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PT Perkebunan Nusantara VIII (PTPN VIII) is a State-Owned Enterprise (BUMN). It operates in the plantation sector. The leading commodity is tea. The demand for tea produced by PTPN VIII is increasing. Thus, planning tea production is necessary. One of the production planning efforts is through forecasting based on previous data. Tea production data is time-series data. It contains seasonal elements and is dependent on other locations. We will analyze data with these criteria using space-time models, one of which is vector autoregressive (VAR). VAR models the relationship between observations on certain variables at one time. It also models the observation of the variable itself at previous times. Additionally, VAR models the relationship between observations and other variables at previous times. This paper explains how to forecast tea production. It uses the reconstituted VAR and Seasonal Autoregressive Moving Average (SARIMA) models. The results showed that the reconstituted VAR model was better than the SARIMA model in predicting tea production. The tea production prediction was at the Sedep and Santosa plantations in Bandung Regency.

The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach’s principle. We discuss Mach’s principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach’s principle holds and that there is a fundamental relation between the gravitational constant G and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven.

This study presents a novel approach for modeling unsaturated flow using deep neural networks (DNNs) integrated with spacetime radial basis functions (RBFs). Traditional methods for simulating unsaturated flow often face challenges in computational efficiency and accuracy, particularly when dealing with nonlinear soil properties and complex boundary conditions. Our proposed model emphasizes the capabilities of DNNs in identifying complex patterns and the accuracy of spacetime RBFs in modeling spatiotemporal data. The training data comprise the initial data, boundary data, and radial distances used to construct the spacetime RBFs. The innovation of this approach is that it introduces spacetime RBFs, eliminating the need to discretize the governing equation of unsaturated flow and directly providing the solution of unsaturated flow across the entire time and space domain. Various error evaluation metrics are thoroughly assessed to validate the proposed method. This study examines a case where, despite incomplete initial and boundary data and noise contamination in the available boundary data, the solution of unsaturated flow can still be accurately determined. The model achieves RMSE, MAE, and MRE values of 10−4, 10−3, and 10−4, respectively, demonstrating that the proposed method is robust for solving unsaturated flow in soils, providing insights beyond those obtainable with traditional methods.

A revived figure of teenage Albert Einstein is confronted at the threshold of the second millennium with a problem of a graphical likeness of the Lambert W function-based cosmological equations to a logarithmic-exponential discontinuous function that he has just plotted. To puzzle the issue out his mind is put onto an imaginary mathematical-philosophical-physical trail ride around the Universe. Euler’s identity that he invited to ride pillion on his Pegasus of Imagination spanks the cavalier’s horse to carry him on wings of Leibniz’ zero-nothingness unity-infiniteness array towards a non-Euclidean landscape of novel cosmological equations – which describe behaviour of principal cosmological parameters as an exclusive function of the scale factor. Zero, unity, p, and Euler’s number become in the rider’s eyes a quaternion of linesmen – and the imaginary unit the one who as a chief referee opens and controls on the space-time playground a collective mass-energy game. And while the young cavalier observes from a horseback of his mount that within the playground expansion the cosmic match is running into the order of timelessness and spacelessness the Universe with all of its ever existing forms and events, thoughts and memories, unveils to him its all-encompassing face of eternity and immortality attributable to God.

The ontology behind quantum mechanics has been the subject of endless debate since the theory was formulated some 100 years ago. It has been suggested, at one time or another, that the objects described by the theory may be individual particles, waves, fields, ensembles of particles, observers, and minds, among many other possibilities. I maintain that these disagreements are due in part to a lack of precision in the use of the theory’s various semantic designators. In particular, there is some confusion about the role of representation, reference, and denotation in the theory. In this article, I first analyze the role of the semantic apparatus in physical theories in general and then discuss the corresponding ontological implications for quantum mechanics. Subsequently, I consider the extension of the theory to quantum fields and then analyze the semantic changes of the designators with their ontological consequences. In addition to the classical arguments to rule out a particle ontology in the case of non-relativistic quantum field theory, I show how the existence of black holes makes the proposal of a particle ontology in general spacetimes unfeasible. I conclude by proposing a provisional pluralistic ontology of fields and spacetime and discussing some prospects for possible future ontological economies.

