Space-time Point Research Articles

A particle model with extra dimensions from coadjoint Poincar\xe9 symmetry

Starting from the coadjoint Poincaré algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincaré algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in D dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature.

Концепт нелінійності у сучасному музично-педагогічному дискурсі

The article is devoted to the problem of studying the peculiarities of nonlinear thinking, its manifestations in musical and pedagogical activity. The article presents the way of development of the concept of «nonlinear thinking» in the scientific literature, the analysis of historical preconditions of its origin and registration in the context of post-classical methodology. As a result of theoretical analysis of the works of modern philosophers, teachers, musicologists, the concept of nonlinear thinking of the individual in the field of music is substantiated. If we consider creativity, including music, as a process of evolutionary self-organization of the individual, we can find a successful application of the ideas of synergetics and nonlinear thinking in music pedagogy. In the process of professional training of musicians-teachers and concert performers in institutions of higher art education, the disproportion and ambiguity of the development of nonlinear thinking of the individual is especially noticeable. The practice of higher art education institutions shows that there are contradictions between the development of pedagogical innovations with a focus on changes in educational technologies and the lack of research related to the transformation of professional self-awareness of future professionals, the specifics of their thinking. Musical and creative activity has a harmonizing effect on the psychophysical and social processes of the individual, provides ample opportunities for pedagogical creativity. Correct and timely managerial influences on the part of the teacher allow to choose the optimal ways of self-development of the student's personality. According to the principle of resonant excitation, a small but accurately calculated energy injection at the required space-time point is enough for this. In the process of pedagogical regulation of the educational process should take into account their own trends in the development of the student's personality, strive to strengthen his abilities to work independently and to cooperate with the teacher. The presence of feedback, ie the active influence of the results of the student's activities on his personality is a necessary condition for the intensification of the educational process.

Including covariates in a space-time point process with application to seismicity

The paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.

The social field designed by architecture

In the literature disciplinary researches, e.g., physics, studied the behaviour of elements, such as particles, in a context provided with properties, e.g., electromagnetic and gravitational. This context is classically considered as field, i.e., a physical quantity associated to each point of space-time. Social sciences and psychology use the concept of Force Field introduced by the social psychologist Kurt Lewin (1890-1947) The Force Field or life space was assumed to be -in any individual or social group- changing with experience and intended as representation of the environment, personal values, emotions and goals. We may say the cognitive system combined with representations and stimuli of the environment. This short essay focuses on Architecture as design of structures able to represent and induce properties of the cognitive systems possessed by inhabitants as well their transformation processes relating to social processes in progress. The subject is studied by Environmental Psychology, in the conceptual framework of Space Syntax. On one hand, the structure of space created through Architecture both represents and induces the social field within which inhabitants behave. On the other hand, inhabitants behave by using such a social field. Within this conceptual framework we may hypothesise the existence of a process of self-architecture by social systems. We explore the coherence, in such social fields, between different aspects such as architecture, design, fashion, music and painting.

Hierarchy of Linear Light Cones with Long-Range Interactions

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, $\mathcal{O}_x(t) \mathcal{O}_y |\psi\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |\psi\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r) \propto 1/r^{\alpha}$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $\alpha>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha>2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

Symmetry-breaking and zero-one laws

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based.

Financial contagion through space-time point processes

We propose to study the dynamics of financial contagion by means of a class of point process models employed in the modeling of seismic contagion. The proposal extends network models, recently introduced to model financial contagion, in a space-time point process perspective. The extension helps to improve the assessment of credit risk of an institution, taking into account contagion spillover effects.

Out-of-horizon correlations following a quench in a relativistic quantum field theory

One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the “horizon effect” a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the “horizon effect”. We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.

