Journal articles: 'Foundations of gravity theories'

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Lasenby, A. N., and M. P. Hobson. "Scale-invariant gauge theories of gravity: Theoretical foundations." Journal of Mathematical Physics 57, no. 9 (September 2016): 092505. http://dx.doi.org/10.1063/1.4963143.

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Calcagni, Gianluca. "Multifractional theories: An updated review." Modern Physics Letters A 36, no. 14 (April 22, 2021): 2140006. http://dx.doi.org/10.1142/s021773232140006x.

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The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional paradigm to quantum gravity is discussed. We also clarify the issue of unitarity in theories with integer-order derivatives.

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Golovnev, Alexey, and María-José Guzmán. "Foundational issues in f(T) gravity theory." International Journal of Geometric Methods in Modern Physics 18, supp01 (April 8, 2021): 2140007. http://dx.doi.org/10.1142/s0219887821400077.

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We give a short review on the status of research on the theoretical foundations of [Formula: see text] gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future directions to follow.

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Satheeshkumar, V. H., and P. K. Suresh. "Gravity and Large Extra Dimensions." Advances in Astronomy 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/189379.

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The idea that quantum gravity can be realized at the TeV scale is extremely attractive to theorists and experimentalists alike. This proposal leads to extra spacial dimensions large compared to the Planck scale. Here, we give a very systematic view of the foundations of the theories with large extra dimensions and their physical consequences.

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CAPOZZIELLO, S., M. DE LAURENTIS, L. FATIBENE, and M. FRANCAVIGLIA. "THE PHYSICAL FOUNDATIONS FOR THE GEOMETRIC STRUCTURE OF RELATIVISTIC THEORIES OF GRAVITATION: FROM GENERAL RELATIVITY TO EXTENDED THEORIES OF GRAVITY THROUGH EHLERS–PIRANI–SCHILD APPROACH." International Journal of Geometric Methods in Modern Physics 09, no. 08 (October 29, 2012): 1250072. http://dx.doi.org/10.1142/s0219887812500727.

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We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers–Pirani–Schild formalism. This approach provides a natural interpretation of the observables showing how relate them to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f(R)-gravity.

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NI, WEI-TOU, HSIEN-HAO MEI, and SHAN-JYUN WU. "FOUNDATIONS OF CLASSICAL ELECTRODYNAMICS, EQUIVALENCE PRINCIPLE AND COSMIC INTERACTIONS: A SHORT EXPOSITION AND AN UPDATE." Modern Physics Letters A 28, no. 03 (January 23, 2013): 1340013. http://dx.doi.org/10.1142/s0217732313400130.

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We look at the foundations of electromagnetism in this 1st LeCosPA Symposium. For doing this, after some review (constraints on photon mass etc.), we use two approaches. The first one is to formulate a Parametrized Post-Maxwellian (PPM) framework to include QED corrections and a pseudoscalar photon interaction. PPM framework includes lowest corrections to unified electromagnetism-gravity theories based on connection approach. It may also overlap with corrections implemented from generalized uncertainty principle (GUP) when electromagnetism-gravity coupling is considered. We discuss various vacuum birefringence experiments — ongoing and proposed — to measure these parameters. The second approach — the χ-g framework is to look at electromagnetism in gravity and various experiments and observations to determine its empirical foundation. The SME (Standard Model Extension) and SMS (Standard Model Supplement) overlap with the χ-g framework in their photon sector. We found that the foundation is solid with the only exception of a potentially possible pseudoscalar-photon interaction. We discussed its experimental constraints and look forward to more future experiments.

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VACARU, SERGIU I. "PRINCIPLES OF EINSTEIN–FINSLER GRAVITY AND PERSPECTIVES IN MODERN COSMOLOGY." International Journal of Modern Physics D 21, no. 09 (September 2012): 1250072. http://dx.doi.org/10.1142/s0218271812500721.

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We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds, endowed with nonholonomic frame structure. Several generalizations and alternatives to Einstein gravity are considered, including modifications with broken local Lorentz invariance. It is also shown how such theories (and general relativity) can be equivalently re-formulated in Finsler like variables. We focus on prospects in modern cosmology and Finsler acceleration of Universe. Einstein–Finsler gravity theories are elaborated following almost the same principles as in the general relativity theory but extended to Finsler metrics and connections. Finally, some examples of generic off-diagonal metrics and generalized connections, defining anisotropic cosmological Einstein–Finsler spaces are analyzed; certain criteria for the Finsler accelerating evolution are formulated.

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Karam, Sabah E. "Does quantum entanglement turn Rowlands’ ‘principle of duality’ into a ‘law’?" Journal of Physics: Conference Series 2197, no. 1 (March 1, 2022): 012017. http://dx.doi.org/10.1088/1742-6596/2197/1/012017.

