Gravitational Redshift Research Articles

Quantitative Analysis of Rapid Siltation and Erosion Caused Coastline Evolution in the Coastal Mudflat Areas of Jiangsu

Muddy coast due to natural and human-induced factors can be variable over a wide range of different spatiotemporal scales. Our limited capability to understand and especially predict this variability can lead to misinterpretation of muddy coastal change information, which hampers informed decision-making and subsequent design and implementation of engineering interventions. Therefore, the research on the evolution of the historical coastline is particularly important. In this study, annual mean coastlines and causes for the variability and possible evolutions are analyzed in a manner that avoids these effects by averaging the instantaneous coastline positions registered during the same year. A set of coastlines is obtained from Landsat MSS/TM/OLI series of remote sensing images taken between 1985 and 2020 in the Google Earth Engine at Jiangsu muddy coast of China Yellow Sea. The coastline is extracted based on the water body index and the Otsu method, and is classified by fractal dimension, annual rate of change, area calculation, center of gravity shift, and artificial index to calculate the temporal and spatial changes in the coastline. The results showed that most of the coastline advanced seaward due to rapid siltation and coastal development in the past 35 years with only a small portion receding landward. The entire coast experienced segmental changes and different evolutionary characteristics and the coastline shifted from rapid erosion to siltation. The silted banks were mainly distributed in the middle section of the coastline in the radial sandbank. The annual change rate in the coast section was 82.21 m/a and the average annual area increased by 18.07 km2. The artificial coastline increased substantially, while the natural coastline gradually decreased due to rapid erosion. From 1985 to 2020, the proportion of artificial coastline in Jiangsu rose from 14% to 77%. The coastline became more curved and the center of gravity of the coastline moved 5.13 km to the northwest by 61°. Before 2000, the driving force affecting the coastline variability was mainly rapid siltation, while the impact of rapid erosion and human activities gradually increased after 2000 with the natural coastline being continuously cut and straightened. Overall, Jiangsu’s muddy coast was the site with the highest anthropogenic pressure and highest vulnerability. However, it is difficult to generalize the results under other conditions, especially on decadal time scales. Scientific and engineering improvements still require more quantitative insight into the physical mechanisms behind the natural and forced shore behavior responsible for the variability to better explain the change process of the coastline and provide a basis for coastal management and sustainable development.

Combining gravitational lensing and gravitational redshift to measure the anisotropic stress with future galaxy surveys

Galaxy surveys provide one of the best ways to constrain the theory of gravity at cosmological scales. They can be used to constrain the two gravitational potentials encoding time, $\Psi$, and spatial, $\Phi$, distortions, which are exactly equal at late time within general relativity. Hence, any small variation leading to a nonzero anisotropic stress, i.e. a difference between these potentials, would be an indication for modified gravity. Current analyses usually consider gravitational lensing and redshift-space distortions to constrain the anisotropic stress, but these rely on certain assumptions like the validity of the weak equivalence principle, and a specific time evolution of the functions encoding deviations from general relativity. In this work, we propose a reparametrization of the gravitational lensing observable, together with the use of the relativistic dipole of the correlation function of galaxies to directly measure the anisotropic stress with a minimum amount of assumptions. We consider the future Legacy Survey of Space and Time of the Vera C. Rubin Observatory and the future Square Kilometer Array, and show that combining gravitational lensing and gravitational redshift with the proposed approach we will achieve model-independent constraints on the anisotropic stress at the level of $\sim 20\,\%$.

Volatile organic compounds emissions embodied in fixed capital formation in China: Gravity movement and decoupling analysis