Track color space-time interest points in video

Color Space-Time Interest Points (CSTIP) are among all the interesting low-level features which can be extracted from videos; they provide an efficient characterization of moving objects. The CSTIP are simple and can be used for video stabilization, camera motion estimation, and object tracking. In this paper, we show how the resulting features often reflect interesting events that can be used for a compact representation of video data as well as for tracking. To increase the robustness of CSTIP features extraction, we suggest a pre-processing step which is based on a Color Video Decomposition and can decompose the input images into a dynamic color texture and structure components. We compute the new Color Space Time Interest Points (CSTIP) associated to the dynamic color texture components by using the proposed algorithm of the detection of Color Space- Time Interest Points. The point tracker object tracks a set of Color Space-Time Interest Points using the robust Zero-Mean Normalized Cross-Correlation (ZNCC), feature-tracking algorithm. Experimental results are obtained from very different types of videos, namely sport videos and animation movies.

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. We obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

Local first law of gravity

We find a (quasi)local first law of thermodynamics, $\mathrm{\ensuremath{\Delta}}E=T\mathrm{\ensuremath{\Delta}}S\ensuremath{-}W$, connecting gravitational entropy, $S$, with matter energy and work. For Einstein gravity, $S$ is the Bekenstein-Hawking entropy, while for general theories of gravity, $S$ is the Wald entropy, evaluated on the stretched future light cone of any point in an arbitrary spacetime, not necessarily containing a black hole. The equation can be written as $\ensuremath{\rho}\mathrm{\ensuremath{\Delta}}V=T\mathrm{\ensuremath{\Delta}}S\ensuremath{-}p\mathrm{\ensuremath{\Delta}}V$ by regarding the energy-momentum tensor as that of a fluid.

N-dimensional PDM non-linear oscillators: linearizability and Euler–Lagrange or Newtonian invariance

We argue that, under multidimensional position-dependent mass (PDM) settings, the Euler–Lagrange textbook invariance falls short and turned out to be vividly incomplete and/or insecure for a set of PDM-Lagrangians. We show that the transition from Euler–Lagrange component presentation to Newtonian vector presentation is necessary and vital to guarantee invariance. The totality of the Newtonian vector equations of motion is shown to be more comprehensive and instructive than the Euler–Lagrange component equations of motion (they do not run into conflict with each other though). We have successfully used the Newtonian invariance amendment, along with some nonlocal space-time point transformation recipe, to linearize Euler–Lagrange equations and extract exact solutions for a set of n-dimensional nonlinear PDM-oscillators. They are, Mathews-Lakshmanan type-I PDM-oscillators, power-law type-I PDM-oscillators, the Mathews-Lakshmanan type-II PDM-oscillators, the power-law type-II PDM-oscillators, and some nonlinear shifted Mathews-Lakshmanan type-I PDM-oscillators.

Tourism as Form of Personal Liberty and General Communication: Experience of Geo-systems Analysis

T his conceptual paper presents a view of tourism as a form of personal freedom, which returns a holistic perception of the world to a person and the possibility of more complete self-realization, and the tourism sector as a form of global communications necessary to overcome the systemic crisis of civilization associated with the violation of external and internal relations in the system “society – nature of the Earth”, which for 2.5 million years has been developing as a “world without borders”. A s an evidence of the continuous spatial development of the planet, prehistoric heritage objects of navigation purpose (navigation – movement and orientation in space-time) are considered, the instrumental capabilities of which are revealed on the basis of paleo-astronomical and paleo-geographical research methods, as well as geo-system approach, traditionally used in geography for the analysis of territorial systems. In the article we proposed reconstruction of navigation technologies and the most ancient symbols of culture, conceptual models of the evolution of human biological and social nature show the astronomical nature of signs and abstract thinking, which allows us to consider modern navigation and communication technologies (including the development of tourism) as manifestations of the self-regulation of global socio-natural a system that provides sustainability based on maintaining flow and diversity. Navigation methods allow us to replenish the resources of the tourism sector, as well as to increase the level of social adaptation (tolerance) based on a rational interpretation of cultural objects, providing for the selection of a global invariant, regional variations and unique orientation conditions at each point of geographical space-time. T he navigation concept of information modeling of the world provides an understanding of the harmonious development of human as part of the universe, contributes to solving theoretical problems of modern science (refining evolution models; determining the primary purpose of prehistoric cultural heritage objects; reconstructing the semantics of signs and the genesis of sign systems) and can be the methodological basis of interdisciplinary research in the geography of culture.

