Space-time Structure Research Articles

A benchmark of individual auto-regressive models in a massive fMRI dataset

Abstract Dense functional magnetic resonance imaging datasets open new avenues to create auto-regressive models of brain activity. Individual idiosyncrasies are obscured by group models, but can be captured by purely individual models given sufficient amounts of training data. In this study, we compared several deep and shallow individual models on the temporal auto-regression of BOLD time-series recorded during a natural video-watching task. The best performing models were then analyzed in terms of their data requirements and scaling, subject specificity, and the space-time structure of their predicted dynamics. We found the Chebnets, a type of graph convolutional neural network, to be best suited for temporal BOLD auto-regression, closely followed by linear models. Chebnets demonstrated an increase in performance with increasing amounts of data, with no complete saturation at 9 h of training data. Good generalization to other kinds of video stimuli and to resting-state data marked the Chebnets’ ability to capture intrinsic brain dynamics rather than only stimulus-specific autocorrelation patterns. Significant subject specificity was found at short prediction time lags. The Chebnets were found to capture lower frequencies at longer prediction time lags, and the spatial correlations in predicted dynamics were found to match traditional functional connectivity networks. Overall, these results demonstrate that large individual functional magnetic resonance imaging (fMRI) datasets can be used to efficiently train purely individual auto-regressive models of brain activity, and that massive amounts of individual data are required to do so. The excellent performance of the Chebnets likely reflects their ability to combine spatial and temporal interactions on large time scales at a low complexity cost. The non-linearities of the models did not appear as a key advantage. In fact, surprisingly, linear versions of the Chebnets appeared to outperform the original non-linear ones. Individual temporal auto-regressive models have the potential to improve the predictability of the BOLD signal. This study is based on a massive, publicly-available dataset, which can serve for future benchmarks of individual auto-regressive modeling.

Space–time characterization of ultrashort laser pulses: A perspective

The characterization of ultrashort laser pulses has significantly advanced beyond the standard spatial and temporal diagnostics to now include sophisticated spatio-temporal measurement techniques. In this perspective, we provide an overview of the current state of space–time characterization, discussing the theoretical foundations of ultrashort laser pulses, the various measurement techniques and their design trade-offs, and the challenges and opportunities for future development. We explore the extension of these techniques to different wavelength regimes and delve into the unique challenges posed by the characterization of polarization-structured beams. The potential for data-driven analysis to enhance the information extracted from the measurements is highlighted, along with the need for direct measurement of previously inaccessible field components, such as the longitudinal electric field in tightly focused beams. As these diagnostic tools continue to evolve, we anticipate a future where the intricate space–time structure of light can be analyzed on a routine basis, opening up new frontiers in ultrafast science and technology.

Darboux and generalized Darboux transformations for the fractional integrable derivative nonlinear Schrödinger equation

Analytical methods provide crucial mathematical insights into the stable solitary waves hidden in nonlinear phenomena. The nonlinear Schrödinger (NLS) equation is one of the most important typical integrable soliton models. From a mathematical perspective, the essence of the celebrated derivative NLS (DNLS) equation’s difference from the classical NLS equation lies in its cubic potential being differentiated once by the spatial variable and multiplied by the imaginary unit, which leads to the former having some characteristics that the latter cannot have. This paper extends the DNLS equation to the fractional integrable case with conformable derivative operators, and uses Darboux transformations (DTs) and generalized DT (GDT) to solve it exactly. Specifically, Lax pairs generating the fractional DNLS equation are first given. Based on the given Lax pairs, then the n-fold DTs and GDT for the fractional DNLS equation are derived. Some special exact solutions of the fractional DNLS equation are further obtained by employing the derived n-fold DTs and GDT. Finally, several novel space–time structures and dynamical evolutions of the obtained exact solutions are analyzed. This paper reveals through the DT and GDT methods that the double power-law fractional orders in the exact solutions of the fractional DNLS equation can be used to dominate the variable velocity propagation and anomalous diffusion in fractional dimensional media at different geometric scales.

Relativistic Consistency of Nonlocal Quantum Correlations.

What guarantees the "peaceful coexistence" of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.