Volatile organic compounds (VOCs) emissions have increased rapidly in China, but little is known about the characteristics of VOCs emissions embodied in China's fixed capital formation (FCF). We investigate the VOCs emissions embodied in various FCF categories in the economic sectors of 30 Chinese provincial-level regions using the multi-regional input-output (MRIO) method. The gravity theory is combined with the Shapley decomposition method to uncover the gravity movement of embodied VOCs emissions in FCF and regional contributions behind. Besides, the Tapio decoupling index is combined with the logarithmic mean Divisia index (LMDI) method to identify the key drivers of decoupling between embodied VOCs emissions and embodied added value driven by FCF. The results indicate that China's embodied VOCs emissions in FCF increased by 10.9% during 2012–2015 and decreased by 4.2% during 2015–2017. Over 2012–2017, the gravity center of embodied VOCs emissions in gross FCF shifted to the southwest region, with the northwestern and northeastern regions acting as the main engines for the gravity shift. There is a weak decoupling between embodied VOCs emissions and embodied added value in gross FCF. Investment scale and embodied investment efficiency largely inhibit the decoupling, while embodied energy intensity largely promotes the decoupling. Accordingly, we suggest that the northeastern region and northwestern region should be the main targets for VOCs emissions reduction. As such, investment scale, embodied investment efficiency, and embodied emission intensity in FCF should be optimized.

Optical appearance of the Schwarzschild black hole in the string cloud context* *Supported by the National Natural Science Foundation of China (11903025) and the Natural Science Foundation of Sichuan Province, China (2022NSFSC1833)

The image of a black hole (BH) consists of direct and secondary images that depend on the observer position. We investigate the optical appearance of a Schwarzschild BH in the context of a string cloud to reveal how the BH's observable characteristics are influenced by the inclination angle, string cloud parameter, and impact parameter. Following Luminet's work [Astron. Astrophys. 75, 228 (1979)], we adopt a semi-analytic method to calculate the total bending angle of the light ray and derive the direct and secondary images of the Schwarzschild string cloud BH. Our results show that an increase in the inclination angle leads to a more pronounced separation of the images. We consider the gravitational redshift and present the redshift distribution of the direct image while illustrating the flux distribution. We observe that the direct image exhibits blueshift and redshift simultaneously, and the asymmetry of the flux distribution increases with the inclination angle. Finally, we obtain the Schwarzschild string cloud BH image via a numerical simulation, which provides an approximate illustration of the EHT resolution.

The Spin of a Newborn Black Hole: Swift J1728.9-3613

The origin and distribution of stellar-mass black hole spins are a rare window into the progenitor stars and supernova events that create them. Swift J1728.9-3613 is an X-ray binary, likely associated with the supernova remnant (SNR) G351.9-0.9. An NuSTAR X-ray spectrum of this source during its 2019 outburst reveals reflection from an accretion disk extending to the innermost stable circular orbit. Modeling of the relativistic Doppler shifts and gravitational redshifts imprinted on the spectrum measures a dimensionless spin parameter of a = 0.86 ± 0.02 (1σ confidence), a small inclination angle of the inner accretion disk θ < 10°, and a subsolar iron abundance in the disk A Fe < 0.84. This high spin value rules out a neutron star primary at the 5σ level of confidence. If the black hole is located in a still visible SNR, it must be young. Therefore, we place a lower limit on the natal black hole spin of a > 0.82, concluding that the black hole must have formed with a high spin. This demonstrates that black hole formation channels that leave an SNR, and those that do not (e.g., Cyg X-1), can both lead to high natal spin with no requirement for subsequent accretion within the binary system. Emerging disparities between the population of high-spin black holes in X-ray binaries and the low-spin black holes that merge in gravitational wave events may therefore be explained in terms of different stellar conditions prior to collapse, rather than different environmental factors after formation.

What can a detected photon with a given gravitational redshift tell us about the maximum density of a compact star?

Far away observers can in principle bound from below the dimensionless maximum-density parameter $\Lambda\equiv4\pi R^2\rho_{\text{max}}$ of a compact star by measuring the gravitational redshift factor $z\equiv\nu_{\text{e}}/\nu_{\infty}-1$ of photons that were emitted from the {\it surface} of the star: $\Lambda\geq{3\over2}[1-(1+z)^{-2}]$ [here $R$ is the radius of the star and $\{\nu_{\text{e}},\nu_{\infty}\}$ are respectively the frequency of the emitted light as measured at the location of the emission and by asymptotic observers]. However, if photons that were created somewhere {\it inside} the star can make their way out and reach the asymptotic observers, then the measured redshift parameter $z$ may not determine uniquely the surface properties of the star, thus making the above bound unreliable. In the present compact paper we prove that in these cases, in which the creation depth of a detected photon is not known to the far away observers, the empirically measured redshift parameter can still be used to set a (weaker) lower bound on the dimensionless density parameter of the observed star: $\Lambda\geq{3\over2}[1-(1+z)^{-2/3}]$.