In order to study the temporal and spatial occurrence law of coal mine roof accidents in construction operation and the interaction degree of construction operation in the spacetime, 171 roof accident investigation reports have been coded and analyzed to obtain the relationship between roof accident spacetime and construction operation. Based on the complex network theory, the construction operation coupling network in roof accidents based on spacetime was proposed and constructed. The degree centrality and edge weight were used to analyze the association strength between construction operation and spacetime, and the coupling degree of construction operation in roof accidents was calculated by grey relation analysis. The countermeasures for preventing roof accidents in coal mine construction were proposed. The results show that the erection of support and 9:00-10:00, maintenance support and 14:00-15:00, recovery of single hydraulic prop and coal mining face, maintenance support and mining roadway, bolt (cable) support and mining roadway heading face are strongly related in roof accidents. The average coupling degree based on spacetime is high for maintenance support, coal gangue removal, coal gangue or debris removal, pillar erection, shed erection and anchor bolt (cable) support in roof accidents.

This study introduces a deep neural network approach that utilizes radial basis functions (RBFs) to solve forward and inverse problems in the process of diffusion. The input layer incorporates multiquadric (MQ) RBFs, symbolizing the radial distance between the boundary points on the spacetime boundary and the source points positioned outside the spacetime boundary. The output layer is the initial and boundary data given by analytical solutions of the diffusion equation. Utilizing the concept of the spacetime coordinates, the approximations for forward and backward diffusion problems involve assigning initial data on the bottom or top spacetime boundaries, respectively. As the need for discretization of the governing equation is eliminated, our straightforward approach uses only the provided boundary data and MQ RBFs. To validate the proposed method, various diffusion scenarios, including forward, backward, and inverse problems with noise, are examined. Results indicate that the method can achieve high-precision numerical solutions for solving diffusion problems. Notably, only 1/4 of the initial and boundary conditions are known, yet the method still yields precise results.

In current physics there are two Natural constants with meanings that remain unresolved: the Cosmological and the Fine Structure constants. Both are related to the theory of relativity and quantum mechanics. Here we attempt to give meaning to each of these constants and the relationship that can exist between them by proposing a new system of units based on Spacetime Structure. We will extend this new concept to unsolved questions in physics and cosmology, as well as describing the process by which the Spacetime Structure premises were developed to provide a basis for our thesis that Spacetime is quantized in energy-linked equidistant vertices separating the Compton electron wavelength and time. Spacetime is an omni-tensional structure that contains the energy and mass composing the Universe. Within this structure atoms and photons undergo quantized movement from vertex to vertex, where the angle change between structural vertices produces the Spacetime curvature. We propose that the Fine Structure constant (α) is related to Spacetime Structure, and that physical properties of matter and energy can be translated to Structural or Spacetime Units, where Natural constants are described by mathematical relationships between the three pure numbers π, φ and α.

It has been shown that the theory of relativity can be applied physically to the functioning brain, so that the brain connectome should be considered as a four-dimensional spacetime entity curved by brain activity, just as gravity curves the four-dimensional spacetime of the physical world. Following the most recent developments in modern theoretical physics (black hole entropy, holographic principle, AdS/CFT duality), we conjecture that consciousness can naturally emerge from this four-dimensional brain connectome when a fifth dimension is considered, in the same way that gravity emerges from a ‘flat’ four-dimensional quantum world, without gravitation, present at the boundaries of a five-dimensional spacetime. This vision makes it possible to envisage quantitative signatures of consciousness based on the entropy of the connectome and the curvature of spacetime estimated from data obtained by fMRI in the resting state (nodal activity and functional connectivity) and constrained by the anatomical connectivity derived from diffusion tensor imaging.