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Abstract Physical laws are permanently observed. They are universal but not proven. Newton’s universal law of gravitation and three laws of motion, derived from the observations and theories of Copernicus, Kepler, Galileo and others, were used to take astronauts to the moon and return them safely to earth. Theories about the origin of gravity and whether gravitational forces are fundamental, quantum, entropic, induced, emergent, curved spacetime or fields like electromagnetism are still being probed. General relativity is a geometric theory, not a law, about gravity. In a book called Zero to Infinity: The Foundations of Physics Peter Rowlands asserts that physics is “founded entirely on the principle of duality.” Wave-particle duality is one of the most fundamental representations of quantum objects. Photons, electrons, neutrinos and even molecules have been shown to be in superposition and entangled. This paper will examine the role that quantum entanglement plays in the fermion/boson relationship of Rowlands’ nilpotent Dirac equation. Many other entangled physical dualities, identified as being foundational to physics, strongly suggest that his ‘principle of duality’ should be promoted into a physical law.

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Napolitano, Fabrizio, Andrea Addazi, Angelo Bassi, Massimiliano Bazzi, Mario Bragadireanu, Michael Cargnelli, Alberto Clozza, et al. "Underground Tests of Quantum Mechanics by the VIP Collaboration at Gran Sasso." Symmetry 15, no. 2 (February 11, 2023): 480. http://dx.doi.org/10.3390/sym15020480.

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Modern physics lays its foundations on the pillars of Quantum Mechanics (QM), which has been proven successful to describe the microscopic world of atoms and particles, leading to the construction of the Standard Model. Despite the big success, the old open questions at its very heart, such as the measurement problem and the wave function collapse, are still open. Various theories consider scenarios which could encompass a departure from the predictions of the standard QM, such as extra-dimensions or deformations of the Lorentz/Poincaré symmetries. At the Italian National Gran Sasso underground Laboratory LNGS, we search for evidence of new physics proceeding from models beyond standard QM, using radiation detectors. Collapse models addressing the foundations of QM, such as the gravity-related Diósi–Penrose (DP) and Continuous Spontaneous Localization (CSL) models, predict the emission of spontaneous radiation, which allows experimental tests. Using a high-purity Germanium detector, we could exclude the natural parameterless version of the DP model and put strict bounds on the CSL one. In addition, forbidden atomic transitions could prove a possible violation of the Pauli Exclusion Principle (PEP) in open and closed systems. The VIP-2 experiment is currently in operation, aiming at detecting PEP-violating signals in Copper with electrons; the VIP-3 experiment upgrade is foreseen to become operative in the next few years. We discuss the VIP-Lead experiment on closed systems, and the strong bounds it sets on classes of non-commutative quantum gravity theories, such as the θ–Poincaré theory.

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Galetska, Tetiana, Natalia Topishko, and Sergii Galetskyi. "GRAVITY MODEL OF INTERNATIONAL TRADE: ORIGIN AND MODERN APPROACHES." Scientific Notes of Ostroh Academy National University, "Economics" Series 1, no. 27(55) (December 22, 2022): 96–103. http://dx.doi.org/10.25264/2311-5149-2022-27(55)-96-103.

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The article examines the historical origins of the formation of gravity modeling and its use in the study of the intensity of international trade. It is emphasized that the driving forces of international exchange and the search for optimal policy ways of its implementation are based on classical theories of international trade. They are based on a liberal approach to deny the need for state restrictions on the free flow of goods between countries in order to regulate the volume, structure and directions of the country's foreign trade. The contribution of outstanding economists to the development of the theoretical and methodological foundations of the construction of gravity models of international exchange is considered. The features of their application for empirical research in the field of international trade are characterized. Factors affecting international trade flows are identified. An analysis of theoretical and methodological approaches to the formation of an effective gravity model of foreign trade was carried out based on the search for factors that influence it and contribute to the intensification of international trade flows between partner countries. The specificity of the involvement of new additional variables in gravity models is shown. It is emphasized that the bifurcation processes taking place in the modern globalized world form new conditions of international exchange. Attention is focused on the fact that such a situation necessitates the further development of theoretical and methodological bases for forecasting the volume of international trade based on the identification of cause-and-effect dependencies and spatio-temporal relationships. The conducted review of the history of gravity modeling, its use in studies of the international trade intensity, the contribution of prominent economists to the deepening of the theoretical and methodological foundations of the of international exchange gravity models construction showed quite wide opportunities for their further improvement based on taking into account the factors that influence the volume of bilateral trade. It was investigated that the problems are: 1) Selection of variables of the gravity model from the side of export and import for its adaptation to modern conditions of the world trade. The bifurcation processes taking place in the modern globalized world form new conditions of international exchange. 2) Gravitational models are empirical models built on liberal and neoliberal theories of international economic relations. In the conditions of globalization, a high level of interaction and interdependence of countries, the intensification of international trade flows, the movement of resources from a weaker trading partner to rich and powerful states means the flow of resources from underdeveloped and poor countries to stronger and richer ones. Gravitational models of international trade are a reflection and improvement of this process.

