Relativistic Spacetime Research Articles

The Geometrical Trinity of Gravity

The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes, we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory. Based on these three alternative formulations of General Relativity, we then discuss some extensions.

Modeling Inflation and Money Supply using Spatial Vector Autoregressive Model with Calendar Variation: Restricted vs Non-restricted Coefficient

One of the tasks of the government is to maintain price stability reflected in the stability of inflation through the regulation of the money supply. Therefore the government needs to know the forecast of the inflation rate and the money supply. In modeling inflation and the money supply simultaneously in Indonesia, three things need to be accommodated, namely the relationship between variables, the existence of space-time relationships and the effect of Eid al-Fitr. The spatial vector autoregressive model with calendars variation can accommodate these three things. The purpose of this study is to compare two types of spatial vector autoregressive models with calendar variations, namely restricted and non-restricted coefficient to model inflation and the money supply in Surabaya, Malang, Kediri, and Jember simultaneously. Results of this study indicate that the non-restricted spatial vector autoregressive model with calendar variation is better than the restricted one. This can be seen from the value of MSE of the non-restricted model that is smaller than the restricted model.

Смысловое опосредование личностью пространственно-временных характеристик экстремальной ситуации

The paper presents the empirical and theoretical revision of the classical experiments of A.J. DeLong and D. Bobko on the nature of space-time relations while estimating the duration of time intervals. The author proposes the novel interpretation of meaning mediation of the extreme situation significant for human life that determines the subjective assessment of the duration of short time intervals. The data obtained develop the idea of cultural mediation of space-time relations (M. Bakhtin, V. Zinchenko, M. Magomed-Eminov, S. Rubinstein, Yu. Strelkov, N. Tolstykh, A. Ukhtomsky and others), supplement the theory of the meaningful interpretation of the perception of time (P. Fraisse, B. Tsukanov), put the emphasis on the assumptions about slowing down time intervals filled with unpleasant experiences and speeding up intervals with pleasant content. This research develops a spherical model of time and the concept of personality work of the individual with his temporal experience as the construction of temporal identity mediated by the cultural and historical experience of a living unique person (M. Magomed-Eminov).

Against the disappearance of spacetime in quantum gravity

This paper argues against the proposal to draw from current research into a physical theory of quantum gravity the ontological conclusion that spacetime or spatiotemporal relations are not fundamental. As things stand, the status of this proposal is like the one of all the other claims about radical changes in ontology that were made during the development of quantum mechanics and quantum field theory. However, none of these claims held up to scrutiny as a consequence of the physics once the theory was established and a serious discussion about its ontology had begun. Furthermore, the paper argues that if spacetime is to be recovered through a functionalist procedure in a theory that admits no fundamental spacetime, standard functionalism cannot serve as a model: all the known functional definitions are definitions in terms of a causal role for the motion of physical objects and hence presuppose spatiotemporal relations.

Geometrization of Newtonian Dynamics

Riemann’s principle “force equals geometry” provided the basis for Einstein’s General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any conservative force. We introduce the relativity of spacetime : an object lives in its own spacetime, whose geometry is determined by all of the forces affecting it. We also introduce the Generalized Principle of Inertia which unifies Newton’s first and second laws and states that: An inanimate object moves freely, that is, with zero acceleration, in its own spacetime. We derive the metric of an object’s spacetime in two ways. The first way uses conservation of energy to derive a Newtonian metric. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new Relativistic Newtonian Dynamics (RND) for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. In the case of the gravitational field of a static, spherically symmetric mass distribution, this metric turns out to be the Schwarzschild metric. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity. In the second way, we obtain the RND metric directly, without first obtaining a Newtonian metric. Instead of conservation of energy, we use conservation of angular momentum, a carefully defined Newtonian limit and Tangherlini’s condition. The non-static case is handled by applying Lorentz covariance to the static case.