We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. We establish a connection between the property of a vector field on a doubly warped product manifold and its components on the factor manifolds to be Killing or 2-Killing. We also prove that a Killing vector field on the doubly warped product gives rise to a Ricci soliton factor manifold if and only if it is an Einstein manifold. If a component of a Killing vector field on the doubly warped product is of a gradient type, then, under certain conditions, the corresponding factor manifold is isometric to the Euclidean space. Moreover, we provide necessary and sufficient conditions for a doubly warped product to reduce to a direct product. As applications, we characterize the 2-Killing vector fields on the doubly warped spacetimes, particularly on the standard static spacetime and on the generalized Robertson–Walker spacetime.

We demonstrate the emergence of an effective “time” axis in the ground state of a gauged rotational symmetry theory in four-dimensional Euclidean space. In so doing, we remove the necessity of Wick rotation to Lorentz spacetime, an arbitrary and sometimes ill-defined procedure, especially for gravity-related theories. We begin by adapting the Cho-Duan-Ge decomposition to the gauge theory of the four-dimensional rotational symmetry group SO(4), where it identifies the maximal Abelian subgroup SO(2)⊗SO(2) in a gauge covariant manner. We then find the one-loop effective theory to have a stable condensate of monopoles corresponding to the reduction of SO(4) symmetry to SO(2)⊗SO(2). The construction of the condensate ensures that the four-dimensional spatial direction of its field strength must coincide with that of this embedding, and that a magnetic potential must be worked against to divert a trajectory away from this direction. Indeed, movement along this direction represents minimal potential energy. We take it to be the time direction. The gauge-dependent nature of the condensate is such that different gauge choices may lead to different time axes and we show on very general grounds that these different coordinate systems must be relatable by transformations of Lorentz form.

This article introduces a new boundary-type meshless method designed for solving axisymmetric transient groundwater flow problems, specifically for aquifer tests and estimating hydraulic properties. The method approximates solutions for axisymmetric transient groundwater flow using basis functions that satisfy the governing equation by solving the inverse boundary value problem in the spacetime domain. The effectiveness of this method was demonstrated through validation with the Theis solution, which involves transient flow to a well in an infinite confined aquifer. The study included numerical examples that predicted drawdown at various radial distances and times near pumping wells. Additionally, an iterative scheme, namely, the fictitious time integration method, was employed to iteratively determine the hydraulic properties during the pumping test. The results indicate that this approach yielded highly accurate solutions without relying on the conventional time-marching scheme. Due to its temporal and spatial discretization within the spacetime domain, this method was found to be advantageous for estimating crucial hydraulic properties, such as the transmissivity and storativity of an aquifer.

The principle of mental gravity contends that the mind uses physical gravity as a mental model or simulacrum to express the relation between the inner self and the outer world in terms of “UP”-ness and “DOWN”-ness. The simulation of increased gravity characterises a continuum of mental gravity which states includes depression as the paradigmatic example of being down, low, heavy, and slow. The physics of gravity can also be used to model spacetime curvature in depression, particularly gravitational time dilation as a property of MG analogous to subjective time dilation (i.e., the slowing of temporal flow in conscious experience). The principle has profound implications for the Temporo-spatial Theory of Consciousness (TTC) with regard to temporo-spatial alignment that establishes a “world-brain relation” that is centred on embodiment and the socialisation of conscious states. The principle of mental gravity provides the TTC with a way to incorporate the structure of the world into the structure of the brain, conscious experience, and thought. In concert with other theories of cognitive and neurobiological spacetime, the TTC can also work towards the “common currency” approach that also potentially connects the TTC to predictive processing frameworks such as free energy, neuronal gauge theories, and active inference accounts of depression. It gives the up/down dimension of space, as defined by the gravitational field, a unique status that is connected to both our embodied interaction with the physical world, and also the inverse, reflective, emotional but still embodied experience of ourselves.