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Blahun, Ivan S., and Yulian R. Nadvirnianskyi. "The Model of Economic Analysis of International Trade Between Ukraine and the European Union." Business Inform 11, no. 538 (2022): 76–81. http://dx.doi.org/10.32983/2222-4459-2022-11-76-81.

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The equations of gravity have undergone a significant evolution since their initial application in economics. The conception is perceived as originating in physics. However, international trade studies allow to a more thorough analysis of the instances of gravity equations application. The conception of gravity, initially underestimated by economists and devoid of solid theoretical foundations, was rarely used in empirical research. However, at present this conception has become the main instrument of analysis. First of all, this is determined by its empirical utility, ability to take into account many factors that shape trade, and, as a result, flexibility of its application. Over the past few years, the use of the conception of gravity has led to the conclusion that economists are finding more and more accurate methods for evaluating econometric models and taking into account increasingly complex factors. As a result, they go beyond purely economic factors that influence the intensity of trade relations between countries. It is worth noting that the conceptions formulated in early theories of trade, such as absolute advantage, comparative advantage, proportions of the provision of factors of production, and many others are directed towards studying the nature, causes and consequences of international trade. The so-called basis for international trade was seen alternately in various factors: differences in labor productivity, different proportions in the provision of factors of production, the effect of scale, the different position of countries on the so-called ladder of technological progress, etc. Some theories see the reasons for trade in differences between countries, others (for example, intra-industry trade) – in similarities. An important topic is also the role of entities operating with foreign capital in creating the trade flows.

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Singh, Tejinder P. "Outline for a Quantum Theory of Gravity." Zeitschrift für Naturforschung A 74, no. 5 (May 27, 2019): 383–86. http://dx.doi.org/10.1515/zna-2019-0027.

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AbstractBy invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four-dimensional non-commutative curvature scalar (which is torsion dependent), which is sourced by the Nambu–Goto world-sheet action for a string plus the Kalb–Ramond string action. This ‘quantum gravity’ is actually a non-commutative classical matrix dynamics, and the only two fundamental constants in the theory are the square of the Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and ℏ) and quantum general relativity (and G) emerge from the underlying matrix dynamics in the thermodynamic limit. Statistical fluctuations, which are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope to highlight here the deep connection between quantum foundations and the sought-for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!

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Shiralilou, Banafsheh, Tanja Hinderer, Samaya M. Nissanke, Néstor Ortiz, and Helvi Witek. "Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity." Classical and Quantum Gravity 39, no. 3 (January 4, 2022): 035002. http://dx.doi.org/10.1088/1361-6382/ac4196.

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Abstract Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modeling of the expected signals in extensions of general relativity. In this paper we model the gravitational wave emission of inspiralling binaries in scalar Gauss–Bonnet gravity theories. Going beyond the weak-coupling approximation, we derive the gravitational waveform to relative first post-Newtonian order beyond the quadrupole approximation and calculate new contributions from nonlinear curvature terms. We also compute the scalar waveform to relative 0.5PN order beyond the leading −0.5PN order terms. We quantify the effect of these terms and provide ready-to-implement gravitational wave and scalar waveforms as well as the Fourier domain phase for quasi-circular binaries. We also perform a parameter space study, which indicates that the values of black hole scalar charges play a crucial role in the detectability of deviation from general relativity. We also compare the scalar waveforms to numerical relativity simulations to assess the impact of the relativistic corrections to the scalar radiation. Our results provide important foundations for future precision tests of gravity.

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Vanrietvelde, Augustin, Philipp A. Hoehn, Flaminia Giacomini, and Esteban Castro-Ruiz. "A change of perspective: switching quantum reference frames via a perspective-neutral framework." Quantum 4 (January 27, 2020): 225. http://dx.doi.org/10.22331/q-2020-01-27-225.

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Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of \cite{Giacomini:2017zju}, embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.

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Elizalde, Emilio. "Zeta Functions and the Cosmos—A Basic Brief Review." Universe 7, no. 1 (December 30, 2020): 5. http://dx.doi.org/10.3390/universe7010005.

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This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown how these powerful methods are used for the regularization of physical quantities, such as quantum vacuum fluctuations in various contexts. In special, in Casimir effect setups, with a note on the dynamical Casimir effect, and mainly concerning its application in quantum theories in curved spaces, subsequently used in gravity theories and cosmology. The second part of this work starts with an essential introduction to large scale cosmology, in search of the observational foundations of the Friedmann-Lemaître-Robertson-Walker (FLRW) model, and the cosmological constant issue, with the very hard problems associated with it. In short, a concise summary of all these interrelated subjects and applications, involving zeta functions and the cosmos, and an updated list of the pioneering and more influential works (according to Google Scholar citation counts) published on all these matters to date, are provided.

