Space-time Systems Research Articles

Looking for Carroll Particles in the Two-Time Spacetime

We make an attempt to describe Carroll particles with a non-vanishing value of energy (i.e., the Carroll particles which always stay in rest) in the framework of two-time physics, developed in the series of papers by I. Bars and his co-authors. In the spacetime with one additional time dimension and one additional space dimension, where one can localize the symmetry which exists between generalized coordinates and their conjugate momenta. Such a localization implies the introduction of the gauge fields, which, in turn, implies the appearance of some first-class constraints. Choosing different gauge-fixing conditions and solving the constraints, we obtain different time parameters, Hamiltonians, and, generally, physical systems in the standard one-time spacetime. We find a set of gauge fixing conditions which gives the description of a Carroll particle in the one-time world. We construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999.

A thermodynamic study of (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {(2+1)}}$$\\end{document}-dimensional analytic charged hairy black holes with Born–Infeld electrodynamics

This work presents analytical black hole solutions for a coupled Einstein–Born–Infeld–Scalar gravity system in AdS spacetime with two different non-minimal coupling functions f(z). For both solutions, we establish the regularity of the scalar field and curvature scalars outside the horizon. For one of the considered coupling cases, thermodynamic analysis in the canonical ensemble reveals stability across all temperatures, while the other case exhibits the Hawking/Page phase transition between the stable large phase of the black hole and thermal-AdS. We investigate the effect of the scalar hair parameter and black hole charge on the phase transition temperature and observe that the critical values of the scalar hair and the charge parameters constrain the feasibility of Hawking/Page phase transition.

Theory of Everything

Our Theory of Everything is made possible by the discovery of a closed fluid dynamic principle, working in a closed fluid space-time system, (the universe). Through the principle of fluid space-time, almost all of the unexplained mysteries of the universe are revealed. How the universe came into being, with matter and the most basic force, Gravity. Newton’s law of gravity in particular, the inverse square law with distance. (the reason is for appearance of the inverse square law, simultaneously in gravitation and electromagnetism, not a coincidence). Special Relativity is an account of how space contracts, time dilates and mass increases, with velocity. General Relativity is an account of how space-time curves. According to Muhammad’s closed fluid dynamic principle, space actually consists of an extremely fluid substance which we call aether. It is therefore fitting that through the closed fluid dynamic principle, we can arrive at an explanation for one major thorn in the side of Special Relativity, the twin paradox. The problem is, it is the twin who accelerates that gets it wrong. Because his assessment of the age of his brother was done without consideration of the fact that when he turned around, made the return journey, he felt his acceleration but did not employ this in Einstein’s time dilation, which was based on inertial reference frames. The task we are confronted with in this paper is to find out how the time dilation addressed in special relativity comes into proceedings in an accelerated frame. We achieve this.

The Uniqueverse, Natural selection as the unique model of evolutionary development of the Universe

The cosmological theories proposed so far do not postulate a common way of creation that can guide the entire line of growth of the universe, from elementary particles to living beings. But everything consists of the same basic components, combined and regulated differently: elementary particles, atoms and molecules make up celestial bodies, solar systems, single and pluricellular organisms, plants and animals. Common constituents are compatible with a common origin and with an incremental and selective development method. One possible common mode is that the Universe was formed according to an evolutionary method based on natural selection, the same process which then allowed the differentiation of biological species. This unique process may have guided from the beginning the development of the fundamental constituents of matter in the primitive universe and then created the other cosmic structures through the evolution of those elementary particles, up to organic molecules and biological beings. A process of this kind is a slow and gradual process, not based on a sudden event but on the progressive increase in the complexity of the structures present in the Universe, regulated by the selection of the most suitable and stable forms. For the relativistic relationship between energy, mass and velocity, we can think that the Universe was formed at the same time as the formation of elementary structures, slowly in a spacetime that was created in parallel: elementary particles created an initial infinitesimal spacetime system that then grew as more matter formed. The incremental creation of the cosmos would also concern forces and physical laws, which may have undergone the same evolutionary process from the most primordial and simple forms to the present, in proportion to the development of the whole system. This modality could justify the current simultaneous presence of quantum and relativistic laws at different levels (atomic and gravitational), as well as the coexistence of different species in different environments. This evolutionary modality is reflected in the fact that atoms, celestial bodies, chemical compounds, the general structure of the universe, physical laws and biological beings show the presence of stable entities selected among the many theoretically possible or unstable.

The Formal Layer of {Brain and Mind} and Emerging Consciousness in Physical Systems

AbstractWe consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection.