The hole argument has become one of the main issues in the philosophy of space-time after the article by Earman and Norton (1987), according to which a certain version of substantivalism (manifold substantivalism) cannot be defended because it brings about to a radical indeterminism. In this article, we try to show that, first, the naming of manifold substantivalism is not appropriate since as some philosophers have said, manifold points cannot be considered to have an independent identity. Second, with a commitment to ontic structural realism, it is possible to offer a proper understanding of manifold substantivalism, which according to the hole argument, does not lead to the radical indeterminism. As a result, the hole argument does not arise, simply. Thus, the last point is that the fact that structural realism is able to solve the problem of the hole argument can itself be seen as considerable evidence in favor of this philosophical position, and thus, the degree of its confirmation goes up.

A model of spacetime is presented. It has an extension to five dimensions, and in five dimensions the geometry is the dual of the Euclidean geometry w.r.t. an arbitrary positive-definite metric. Dually flat geometries are well-known in the context of information geometry. The present work explores their role in describing the geometry of spacetime. It is shown that the positive-definite metric with its flat 5-d connection can coexist with a pseudometric for which the connection is that of Levi–Civita. The 4-d geodesics are characterized by five conserved quantities, one of which can be chosen freely and is taken equal to zero in the present work. An explicit expression for the parallel transport operators is obtained. It is used to construct a pseudometric for spacetime by choosing an arbitrary possibly degenerate inner product in the tangent space of a reference point, for instance, that of Minkowski. By parallel transport, one obtains a pseudometric for spacetime, the metric connection of which extends to a 5-d connection with vanishing curvature tensor. The de Sitter space is considered as an example.

All differences between the role of space and time in nature are explained by proposing principles in which none of the spacetime coordinates has an a priori special role. Spacetime is treated as a non-dynamical manifold, with a fixed global RD topology. The dynamical theory of gravity determines only the metric tensor on a fixed manifold. All dynamics is treated as a Cauchy problem, so it follows that one coordinate takes a special role. It is proposed that any boundary condition that is finite everywhere leads to a solution which is also finite everywhere. This explains the (1,D−1) signature of the metric, the boundedness of energy from below, the absence of tachyons, and other related properties of nature. The time arrow is explained by proposing that the boundary condition should be ordered. The quantization is considered as a boundary condition for field operators. Only the physical degrees of freedom are quantized.

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements (which must include initial conditions), identifies four possible options for a Theory of Everything. Quotes from prominent physicists express divergent views on each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery.

We introduce two-dimensional space plus time (2D+1) structure and numerically investigate it using a developed multilayer simulation framework, for the first time. The new structure is consisting of crossed grating with time-varying permittivity which is inspired from 1D+1. In this regard, we extend Fourier Modal Method (FMM) in a general approach for spacetime multilayer states. Our proposed framework is fast, robust, and powerful compared to various finite difference methods. We use the scattering matrix technique to develop the proposed spacetime simulation method for multilayer structures using a non-uniform stack of layers. The method is perfectly suitable to investigate the spatiotemporal effects of surfaces/metasurfaces which covers both the transverse electric and magnetic (TE & TM) polarizations. The results show more freedom to control the optical outcomes of the multilayer considering two spatial periodicities in addition to the modulation frequency to reach nonreciprocity as one of the main consequences of the proposed structure. Moreover, we investigate the condition and limitation of breaking the Lorentz rule for spacetime structures. 2D+1 structure is more controllable than the 1D+1 due to its greater ability to adjust spatial manipulation in addition to temporal variations to reach nonreciprocity applications, digital coding, beam steering, etc.

In this study, a radical hypothesis concerning the wave-particle duality exhibited by extremely small objects in nature is explored by developing a Planck lattice model of space–time that grapples with the uncertain dynamic quantum structure of space–time at the Planck scale. Upon applying the Planck lattice model to two notable experiments that most clearly demonstrate the essence of wave-particle duality, one immediately finds that it successfully shows in a relatively straightforward and physically consistent manner how parcels of matter and energy, i.e., electrons and photons, respectively, can behave like waves. The heuristic concepts regarding the underlying structure of space–time contained herein are intended to show the classical particle description of matter and energy as fundamental, while at the same time doing away with the widely held notion of a continuous space–time.