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Xu, Ping, Yiqiu Ma, Ji-Gang Ren, Hai-Lin Yong, Timothy C. Ralph, Sheng-Kai Liao, Juan Yin, et al. "Satellite testing of a gravitationally induced quantum decoherence model." Science 366, no. 6461 (September 19, 2019): 132–35. http://dx.doi.org/10.1126/science.aay5820.

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Quantum mechanics and the general theory of relativity are two pillars of modern physics. However, a coherent unified framework of the two theories remains an open problem. Attempts to quantize general relativity have led to many rival models of quantum gravity, which, however, generally lack experimental foundations. We report a quantum optical experimental test of event formalism of quantum fields, a theory that attempts to present a coherent description of quantum fields in exotic spacetimes containing closed timelike curves and ordinary spacetime. We experimentally test a prediction of the theory with the quantum satellite Micius that a pair of time-energy–entangled particles probabilistically decorrelate passing through different regions of the gravitational potential of Earth. Our measurement results are consistent with the standard quantum theory and hence do not support the prediction of event formalism.

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Lämmerzahl, Claus, and Angela Di Virgilio. "Experimental gravitation." International Journal of Modern Physics D 25, no. 10 (August 25, 2016): 1630022. http://dx.doi.org/10.1142/s0218271816300226.

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100 years after the invention of General Relativity (GR) and 110 years after the development of Special Relativity (SR) we have to state that until now no single experiment or observation allows any doubt about the validity of these theories within the accuracy of the available data. Tests of GR can be divided into three categories: (i) test of the foundations of GR, (ii) tests of the consequences of GR, and (iii) test of the interplay between GR and quantum mechanics. In the first category, we have tests of the Einstein Equivalence Principle and the structure of the Newton axioms, in the second category we have effects like the gravitational redshift, light defection, gravitational time delay, the perihelion shift, the gravitomagnetic effects as the Lense–Thirring and Schiff effect, and gravitational waves. Tests of the effects of gravity on quantum systems are a first step towards experiments searching for a quantum gravity theory. In this paper, we also highlight practical applications in positioning, geodesy, and the International Atomic Time. After 100 years, GR can now definitely be regarded also as practical and applied science.

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Ni, Wei-Tou. "Genesis of general relativity — A concise exposition." International Journal of Modern Physics D 25, no. 14 (December 2016): 1630004. http://dx.doi.org/10.1142/s0218271816300044.

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This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).

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Palmer, T. N. "The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2110 (July 29, 2009): 3165–85. http://dx.doi.org/10.1098/rspa.2009.0080.

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A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I , invariant under the action of some subordinate deterministic causal dynamics D I . An exploratory analysis is made of a possible causal realistic framework for quantum physics based on key properties of I . For example, sparseness is used to relate generic counterfactual states to points p ∉ I of unreality, thus providing a geometric basis for the essential contextuality of quantum physics and the role of the abstract Hilbert Space in quantum theory. Also, self-similarity, described in a symbolic setting, provides a possible realistic perspective on the essential role of complex numbers and quaternions in quantum theory. A new interpretation is given to the standard ‘mysteries’ of quantum theory: superposition, measurement, non-locality, emergence of classicality and so on. It is proposed that heterogeneities in the fractal geometry of I are manifestations of the phenomenon of gravity. Since quantum theory is inherently blind to the existence of such state-space geometries, the analysis here suggests that attempts to formulate unified theories of physics within a conventional quantum-theoretic framework are misguided, and that a successful quantum theory of gravity should unify the causal non-Euclidean geometry of space–time with the atemporal fractal geometry of state space. The task is not to make sense of the quantum axioms by heaping more structure, more definitions, more science fiction imagery on top of them, but to throw them away wholesale and start afresh. We should be relentless in asking ourselves: From what deep physical principles might we derive this exquisite structure? These principles should be crisp, they should be compelling. They should stir the soul. Chris Fuchs ( Gilder 2008 , p. 335)

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Balachandran, A. P., and S. Vaidya. "Emergent Chiral Symmetry: Parity and Time Reversal Doubles." International Journal of Modern Physics A 12, no. 29 (November 20, 1997): 5325–57. http://dx.doi.org/10.1142/s0217751x97002851.

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There are numerous examples of approximately degenerate states of opposite parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity doubles occur in nuclear physics as well, among nuclei with odd A ~ 219–229. We have also suggested elsewhere that such doubles occur in particle physics for baryons made up of cbu and cbd quarks. In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born–Oppenheimer approximation, and emphasizing their bundle-theoretic and topological underpinnings. Starting with certain "low energy" effective theories in which classical symmetries like parity and time reversal are anomalously broken on quantization, we show how these symmetries can be restored by judicious inclusion of "high-energy" degrees of freedom. This mechanism of restoring the symmetry naturally leads to the aforementioned doublet structure. A novel byproduct of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also discuss the implications of this mechanism for Skyrmion physics, monopoles, anomalies and quantum gravity.

