Gravitational Redshift Research Articles

Non-linear media in weakly curved spacetime: optical solitons and probe pulses for gravimetry

That light propagating in a gravitational field gets frequency-shifted is one of the basic consequences of any metric theory of gravity rooted in the equivalence principle. At the same time, also a time dependent material’s refractive index can frequency-shift light propagating in it. The mathematical analogy between the two effects is such that the latter has been used to study the optical analogue of a black-hole spacetime. Here, we combine these two effects by showing that light propagation in non-linear media in the presence of a moving refractive index perturbation can lead to a gravity-dependent blueshift. We find that the predicted blueshift surpasses the gravitational redshift even if the medium is considered to be perfectly stiff. In realistic scenarios, by far the strongest frequency shift arises due to the deformation of the dielectric medium and the corresponding photoelastic change of refractive index. This has the potential to facilitate optical sensing of small gravity gradients.

Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

Dynamics and advanced active disturbance rejection control of tethered UAV

Due to its vast potential for applications in agricultural harvesting, the tethered unmanned aerial vehicle (UAV) has garnered considerable interest. However, the anti-disturbance control of this system remains fraught with obstacles, stemming primarily from its inherent nonlinearity, unpredictable airflow disturbances, unmeasurable tether tension, and the changes in the center of gravity during operation. We propose a comprehensive dynamic model for the operational tethered unmanned aerial vehicle with considering the center of gravity shift. Because of obstructions caused by branches and leaves, the tethered UAV can't reach fruits inside the tree. Therefore, two deformation functions of the tethered quadcopter are considered. Additionally, in order to enhance the effectiveness of traditional Active Disturbance Rejection Control, we present an optimized controller combining a phase compensation algorithm with a nonlinear function. The proposed Controller is validated in a high-fidelity simulation environment, considering internal interference, wind field interference and reactive force from produces. Besides, the simulation is specifically developed for picking operation, The results underscore the better observation capabilities of the enhanced controller proposed in this study. Moreover, when deployed in a simulated picking environment, the improved controller exhibits remarkable resistance to the interference and significantly mitigates chattering issues.

Local versus Global Time in Early Relativity Theory.

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity.

Single-Photon Interference over 8.4km Urban Atmosphere: Toward Testing Quantum Effects in Curved Spacetime with Photons.

The emergence of quantum mechanics and general relativity has transformed our understanding of the natural world significantly. However, integrating these two theories presents immense challenges, and their interplay remains untested. Recent theoretical studies suggest that the single-photon interference covering huge space can effectively probe the interface between quantum mechanics and general relativity. We developed an alternative design using unbalanced Michelson interferometers to address this and validated its feasibility over an 8.4km free-space channel. Using a high-brightness single-photon source based on quantum dots, we demonstrated single-photon interference along this long-distance baseline. We achieved a phase measurement precision of 16.2mrad, which satisfied the measurement requirements for a gravitational redshift at the geosynchronous orbit by 5 times the standard deviation. Our results confirm the feasibility of the single-photon version of the Colella-Overhauser-Werner experiment for testing the quantum effects in curved spacetime.

Redshift and Photon Energy Attenuation Constant in Vacuum

There obtained an estimate of the minimum value of the photon energy attenuation constant in vacuum α: α = 8 · 10–19 m–1 based on quantum concepts of the structure of vacuum and data on the red shift of the emitter spectra of distant galaxies. Presumably, the cosmic microwave radiation is partly the thermal vacuum radiation heated by the photon fluxes from the infinite universe. Despite the universe infinity, the sky is dark precisely due to the photon’s energy absorption from distant and ultra-distant galaxies in vacuum, and not only the photon absorption during various interactions with the gas or dust components of intergalactic clusters. Thus, the emission spectrum of these ultra-distant objects is transformed into the microwave range, which complements the intensity of thermal radiation in this range. The inconsistency of alternative explanations for the red shift is shown: the Doppler effect in the cosmological model of the expanding universe and the Big Bang, and the gravitational shift.

Preliminary sensitivity study for a gravitational redshift measurement with China’s Lunar exploration project

General relativity (GR) is a highly successful theory that describes gravity as a geometric phenomenon. The gravitational redshift, a classic test of GR, can potentially be violated in alternative gravity theories, and experimental tests on this effect are crucial for our understanding of gravity. In this paper, considering the space-ground clock comparisons with free-space links, we discuss a high-precision Doppler cancellation-based measurement model for testing gravitational redshift. This model can effectively reduce various sources of error and noise, reducing the influences of the first-order Doppler effect, atmospheric delay, Shapiro delay, etc. China’s Lunar Exploration Project (CLEP) is proposed to equip the deep-space H maser with a daily stability of 2×10−15 , which provides an approach for testing gravitational redshift. Based on the simulation, we analyze the space-ground clock comparison experiments of the CLEP experiment, and simulation analysis demonstrates that under ideal condition of high-precision measurement of the onboard H-maser frequency offset and drift, the CLEP experiment may reach the uncertainty of 3.7×10−6 after a measurement session of 60 days. Our results demonstrate that if the issue of frequency offset and drift is solved, CLEP missions have a potential of testing the gravitational redshift with high accuracy.