Circular motion analogue Unruh effect in a thermal bath: robbing from the rich and giving to the poor

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration experiences the Minkowski vacuum as a thermal state at temperature . An observer in uniform circular motion experiences a similar effective temperature, operationally defined in terms of excitation and de-excitation rates, and physically interpretable in terms of synchrotron radiation, but this effective temperature depends not just on the acceleration but also on the orbital speed and the excitation energy. In this paper we consider an observer in uniform circular motion when the Minkowski vacuum is replaced by an ambient thermal bath, and we address the interplay of ambient temperature, Doppler effect, acceleration, and excitation energy. Specifically, we consider a massless scalar field in spacetime dimensions, probed by an Unruh–DeWitt detector, in a Minkowski (rather than proper) time formulation: this setting describes proposed analogue spacetime systems in which the effect may become experimentally testable, and in which an ambient temperature will necessarily be present. We establish analytic results for the observer’s effective temperature in several asymptotic regions of the parameter space and provide numerical results in the interpolating regions, finding that an acceleration effect can be identified even when the Doppler effect dominates the overall magnitude of the response. We also identify parameter regimes where the observer sees a temperature lower than the ambient temperature, experiencing a cooling Unruh effect.

Is the Quality of Life Objectively Evaluable on Naturalism?

Abstract This article examines one of the sources of David Benatar’s anti-natalism. This is the view that ‘all procreation is [morally] wrong.’ (Benatar and Wasserman, 2015:12) One of its sources is the claim that each of our lives is objectively bad, hence bad whether we think so or not. The question I will pose is whether the constraints of metaphysical naturalism allow for an objective devaluation of human life sufficiently negative to justify anti-natalism. My thesis is that metaphysical naturalism does not have the resources to support such a negative evaluation. Metaphysical naturalism is the view that causal reality is exhausted by nature, the space-time system and its contents. The gist of my argument is that the ideal standards relative to which our lives are supposed to be axiologically substandard cannot be merely subjective expressions of our desires and aversions; they must be (i) objectively binding standards that are (ii) objectively possible in the sense of concretely realizable. The realizability condition, however, cannot be satisfied on metaphysical naturalism; ergo, failure to meet these ideal standards cannot show that our lives are objectively bad.

Biological mass spectrometry enables spatiotemporal 'omics: From tissues to cells to organelles.

Biological processes unfold across broad spatial and temporal dimensions, and measurement of the underlying molecular world is essential to their understanding. Interdisciplinary efforts advanced mass spectrometry (MS) into a tour de force for assessing virtually all levels of the molecular architecture, some in exquisite detection sensitivity and scalability in space-time. In this review, we offer vignettes of milestones in technology innovations that ushered sample collection and processing, chemical separation, ionization, and 'omics analyses to progressively finer resolutions in the realms of tissue biopsies and limited cell populations, single cells, and subcellular organelles. Also highlighted are methodologies that empowered the acquisition and analysis of multidimensional MS data sets to reveal proteomes, peptidomes, and metabolomes in ever-deepening coverage in these limited and dynamic specimens. In pursuit of richer knowledge of biological processes, we discuss efforts pioneering the integration of orthogonal approaches from molecular and functional studies, both within and beyond MS. With established and emerging community-wide efforts ensuring scientific rigor and reproducibility, spatiotemporal MS emerged as an exciting and powerful resource to study biological systems in space-time.

Modeling the Spatial Development of the US Cross-Border Regions as Mesolevel Socio-Economic Systems

The cross-border nature of the spatial development of economically and socially significant regions identified in the geospace of the largest federal states of the modern world necessitates their study from the standpoint of the mesoeconomics of development as complex, open and dynamic systems in space-time. The object of this study is the cross-border regions of the United States with Mexico and Canada, which are distinguished by a characteristic set of specific properties of both system-structural and socio-economic nature. According to the systemic economic theory, the identified cross-border regions of the United States show the principle of duality of spatial development, and within the framework of evolutionary theory – ​a specific “socio-economic genotype” of the territory. Using elements of mesoeconomic modeling, the author identified and substantiated some trends in the spatial development of different groups of cross-border regions of the United States over a long time period of 1970–2020 and as a forecast until 2030. Based on a comparative analysis carried out on the results of modeling and testing, the author's hypothesis about a multidirectional change in the dynamics of indicators of socio-economic spatial development, which depends on the regional features of the spatiotemporal evolution of specific transboundary territories, is confirmed – ​as socio-economic systems of the mesolevel. The obtained results, revealing the spatial dependence of the data, indicate the growth of spatial relationships of both social and economic nature within the studied cross-border regions of the United States, which determine the spatiotemporal evolution of the latter in the geoeconomic and geocultural space of the United States and neighboring states. Based on the results of mesoeconomic modeling, the existence of an evolutionary-cyclical nature and duality of the studied mesosystems is empirically confirmed, having their own socio-economic genotype of territories, depending on the insurmountable specifics of spatial diversity and unevenness in the conditions of the market organization of American society. The main conclusion is that regional interest, which has dialectical unity and variability, manifested over time, causes different directions and levels of spatial development of specific regions of the United States as integral dynamic and open socio-economic systems of the mesoterritorial level, reflecting the gradual increase in economic regionalization. The approach used, taking into account the specifics of spatial development, is of interest for the study of similar subject issues in relation to large federal states that have a transboundary nature of genetically determined socio-economic interaction.