This is a comprehensive review of new developments in entropic gravity in light of the Relativistic Transactional Interpretation (RTI). A transactional approach to spacetime events can give rise in a natural way to entropic gravity (in the way originally proposed by Eric Verlinde) while also overcoming extant objections to that research program. The theory also naturally gives rise to a Cosmological Constant and to Modified Newtonian Dynamics (MOND) and thus provides a physical explanation for the phenomena historically attributed to ‘dark energy’ and ‘dark matter’.

● Phenomenon of Research: Recent term (spacetime) and this term is not new, but he appeared with zhoraalm peerless genius impact in our lives so far with his theories and sisal affects us several years to come, the world is ' Einstein and his theory of relativity, and may collect the time and place of the movement in one term is ' space ' was For the term close connection and basic with everything in our lives and his close relationship with industrial design product design, where everything is doing better with time, and the time since the beginning of time influence our life, and that is what petitioners would explain search. ● Claim of Research: Claims that there is a close relationship between factor (time) ' fourth dimension ' and industrial design products to detect this relationship will improve and develop product design. Of Research: Objective● Detect relationship between the fourth dimension (time) and designing products which contribute to improve and develop the design process, clarify and detect four-dimensional techniques and add it at the stage of product and determine design alternatives. of Research:Problematic● There is a relationship between time and product and are opaque relationship need to clarify and prove with evidence, and that there were four-dimensional techniques techniques rely on ' time ' featured related product design almost a fantasy. What are those techniques and how pragmatism in the process showing and modeling product. of Research:Methodology ● Exploratory curriculum. ● Plan of Research: To prove the prosecution must follow a plan to reach the goal: human thinking when faced with problematic, if some information concerning problematic the seeker based on this information, and more may be required to reach the unknown elements in problematic, and pass on this in the language of logic by saying: the thinker Moving from the introductions to the results, this is inferred. So the conclusion in General is a mental process which is done by her transition from the unknown to the known, you must first identify the date when the term ' space '.

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.

This paper looks at several key motivations behind the prisoner of time objection and a view against which it is leveled, the Oxford School of divine temporality, with respect to the Christian God. Shared between these opposing views are concerns for divine freedom and sovereignty. While the objection, coming from divine atemporalists, has in its background a concern for the creator–creature distinction, the Oxford School prizes the authenticity of temporal God–talk in the Scriptures and the coherency of human God–talk more generally. By following these motivations closely in conversation with M–theory discussions about the nature of time as a dimension of spacetime, I propose a new model of God’s relation to time called transcendent temporality. In it, God is transcendently present in our temporal dimension, so that he is temporal but experiences our time differently than we do. Moreover, God has his own time which is distinct from but correlated to our time. God, on this view, is temporal, but in a way that he can experience succession in different ways than our one–directional and linear experience of succession. I conclude by unpacking some implications of this model and addressing possible objections.

Considering that the propagation speed of action potentials in the brain connectome has a finite limit and that present is ill-defined in the brain we apply concepts borrowed from the theories of special and general relativity to introduce the view that time and space are tightly blended in the brain. It is shown that the brain functional and structural features can be unified through a combined brain “spacetime”. This 4-dimensional brain spacetime presents a functional curvature generated by brain activity, in a similar way gravitational masses give our 4-dimensional Universe spacetime its curvature. After laying its foundations and developing this framework using a relativistic pseudo-diffusion model of neural propagation, we explore how this whole-brain framework may shed light on brain functional features and dysfunction phenotypes (clinical expression of diseases) observed in some neuropsychiatric and consciousness disorders. Statement of Significance: Because action potentials in the brain connectome propagate with a finite velocity limit, simultaneity across brain nodes is only relative. A new concept is emerging where time and space in the brain, as in the Universe, are tightly mingled through a combined “spacetime”. This 4-dimensional spacetime merging brain structure and function presents a curvature generated by brain activity, in a similar way gravitational masses give our Universe spacetime its curvature, driving activity flow within the brain.