Long-distance chronometric leveling with a portable optical clock

We have measured the geopotential difference between two locations separated by 457 km by comparison of two optical lattice clocks via an interferometric fiber link, utilizing the gravitational redshift of the clock transition frequency. The 87Sr clocks have been compared side-by-side before and after one of the clocks was moved to the remote location. The chronometrically measured geopotential difference of 3918.1(2.6)m2s−2 agrees with an independent geodetic determination of 3915.88(0.30)m2s−2. The uncertainty of the chronometric geopotential difference is equivalent to an uncertainty of 27cm in height. Published by the American Physical Society 2024

About Newton’s Law of Gravitation and the Energy Momentum Relations

Newtonian dynamics was based on the assumption of instantaneous propagation of interaction. Roamer’s studies showed that the velocity of interaction cannot exceed the velocity of light in free space. (c=3x108 mps). Lorentz’ electron theory and electrodynamics take this fact into account. It is possible to rectify the defects of Newtonian theory by deriving Maxwell-Lorentz equations and the Lorentz Force equation for the gravitational field and hence the modified Newtonian dynamics can explain (i) The Perihelion Shift of the orbit of the Planet Mercury (ii) Deflection of light by the Sun (iii) The Gravitational Redshift [1]. It is shown that the use of centre of mass coordinate system also implies a non-elliptic orbit in general, so that the inverse square law of Newton/Coulomb is always valid. Next, the energy and momentum of a dynamical system are shown to satisfy Finally, the Schrodinger’s wave function is interpreted as a quantum mechanical energy density [2].

River valley urban network and morphology: A study on the urban morphology evolution of Lanzhou.

The present study investigates the dynamic evolution characteristics of urban spatial morphology by analyzing real road network data from 2000, 2010, and 2020, along with nighttime lighting data employing spatial analysis methods and spatial syntax models. Accordingly, two separate dimensions of urban morphology: internal and external, are covered. First, the integration and synergy of interior morphology features are analyzed using spatial syntactic modeling. Subsequently, the spatial compactness, fractal dimension, and level of center of gravity shift of the city are assessed by combining the nighttime lighting data with the earlier dataset. This analysis facilitated the deep exploration of the spatiotemporal evolution of the city's external morphology. Building upon this foundation, the interaction between the "internal and external" domains was analyzed further. The main findings of the study reveal a synchronous pattern of urban expansion throughout the evolution of urban spatial morphology. Furthermore, the urban form was observed to undergo a progressive transformation, transitioning from a "single core" morphology to a "primary and secondary double core" morphology. Over time, this development progressed and evolved into a "belt-like multi-core" structure. Additionally, the coupling characteristics further validate the relationship between the structure of the road network and the urban morphology in river valley-type cities. In particular, accessibility of dense and horizontally distributed transportation network was found to significantly influence the spatial development of these cities. As observed, the findings provides valuable insights into understanding the characteristics of internal and external associations regarding urban spatial patterns.

Kinematic Age of the β-Pictoris Moving Group

Accurate age estimation of nearby young moving groups (NYMGs) is important as they serve as crucial testbeds in various fields of astrophysics, including the formation and evolution of stars and planets, as well as loose stellar associations. The β-Pictoris moving group (BPMG), being one of the closest and youngest NYMGs, has been extensively investigated, and its estimated ages have a wide range from ∼10–25 Myr, depending on the age estimation methods and data used. Unlike other age dating methods, kinematic traceback analysis offers a model-independent age assessment hence the merit in comparing many seemingly discordant age estimates. In this study, we determine the kinematic ages of the BPMG using three methods: probabilistic volume calculation, mean pairwise distance calculation, and covariance matrix analysis. These methods yield consistent results, with estimated ages in the range of 14–20 Myr. Implementing corrections to radial velocities due to gravitational redshift and convectional blueshift increases the ages by ∼2–4 Myr. Conversely, considering data uncertainties decreases the estimated ages by 1–2 Myr. Taken together, our analysis determined the kinematic age of the BPMG to be 16.3−2.1+3.4 Myr. This age is significantly younger than the commonly accepted age of the BPMG (∼24 Myr) determined primarily from the lithium depletion boundary analysis. This younger kinematic age may point to the discrepancy between the luminosity evolution and lithium depletion models or the presence of unaccounted systematic error in the method. This result underscores the necessity for systematic reevaluations of age-dating methods for nearby, young moving groups.