Null test for cosmic curvature using Gaussian process* *Supported by the National SKA Program of China (2022SKA0110200, 2022SKA0110203) and the National Natural Science Foundation of China (11975072, 11835009, 11875102)

The cosmic curvature , which determines the spatial geometry of the universe, is an important parameter in modern cosmology. Any deviation from would have a profound impact on the primordial inflation paradigm and fundamental physics. In this work, we adopt a cosmological model-independent method to test whether deviates from zero. We use the Gaussian process to reconstruct the reduced Hubble parameter and the derivative of the distance from observational data and then determine with a null test relation. The cosmic chronometer (CC) Hubble data, baryon acoustic oscillation (BAO) Hubble data, and supernovae Pantheon sample are considered. Our result is consistent with a spatially flat universe within the domain of reconstruction , at the confidence level. In the redshift interval , the result favors a flat universe, while at , it tends to favor a closed universe. In this sense, there is still a possibility for a closed universe. We also carry out the null test of the cosmic curvature at using the simulated gravitational wave standard sirens, CC+BAO, and redshift drift Hubble data. The result indicates that in the future, with the synergy of multiple high-quality observations, we can tightly constrain the spatial geometry or exclude the flat universe.

Empirical neutron star mass formula based on experimental observables

We derive the empirical formulae expressing the mass and gravitational redshift of a neutron star, whose central density is less than threefold the nuclear saturation density, as a function of the neutron-skin thickness or the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $, especially focusing on the 8 Skyrme-type effective interactions. The neutron star mass and its gravitational redshift can be estimated within $ \approx 10 \, \% $ errors with our formulae, while the neutron star radius is also expected within a few $\%$ errors by combining the derived formulae. Owing to the resultant empirical formulae, we find that the neutron star mass and radius are more sensitive to the neutron-skin thickness of $ {}^{208} \mathrm{Pb} $ than the dipole polarizability of $ {}^{208} \mathrm{Pb} $ or $ {}^{132} \mathrm{Sn} $.

The appearance of a merging binary black hole very close to a spinning supermassive black hole

ABSTRACTThe mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within 10 gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of zcos = (10−2–10−1) and composed of BHs of $(10\!-\!20)\, \mathrm{M}_\odot$ could masquerade as a BBH at a redshift of zcos ∼ 1 and containing BHs as large as $(44\!-\!110)\, \mathrm{M}_\odot$. In the case of extreme demagnification, we also find that the same BBH could appear to be at zcos &amp;gt; 10 and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.

Probing a polymerized black hole with the frequency shifts of photons

As is well-known, black hole plays an important role in probing the quantum effects of gravity in the strong-field regime. In this paper, we focus on a polymerized black hole and investigate the quantum effects on the redshift, blueshift and gravitational redshift of photons emitted by massive particles revolving around this black hole. With a general relativistic formalism, we obtain two elegant and concise expressions for the mass of the black hole and the quantum parameter in terms of few direct observables, and find that all the frequency shifts of photons decrease with the quantum parameter. By expanding the total frequency shift for large orbit of the emitter, low peculiar redshift, and small azimuthal angle, we find that the leading contributions to the frequency shift are originated from the kinematic shift and peculiar shift, and the quantum effects make a negligible contribution. In addition, we study the effects of the plasma on the redshift/blueshift for the first time, and conclude that the presence of plasma results in the decrease of the redshift/blueshift.