Space-Time FEM for the Vectorial Wave Equation under Consideration of Ohm’s Law

Abstract The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods. In this paper, we will treat time as another space direction, which is the main idea of space-time methods. First, we will briefly discuss how exactly the vectorial wave equation is derived from Maxwell’s equations in a space-time structure, taking into account Ohm’s law. Then we will derive a space-time variational formulation for the vectorial wave equation using different trial and test spaces. This paper has two main goals. First, we prove unique solvability for the resulting Galerkin–Petrov variational formulation. Second, we analyze the discrete equivalent of the equation in a tensor product and show conditional stability, i.e., under a CFL condition. Understanding the vectorial wave equation and the corresponding space-time finite element methods is crucial for improving the existing theory of Maxwell’s equations and paves the way to computations of more complicated electromagnetic problems.

Theoretical Analysis of Moving Galaxies in the Large Scale Structure of SpaceTime

In this paper we will make further theoretical analysis for the validity of the accelerating universe based on General Relativity and three new problems of the standard model of the universe are presented from different perspectives. The first part, analyzed the explosion mechanism of the cosmic initial singularity and put forward a different view from the rest. It’s virtually impossible to start with a giant explosion, the big bang by now cosmologists had refined the idea. The second part devised a new model of the twin paradox. It’s one in which people have been consider to include both special and general relativity in the calculations to expose the counterintuitive weirdness of relativity theory. It seems to has a curious coincidence with the cat-a feline in a locked box that is both dead and alive until the box is opened-was a thought experiment devised by physicist Schr ö dinger. In part three the author makes determination on the cosmological deceleration parameter q0 by using mathematical derivation, and based on which to construct a thought experiment on cosmological redshift. It is needed to make a static model of the universe that both conforms to the Copernican principle and satisfies Hubble’s law and it’s possible to make us a fresh perspective and thought process.

Testing space-time non-commutativity with TianQin

The direct detection of gravitational waves offers a powerful tool to explore the nature of gravity and the structure of space-time. This paper focuses on the capabilities of space-based gravitational wave detectors in testing space-time non-commutativity. Our findings indicate that TianQin has the potential to impose constraints on the non-commutative scale at a sub-Planckian level using massive black hole binaries. Additionally, we have developed a pipeline tailored to this specific topic.

The Double-slit Experiment in The Six-dimensional Space-Time

Young's two-slit test can be interpreted over time. Classical events have a quantum behaviour over time. Based on the findings of this research, Quantum Phenomena have a classical interpretation. The role of time has been neglected in the understanding of quantum mechanics phenomena. By examining classical events over time, Quantum Phenomena were simulated. Entanglement, particle-wave phenomenon, etc. are intertwined in the space-time structure. The role of the arrow of time in solving physics problems can be considered.

Rotating kiselev black holes in f(R, T) gravity

Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the f(R, T) gravity framework using the revised Newman-Janis algorithmthe f(R, T) gravity-motivated rotating Kiselev black holes (FRKBH) with additional parameter quintessence parameter ω and state parameter γ, apart from mass M and spin a, which encompasses, as exceptional cases, Kerr (K = 0) and effective Kerr-Newman (K = Q 2) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the w for viable choices for the f(R, T) function. From the parameter space or domain of existence of black holes defined by a and γ for FKRBH, we discover that when a 1 < a < a 2, there is a critical value γ = γ E which corresponds to extreme value black holes portrayed by degenerate horizons. When a < a 1 (a > a 2), we encounter two distinct critical values γ = γ E1, γ E2 with γ E1 > γ E2 (or γ = γ E3, γ E4 with γ E3 > γ E4). We discuss the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters w and γ. This exploration is motivated by the remarkable effects of f(R, T) gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.

Testing the weak cosmic censorship conjecture in short haired black holes

The weak cosmic censorship conjecture is a hypothesis about the nature of event horizons and singularities during the formation of black holes. It posits that singularities are always enveloped by the event horizons of black holes, thereby preventing naked singularities from affecting the causal structure of spacetime. In this paper, we study the effect of rotating short haired black holes on the weak cosmic censorship conjecture. Discussion of whether the event horizons of a rotating short haired black hole is disrupted by studying incident neutral test particles and scalar fields. In the context of short haired black holes, when incident neutral test particles are considered for extreme and near extreme cases, our research results indicate that neutral test particles can destroy the event horizons of short haired black holes, violating the weak cosmic censorship conjecture. In the case of scalar field incidence in short haired black holes, for extreme situations, when the incident wave modes fall within the range of 12κM+βMκ<ωm<12Mκ+βMκ-12κ,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2\\kappa M+\\frac{\\beta }{M\\kappa }}<\\frac{\\omega }{m}<\\frac{1}{2M\\kappa + \\frac{\\beta }{M\\kappa }-\\frac{1}{2\\kappa }},$$\\end{document} the results indicate that the event horizons of rotating short haired black holes is disrupted. For near extreme cases, the presence of hair allows for the disruption of the event horizons of rotating short haired black holes, as indicated by our results. Therefore, these conclusions are intriguing and will provide new insights for us to further understand the weak cosmic censorship conjecture and explore the properties of short haired black holes.