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HAN, MUXIN, YONGGE MA, and WEIMING HUANG. "FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY." International Journal of Modern Physics D 16, no. 09 (September 2007): 1397–474. http://dx.doi.org/10.1142/s0218271807010894.

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In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

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Anderson, Edward. "Lie Theory Suffices to Resolve the Local Classical Problem of Time." Geometry, Integrability and Quantization 22 (2021): 43–63. http://dx.doi.org/10.7546/giq-22-2021-43-63.

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The problem of time - a foundational question in quantum gravity - is due to conceptual gaps between GR and physics' other observationally-confirmed theories. Its multiple facets originated with Wheeler-DeWitt-Dirac over 50~years ago. They were subsequently classified by Kucha\v{r}-Isham, who argued that most of the problem is facet interferences and posed the question of how to order the facets. We show the local classical level facets are two copies of Lie theory with a Wheelerian two-way route therebetween. This solves facet ordering and facet interference. Closure by a Lie algorithm generalization of Dirac's algorithm is central.

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Höhn, Philipp A., Marius Krumm, and Markus P. Müller. "Internal quantum reference frames for finite Abelian groups." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 112207. http://dx.doi.org/10.1063/5.0088485.

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Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories, and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work [M. Krumm, P. A. Höhn, and M. P. Müller, Quantum 5, 530 (2021)]. The simplicity of this setup admits a fully rigorous quantum information–theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information–theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the “physical Hilbert space”—the arena of the “perspective-neutral” approach—as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the “perspective-neutral” and the “alignability” approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described “relative to one of the subystems.”

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Ferrándiz, José M., Sadegh Modiri, Santiago Belda, Mikhail Barkin, Mathis Bloßfeld, Robert Heinkelmann, and Harald Schuh. "Drift of the Earth’s Principal Axes of Inertia from GRACE and Satellite Laser Ranging Data." Remote Sensing 12, no. 2 (January 18, 2020): 314. http://dx.doi.org/10.3390/rs12020314.

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The location of the Earth’s principal axes of inertia is a foundation for all the theories and solutions of its rotation, and thus has a broad effect on many fields, including astronomy, geodesy, and satellite-based positioning and navigation systems. That location is determined by the second-degree Stokes coefficients of the geopotential. Accurate solutions for those coefficients were limited to the stationary case for many years, but the situation improved with the accomplishment of Gravity Recovery and Climate Experiment (GRACE), and nowadays several solutions for the time-varying geopotential have been derived based on gravity and satellite laser ranging data, with time resolutions reaching one month or one week. Although those solutions are already accurate enough to compute the evolution of the Earth’s axes of inertia along more than a decade, such an analysis has never been performed. In this paper, we present the first analysis of this problem, taking advantage of previous analytical derivations to simplify the computations and the estimation of the uncertainty of solutions. The results are rather striking, since the axes of inertia do not move around some mean position fixed to a given terrestrial reference frame in this period, but drift away from their initial location in a slow but clear and not negligible manner.

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Yadav, Ranjit Prasad. "Theory of General Relativity: Historical Perspective." Academic Voices: A Multidisciplinary Journal 4 (March 28, 2015): 49–52. http://dx.doi.org/10.3126/av.v4i0.12358.

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General relativity was developed by Albert Einstein near about 100 Years ago. This article attempt to give an outline about the brief history of general theory of relativity and to understand the background to the theory we have to look at how theories of gravitation developed. Before the advent of GR, Newton's law of gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses i.e. gravity was the result of an attractive force between massive objects. General relativity has developed in to an essential tool in modern astrophysics. It provides the foundation for the understanding of black holes, regions of space where gravitational attraction is strong that not even light can escape and also a part of the big bang model of cosmology.DOI: http://dx.doi.org/10.3126/av.v4i0.12358Academic Voices Vol.4 2014: 49-52

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Wang, Yong Zhi, Yun Long Wang, Zhuo Shi Chen, and Xiao Ming Yuan. "Underground Space Form Design of Large Centrifugal Shaker System and Analysis of Machine Foundation Vibration." Applied Mechanics and Materials 238 (November 2012): 795–98. http://dx.doi.org/10.4028/www.scientific.net/amm.238.795.

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Centrifugal shakers are accounted the most effective and the most advanced test method of geotechnical earthquake engineering and soil dynamics, for a unique ability of exerting dynamic loads of sine waves and seismic waves on models while the same gravity stress as prototype is produced. Large centrifugal shakers are necessary to countries of frequent earthquake occurrences, but no one has been built in China. As state-of-the-art test equipments, its construction absolutely has many challenges. In the machine foundation design, its underground space employed a narrow rectangle as usual can’t satisfy the required space of facilities, while the imbalance force of equipments against foundation stability is inherently high. For no relevant research findings can be available, the paper states the general layout of a large centrifugal shaker and the fiendish problems between two space forms. By theories of mass-spring-damper and elastic half-space, two foundation vibration mathematical models for large centrifugal shakers are proposed. The calculation results of both underground space forms show that a round space meeting the required space of facilities doesn’t significantly increase foundation vibration, and is more ideal. Moreover the view of a narrow rectangular underground space more stable to large centrifugal shakers by experience is not true.