Micro-kinetics of non-oxidative methane coupling to ethylene over Pt/CeO2 catalyst

A single atom Pt/CeO2 catalyst for the direct non-oxidative methane coupling (NOCM) operation to C2 hydrocarbon product species was prepared, mechanisms were evaluated, and kinetics based on elementary step reaction scheme equations were determined. The catalyst was characterized by a number of techniques; scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS) were implemented. CO DRIFTS showed the presence of single Pt atoms. Temperature, CH4 flow and functional weight hourly space velocity were varied in the ranges of 780–910 °C, 0.9–2.6 mL min-1 and 0.094–0.29 h−1, respectively. The applied total pressure, used was 1.5 bar. The highest reactant conversion achieved was 4.3 mol.%, the selectivity to C2 was 60 mol.%, and to ethene alone, maximally 80 mol.% among C2 products. Also some coke was forming, but processing remained stable for 245 h of the time on stream. System’s kinetic parameters were fitted to quantitative data values, non-linear regression analyses were being reiterated, and a relatively good agreement with the space–time point sets for CH4, ethylene, acetylene and hydrogen was reached. The sensitivity analysis of fixed rate constants showed which reaction steps influence reacting CH4, the reactivity towards transformed C2 and yields the most. It was shown that the important physico-chemical transformations are CH4 adsorption, the abstraction of the first H• from its neutral CH4 molecule on the surface and the sorption/desorption of H2. Fast C–C bond processes only have a limited measurable effect on CH4 converted. C2 are primarily affected by the Pt adhesion/release of CH4, synthesized C2 and H2. Modelling may be translated to other catalytic NOCM understanding, designing and optimizing, as an alternative to steam methane reforming.

Signature-causality reflection generated by Abelian gauge transformations

In this paper, we want to better understand the causality reflection that arises under a subset of Abelian local gauge transformations in geometrodynamics. We proved in previous papers that in Einstein–Maxwell spacetimes, there exist two local orthogonal planes of gauge symmetry at every spacetime point for non-null electromagnetic fields. Every vector in these planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. The vectors that span these local orthogonal planes are dependent on electromagnetic gauge. The local group of Abelian electromagnetic gauge transformations has been proved isomorphic to the local groups of tetrad transformations in these planes. We called LB1 the local group of tetrad transformations made up of SO(1, 1) plus two different kinds of discrete transformations. One of the discrete transformations is the full inversion two by two which is a Lorentz transformation. The other discrete transformation is given by a matrix with zeroes on the diagonal and ones off-diagonal two by two, a reflection. The group LB1 is realized on this plane, we call this plane one, and is spanned by the time-like and one space-like vectors. The other local orthogonal plane is plane two and the local group of tetrad transformations, we call this LB2, which is just SO(2). The local group of Abelian electromagnetic gauge transformations is isomorphic to both LB1 and LB2, independently. It has already been proved that a subset of local electromagnetic gauge transformations that leave the electromagnetic tensor invariant induces a change in sign in the norm of the tetrad vectors that span the local plane one. The reason is that one of the discrete transformations on the local plane one that belongs to the group LB1 is not a Lorentz transformation, it is a flip or reflection. It is precisely on this kind of discrete transformation that we have an interest since it has the effect of changing the signature and the causality. This effect has never been noticed before.

Spatially covariant gravity theories with two tensorial degrees of freedom: The formalism

Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are tensorial and one is of the scalar type. Through a detailed Hamiltonian analysis, we find two necessary and sufficient conditions to evade the scalar type degree of freedom. The first condition implies that the lapse-extrinsic curvature sector must be degenerate. The second condition ensures that the dimension of the phase space at each spacetime point is even, so that the scalar type degree of freedom is eliminated completely. We also compare our results with the previous studies, and apply our formalism to a simple example, in which the Lagrangian is quadratic in the extrinsic curvature.