Integrated Spatial Modulation and STBC-VBLAST Design toward Efficient MIMO Transmission.

In this contribution, the concept of spatial modulation (SM) is firstly integrated into the structure of space-time block codes (STBC)-aided vertical Bell-labs layered space-time (VBLAST) systems, in order to strike a balanced tradeoff among bit error ratio (BER), spectral efficiency and computational complexity. First of all, in order to enhance the BER performance of STBC-VBLAST, we advocate an effective transmit power allocation (TPA) scheme with negligible implementation costs, while dividing the STBC and VBLAST layers with alleviated interference, so as to facilitate combination with SM. Then, we further utilize the unique structure of SM for enhancing the spectral efficiency of original STBC-VBLAST, wherein the information is conveyed by not only the amplitude/phase modulation (APM) symbols but also the antenna indices. In addition, constellation sets of STBC symbols are specifically designed to be rotated to make full use of the degrees of freedom. Finally, the performance advantages of the above-mentioned structures over traditional STBC-VBLAST are demonstrated by the theoretical derivation of a closed-form expression for the union bound on the bit error probability for various spectral efficiencies, and they are supported by simulation results.

A multi-optimization-based genetic algorithm mapper design for three transmit uncoded space-time diversity systems

Three transmit antennas Uncoded Space-Time Labeling Diversity (USTLD) systems were recently proposed as a direct extension to the two transmit antennas USTLD system. By employing more antennas at the transmitter, antenna — as well as — labeling diversity (LD) can be further achieved. Existing mapper designs for three transmit antennas USTLD systems are based on symmetrical heuristics, and hence no asymmetrical mapper designs can be produced. This paper proposes a multi-function optimization genetic algorithm for the three transmit antennas USTLD system that produces mapper designs irrespective of size or symmetry. The genetic algorithm was tested on 16-, 32QAM, 16-, 32APSK and 16APSK constellations that do not exhibit diagonal symmetry. The proposed genetic algorithm had produced mapper designs that match but did not improve upon existing mapper designs for 16QAM and 32QAM, respectively. The 16APSK and 32APSK mapper designs produced achieved diversity gains of [Formula: see text] and [Formula: see text] when compared to existing third mapper designs, as well as [Formula: see text] and [Formula: see text] gain over the two transmit antennas USTLD scheme at the BER of [Formula: see text]. Furthermore, when tested on 16APSK constellations that do not exhibit diagonal symmetry, these mappers achieved diversity gains between [Formula: see text], [Formula: see text] and [Formula: see text] over the two-transmit USTLD scheme at the BER of [Formula: see text], respectively. The computational complexity of the proposed genetic algorithm was analyzed based on a previous study, which was shown to be [Formula: see text].

Relativistic Landau quantization for a composite system in the spiral dislocation spacetime

Relativistic Landau quantization for a composite system in the spiral dislocation spacetime

Gravitational radiation from a binary system in odd-dimensional spacetime

We explore possible manifestations of an odd number of extra dimensions in gravitational radiation, which are associated with violation of Huygens' principle in flat odd-dimensional spacetime. Our setup can be regarded as the limit of an infinite compactification radius in ADD model and is not viable as realistic cosmology, but it still may be useful as a simple analytically solvable model catching certain features of more realistic scenarios. The model consists of two point masses moving inside a flat three-dimensional brane, embedded in a five-dimensional Minkowski space and interacting only through a massless scalar field localized on the same brane, while gravitational radiation is emitted into the bulk. This setup avoids the difficulties associated with taking into account the gravitational stresses binding the system, which require the cubic terms in the perturbative gravitational Lagrangian, and permits to limit ourselves to linearized theory. We calculate radiation in a linearized five-dimensional gravity generalizing the Rohrlich-Teitelboim approach to extract the emitted part of the retarded gravitational field. The source term consists of a local contribution from point particles and a non-local contribution from scalar field stresses, which is calculated using the DIRE approach to post-Newtonian expansions. In the nonrelativistic limit, we find an analog of the quadrupole formula containing an integral over the history of the particles' motion preceding the retarded time. We also show that, for an observer on the brane, the radiation contains a third polarization: the breathing mode.