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Stiening, Gideon. "Von der mathematischen zur kritischen Metaphysik der Natur. Lambert und Kant." Kantian journal 41, no. 2 (2022): 42–67. http://dx.doi.org/10.5922/0207-6918-2022-2-2.

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In the mid-1760s, Johann Heinrich Lambert wrote a letter to Kant who offered cooperation with a view to reforming metaphysics. Based on the short correspondence between the two philosophers, it can be shown that this cooperation could never really come about. Nevertheless the thesis was sometimes put forward in research that Lambert had a defining influence on Kant’s Metaphysical Foundations of Natural Science, also, and above all, with regard to the Newton-critical moments of this natural theory. However, this thesis can only be confirmed in relation to individual theorems, such as the relationship between attraction and repulsion force, even though the reasons for Lambert and Kant’s deviation from Newton’s theory of gravity also differ. For in its main features the transcendental metaphysics of Kant’s nature is substantially different from the mathematical methodology of Lambert’s theory of nature. In addition, Lambert stuck throughout his life to a theonomous natural teleology in the succession of Wolff, which was fundamentally made impossible by the Critique of Pure Reason: because the wise “intention of the creator”, which Lambert’s empirical-rationalistic cosmology could not and did not want to do without, could no longer be referred to in a rational context according to the Critique of Pure Reason. Even if Lambert certainly had moments of the Kantian theory of matter or — as Kant himself admitted — elements of the spatial theory of the first Critique, there is no way from his mathematisation of metaphysics and his natural teleology to the fundamental innovation of the Metaphysical Foundations.

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Xiao, Wen Sheng, Xiu Juan Lin, and Hong Yan Wang. "Mechanical Stability Analysis of Subsea Wellhead for Deepwater Production to Earthquake Load." Applied Mechanics and Materials 44-47 (December 2010): 1061–65. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.1061.

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Subsea wellhead for deepwater production subjects to axial force, lateral force and bending moment under the seismic loading, the effect of subsea christmas tree and casing string’s gravity. Joint action of these forces makes it is possible that horizontal displacement exceeds the limitation and thus loses the stability. A mechanical analytical model of subsea wellhead for deepwater production is established on the basis of the pile foundation theories and material mechanics, the seismic load and behavior between casing string and formation are considered. The analyses on lateral displacement, angular distortion, bending moment and shear force show that the affection of lateral load is focus on the upper section of casing string, and the lateral displacement of subsea wellhead for deepwater production increases along with earthquake load and thus decreases stability. The stability improves notably with the increase of coefficient of soil reaction. Therefore it is necessary to obtain the on-the-spot geological data in shallow formation. The wellhead stability may be improved to different degrees by taking measures such as minimizing axial load, enhancing the conductor bending strenth, increasing the depth of the casing string in soil, reducing the outcropping length of the casing string.

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He, Yan Yan, Alan W. Roberts, and Jan Dirk Prigge. "Investigation of Flow Channel Geometry and Draw-Down in Funnel-Flow Bins and Stockpiles." Advanced Materials Research 508 (April 2012): 16–20. http://dx.doi.org/10.4028/www.scientific.net/amr.508.16.

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Over the past 50 years, a strong foundation for the professional discipline of bulk solids handling has been provided, but so far, the theories for predicting funnel-flow are still quite empirical. In most cases, only two-dimensional stress field models are applied, which overestimate the stable pipe or rathole dimensions defining the core of the funnel and lead to draw-down and live capacity determinations, which are too conservative. More recently, Roberts [ introduced a new, more realistic, hoop stress theory based on the three-dimensional stress state occurring in a rathole. To verify the validity of the new theory, the current research upon which this paper is based, involves an experimental study of rathole formation in laboratory scale model funnel-flow bins and gravity reclaim stockpiles. A two-dimensional laser line scanner is used to depict rathole profiles, while load cells and pressure sensors are applied to determine instantaneous loads and pressure conditions during filling, storage and discharge. Iron ore fines are used as the test material, with the test program including flat-bottom bins with different diameters as well as varying filling levels and outlet diameters and stockpiles with variable heights and outlet diameters. The tests demonstrate the capability of laser scanning to describe rathole profiles. In addition, the suitability of the load cells and pressure sensors to describe the relevant funnel-flow parameters is shown.

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Guinan, Edward F., Petr Harmanec, and William Hartkopf. "Introduction & Overview to Symposium 240: Binary Stars as Critical Tools and Tests in Contemporary Astrophysics." Proceedings of the International Astronomical Union 2, S240 (August 2006): 5–16. http://dx.doi.org/10.1017/s1743921307003730.