Addressing Systematics in the Traceback Age of the β Pictoris Moving Group

We characterize the impact of several sources of systematic errors on the computation of the traceback age of the β Pictoris moving group (βPMG). We find that uncorrected gravitational redshift and convective blueshift bias absolute radial velocity measurements by ∼0.6 km s−1, which leads to erroneously younger traceback ages by ∼2 Myr. Random errors on parallax, proper motion, and radial velocity measurements lead to an additional bias of ∼0.6 Myr on traceback ages. Contamination of astrometric and kinematic data by kinematic outliers and unresolved multiple systems in the full input sample of 76 members and candidates of βPMG also erroneously lowers traceback ages by ∼3 Myr. We apply our new numerical traceback analysis tool to a core sample of 25 carefully vetted members of βPMG using Gaia Data Release 3 data products and other kinematic surveys. Our method yields a corrected age of 20.4 ± 2.5 Myr, bridging the gap between kinematic ages (11–19 Myr) and other age-dating methods, such as isochrones and lithium depletion boundary (20–26 Myr). We explore several association size metrics that can track the spatial extent of βPMG over time, and we determine that minimizing the variance along the heliocentric curvilinear coordinate (i.e., toward the Galactic Center) offers the least random and systematic errors, due to the wider UVW space velocity dispersion of members of βPMG along the U-axis, which tends to maximize the spatial growth of the association along the -axis over time.

Tolman VI Fluid Sphere in f(R,T) Gravity

We analyze the behavior of relativistic spherical objects within the context of modified f(R,T) gravity considering Tolman VI spacetime, where the gravitational Lagrangian is a function of the Ricci scalar (R) and trace of energy momentum tensor (T), i.e, f(R,T) = R + 2βT, for some arbitrary constant β. For developing our model, we have chosen £m = −p, where £m represents the matter Lagrangian. For this investigation, we have chosen three compact stars, namely PSR J1614-2230 (Mass = (1.97 ± 0.4)M⊙; Radius = 9.69+0.02−0.02 km), Vela X-1 (Mass = (1.77 ± 0.08)M⊙; Radius = 9.560+0.08−0.08 km) and 4U 1538-52 (Mass = (9.69)M⊙; Radius = 1.97 km). In this theory, the equation of pressure isotropy is identical to the standard Einstein’s theory. So, all known metric potential solving Einstein’s equations are also valid here. In this paper, we have investigated the effort of a coupling parameter (β) on the local matter distribution. The sound of speed and adiabatic index are higher with grater values of β, while on the contrary, the mass function and gravitational redshift are lower with higher values of β. For supporting the theoretical results, graphical representations are also employed to analyze the physical viability of the compact stars.

High-accuracy open-loop velocity measurement and gravitational redshift verification design analysis based on the Chang&amp;rsquo;E-5 probe

嫦娥五号（CE-5）任务具有天地联合的优势测控资源，为地基无线电测量新方法验证、工程应用与科学研究提供了优越条件。本文重点开展CE-5探测器开环测速精细提取及应用。首先，提出了基于信号重构互相关的开环测速多普勒频率提取算法，建立了从信号输入、信号处理到观测量输出的完整实现步骤；然后，基于中国深空网开展了CE-5轨道器开环测速试验，经信号处理分析结果表明：CE-5轨道器开环测速精度达到2~3mHz水平，优于深空站基带测速精度3~4倍；其次，通过CE-5轨道器精密定轨，有效验证开环测速观测量应用效果，结果表明：开环测速的定轨残差为0.12mm/s，基带测速的定轨残差为0.46mm/s；最后，提出了基于深空探测器的多体问题引力红移验证方法，从理论上分析了高精度开环测速在引力红移验证方面潜在应用可行性，初步设计了引力红移验证设想方案，评估了以现有CE-5轨道器开环测速结果为依据，建议可考虑开展引力红移验证专项试验，有望实现10-4~10-5水平的引力红移验证精度。

Gravitational redshift test using Rb clocks of eccentric GPS satellites

This paper reports a test of gravitational redshift, which is a consequence of the Einstein equivalence principle, using the Rb clocks of GPS Block IIF satellites. The fractional deviation in the gravitational redshift was measured using 6,640 days of data from three Rb clocks onboard GPS Block IIF satellites. The systematic effects related to orbital uncertainty, temperature, and magnetic field were modeled conservatively. The fractional deviation in the gravitational redshift from the general relativity prediction was measured with (0.23±1.34)×10−3 at one sigma.