Abstract We combine the asynchronous spacetime discontinuous Galerkin (aSDG) method, an interfacial-damage fracture model, and a dynamic contact model to simulate dynamic fracture and crack closure in brittle materials. The contact model enforces specialized Riemann solutions for bonded, separation, slip and stick conditions while preserving elastodynamic characteristic structure across fracture interfaces. Powerful adaptive spacetime meshing tracks dynamic evolution of fracture-surface networks and captures moving solution features. We present numerical examples to demonstrate the model’s ability to reveal fine details of fracture response in problems that range from dynamic crack initiation, growth, closure, and arrest along a pre-defined planar path to fragmentation of rock by an explosively loaded wellbore with stochastic nucleation, free propagation, and coalescence of fracture surfaces.

Symmetry (and group theory) is a fundamental principle of theoretical physics. Finite symmetries, continuous symmetries of compact groups, and infinite-dimensional representations of noncompact Lie groups are at the core of solid physics, particle physics, and quantum physics, respectively. The latter groups now play an important role in many branches of mathematics. In more recent years, we have been faced with the impact of topological quantum field theory (TQFT). Topology and symmetry have deep connections, but topology is inherently broader and more complex. While the presence of symmetry in physical phenomena imposes strong constraints, topology seems to be related to low-energy states and is very likely to provide information about the different dynamical trajectories and patterns that particles can follow. For example, regarding the relationship of topology to low-energy states, Hodge’s theory of harmonic forms shows that the zero-energy states (for differential forms) correspond to the cohomology. Regarding the relationship of topology to particle trajectories, a topological knot can be seen as an orbit with complex properties in spacetime. The various deformations or embeddings of the knot, performed in low or high dimensions, allow defining different equivalence classes or topological types, and interestingly, it is possible from these types to study the symmetries associated with the deformations and their changes. More specifically, in the present work, we address two issues: first, that quantum geometry deforms classical geometry, and that this topological deformation may produce physical effects that are specific to the quantum physics scale; and second, that mirror symmetry and the phenomenon of topological change are closely related. This paper was aimed at understanding the conceptual and physical significance of this connection.

We propose a new event ontology of the world, which is part of a general approach to philosophy based on combining ideas from science, ontology, and the philosophy of nature. While the position advocated here is grounded in science and philosophy, it attempts to move beyond each of them by devising and exploring a series of technical (naturalized or naturalistic) ontological concepts such as Interconnectedness, the Whole, the Global, Chaos, the event assemblage, and Nonspace. A central theme in our event ontology is the mapping out of a fundamental critique of the theory of the organism and organization, especially when the latter two are viewed as processes in spacetime. In particular, and following earlier leads, we criticize the spacetime doctrine by arguing that it is not ontologically fundamental, where we suggest its replacement by more primordial naturalized ontological concepts of space such as ontospace and Nonspace. The event ontology of nature can be considered a radical alternative attitude toward the relation between the human and nature, an attitude, in fact, that has been repeatedly explored, though under very different headings, by numerous scattered thinkers throughout the history of ideas. We examine some of the past thinkers who contributed to this general but still incoherent body of thought, including Leibniz, Heidegger, Simondon, Ruyer, Deleuze, Whitehead, and Guattari. The goal of this article is to provide a condensed high-level view on this very complex and still evolving subject intended for a large audience, not necessarily only philosophers, but also scientists, mathematicians, technologists, theologians, sociologists, artists, and psychologists.