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AbstractAn overview is presented of the many new and exciting developments in binary and multiple star studies that were discussed at IAU Symposium 240. Impacts on binary and multiple star studies from new technologies, techniques, instruments, missions and theory are highlighted. It is crucial to study binary and multiple stars because the vast majority of stars (>60%) in our Galaxy and in other galaxies consist, not of single stars, but of double and multiple star systems. To understand galaxies we need to understand stars, but since most are members of binary and multiple star systems, we need to study and understand binary stars. The major advances in technology, instrumentation, computers, and theory have revolutionized what we know (and also don't know) about binary and multiple star systems. Data now available from interferometry (with milliarcsecond [mas] and sub-mas precisions), high-precision radial velocities (∼1-2 m/s) and high precision photometry (<1–2 milli-mag) as well as the wealth of new data that are pouring in from panoramic optical and infrared surveys (e.g., > 10,000 new binaries found since 1995), have led to a renaissance in binary star and multiple star studies. For example, advances have lead to the discovery of new classes of binary systems with planet and brown dwarf components (over 200 systems). Also, extremely valuable data about binary stars are available across the entire electromagnetic spectrum — from gamma-ray to IR space missions and from the ground using increasingly more powerful and plentiful optical and radio telescopes as well as robotic telescopes. In the immediate future, spectral coverage could even be extended beyond the radio to the first detection of gravity waves from interacting close binaries. Also, both the quality and quantity of data now available on binary and multiple stars are making it possible to gain unprecedented new insights into the structure, and formation and evolution of binary stars, as well as providing valuable astrophysical information (like precise stellar masses, radii, ages, luminosities and distances) to test and constrain current astrophysical theory. These major advances permit tests of current theories and ideas in stellar astrophysics and provide the foundations for the next steps in modeling and improvements in theory to be taken.

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R�hrl, Helmut. "Convexity theories 0. Foundations." Applied Categorical Structures 2, no. 1 (1994): 13–43. http://dx.doi.org/10.1007/bf00878500.

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Souza, Cynelle Olívia de. "Complements to Gravity Theories." International Journal of Innovative Science and Research Technology 5, no. 7 (July 31, 2020): 673–78. http://dx.doi.org/10.38124/ijisrt20jul535.

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Gravity, electricity, magnetism and strong and weak nuclear forces form the fundamental energies and force fields for the organization of matter in the universe. All visible matter emits electromagnetic waves at specific frequencies; dark matter does not emit them. It is assumed, or else, that it can be formed by particles like the neutrino, which subtly interact with electromagnetic waves and with matter. Under the action of strong energy, the neutrino can theoretically reach speeds greater than that of light. Such an effect can occur when this particle becomes detached from electromagnetic interference, which is very difficult to observe. Sound also participates in the transport of matter and energy and can participate as the main means of coupling neutrinos and transmitting their information.

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Capozziello, Salvatore, and Mariafelicia De Laurentis. "Extended Theories of Gravity." Physics Reports 509, no. 4-5 (December 2011): 167–321. http://dx.doi.org/10.1016/j.physrep.2011.09.003.

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34

Butterfield, Jeremy. "Foundations of Space-Time Theories." International Studies in Philosophy 19, no. 3 (1987): 77–78. http://dx.doi.org/10.5840/intstudphil198719379.

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Kleisli, H., and H. Röhrl. "Convexity theories 0 fin. foundations." Publicacions Matemàtiques 40 (July 1, 1996): 469–96. http://dx.doi.org/10.5565/publmat_40296_16.

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36

Healey, Richard, and Michael Friedman. "Foundations of Space-Time Theories." Noûs 21, no. 4 (December 1987): 595. http://dx.doi.org/10.2307/2215674.

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37

O'Connor, Tony. "Foundations, Intentions and Competing Theories." Journal of the British Society for Phenomenology 25, no. 1 (January 1994): 14–26. http://dx.doi.org/10.1080/00071773.1994.11007044.

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38

Haselschwerdt, Megan L. "Family Theories: Foundations and Applications." Journal of Family Theory & Review 10, no. 3 (May 30, 2018): 692–97. http://dx.doi.org/10.1111/jftr.12282.

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H. Krieger, Martin. "Foundations of Complex-Systems Theories." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32, no. 1 (March 2001): 135–36. http://dx.doi.org/10.1016/s1355-2198(00)00006-x.

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Liu, Tao, Tianshuang Qiu, and Shengyang Luan. "Cyclic Correntropy: Foundations and Theories." IEEE Access 6 (2018): 34659–69. http://dx.doi.org/10.1109/access.2018.2847346.

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Backerra, Anna C. M. "The quantum-mechanical foundations of gravity." Physics Essays 27, no. 3 (September 17, 2014): 380–97. http://dx.doi.org/10.4006/0836-1398-27.3.380.