Gravitational redshift explained as a Doppler Effect in uniformly accelerated frames

Einstein predicted a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional with the distance from the gravitational source. In the following, we will present an approach to the experiment relying on the Einstein Equivalence Principle and on the recently derived expressions of the Doppler Effect for uniformly accelerated motion of the source and the receiver. We will conclude with a chapter on the numerical limits of applicability of the described method.

Observational tests of 4D double field theory

Although General Relativity (GR) is a very successful theory of gravity, it cannot explain every observational phenomenon. People have tried many kinds of modified gravity theory to explain these phenomena which GR cannot explain very well, such as string theory. In recent years Double Field Theory (DFT) has been an exciting research area in string theory. The most general, spherically symmetric, asymptotically flat, static vacuum solution to D=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=4$$\\end{document} double field theory has been derived by S.M. Ko, J.H. Park and M. Suh. In this article, we calculate the minor corrections to the three predictions in GR: optical deflation, planet precession and gravitational redshift. These three predictions should be able to tested by observations and find the discrepancies between GR and DFT in the future.

Investigating the Effects of Center of Gravity (CoG) Shift Due to a Simulated Exploration Extravehicular Mobility Unit (xEMU) Suit on Balance

Maintaining balance is critical to minimizing astronauts’ risk of falling and reducing injury or suit damage. Previous studies involving spacesuits have not examined the effects of the superior shift of the center of gravity (CoG) on astronauts’ ability to balance. Here, the purpose of our study was to investigate the effects of CoG shift due to a simulated Extravehicular Mobility Unit (xEMU) on balance. Seventeen participants’ standing balance was examined for three test configurations: unsuited, weighted with an Extravehicular Mobility Unit (xEMU) vest, and xEMU hard upper body torso (HUT). Using a Tekscan forceplate walkway, the CoG locations were determined. Balance assessments were performed to determine the limits of stability and standing balance performance during wide or tandem stances with eyes open/closed. The center of pressure (CoP) time series was examined in terms of displacement, velocity, and frequency measures. During the eyes-open wide stance, the xEMU vest significantly increased the mediolateral balance parameters, while the HUT significantly increased the total displacement (TOTEX), mean velocity (MVELO), and mean frequency (MFREQ) of the CoP. In the eyes-closed wide stance, the HUT significantly increased these parameters. In the eyes-closed tandem stance, the xEMU vest significantly decreased the parameters. The xEMU vest significantly reduced the TOTEX, MVELO, and MFREQ (improved standing balance), while the HUT decreased standing balance ability, seen with significant increases in said parameters. By quantifying CoG’s effect on balance, our results form the basis for future balance and posture studies of xEMU spacesuits.

Finite pulse-time effects in long-baseline quantum clock interferometry

Quantum-clock interferometry has been suggested as a quantum probe to test the universality of free fall and the universality of gravitational redshift. In typical experimental schemes, it seems advantageous to employ Doppler-free E1–M1 transitions which have so far been investigated in quantum gases at rest. Here, we consider the fully quantized atomic degrees of freedom and study the interplay of the quantum center-of-mass (COM)—that can become delocalized—together with the internal clock transitions. In particular, we derive a model for finite-time E1–M1 transitions with atomic intern–extern coupling and arbitrary position-dependent laser intensities. We further provide generalizations to the ideal expressions for perturbed recoilless clock pulses. Finally, we show, at the example of a Gaussian laser beam, that the proposed quantum-clock interferometers are stable against perturbations from varying optical fields for a sufficiently small quantum delocalization of the atomic COM.

Gravitational redshift constraints on the effective theory of interacting dark energy

Upcoming galaxy surveys provide the necessary sensitivity to measure gravitational redshift, a general relativistic effect that generates a dipole in galaxy clustering data when correlating two distinct populations of galaxies. Here, we study the constraining power of gravitational redshift within the framework of the effective theory of interacting dark energy. This formalism describes linear cosmological perturbations in scalar-tensor theories of gravity with a limited number of free functions, and allows each particle species to be coupled differently to the gravitational sector. In this work, we focus on Horndeski theories with a non-minimal coupling of dark matter to the scalar degree of freedom, yielding a breaking of the weak equivalence principle for this cosmic component, a scenario that is yet untested. We show that the dipole generated by gravitational redshift significantly breaks degeneracies and tightens the constraints on the parameters of the effective theory compared to the standard redshift-space distortion analysis solely based on the even multipoles in the galaxy correlation function, with an improvement of up to ∼ 50% for populations with a galaxy bias difference equal to 1. We make the Python package EF-TIGRE (Effective Field Theory of Interacting dark energy with Gravitational REdshift) developed for this work publicly available (https://github.com/Mik3M4n/EF-TIGRE).