Diffeomorphism Group Representations in Nonrelativistic and Relativistic Quantum Theory: Some Future Directions

Diffeomorphism groups and their unitary representations unify the description of a wide variety of diverse nonrelativistic (Galilean) quantum systems. In recent work, we have suggested an approach to relativistic quantum field theory that begins with hierarchies of diffeomorphism group representations and the corresponding current densities. We introduce (noncovariant) creation and annihilation fields that intertwine the representations, and restore the (relativistic) spacetime symmetry by redefining local quantum fields and the Hamiltonian operator in terms of the intertwining fields and current densities. Here we outline the main ideas, and point to next steps and possible future directions of this line of inquiry.

Integration schemes with substepping algorithms for creep analysis in geomaterials

SummaryThis paper describes a robust and efficient methodology for predicting displacements, deformations, and stresses in geomaterials that are susceptible to creep. The methodology is based on two integration schemes, which consider substepping algorithms. The first scheme is used for integrating space‐time relations in a global sense, whereas the second scheme is used for integrating stress‐stain relations in a local sense. Different from previous studies, both integration schemes are easy to implement and general in the sense that they can be applied to any type of creep law. Through an in‐house finite element simulator, several numerical tests are performed. They include triaxial and wellbore closure analyses considering soft soils and salt rocks. The results show that the combination of both schemes leads to stable and accurate solutions with reduced computational time.

Relativistic spacetimes and definitions of determinism

I discuss candidates for definitions of determinism in the context of general relativistic spacetimes, and argue that a definition which does not make recourse to any particular region of spacetime should be preferred over alternatives; one such notion is discussed in detail in the light of various physical examples. The emerging picture of determinism is a pluralist one: sometimes there is no unique way of making our intuitive concept of determinism precise. Instead, what is crucial for assessment of determinism of the theory are auxiliary conditions under which it counts as deterministic or indeterministic, and justification for using them in a given situation.

Spatio-temporal neural networks for space-time data modeling and relation discovery

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for modeling time series of spatial processes, i.e., series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts the observations from the latent representations. We consider several variants of this model, corresponding to different prior hypothesis about the spatial relations between the series. The model is used for the tasks of forecasting and data imputation. It is evaluated and compared to state-of-the-art baselines, on a variety of forecasting and imputation problems representative of different application areas: epidemiology, geo-spatial statistics, and car traffic prediction. The experiments also show that this approach is able to learn relevant spatial relations without prior information.

Elastic scattering in general relativistic ray tracing for neutrinos

We present a covariant ray tracing algorithm for computing high-resolution neutrino distributions in general relativistic numerical spacetimes with hydrodynamical sources. Our formulation treats the very important effect of elastic scattering of neutrinos off of nuclei and nucleons (changing the neutrino's direction but not energy) by incorporating estimates of the background neutrino fields. Background fields provide information about the spectra and intensities of the neutrinos scattered into each ray. These background fields may be taken from a low-order moment simulation or be ignored, in which case the method reduces to a standard state-of-the-art ray tracing formulation. The method handles radiation in regimes spanning optically thick to optically thin. We test the new code, highlight its strengths and weaknesses, and apply it to a simulation of a neutron star merger to compute neutrino fluxes and spectra, and to demonstrate a neutrino flavor oscillation calculation. In that environment, we find qualitatively different fluxes, spectra, and oscillation behaviors when elastic scattering is included.

Models of exotic interferometer cross-correlations in emergent space-time

A Lorentz invariant framework is developed to model the cross spectrum of two interferometers in a space-time that emerges from a Planck scale quantum system with exact causal symmetry and holographic spacelike rotational correlations. Space-time relationships between world lines are generated by entanglement of geometrical states on causal diamonds. The entanglement is tied to a unique observable signature: an exotic imaginary broad band cross spectrum, with a frequency structure determined by the layout of the interferometers. The models will be used to interpret data from the reconfigured Fermilab Holometer, and for conceptual design of future experiments.

