's principle of infinite primes, equivalent transformation principle, and the idea of normalization of set element operation, this paper proves that Goldbach's conjecture, twin primes conjecture and Polignac conjecture are completely correct. In order to strictly prove a conjecture about the solution of positive integers of indefinite equations proposed by French scholar Ferma around 1637 (usually called Ferma's last theorem) from the perspective of pure mathematics, this paper uses the general solution principle of functional equations and the idea of symmetric substitution, as well as the inverse method. It proves that Fermar's last theorem is completely correct.

An efficient electromagnetic scattering character restoration solution for UAV swarm targets

ABSTRACT Swarm formulations are new UAV (unmanned aerial vehicle) derivations with high application significances. UAV swarms are nonrigid, deformable, extended targets with multimodality property in radar viewpoint. This brings higher radar cross section (RCS) variety and statistical uncertainty. Conventional full-wave electromagnetic solvers are not applicable for massive UAV swarm RCS simulation. This paper introduces an efficient RCS restoration solution using EPA (equivalent principle algorithm) and EIM (empirical interpolation method). Parameter and solution spaces are constructed to extract interpolation points and basis functions. Specific parameter selection and solution initialization methods enable solution restoration. The quadcopter drone swarm model is developed for numerical verification. RCS restoration accuracy and efficiency evaluation results indicate that the proposed method enables the possibility for massive UAV swarm RCS simulations with prominent efficiency advantages.

A Pilot Study to Predict Lifetime of Resin-Based Materials for Denture: Presentation of an In Vitro Thermally-Accelerated Ageing Method.

The aim of this article was to present a method for predicting dental materials lifetime, using in vitro thermally accelerated ageing. The technique was tested to compare the behavior of 3 resin base materials for denture. Bar-shaped samples of the poly(methyl methacrylate) PMMA based-resin Probase Hot (Probase), CAD/CAM disc Ivobase CAD (IvoCAD) and high-impact resin IvoCAP were aged in artificial saliva for 15, 30, 45, 60, 90, 120 and 180 days at 55°C, 75°C and 90°C. Flexural strength and surface roughness of the 3 resins for each ageing duration and temperature were measured for 3 samples (n=189). Using the time-temperature equivalence principle and the Arrhenius model, a master curve was constructed, the activation energy of the simulated ageing process was calculated and the lifetime of each material was estimated, based on degradation of flexural strength value over time. The mean initial flexural strength was 87.98 ± 7.37, 79.35 ± 10.01 and 97.31 ± 4.97 MPa for IvoCAD, IvoCAP and Probase, respectively. Activation energies of the ageing in artificial saliva were measured at 81.9, 82.6 and 66.2 kJ/mol, respectively, and average lifetimes at 37°C were estimated at 19.5, 14.4 and 9.2 years. In this first approach to estimating the in vitro lifetime in artificial saliva of resin-based materials for dentures, the three materials met the expected criteria, validating the estimation method. Therefore, thermally-accelerated ageing and the Arrhenius model could be an interesting tool to add to routine tests used to validate new polymer materials and manufacturing processes.

Characteristic Analysis and Error Compensation Method of Space Vector Pulse Width Modulation-Based Driver for Permanent Magnet Synchronous Motors.

Permanent magnet synchronous motors (PMSMs) are widely used in a variety of fields such as aviation, aerospace, marine, and industry due to their high angular position accuracy, energy conversion efficiency, and fast response. However, driving errors caused by the non-ideal characteristics of the driver negatively affect motor control accuracy. Compensating for the errors arising from the non-ideal characteristics of the driver demonstrates substantial practical value in enhancing control accuracy, improving dynamic performance, minimizing vibration and noise, optimizing energy efficiency, and bolstering system robustness. To address this, the mechanism behind these non-ideal characteristics is analyzed based on the principles of space vector pulse width modulation (SVPWM) and its circuit structure. Tests are then conducted to examine the actual driver characteristics and verify the analysis. Building on this, a real-time compensation method is proposed, physically matched to the driver. Using the volt-second equivalence principle, an input-output voltage model of the driver is derived, with model parameters estimated from test data. The driving error is then compensated with a voltage method based on the model. The results of simulations and experiments show that the proposed method effectively mitigates the influence of the driver's non-ideal characteristics, improving the driving and speed control accuracies by 88.07% (reducing the voltage error from 0.7345 V to 0.0879 V for a drastic command voltage with a sinusoidal amplitude of 10 V and a frequency of 50 Hz) and 53.08% (reducing the speed error from 0.0130°/s to 0.0061°/s for a lower command speed with a sinusoidal amplitude of 20° and a frequency of 0.1 Hz), respectively, in terms of the root mean square errors. This method is cost-effective, practical, and significantly enhances the control performance of PMSMs.