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Whitehouse, Richard J. S., James Sutherland, and John M. Harris. "Evaluating scour at marine gravity foundations." Proceedings of the Institution of Civil Engineers - Maritime Engineering 164, no. 4 (December 2011): 143–57. http://dx.doi.org/10.1680/maen.2011.164.4.143.

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NI, WEI-TOU. "EMPIRICAL FOUNDATIONS OF THE RELATIVISTIC GRAVITY." International Journal of Modern Physics D 14, no. 06 (June 2005): 901–21. http://dx.doi.org/10.1142/s0218271805007139.

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In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3–6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter γ to be 1.000021 ± 0.000023 of general relativity — a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense–Thirring effect on the LAGEOS and LAGEOS2 satellites to be 0.99 ± 0.10 of the value predicted by general relativity. In April 2004, Gravity Probe B (Stanford relativity gyroscope experiment to measure the Lense–Thirring effect to 1%) was launched and has been accumulating science data for more than 170 days now. μSCOPE (MICROSCOPE: MICRO-Satellite à trainée Compensée pour l'Observation du Principle d'Équivalence) is on its way for a 2008 launch to test Galileo equivalence principle to 10-15. LISA Pathfinder (SMART2), the technological demonstrator for the LISA (Laser Interferometer Space Antenna) mission is well on its way for a 2009 launch. STEP (Satellite Test of Equivalence Principle), and ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) are in good planning stage. Various astrophysical tests and cosmological tests of relativistic gravity will reach precision and ultra-precision stages. Clock tests and atomic interferometry tests of relativistic gravity will reach an ever-increasing precision. These will give revived interest and development both in experimental and theoretical aspects of gravity, and may lead to answers to some profound questions of gravity and the cosmos.

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Rovelli, Carlo. "The Structural Foundations of Quantum Gravity." Classical and Quantum Gravity 24, no. 17 (August 21, 2007): 4539–41. http://dx.doi.org/10.1088/0264-9381/24/17/b01.

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Catren, Gabriel. "Geometric foundations of Cartan gauge gravity." International Journal of Geometric Methods in Modern Physics 12, no. 04 (April 2015): 1530002. http://dx.doi.org/10.1142/s0219887815300020.

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We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection ω and the soldering form θ that define the fundamental variables of the Palatini formulation of general relativity can be understood as different components of a single field, namely a Cartan connection A = ω + θ. In order to stress both the similarities and the differences between the notions of Ehresmann connection and Cartan connection, we explain in detail how a Cartan geometry (PH → M, A) can be obtained from a G-principal bundle PG → M endowed with an Ehresmann connection (being the Lorentz group H a subgroup of G) by means of a bundle reduction mechanism. We claim that this reduction must be understood as a partial gauge fixing of the local gauge symmetries of PG, i.e. as a gauge fixing that leaves "unbroken" the local Lorentz invariance. We then argue that the "broken" part of the symmetry — that is the internal local translational invariance — is implicitly preserved by the invariance under the external diffeomorphisms of M.

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Flanagan, Éanna É. "Higher-order gravity theories and scalar–tensor theories." Classical and Quantum Gravity 21, no. 2 (December 4, 2003): 417–26. http://dx.doi.org/10.1088/0264-9381/21/2/006.

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Klauder, John R. "Noncanonical quantization of gravity. I. Foundations of affine quantum gravity." Journal of Mathematical Physics 40, no. 11 (November 1999): 5860–82. http://dx.doi.org/10.1063/1.533059.

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Fatibene, Lorenzo, and Simon Garruto. "Extended gravity." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460018. http://dx.doi.org/10.1142/s0219887814600184.

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We shall show equivalence between Palatini-f(ℛ) theories and Brans–Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by introducing the Helmholtz Lagrangian associated to Palatini-f(ℛ) theory and then performing frame transformations in order to recover Einstein frame and BD frame. This clarifies the relation among different formulations and the transformations among different frames. Additionally, it defines a formulation a lá Palatini for the BD theory which is dynamically equivalent to metric BD (unlike the standard Palatini-formulation of metric BD theory which are not dynamically equivalent). In conclusion, we discuss interpretation of extended theories of gravitation and perspectives.

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Myrzakulov, Nurgissa, Ratbay Myrzakulov, and Lucrezia Ravera. "Metric-Affine Myrzakulov Gravity Theories." Symmetry 13, no. 10 (October 3, 2021): 1855. http://dx.doi.org/10.3390/sym13101855.

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In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître–Robertson–Walker background to study cosmological aspects and applications. Historical motivation for this research is thoroughly reviewed and specific physical motivations are provided for the aforementioned family of alternative theories of gravity.

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Heisenberg, Lavinia. "Scalar-vector-tensor gravity theories." Journal of Cosmology and Astroparticle Physics 2018, no. 10 (October 29, 2018): 054. http://dx.doi.org/10.1088/1475-7516/2018/10/054.

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Journal articles on the topic 'Foundations of gravity theories'

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