Quantum fields and gravity: Expanding space-times

We discuss a proposal for a somewhat new formulation of quantum field theory (set in a four-dimensional manifold, the space-time) that includes an analysis of its implications for the evolution of Einstein-Friedmann cosmological models. The proposed theory displays two peculiar features: (i) a local Hilbert-Fock space is associated with each space-time point: we are dealing with a vector bundle whose fibers are Hilbert spaces; the operator-valued sections of the bundle are the quantum fields; (ii) the vacuum energy density is finite, being regularized in a space-time curvature dependent way, independently at each point. In fact everything is finite: self-masses, self-charges, quantum fluctuations: they depend on the space-time curvature and diverge only for a flat metric. In an Einstein-Friedmann model the vacuum (zero-point) energy density is consequently time-dependent and in general not negligible. Then it is shown that, for some choices of the parameters of the theory, the big-bang singularity is resolved and replaced by a bounce driven by the vacuum energy density, which becomes (very) large and negative near the bounce (negative by the contribution of the Fermi fields). But for large times (now, say) the Bose fields’ positive vacuum energy eventually overcomes the negative one and we are finally left with the present vacuum energy: positive and reasonably small.

Relativistic Gravitation Based on Symmetry

We present a Relativistic Newtonian Dynamics ( R N D ) for motion of objects in a gravitational field generated by a moving source. As in General Relativity ( G R ), we assume that objects move by a geodesic with respect to some metric, which is defined by the field. This metric is defined on flat lab spacetime and is derived using only symmetry, the fact that the field propagates with the speed of light, and the Newtonian limit. For a field of a single source, the influenced direction of the field at spacetime point x is defined as the direction from x to the to the position of the source at the retarded time. The metric depends only on this direction and the strength of the field at x. We show that for a static source, the R N D metric is of the same form as the Whitehead metric, and the Schwarzschild metric in Eddington–Finkelstein coordinates. Motion predicted under this model passes all classical tests of G R . Moreover, in this model, the total time for a round trip of light is as predicted by G R , but velocities of light and object and time dilation differ from the G R predictions. For example, light rays propagating toward the massive object do not slow down. The new time dilation prediction could be observed by measuring the relativistic redshift for stars near a black hole and for sungrazing comets. Terrestrial experiments to test speed of light predictions and the relativistic redshift are proposed. The R N D model is similar to Whitehead’s gravitation model for a static field, but its proposed extension to the non-static case is different. This extension uses a complex four-potential description of fields propagating with the speed of light.

Cognition According to Quantum Information: Three Epistemological Puzzles Solved

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum in-variance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics.

Dark Future for Dark Matter

The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is based on the Einstein gravitational field equation. However, a thorough scrutiny of the underlying theory calls into question the suitability of the field equation, which states that the Einstein tensor Gμv is a constant multiple of the stress-energy tensor Tμv when they both are evaluated at the same 4D space-time point: Gμv = 8πkTμv, where k is the gravitational constant. Notwithstanding its venerable provenance, this equation is incorrect unless the cosmic pressure is p = 0; but then all that remains of the Einstein equation is the Poisson equation which models the Newtonian gravity field. This shortcoming is not resolved by adding the cosmological constant term to the field equation, Gμv +Λ gμv =8πkTμv, as in the ΛCDM model, because then p = Λ, so the pressure is a universal constant, not a variable. Numerous studies support the concept of a linearly expanding universe in which gravitational forces and accelerations are negligible because the baryonic mass density of the universe is far below its critical density. We show that such a coasting universe model agrees with SNe Ia luminosity vs. redshift distances just as well or even better than the ΛCDM model, and that it does so without having to invoke dark matter or dark energy. Occam’s razor favors a coasting universe over the ΛCDM model.