Fluid-structure interaction dynamic analysis of large civil aircraft tank sloshing

To meet the requirements of passengers, the tank volume of large civil aircraft is gradually increasing, which brings certain risks. Under different 0 pertaining conditions during the flight, the liquid in the tank will cause structural failure and affect the aircraft’s safety. Therefore, based on the assumption of an ideal fluid, the smooth particle method (SPH) combined with the finite element method (FEM) is used to establish the coupling dynamic equation between the tank and the liquid. The effects of sloshing impact on the water tank under different filling rates were studied, and the influences of the water wave shape, the center of gravity shift, stress distribution, and deformation of the tank were obtained. The results show that the mass accumulation of water particles occurs in the acceleration stage, the relative center of gravity changes greatly in less water, and the accumulated liquid greatly influences the tank under the action of inertia. The more liquid in the tank is, the more the impact effect on the tank increases. The analysis results provide some reference for the analysis and design of tank anti-sway plates and flight attitude adjustment.

Bulk Properties of PSR J0030+0451 Inferred with the Compactness Measurement of NICER

In 2019, the Neutron star Interior Composition ExploreR (NICER) mission released its findings on the mass and radius of the isolated neutron star (INS) PSR J0030+0451, revealing a mass of approximately 1.4 solar masses (M ⊙) and a radius near 13 km. However, the recent reanalysis by the NICER collaboration suggests that the available data primarily yield a precise inference of the compactness for this source while the resulting mass and radius are strongly model-dependent and diverse (the 68.3% credible regions just overlap slightly for the ST+PDT and PDT-U models). By integrating this compactness data with the equation of state (EOS) refined by our latest investigations, we have deduced the mass and radius for PSR J0030+0451, delivering estimates of M=1.48−0.10+0.09M⊙ and R=12.38−0.70+0.51km for the compactness found in the ST+PDT model, alongside M=1.47−0.20+0.14M⊙ and R=12.37−0.69+0.50km for the compactness in the PDT-U model. These two groups of results are well consistent with each other and the direct X-ray data inference within the ST+PDT model seems to be favored. Additionally, we have calculated the tidal deformability, moment of inertia, and gravitational binding energy for this neutron star. Furthermore, employing these refined EOS models, we have updated mass–radius estimates for three INSs with established gravitational redshifts.

Space, Gravity-Time

Space and time, from Newton's point of view, were considered as two separate and absolute concepts, and gravity was also defined as a force that varies according to the mass of two objects and their distance from each other. However, Hermann Minkowski, using Einstein's theory of relativity, offered a geometric interpretation of special relativity, integrating time and the three dimensions of space into a unified four-dimensional model now known as Minkowski space. In the theory of general relativity, gravity is also defined as a geometric function and a consequence of the curvature of space-time, which itself arises from the uneven distribution of mass and energy. One of the key outcomes of the theory of general relativity is that the motion of celestial bodies orbiting around other bodies in curved paths is not driven by a force known as gravity. Instead, bodies are actually following the closest objects to them through curved space-time, a bending that gravity is a result of. This movement happens along the shortest path, known as a geodesic. In contrast to Newton's view, the theory of relativity has shown that the speed at which gravity acts is limited to the speed of light. Modern physics proposes that this transmission of gravity might be carried out by hypothetical particles called gravitons. Another prediction of this theory is the concept of a gravitational potential well, which explains why the frequency of light increases or decreases as it falls into or escapes from this well, due to the curvature of space-time caused by a massive object. Time dilation near a massive object is also a phenomenon that occurs due to the strong gravitational field of that object. In this regard, Einstein's theory of special relativity explains how the laws of physics are the same for all observers moving at the same velocity and how the speed of light is constant in a vacuum. One of the consequences of this theory is that mass and energy are considered equivalent and interchangeable according to the famous E=mc2 equation. However, in the theories of T-Consciousness Cosmology, space is conceptualized independently and as a principle, in the form of a mesh, and time is described as an entropic force that acts opposite to gravity to break down objects that cause space to contract. In other words, the entropic force of time is introduced as a force that arises from mass to release space from stress, not as a fourth dimension perpendicular to the dimensions of space. Furthermore, this perspective considers varying viscosities for the space surrounding celestial objects. It introduces gravity as a force that is equivalent to the viscosity of space, rather than as a consequence of curved geometry, as typically presented in relativity. Gravity functions in accordance with the structure of space mesh. Consequently, phenomena such as gravitational redshift or blueshift are interpreted as outcomes of the viscosity of space. This perspective states that as light enters black holes, the mass-energy equivalence principle is violated because of the energetic resonance of the wave during its gravitational blackshift; implying that black holes are matter production factories. Furthermore, the mass-energy equivalence principle and the law of conservation of matter and energy do not hold true in the Cosmic Black Hole, which is the beginning of the cosmos, or after the final stage of space Rebound.

Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

Mass-energy equivalence and the gravitational redshift: Does energy always have mass?