Volumetric mix-design modification and vibration attenuation analysis of rubberised epoxy asphalt track for railway

Rubberized asphalt mixture effectively reduces vibrations in railway track due to the elasticity of crumb rubber (CR) and the viscoelasticity of asphalt binder. This study aims to design a rubberized epoxy asphalt mixture using the modified volumetric mix-design method named the multi-point supported skeleton for asphalt mixtures (V-S method). The feasibility and vibration attenuation of the precast epoxy asphalt track was evaluated through a 3D FEM simulation at a 350 km/h speed. By combining the V-S method with the equivalent volume replacement principle between CR and coarse aggregate, four types of rubberized epoxy asphalt mixtures were proposed using the dry method. Indoor test results confirm that these mixtures meet the required specifications. The FEM results demonstrate that the designed epoxy asphalt track meets the design criteria and the components of the EA-4CR track structure demonstrate superior vibration reduction performance among the cases with the same increment in CR content.

Mitigação dos princípios cambiários pelos títulos de crédito escriturais

The present study presents the theme of scriptural credit bonds based on a reinterpretation of the principles of credit bonds, notably Cartularity, Documentability and Functional Equivalence, considering their electronic circulation system. The regulation of exchange rate circulation is scrutinized in a written manner, instrumentalized by technologies, despite the mismatch between the legislative tool, technological evolution and the apparent conflict between the aforementioned principles of credit bonds. The aim is to verify whether the demand of the economic agents involved in the exchange rate relationship is effectively being met; confirming or refuting the negative premise posed to the questions whether such principles were suppressed, as well as whether the circulation of credit securities in book-entry form justifies a possible revocation of the guidelines that regulate the issuance of certificated securities. Inquiring into the hypotheses characterized by the negative nature of the inquiries, in the end, it appears that there was no suppression of the circulation of credit securities in written form nor the revocation of the determinations that regulate the issuance of certificates of exchange securities.

Comment on “Determining the difference between local acceleration and local gravity: Applications of the equivalence principle to relativistic trajectories” [Am. J. Phys. 92(6), 444–449 (2024)]

Comment on “Determining the difference between local acceleration and local gravity: Applications of the equivalence principle to relativistic trajectories” [Am. J. Phys. <b>92</b>(6), 444–449 (2024)]

Inflation and the principle of equivalence

Abstract A formal, mathematical statement of the principle of equivalence in general relativity is that one must always be able to find – at each location within a curved spacetime – the local free-falling frame against which one can measure the acceleration-induced time dilation and degree of curvature relative to flat spacetime. In this article, we use this theorem to prove that a de Sitter expansion, required during cosmic inflation, does not satisfy this condition and is therefore inconsistent with the PoE. To emphasize the importance – and reality – of this outcome, we contrast it with the analogous derivation for the Schwarzschild metric, which instead satisfies this requirement completely. We point out that this failure by de Sitter results from its incorrect handling of the Friedmann–Lemaître–Robertson–Walker (FLRW) lapse function, g tt {g}_{{\rm{tt}}} . Our conclusion calls into question whether a period of inflated expansion could have even been possible in the context of FLRW cosmologies, and is noteworthy in light of recent, high-precision measurements showing that inflation could not have solved the temperature horizon problem while simultaneously producing the observed primordial power spectrum.

Fast prediction of the melting of FeH[formula omitted] in planetary interiors

FeHx is a crucial mineral in geophysics, but its melting properties remain poorly understood at high pressures. In this Short Communication, we introduce a simple analytical model to access the solid–liquid boundary of FeHx with minimal time and cost. Inspired by the work-heat equivalence principle, our model allows geophysicists to effectively exploit available ab initio resources to directly deduce the melting temperature of FeHx from its equation of state. The obtained results agree quantitatively with cutting-edge atomistic simulations throughout a wide range of hydrogen content and hydrostatic pressure. Therefore, our analyses would have implications for elucidating the internal dynamics of rocky worlds within and beyond our Solar System.