In this review article, the study of the development of relativistic cosmology and the introduction of inflation in it as an exponentially expanding early phase of the universe is carried out. We study the properties of the standard cosmological model developed in the framework of relativistic cosmology and the geometric structure of spacetime connected coherently with it. The geometric properties of space and spacetime ingrained into the standard model of cosmology are investigated in addition. The big bang model of the beginning of the universe is based on the standard model which succumbed to failure in explaining the flatness and the large-scale homogeneity of the universe as demonstrated by observational evidence. These cosmological problems were resolved by introducing a brief acceleratedly expanding phase in the very early universe known as inflation. The cosmic inflation by setting the initial conditions of the standard big bang model resolves these problems of the theory. We discuss how the inflationary paradigm solves these problems by proposing the fast expansion period in the early universe. Further inflation and dark energy in fR modified gravity are also reviewed.

The concept of spacetime has long been used in physics to refer to models that integrate 3D space and time as a single 4D continuum. We argue in this paper that it is also advantageous to use this concept in a practical geographic context by realizing a true 4D model, where time is modeled and implemented as a dimension in the same manner as the three spatial dimensions. Within this paper we focus on 4D vector objects, which can be implemented using dimension-independent data structures such as generalized maps. A 4D vector model allows us to create and manipulate models with actual 4D objects and the topological relationships connecting them, all of which have a geometric interpretation and can be constructed, modified, and queried. In this paper we discuss where such a 4D model fits with respect to other spatiotemporal modeling approaches, and we show concretely how higher-dimensional modeling can be used to represent such 4D objects and topological relationships. In addition, we explain how the 4D objects in such a system can be created and manipulated using a small set of implementable operations, which use simple 3D space and 1D time inputs for intuitiveness and which modify the underlying 4D model indirectly.

Often times the language of mathematics is used to formulate physical theories. For example, as in this paper, while Minkowski space or the theory of special relativity were studying, their formulation was given by means of mathematical methods. In this manuscript, we study spacelike normal curves lying entirely in the 2-dimensional and 3-dimensional lightlike cone. In particular, some related theorems and definitions are also given. The study of representations of spacelike normal curves in the lightlike cone has led to the existence of different areas of mathematics and physics.

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts—instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.

Space is something. Space inherently contains laws of nature: universal rules (mathematics, space dimensions, types of forces, types of fields, and particle species), laws (relativity, quantum mechanics, thermodynamics, and electromagnetism) and symmetries (Lorentz, Gauge, and symmetry breaking). We have significant knowledge about these laws of nature because all our scientific theories assume their presence. Their existence is critical for developing either a unique theory of our universe or more speculative multiverse theories. Scientists generally ignore the laws of nature because they “are what they are” and because visualizing different laws of nature challenges the imagination. This article defines a conceptual model separating space (laws of nature) from the universe’s energy source (initial conditions) and expansion (big bang). By considering the ramifications of changing the laws of nature, initial condition parameters, and two variables in the big bang theory, the model demonstrates that traditional fine tuning is not the whole story when creating a universe. Supporting the model, space and “nothing” are related to the laws of nature, mathematics and multiverse possibilities. Speculation on the beginning of time completes the model.

Physicists usually admit a rather naive concept of physical reality: it is the object they are investigating using experiments understood as actions in the real world. In theoretical physics, the object of investigation is not the real world itself but its mathematical description which is considered as describing physical reality as exactly as possible. I present arguments from philosophy of science and from recent work in the theory of gravitational physics which indicate a possibility to defend also antirealistic views, and clarify in which sense both standpoints can be viable.

The Fundamental U-Theory of Time (Part 1) is an original theory that aims to unravel the mystery of what exactly is ‘time’. To date very few explanations, from the branches of physics or cosmology, have succeeded to provide an accurate and comprehensive depiction of time. Most explanations have only managed to provide partial understanding or at best, glimpses of its true nature. The U-Theory uses ‘Thought Experiments’ to uncover the determining characteristics of time. In part 1 of this theory, the focus is not on the mathematics as it is on the accuracy of the depiction of time. Moreover, it challenges current views on theoretical physics, particularly on the idea of ‘time travel’. Notably, it is a theory seeking to present a fresh approach for reviewing Einstein’s Theory of Relativity, while unlocking new pathways for upcoming research in the field of physics and cosmology.