The Nonextensive Thermodynamics of Q-Deformed Spacetime in General Relativity

Recently we discussed several models of apriori q-deformed spacetimes and spacetime metrics, arguing that the resulting q-diffusion tensors of the propagation were also the (inverse) q-strain or when unreferenced the metric tensors in 3D and q-(fundamental) metric in 4D deformed Minkowski spacetime. The topology of q-deformed tensors in the usual way resulted in non-zero Riemann tensors, Ricci tensors upon contraction and non-zero q-scalar 'curvature' like terms that modified otherwise flat spacetime. We stated that these results obtained gravitational-like metric tensors, Ricci tensors and then Einstein tensors and equations relating q-deformed geometry to non-zero stress-energy tensors. In this letter we apply thermodynamics to the 4D (nD generally) q-deformed spacetime(s) as we have represented them in the above q-deformed topology. Specifically we will discuss the relation between entropy and stress-strain and internal energy. And as entropy can be written as an extensive composition e.x. the Gibbs-Boltzmann or Von Neumann logarithmic form or as a nonextensive composition such as the Tsallis q-power law type, we seek to also connect to the idea of q-deformed (general) relativistic spacetime to nonextensive entropy and thermodynamics.

Acoustics of noise, vibration, and harshness

In this paper, we will go to a more fundamental level of treating acoustics. We introduced the gauge invariance into the acoustic wave equation of motion in 2007. This is an important milestone in the history of gauge invariance. The earliest gauge invariance is shown by Maxwell’s electromagnetic wave equations. The root of acoustics originated from fluid mechanics. We show that the usual form of acoustic wave equation for fluids is in fact the linearized form of the Navier Stokes equations. Hence there is in fact, no need to use acoustic analogy to derive the formula for the jet noise which was done by James Lighthill. In this paper we also treat finite amplitude sound wave and finite amplitude vibration using the deductive approach. This is a generalization of the linear theory to the nonlinear theory using relativistic and curvilinear spacetime treatment. This produces the linear case as a special case of the nonlinear case. The usual method is the reverse which starts from the linear theory and extend to the nonlinear theory. This will miss out some useful information. The treatment of vibration will need to incorporate the theory of elasticity. This paper is also the first introduction of singularities into vibration. Singularities is mathematically more sophisticated than resonance.

How to Be a Relativistic Spacetime State Realist

According to spacetime state realism (SSR), the fundamental ontology of a quantum mechanical world consists of a state-valued field evolving in four-dimensional spacetime. One chief advantage it claims over rival wave-function realist views is its natural compatibility with relativistic quantum field theory (QFT). I argue that the original density operator formulation of SSR cannot be extended to QFTs where the local observables form type III von Neumann algebras. Instead, I propose a new formulation of SSR in terms of a presheaf of local state spaces dual to the net of local observables studied by algebraic QFT. 1. Introduction2. Spacetime State Realism in Quantum Field Theory 2.1. Equivalence thesis3. Entanglement and the Type III Property 3.1. No-Go Lemma 13.2. No-Go Lemma 24. State Space Axioms for Quantum Field Theory 4.1. Revised equivalence thesis5. Discussion

Statistical evidence for long-range space-time relationships between large earthquakes

Whether large earthquakes are triggered by other large earthquakes at very large distances, and at time scales where the triggered event is delayed by more than several days or weeks, is an open question. Here I provide statistical evidence to show that large earthquakes near the subduction zones of the Pacific plate boundary lessen significantly the average time until the next large earthquake that occurs near the boundaries of the smaller and adjacent Nazca and Cocos plates in the eastern Pacific Ocean. In addition, the existence and importance of this relationship is enriched by the finding that the larger the magnitude of the Pacific plate earthquake, the more likely it becomes that the time until the next earthquake in the distant triggered zone is less than the time since the last earthquake in the triggered zone. There are also specific regions along the western and northern Pacific plates where these relationships appear to be particularly prominent. The findings call into question the notion that the hazard of large earthquakes in distant regions is not raised following other large earthquakes, and they provide statistical evidence for relationships between earthquakes occurring months apart on different plates.

Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids

We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations, and are obtained from standard relativistic hydrodynamics in the limit of infinite or vanishing velocity of light. All dissipative phenomena such as friction and heat conduction are included in our description. Part of our work consists in designing the appropriate coordinate frames for relativistic spacetimes, invariant under Galilean or Carrollian diffeomorphisms. The guide for the former is the dynamics of relativistic point particles, and leads to the Zermelo frame. For the latter, the relevant objects are relativistic instantonic space-filling branes in Randers–Papapetrou backgrounds. We apply our results for obtaining the general first-derivative-order Galilean fluid equations, in particular for incompressible fluids (Navier–Stokes equations) and further illustrate our findings with two applications: Galilean fluids in rotating frames or inflating surfaces and Carrollian conformal fluids on two-dimensional time-dependent geometries. The first is useful in atmospheric physics, while the dynamics emerging in the second is governed by the Robinson–Trautman equation, describing a Calabi flow on the surface, and known to appear when solving Einstein’s equations for algebraically special Ricci-flat or Einstein spacetimes.

Spacetime is as spacetime does

Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must establish how relativistic spacetime emerges from their non-spatiotemporal structures. We argue that in order to secure this emergence, it is sufficient to establish that only those features of relativistic spacetimes functionally relevant in producing empirical evidence must be recovered. In order to complete this task, an account must be given of how the more fundamental structures instantiate these functional roles. We illustrate the general idea in the context of causal set theory and loop quantum gravity, two prominent approaches to quantum gravity.

On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm!

The biggest and most lasting among David Bohm’s (1917–1992) many achievements is to have proposed a picture of reality that explains the empirical rules of quantum mechanics. This picture, known as pilot wave theory or Bohmian mechanics among other names, is still the simplest and most convincing explanation available. According to this theory, electrons are point particles in the literal sense and move along trajectories governed by Bohm’s equation of motion. In this paper, I describe some more recent developments and extensions of Bohmian mechanics, concerning in particular relativistic space-time and particle creation and annihilation.

ARTISTIC CHRONOTOPE IN E. T. A. HOFFMANN’S NOVELLA «THE GOLDEN POT»

The article is devoted to the problem of studying the chronotope in an artistic work. The research based on the material of E. T. A. Hoffmann’s novelette that is stated in the title.Scientific research begins with systematization of the main literary approaches to understanding the spatial and temporal unity of artistic work. The background of emergence and genesis of the term «chronotope» is analyzed. The author pointed out the significant contribution of foreign and domestic scientists to the identified problem. While comparing the classical interpretation of the chronotope problem by M. M. Bakhtin with the works of domestic scientists, it was discovered that the modern view on the term «chronotope» is theoretically and practically enriched by a large number of its possible transformations. Specified on author’s storyline and genre-forming functions of chronotope.It is determined that artistic chronotope has a subjective nature and is realized in the author, characters and reader’s of literary text consciousness. Novelists confirmed that the free use of the artistic chronotope in literature destroyed the boundaries between the past, the present and future time of the literary work, and opened the way for the image of characters in all circumstances of time and space. Therefore, the chronotope of a romantic work is always conditional and mysterious.In the creative work of the German writer E. T. A. Hoffman, the concept of linear (real) and fantastic (ideal) chronotop is decisive. Сhronotop as a kind of artistic thinking, expressed in such forms: author’s, real, unreal, linear, fantastic, fairy-tale, mythopoetic and psychological.The mentioned types and forms of time-space relations are intertwined and interact with each other so that it contributes to a deeper understanding of the literary work artistic nature and gives an opportunity to detail the peculiarities of the writer’s individual style.

Produção discursiva de espaços-tempos em relatos de professores: sentidos reorientadores de formação

RESUMO O objetivo deste estudo é analisar, em relatos escritos de professores em formação, como as trajetórias de vida destes sujeitos se atualizam em seus discursos, através de referências a coordenadas espaço-temporais. As relações espaço-temporais inscritas nos relatos são apreendidas, nas análises, como dimensões históricas orientadoras de representações que esses sujeitos constroem de sua posição no mundo. Em se tratando de professores participantes de uma particular história de migração para uma região brasileira ainda marcada por processos de negação de direitos, suas práticas discursivas trazem índices desta trajetória e elas devem constituir bases para os próprios processos formativos, uma vez que nelas se forjam modos de constituir-se professor, de assumir a profissão, de desenvolver novos processos formativos. Os relatos apontam para cronotopos que indiciam a relação entre as experiências e a memória regida pela força das condições históricas, ao mesmo tempo que oferecem contornos de produção de identidades e de subjetividades.