Coupled Elastic–Plastic Damage Modeling of Rock Based on Irreversible Thermodynamics

Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate b, damage evolution rate Bω, weighting factor r, and damage softening parameter a. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas.

Study on the equivalent model considering in-plane and out-of-plane mechanical properties for a curved sandwich structure with square honeycomb core

The curved honeycomb sandwich structure has larger surface area, effectively reducing the number of fasteners and parts of civil airplane fuselages, engine cowls, and ship’s hulls. Its equivalent model building can significantly shorten the simulation analysis time and improve the efficiency of optimal design and performance prediction, but the reliability and precision of the model are closely related to the calculation accuracy of equivalent elastic parameters. In the present study, an equivalent model considering the in-plane and out-of-plane mechanical properties of the core is developed for a curved square honeycomb sandwich structure. The in-plane and out-of-plane equivalent elastic parameters of the honeycomb core composed of hollow quadrangular frustum cells with symmetrical rectangular sides (i.e. square cell) are derived by analytical method, equivalent strain energy principle, and equivalent stiffness principle. And then combined with the sandwich panel theory, an equivalent model of the curved sandwich structure is established. The three-dimensional (3D) geometric models of planar honeycomb cores with hollow quadriprism cells are built by SolidWorks software, and the 3D printing is performed using Polylactic Acid (PLA) material. The three-point bending tests are conducted on the planar honeycomb sandwich structures with carbon fiber composite face sheets, and the test data are compared with the numerical results of this structure and its equivalent model. Based on ANSYS Workbench, the static analysis under bending and compression conditions, modal analysis, and harmonic response analysis are implemented on honeycomb sandwich structures with different bending degrees and their equivalent models. The results show that the load-displacement test curves of planar sandwich structures agree well with the finite element results of these structures and their equivalent models, and the equivalent models of curved sandwich structures accurately reflect the bending and vibration characteristics, fully verifying the feasibility of the presented equivalent model. This study provides important references and guidance for establishing the equivalent model of curved honeycomb sandwich structures.

Design of a novel state-feedback robust \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_2/H_{\\infty }$$\\end{document} sliding-mode controller for a hydraulic turbine governing system

This paper presents a novel state-feedback robust sliding-mode controller (SFRSMC) based on a mixed H2/H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_2/H_{\\infty }$$\\end{document} approach to enhance the control performance of hydraulic turbine governing systems (HTGS) with complex conduit systems under external load disturbances and control signal uncertainties. A state-space model incorporating the dynamic responses of the HTGS is developed. The SFRSMC is designed using the sliding-mode equivalent control principle, with a disturbance observer to estimate and mitigate unknown disturbances. To balance robustness and optimality, mixed H2/H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_2/H_{\\infty }$$\\end{document} linear matrix inequalities (LMIs) are utilized to determine the critical performance sliding matrix via an auxiliary feedback control method. The effectiveness of the proposed control scheme is validated through time-domain simulations under various operating scenarios, including different parameter variations of the HTGS.

Explanation of the exceptionally strong timing noise of PSR J0337+1715 by a circum-ternary planet and consequences for gravity tests

Timing of pulsar PSR J0337+1715 provides a unique opportunity to test the strong equivalence principle (SEP) with a strongly self-gravitating object. This is due to its unique situation in a triple stellar system with two white dwarfs. Our previous study suggested the presence of a strong low-frequency residual signal in the timing data, and we set out to model this signal on a longer dataset in order to determine its nature and improve accuracy. We considered three models: chromatic red noise, achromatic red noise, and a small planet in a hierarchical orbit with the triple stellar system. These models were implemented in our numerical timing model. We performed Bayesian inference of posterior distributions. Best fits were compared using information-theoretic criteria. We rule out chromatic red noise from dispersion-measure variations. Achromatic red noise or a planet in Keplerian orbit provide the best fits. If the residual signal is red noise, then it appears exceptionally strong. When assuming the presence of a planet, we obtained a marginal detection of mutual interactions that allowed us to constrain its mass to $ Moon $ as well as its inclination. The latter is intriguingly coincident with a Kozai resonance. We show that a longer observation span will ultimately lead to a clear signature of the planet model due to its mutual interactions with the triple system. We produce new limits on SEP violation: $| $ or $| $ at a 95&lt;!PCT!&gt; confidence level under the planet or red-noise hypothesis, respectively. This model dependence emphasises the need for additional data and model selection. As a by-product, we estimated a rather low supernova kick velocity of $ km/s$, strengthening the idea that it is a necessary condition for the formation of pulsar triple systems.