Without the mass-energy equivalence available on Minkowski spacetime M, it is not possible on 4-dimensional non-relativistic Galilei/Newton spacetime G to combine 3-momentum and total mass-energy in a single tensor object. However, given a fiducial frame, it is possible to combine 3-momentum and kinetic energy into a linear form (particle) or (1,1) tensor (continuum) in a manner that exhibits increased unity of classical mechanics on flat relativistic and non-relativistic spacetimes M and G. As on M, for a material continuum on G, the first law of thermodynamics can be considered a consequence of a unified dynamical law for energy-momentum rather than an independent postulate.

Various experimentally verified values of physical parameters indicate that the universe evolves close to the topological phase of exotic smoothness structures on R 4 and K3 surface. The structures determine the α parameter of the Starobinski model, the number of e-folds, the spectral tilt, the scalar-to-tensor ratio and the GUT and electroweak energy scales, as topologically supported quantities. Neglecting exotic R 4 and K3 leaves these free parameters undetermined. We present general physical and mathematical reasons for such preference of exotic smoothness. It appears that the spacetime should be formed on open domains of smooth K 3 # C P 2 ¯ at extra-large scales possibly exceeding our direct observational capacities. Such potent explanatory power of the formalism is not that surprising since there exist natural physical conditions, which we state explicitly, that allow for the unique determination of a spacetime within the exotic K3.

The debate on the ontological status of spacetime in General Relativity has historically seen two principal philosophical contenders: substantivalism, roughly the view that holds that spacetime exists apart from the material contents of the universe, and relationism, the doctrine that spacetime does not exist, i.e., it is a mere abstract web of spatiotemporal relations among bodies. This dispute, however, has rarely been fought on a cosmological battlefield. In this paper an attempt in this direction is made. The question at issue is the following: is there any feature of our universe that requires or is best explained in terms of a substantival space? I claim that there is indeed: the expansion of the universe, perhaps the most important phenomenon in cosmology, can play such a role.

There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.

Ted Sider argues that nihilism about objects is incompatible with the metaphysical possibility of gunk and takes this point to show that nihilism is flawed. I shall describe one kind of nihilism able to answer this objection. I believe that most of the things we usually encounter do not exist. That is, I take talk of macroscopic objects and macroscopic properties to refer to sets of fundamental properties, which are invoked as a matter of linguistic convention. This view is a kind of nihilism: it rules out the existence of objects; that is, from an ontological point of view, there are no objects. But unlike the moderate nihilism of Mark Heller, Peter van Inwagen and Trenton Merricks that claims that most objects do not exist, I endorse a radical nihilism according to which there are no objects in the world, but only properties instantiated in spacetime. As I will show, radical nihilism is perfectly compatible with the metaphysical possibility of gunk. It is also compatible with the epistemic possibility that we actually live in a gunk world. The objection raised by Ted Sider only applies to moderate nihilism that admits some objects in its ontology.

The main aim of this paper is to provide an interpretative application of Józef Życiński’s philosophical work. I claim that one can find in Życiński’s thought criteria for evaluating certain positions which use platonistic concepts in order to solve specific problems in the context of philosophy of physics, especially philosophy of spacetime. After reconstructing Życiński’s philosophy, I use the derived criteria to evaluate positions of Howard Stein’s and Max Tegmark’s. I conclude that, according to criteria taken from Życiński’s philosophy, the former’s views are more plausible, and so create a better starting point in developing a platonistic structuralist position.

The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.

Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank–Shor–Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Our protocol includes decoding whose gate complexity scales linearly with the number of causal diamonds. Our thorough framework for quantum summoning enables full specification of the protocol, including spatial and temporal implementation and costs, which enables quantum summoning to be a well posed protocol for relativistic quantum communication purposes.

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.

The electromagnetic implementation of cloaking, the hiding of objects from sight by diverting and reassembling illuminating electromagnetic fields has now been with us ten years, while the notion of hiding events is now five. Both schemes as initially presented neglected the inevitable dispersion that arises when a designed medium replaces vacuum under transformation. