Gravitational Energy and the Casimir Effect

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Lateral changes of lithospheric density structure and associated topography create spatial variations of Gravitational Potential Energy (GPE) that exert a primary control on the direction and magnitude of crustal stresses, the style of active faulting and, therefore, the location, spatial density and magnitude of crustal earthquakes. Zones of positive/negative GPE with respect to a stable region, should be characterized by an extensional/compressional stress regime, driving crustal deformation toward an ideal situation of spatially homogeneous GPE with no lateral gradients. Along active continental margins, these relationships can be altered by forces associated to subduction, namely the far-field tectonic forces due to plate convergence, elevated shear stresses along the interplate megathrust and basal drags driven by mantle wedge flow. Testing the role of GPE on crustal stresses and seismicity requires an adequate representation of the 3D density structure and a large dataset of stress field indicators and focal mechanism to allow a significant statistical comparison between model predictions and observations, both of which are commonly scarce.In this contribution we will show results of a study performing this test along the Central and Southern Andean margin (5º-45ºS) that use a refined geophysically-constrained 3D density model, complemented by an analysis of Geoid anomalies, and a recently compiled dataset of several hundred stress tensors derived from Pliocene-to-Recent fault slip data and shallow earthquake focal mechanisms. These results show a strong first-order correlation between GPE anomalies and the large-scale stress field with positive/negative GPE correlating with normal/reverse faulting and near neutral GPE associated to strike-slip faulting. However, local misorientation of existing crustal faults with respect to this field causes stress rotations. First- and second-order partial derivatives of GPE are associated to the 2D stress tensor and compares well with the maximum horizontal stresses SHmax derived from the available data, confirming the main role of GPE on driving crustal deformation. This is further analyzed verifying a correlation between the spatial density of crustal seismic events and the magnitude of GPE gradients, which shed light about the level of stresses at crustal faults and the mechanism of their seismic activation. These results have important implications for understanding the forces driving crustal deformation and the controls on crustal seismicity in active orogenic systems.

Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field [Formula: see text], which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy–momentum of the gravitational field. It solves the problem of the nonlocalization of gravitational energy–momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully–Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein–Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.

We review current observations of the homogeneous cosmological expansion which, because they measure only kinematic variables, cannot determine the dynamics driving the recent accelerated expansion. The minimal fit to the data, the flat ACDM model, consisting of cold dark matter and a cosmological constant, interprets 4? geometrically as a classical spacetime curvature constant of nature, avoiding any reference to quantum vacuum energy. (The observed Uehling and Casimir effects measure forces due to QED vacuum polarization, but not any quantum material vacuum energies.) An Extended Anthropic Principle, that Dark Energy and Dark Gravity be indistinguishable, selects out flat ACDM. Prospective cosmic shear and galaxy clustering observations of the growth of fluctuations are intended to test whether the 'dark energy' driving the recent cosmological acceleration is static or moderately dynamic. Even if dynamic, observational differences between an additional negative-pressure material component within general relativity (Dark Energy) and low-curvature modifications of general relativity (Dark Gravity) will be extremely small.

The motion and deformation of the lithosphere result from forces and stresses that are driven by lateral variations in gravitational potential energy (GPE). In turn, GPE variations derive from lateral differences in the thermal or lithological density distribution. The recent development of global lithospheric models allows us to take a step forward towards consistent estimates of Horizontal Gravitational Tractions (HGTs) that arise from lateral gradients in GPE. We find that lithospheric model LithoRef18 [Afonso et al. 2019] yields unrealistic GPE and HGT results. Our preferred HGT field uses lithosphere model WINTERC-G [Fullea et al. 2021] to incorporate horizontal GPE gradients with a laterally variable Lithosphere-Asthenosphere Boundary (LAB). The azimuth of HGTs is most strongly correlated with the azimuth of topographic gradients, while the HGT magnitudes correlates best with topography gradient magnitude for HGTs larger than 10MPa. The most significant HGT magnitudes, exceeding 100 MPa, occur along the edges of the Andes and Tibetan plateaus. Tractions in cratonic regions are generally low, except where surface, Moho, or LAB topology gradients are large. Our attempt to isolate the HGT of the overriding plate yields moderate oceanward HGTs in the forearc along all convergence zones, which may be interpreted as trench suction. We explore the sensitivity of the HGT to classical integration limits of the deepest Moho or 100km depth to find that HGT magnitudes are markedly different and that HGT directions are relatively insensitive to integration depth. Afonso, J.C., Salajegheh, F., Szwillus, W., Ebbing, J. Gaina, C. (2019), A global reference model of the lithosphere and upper mantle from joint inversion and analysis of multiple data sets, Geophys. J. Int., 217(3), 1602–1628.Fullea, J., Lebedev, S., Martinec, Z., Celli, N.L. (2021), WINTERC-G: mapping the upper mantle thermochemical heterogeneity from coupled geophysical–petrological inversion of seismic waveforms, heat flow, surface elevation and gravity satellite data, Geophys. J. Int., 226(1), 146–19.

Within an optimization framework, we model the mechanical and electrical components of a novel energy storage system. The system is based on the possibility of storing large amounts of energy in the form of gravitational potential energy if large masses are elevated to a higher altitude through any efficient method, specifically, through a dedicated railway system; later, this energy can be retrieved using regenerative braking in the dedicated railway system. In order to obtain a more general model, we have included in the system a renewable energy plant located nearby, and a conventional railway line that is able to exchange energy with the storage system; the operation of all these facilities together is beneficial for all the agents involved. Moreover, we have also included a connection to an electrical network, thus allowing for exchanges among all the elements in the system. In this setup, we try to determine the optimal operation in order to maximize the profit obtained by the owner of the systems.

In general relativity there is a long-standing problem of defining momentum and angular momentum in a general curved space-time. In this chapter, we describe an application of twistor theory which aims to provide a solution to this problem. As we shall see, this aim is not entirely achieved and the programme has both successes and failures. We recall that in general relativity, all the local matter content is described by the stress–energy tensor T ab . Gravitational energy, whether in gravitational waves or in the form of gravitational potential energy, is notoriously non-local and one cannot expect to characterise it by a local density. Instead, Penrose (1982) has suggested that one should seek a non-local invariant associated to any two-surface S and representing the total momentum–angular momentum flux through that surface. This non-local invariant will be constructed by twistorial techniques tailored to give the right answer for linearised general relativity where there is a clear right answer. We begin by reviewing the definition of momentum and angular momentum in special relativity and in linearised general relativity. A material system in special relativity is defined by its stress–energy tensor T ab which we may suppose for definiteness to have support within a world tube W in Minkowski space, M . (The case of say electromagnetic fields spread throughout M is a simple generalisation.)

A new formulation of the general problem of the large‐scale energetics for the global oceans is presented and analyzed. Using a variety of ocean surface observations, some of the terms in the energy balance equations, such as the time rates of change, the generation rates of available gravitational potential energy G(P) and kinetic energy G(K), and the conversion rate from available gravitational potential energy into kinetic energy C(P, K), are estimated for annual and seasonal mean conditions. An attempt is also made to measure the uncertainty of these terms in order to assess the reliability of the results. The interseasonal variability is analyzed showing that the winter hemisphere represents the most active region of the globe. Using the data and some reasonable assumptions, pictures of the energy cycle in the global oceans for yearly and seasonal conditions are constructed. The hemispheric and global dissipation rates of available gravitational potential energy D(P) and of kinetic energy D(K) are estimated as residuals, assuming that the contribution from the internal energy C(I, K) is only a minor factor. After analyzing the general consistency of the picture of the energy cycle for the oceans, the conclusion is reached that the G(P) and G(K) terms are about equally important terms needed to describe and understand the structure and dynamics of the global ocean circulation.

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere‐ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing thus play complementary roles in sustaining the large‐scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (−0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by nonlinearities in the equation of state.

A major source of lithospheric stresses is believed to be in variations of surface topography and lithospheric density. The traditional approach to stress estimation is based on direct calculations of the Gravitational Potential Energy (GPE), the depth integrated density moment of the lithosphere column. GPE is highly sensitive to density structure which, however, is often poorly constrained. Density structure of the lithosphere may be refined using methods of gravity modeling. However, the resulted density models suffer from non-uniqueness of the inverse problem. An alternative approach is to directly estimate lithospheric stresses (depth integrated) from satellite gravimetry data. Satellite gravity gradient measurements by the ESA GOCE mission ensures a wealth of data for mapping lithospheric stresses if a link between data and stresses or GPE can be established theoretically. Following (Camelbeeck et al., 2013), we adopt the method that constrains lithospheric stresses by direct utilization of the gravity gradient tensor. For comparison, we use more traditional methods as well: (2) the filtered geoid approach (e.g., Chase et al., 2002; Coblentz et al., 2015), and (3) the direct thin-sheet approximation based on depth integration of density moment (e.g., Medvedev, 2016). Whereas the last two approaches (2)-(3) calculate GPE and utilize a computationally expensive finite element mechanical modeling to calculate stresses, the approach (1) uses a much simpler numerical treatment but requires simplifying assumptions that yet to be tested. We applied all methods to the North Atlantic region where reliable additional constraints are available and tested results against the World Stress Map.

This paper describes an investigation into student reasoning about potential energy in the context of introductory electrostatics. Similar incorrect reasoning patterns emerged both in written questions administered after relevant instruction and in one-on-one interviews. These reasoning patterns are also prevalent in responses to questions posed about gravitational potential energy in the context of universal gravitation in introductory mechanics. This finding is relevant for interdisciplinary research, because many courses in multiple disciplines first introduce the concept of electric potential energy in analogy to gravitational potential energy. The results suggest that in introductory courses students do not gain an understanding of potential energy that is sufficiently robust to apply in more advanced physics courses or in disciplines other than physics, in which students must frequently reason with energy in the context of interactions between atoms and molecules.

We investigate the interaction between dark energy and dark matter in the framework of irreversible thermodynamics of open systems with matter creation/annihilation. We consider dark energy and dark matter as an interacting two-component (scalar field and ``ordinary'' dark matter) cosmological fluid in a homogeneous spatially flat and isotropic Friedmann-Robertson-Walker Universe. The thermodynamics of open systems as applied together with the gravitational field equations to the two-component cosmological fluid leads to a generalization of the elementary dark energy-dark matter interaction theory, in which the decay (creation) pressures are explicitly considered as parts of the cosmological fluid stress-energy tensor. Specific models describing coherently oscillating scalar waves, leading to a high particle production at the beginning of the oscillatory period, and models with a constant potential energy scalar field are considered. Furthermore, exact and numerical solutions of the gravitational field equations with dark energy-dark matter interactions are also obtained.

Blackhole and cosmology-sink as source

The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

We build a mechanism of gravitational symmetry breaking (GSB) of a global\nU(1) symmetry based on the relaxation of the equivalence principle due to the\nmass variation of pseudo Nambu-Goldstone dark matter (DM) particles. This GSB\nprocess is described by the modified cosmological convergence mechanism of the\nAbnormally Weighting Energy (AWE) Hypothesis previously introduced by the\nauthors. Several remarkable constraints from the Hubble diagram of far-away\nsupernovae are derived, notably on the explicit and gravitational symmetry\nbreaking energy scales of the model. We then briefly present some consequences\non neutrino masses when this mechanism is applied to the particular case of the\nbreaking of lepton number symmetry.\n