(2 + 1)-Maxwell Equations in Split Quaternions

The properties of spinors and vectors in (2 + 2) space of split quaternions are studied. Quaternionic representation of rotations naturally separates two SO(2,1) subgroups of the full group of symmetry of the norms of split quaternions, SO(2,2). One of them represents symmetries of three-dimensional Minkowski space-time. Then, the second SO(2,1) subgroup, generated by the additional time-like coordinate from the basis of split quaternions, can be viewed as the internal symmetry of the model. It is shown that the analyticity condition, applying to the invariant construction of split quaternions, is equivalent to some system of differential equations for quaternionic spinors and vectors. Assuming that the derivatives by extra time-like coordinate generate triality (supersymmetric) rotations, the analyticity equation is reduced to the exact Dirac–Maxwell system in three-dimensional Minkowski space-time.

Anomaly and superconnection

Abstract We study anomalies of fermions with spacetime-dependent mass. Using Fujikawa’s method, it is found that the anomalies associated with the U(N)+ × U(N)− chiral symmetry and U(N) flavor symmetry for even and odd dimensions, respectively, can be written in terms of superconnections. In particular, the anomaly for a vector-like U(1) symmetry is given by the Chern character of the superconnection in both even- and odd-dimensional cases. It is also argued that the non-Abelian anomaly for a system in D-dimensional spacetime is characterized by a (D + 2)-form part of the Chern character of the superconnection which generalizes the usual anomaly polynomial for the massless case. These results enable us to analyze anomalies in the systems with interfaces and spacetime boundaries in a unified way. Applications to index theorems, including the Atiyah–Patodi–Singer index theorem and a Callias-type index theorem, are also discussed. In addition, we give a natural string theory interpretation of these results.

Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation

We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion

In recent times, there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some concerns that the nonlinearities might produce pathological properties for composite/multiparticle systems. We here focus on kinematics in the [Formula: see text]-Minkowski noncommutative spacetime, the quantum spacetime which has been most studied from this perspective and compare the implications of the alternative descriptions of the total momentum of a multiparticle system which have been so far proposed. We provide evidence suggesting that priority should be given to defining the total momentum as the standard linear sum of the momenta of the particles composing the system. We also uncover a previously unnoticed feature concerning some (minute but conceptually important) effects on center-of-mass motion due to properties of the motion of the constituents relative to the center of mass.

A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

Low complexity decoding algorithm for differential space-time block coding transmission systems

Low complexity decoding algorithm for differential space-time block coding transmission systems

A novel signal detection algorithm of multiple-input multiple-output Vertical-Bell Laboratories Layered Space-Time for underwater acoustic networks based on the improved minimum mean square error

Multiple-input multiple-output is a commonly used technology supporting for high-rate transmission over frequency-selective fading channels with multiple antennas. Vertical-Bell Laboratories Layered Space-Time is a detection method of a multiple-input multiple-output system, which establishes a direct correspondence between antennas and layers. Studies demonstrate that multiple-input multiple-output Vertical-Bell Laboratories Layered Space-Time is a meaningful way for underwater acoustic networks of high performance. However, considering the hardware constraints and energy consumption, achieving a trade-off between the bit error ratio and complexity is a crucial issue for underwater acoustic networks of multiple-input multiple-output Vertical-Bell Laboratories Layered Space-Time systems. This article proposes a novel signal detection algorithm of multiple-input multiple-output Vertical-Bell Laboratories Layered Space-Time. First, we address the unitary matrix of the underwater acoustic channel by LDLHdecomposition. Second, we order the detection sequence based on the permutation matrix. Third, we detail the implementation of interference cancelation and slice processing. Finally, we perform experiments for comparing the bit error ratio, energy consumption, processing delay, and complexity of the proposed algorithm with zero-forcing Vertical-Bell Laboratories Layered Space-Time, minimum mean square error Vertical-Bell Laboratories Layered Space-Time, and maximum likelihood Vertical-Bell Laboratories Layered Space-Time. Results indicate that our algorithm maintains bit error ratio and the processing delay to that of maximum likelihood Vertical-Bell Laboratories Layered Space-Time algorithm. However, it reduces the energy consumption, which achieves a good trade-off between performance and complexity. This work supports on constructing underwater acoustic networks of multiple-input multiple-output Vertical-Bell Laboratories Layered Space-Time system.