Observational signatures of charged rotating traversable wormhole: shadows and light rings with different accretions

In this work, we investigate the optical appearance of qualitatively new observational features of accretion disk images around the charged rotating traversable wormhole (TWH) space-time for different spin, throat, and charge values. To accomplish this, we first consider the Hamilton–Jacobi method to derive the geodesic equations for the motion of photons and study the effects of parameters on the photon orbit in the observer’s sky. We found that each parameter affects the size and shape of the wormhole (WH) shadow and flatness is observed in the shadow because of spin and other parameters. To produce shadow images of sufficient visual quality but within manageable computational times, we adopt the ray-trace procedure and characterize the significant features of light trajectories on the observer’s screen, depending on the interaction between the space-time structure and the accretion disk. In addition, we consider the static spherically symmetric accretion flow model to observe the specific intensity around the traversable WH space-time geometry. It is found that the intensity and positions of the photon ring vary with respect to the involved parameters. In future observation, this type of study may provide a fertile playground to test the nature of compact objects, specifically the WH in the strong-field regime.

Singular space-times with bounded algebraic curvature scalars

We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the analysis of such scalars to assess the regularity of a given space-time. This conclusion follows from the analysis of incomplete geodesics within the internal region of asymmetric wormholes supported by scalar matter which arise in two distinct metric-affine gravity theories. These wormholes have bounded algebraic curvature scalars everywhere, which highlights that their finiteness does not prevent the emergence of pathologies (singularities) in the geodesic structure of space-time. By analyzing the tidal forces in the internal wormhole region, we find that the angular components are unbounded along incomplete radial time-like geodesics. The strength of the singularity is determined by the evolution of Jacobi fields along such geodesics, finding that it is of strong type, as volume elements are torn apart as the singularity is approached. Lastly, and for completeness, we consider the wormhole of the quadratic Palatini theory and present an analysis of the tidal forces in the entire space-time.

Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics

We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing four-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by gluing such four-frusta in spatial and temporal direction, we find causality violations if the sub-cells connecting spatial slices are spacelike. A Wick rotation to the Euclidean theory can be defined globally by a complexification of the variables and an analytic continuation of the action. Introducing a discrete free massless scalar field, we study its equations of motion and show that it evolves monotonically. Furthermore, in a continuum limit, we obtain the equations of a homogeneous scalar field on a spatially flat Friedmann background. Vacuum solutions to the causally regular Regge equations are static and flat and show a restoration of time reparametrisation invariance. In the presence of a scalar field, the height of a frustum is a dynamical variable that has a solution if causality violations are absent and if an inequality relating geometric and matter boundary data is satisfied. Edge lengths of cubes evolve monotonically, yielding a contracting or an expanding branch of the Universe. In a small deficit angle expansion, the system can be deparametrised via the scalar field and a continuum limit of the discrete theory can be defined which we show to yield the relational Friedmann equation. These properties are obstructed if higher orders of the deficit angle are taken into account. Our results suggest that the inclusion of timelike sub-cells is necessary for a causally regular classical evolution in this symmetry restricted setting. Ultimately, this works serves as a basis for forthcoming investigations on the cosmological path integral within the framework of effective spin foams.

Electromagnetic entrapment in gravity

We derive specific properties of electromagnetism when gravitational effects are not negligible and analyze their impact on new physics at the horizons of black holes. We show that a neutral configuration of charges in a region of high redshift, characterized by a large gtt, produces a highly localized electromagnetic field that vanishes just beyond that region. This phenomenon implies the existence of extensive families of spacetime structures generated by electromagnetic degrees of freedom that are as compact as black holes. We construct neutral bound states of extremal black holes in four dimensions and in five dimensions, where one direction is compact. These geometries are indistinguishable from a neutral black hole, referred to as distorted Schwarzschild, except in an infinitesimal region near its horizon where the entrapped electromagnetic structures start to manifest. The five-dimensional solutions satisfy various criteria for describing black hole microstructure: they increase in size with the Newton constant, are as compact as the Schwarzschild black hole, and have an entropy that scales like M2.