Radial pulsations, moment of inertia and tidal deformability of dark energy stars

We construct dark energy stars with Chaplygin-type equation of state (EoS) in the presence of anisotropic pressure within the framework of Einstein gravity. From the classification established by Iyer et al. (Class Quantum Grav 2:219, 1985), we discuss the possible existence of isotropic dark energy stars as compact objects. However, there is the possibility of constructing ultra-compact stars for sufficiently large anisotropies. We investigate the stellar stability against radial oscillations, and we also determine the moment of inertia and tidal deformability of these stars. We find that the usual static criterion for radial stability dM/drho _c >0 still holds for dark energy stars since the squared frequency of the fundamental pulsation mode vanishes at the critical central density corresponding to the maximum-mass configuration. The dependence of the tidal Love number on the anisotropy parameter alpha is also examined. We show that the surface gravitational redshift, moment of inertia and dimensionless tidal deformability undergo significant changes due to anisotropic pressure, primarily in the high-mass region. Furthermore, in light of the detection of gravitational waves GW190814, we explore the possibility of describing the secondary component of such event as a stable dark energy star in the presence of anisotropy.

Effect of nucleon coupling constants on the mass radius ratio of proto neutron star PSR J0737-3039A

The effect of the nucleon coupling constants on the mass radius ratio (further, the surface gravitational redshift) of proto neutron star (PNS) PSR J0737-3039A is examined with relativistic mean field theory in consideration of a baryon octet. Here, five sets of nucleon coupling constants DD-MEI, GL85, GL97, GM1 and NL2 are used. The PNS’s temperature is assumed to be [Formula: see text] MeV and the mass the PNS PSR J0737-3039A is chosen as [Formula: see text]. The radius and the mass radius ratio of the PNS PSR J0737-3039A calculated by the five groups of nucleon coupling constants above are [Formula: see text] km and [Formula: see text]/km, respectively. The surface gravitational redshift [Formula: see text] of the PNS PSR J0737-3039A calculated from the above five groups of nucleon coupling constants is [Formula: see text].

Spatiotemporal coupling of multidimensional urbanization and resource–environment performance in the Yangtze River Delta urban agglomeration of China

Realizing the coordinated development of urbanization and resource–environment performance is a crucial way to ensure regional high-quality development.By clarifying the interaction between multidimensional urbanization (MUR) and resource–environment performance (REP), this study used multiple approaches—the coupling degree model, center of gravity shift analysis, scissors difference analysis, and the Tobit model—to discuss their coupling coordination degree, spatiotemporal evolution characteristics, and core driving factors in the Yangtze River Delta urban agglomeration (YRDUA) from 2008 to 2018. Results show that (1) the multidimensional urbanization was high in the east and low in the west, while the resource–environment performance showed a trend in which the high-level area is decreasing and the low-level area is moving to the east. (2) In terms of the temporal sequence evolution, the multidimensional urbanization lagging cities in the study area dominated, but the number of resource–environment performance lagging cities represented by Shanghai, gradually expanded. (3) The range of the center of gravity in the multidimensional urbanization and resource–environment performance coupling degree in terms of longitude and latitude was 119.675° E−119.708° E and 30.983° N-31.008° N, respectively. Generally, the center of gravity shifts to the northwest, but the total migration distance was only 5.489 km. (4) The obstacles restricting improvement of the multidimensional urbanization and resource–environment performance coupling coordination degree mainly come from the population factor, while technological, ecological, spatial, and economic factors all play positive roles. Among them, the technical factor has the greatest impact, where the coupling coordination degree increases by 0.5198% for every 1% increase.

Testing general relativity: New measurements of gravitational redshift in galaxy clusters