The Concept of Weight as Reflecting the Epistemological Changes in Physics

AbstractThe goal of this study was to elicit and juxtapose the account of the concept of weight in history vis a vis physics education. The results reveal the problem of consistency in the currently employed teaching materials. The weight concept is very old and remains ubiquitous in science. Its history reflects the maturation of scientific methodology. The latter implied three periods of its development: old, classical, and modern. The “old” weight designated heaviness, or gravity, of bodies and the quantity of matter, both measured through weighing by balance. The “old” weight served as the basis for trade and technology. “Old” weight split in the scientific revolution of the seventeenth century into mass and gravitational force that explained the weight of massive objects—weight was identified with gravitational force. The third period followed the scientific revolution of the twentieth century. Classical Mechanics adopted the equivalence principle and included the accelerated observers. This implied redefinition of weight by the operational definition as the result of weighing. Thus, weight was distinguished from the gravitational force. All three periods reflect the change of physics methodology. In education, physics textbooks are currently divided between the contradictory accounts of the second and third periods of weight history. The weight concept is often confused by students who show numerous related misconceptions. Facing this complexity, we argue for using weight teaching as a tool for promoting the modern perspective of knowledge construction in physics, its epistemology, that is, revealing the nature of science, the need for a reliable operational definition alongside a theoretical one, to the students. The teaching in accordance with the discipline-culture paradigm emphasizes the discursive nature of science, reveals the conceptual dialogue, and suggests its presentation in science/physics classes.

Vibration Measurement and Numerical Simulation of the Effect of Non-Structural Elements on Dynamic Properties of Large-Span Structures

Non-structural elements have been demonstrated to be essential for the dynamic performance of large-span structures. However, how to quantify their effect has not yet been fully understood. In this study, the contribution of non-structural elements to dynamic properties of large-span structures is systematically investigated via both field measurement and numerical simulation methods. Modal testing of an indoor stadium and an elevated highway bridge was conducted during different construction phases, and the corresponding modal characteristics were identified. Results show that the traditional capacity-based models are incapable of reflecting the actual dynamic characteristics of in-service structures since neglecting the effect of non-structural elements would result in remarkable discrepancies in modal properties. A general modeling framework incorporating the contribution of slab/deck pavement, infill walls (or crash barriers), and joints/connections for large-span structures is developed to quantitatively consider the effect of non-structural elements based on the principle of equivalence of stiffness and mass to the actual structure. The effectiveness of the method is validated by vibration measurement results.

An accelerated corrosion-fatigue testing method for marine high-strength steel based on equivalence principle of fatigue crack growth

The corrosion-fatigue test is widely used to assess marine equipment. However, due to the low-frequency and high-cycle loading of marine equipment in service, conventional test methods require long cycle times and high costs. This makes it challenging to meet the rapid evaluation demands associated with equipment development effectively. In this study, an accelerated corrosion test method was proposed for steel by adjusting the composition, temperature, pH and H2O2 concentration of environment. Fatigue crack growth tests were conducted under various corrosion environments and load frequencies. The matching relationships between corrosion fatigue acceleration multiplier, corrosion environment parameters and load parameters were established. Additionally, a corrosion fatigue acceleration test method was proposed based on the equivalent principle of fatigue crack growth. The results show that effective coupling between corrosion and fatigue can be achieved by gradually reducing the load frequency as the stress intensity factor amplitude increases throughout the crack growth process. It is consistent with the trend of fatigue crack growth rate in the seawater environment. The 4.85% fatigue life deviation and the 15.68 times corrosion fatigue acceleration can be achieved by our method. This work improves the accuracy and reliability of fatigue performance evaluation for offshore equipment.