Manipulating the McGinty Equation to Create Stable Micro-Wormholes

Fractal wormholes represent a novel theoretical concept at the intersection of classical physics and quantum mechanics. This article introduces the ΨFractal equation, a theoretical construct that seeks to describe these hypothetical entities. The equation integrates fundamental constants with parameters like mass, charge, and fractal dimension, suggesting intriguing properties and interactions with the cosmos. The McGinty equation, Ψ(x,t) = ΨQFT(x,t) + ΨFractal(x,t,D,m,q,s), can be used to help explain the fractal structure of space-time. The ΨFractal(x,t,D,m,q,s) term in the equation represents the fractal properties of space-time, where D represents the fractal dimension, m represents the mass of the system, q represents the charge, and s represents the spin. By manipulating the values of these variables, scientists can create a stable micro-wormhole in a controlled environment. The fractal dimension D, for example, can be used to control the size and stability of the wormhole. A higher fractal dimension value would result in a larger and more stable wormhole, while a lower value would result in a smaller and less stable wormhole. The mass of the system, represented by the variable m, can also play a role in the stability of the wormhole. A higher mass would result in a more stable wormhole, while a lower mass would result in a less stable wormhole. The charge and spin of the system, represented by the variables q and s, respectively, can also have an effect on the stability of the wormhole. A higher charge would result in a more stable wormhole, while a lower charge would result in a less stable wormhole. Similarly, a higher spin would result in a more stable wormhole, while a lower spin would result in a less stable wormhole. By manipulating the values of these variables, scientists can create a stable micro-wormhole in a controlled environment. This leads to advancements in fractal engine technology which in turn leads to the development of practical applications for faster-than-light travel, such as faster communication and interstellar exploration. For example, if we consider the equation for a fractal wormhole, ΨFractal(x,t,D,m,q,s) = [(G * m^2 * D) / (h * q * s)] * e^-(D * m * x^2) Where G is the gravitational constant, h is the Planck constant, and x is distance. By manipulating the value of D, m, q and s, scientists can control the size and stability of the wormhole, which in turn can be used for faster than light communication and interstellar travel.

Merger estimates for a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories* *Supported by the National Key Research and Development Program of China (2020YFC2201400), and the National Natural Science Foundation of China (12275079, 12035005, 12275078)

We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories. In the ringdown stage of the black hole merger, for the prograde orbit, the real part of the quasinormal modes decreases with an increase in the disformal parameter, and the imaginary part also decreases, except in the Kerr case for a large spin parameter. However, for the retrograde orbit, the real part increases with an increase in the disformal parameter, and the imaginary part always decreases with it. For the approximate final spin, regardless of an equal spin, unequal spin, or generic spin configuration merger, the final black hole spin always increases with an increase in the disformal parameter. Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger, which suggests the differences between these two spacetime structures.

Pion Interferometry with Lévy-Stable Sources in sNN = 200 GeV Au + Au Collisions at STAR

Measurements of femtoscopic correlations in high-energy heavy-ion collisions are used to unravel the space–time structure of the particle-emitting source (the quark–gluon plasma). Recent results indicate that the pion pair source exhibits a power law behavior and can be described well by a Lévy distribution. In this study, Lévy fits were applied to the measured one-dimensional two-pion correlation functions in Au + Au collisions at sNN = 200 GeV. The three extracted source parameters are the Lévy scale parameter, R, which relates to the size of the source; the correlation strength parameter, λ; and the Lévy exponent, α, which characterizes the power law tail of the source. In this paper, we report the current status of the analysis of the extracted Lévy source parameters and present their dependence on average transverse mass, mT, and on centrality.

Gödel’s Undecidability Theorems and the Search for a Theory of Everything

I investigate the question whether Gödel’s undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether a given theory is the final one or not. This is relevant for both canonical quantum gravity and string theory. Slightly elaborated version of a Prize winning essay awarded by the Kurt Gödel Circle of Friends Berlin with the support of the University of Wuppertal, first published in https://kurtgoedel.de/kurt-goedel-award-2023/

Spacetime geometry of acoustics and electromagnetism

Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The resulting extensions are geometrically complete and phase-invariant (i.e., dual-symmetric) formulations that span all five grades of spacetime, with dynamical potentials and measurable fields spanning complementary grades that are related by a spacetime vector derivative (i.e., the quantum Dirac operator). These complete representations correct the equations of motion, energy–momentum tensors, forces experienced by probes, Lagrangian densities, and allowed gauge freedoms, while making manifest the deep structural connections to relativistic quantum field theories. Finally, we discuss the implications of these corrections to experimental tests.

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.