Context. The peculiar velocity distribution of cluster member galaxies provides a powerful tool to directly investigate the gravitational potentials within galaxy clusters and to test the gravity theory on megaparsec scales. Aims. We exploit spectroscopic galaxy and galaxy cluster samples extracted from the latest releases of the Sloan Digital Sky Survey (SDSS) to derive new constraints on the gravity theory. Methods. We considered a spectroscopic sample of 3058 galaxy clusters, with a maximum redshift of 0.5 and masses between 1014 − 1015 M⊙. We analysed the velocity distribution of the cluster member galaxies to make new measurements of the gravitational redshift effect inside galaxy clusters. We accurately estimated the cluster centres, computing them as the average of angular positions and redshifts of the closest galaxies to the brightest cluster galaxies. We find that this centre definition provides a better estimation of the centre of the cluster gravitational potential wells, relative to simply assuming the brightest cluster galaxies as the cluster centres, as done in past literature works. We compared our measurements with the theoretical predictions of three different gravity theories: general relativity (GR), the f(R) model, and the Dvali–Gabadadze–Porrati (DGP) model. A new statistical procedure was used to fit the measured gravitational redshift signal, and thus to discriminate among the considered gravity theories. Finally, we investigated the systematic uncertainties that possibly affect the analysis. Results. We clearly detect the gravitational redshift effect in the exploited cluster member catalogue. We recover an integrated gravitational redshift signal of −11.4 ± 3.3 km s−1, which is in agreement, within the errors, with past literature works. Conclusions. Overall, our results are consistent with both GR and DGP predictions, while they are in marginal disagreement with the predictions of the considered f(R) strong field model.

Modified Gravitation and Mach's Principle: An Alternative to the Dark Matter and Dark Energy Cosmological Paradigm

The general approach is that all particles with non-null rest mass are subject to the force of gravity through the inverse square law of gravitation, plus an additional term that varies with the comoving distance (UYF-Field). The model is an ΛFRW-Cosmology starting from the modification of the gravity by explicitly incorporating Mach's Principle through an additional term large-scale in the gravitation; the source of this field is the ordinary baryonic matter. It`s deduced from the Matter-radiation decoupling in the early universe. This additional term of gravity UYF result null in the inner solar system, weakly attractive in interstellar ranges, very attractive in ranges comparable to the clusters of galaxies, and repulsive in cosmic scales, in agreement with astronomical and laboratory observables. This term explains dark energy, removes the incompatibility between the density of matter and the flatness of the universe in ᴧFRW-Cosmology; allows the theoretical deduction of the Hubble-Lemaitre Law, between other relevant consequences. Additionally to discuss other relevant astrophysics consequences: Birkhoff Theorem, Virial Theorem, the missing mass of Zwicky, gravitational lenssings, the BAO and the gravitational redshift in AGN, provides an additional contribution for the gravitational redshift that increase the until an factor of ~4, which has resolved the Arp controversy. Also we show the crude explanations of Pioneer anomaly, we obtain as the additional contribution of the acceleration of gravity due to UYF-Field. It is concluded that the dark energy and the missing dark mass can be approached with the usual physics as the large-scale modification of the Gravitation.

Космология между физикой и философией

It is shown that the canonical cosmological model of the Universe – Big Bang Theory (BBT) contains unacceptably many unsolvable contradictions either to facts, or logic, or, finally, to physics. They can be categorized into several groups: 1) unacceptable, 2) unsubstantiated, and 3) multivalued. To the unac­ceptable fragments of the concept of BBT it is reasonable to include ideas about: a) “singularity”; b) “cosmological inflation”; c) “infinite death of Nature”. Un­reasonable include: a) hypothesis about materiality of space-time, b) recognition of the possibility of their birth and death. Among the interpretations admitting other ones with high probability are: a) the principle of equivalence of the iner­tial and gravitational masses, b) the gravitational redshift, c) the effect of deflec­tion of light near large masses. Among the interpretations, which do not cause doubts, it is possible to note an explanation of the black hole nature, following from Newton’s classical theory of gravitation. The source of insoluble contradic­tions of the BBT was Einstein’s General Theory of Relativity (GTR), which was created on the basis of strictly deterministic classical mechanics. The underde­velopment of quantum mechanics at the beginning of the twentieth century mis­led the author of the GTR about the equivalence of inertial and gravitational masses. A consequence of this delusion was the erroneous recognition of space-time as material substances. It, in turn, led to a lot of unexplained events in the past of the Universe, and fantastic predictions about its future. But the most striking thing that distinguishes GTR is its violation of the fundamental law of conservation of energy, which cosmological theorists turn a blind eye to. This allows us to consider it a legacy of classical physics of the nineteenth century, unsatisfactory from the perspective of probabilistic physics of the twenty-first century.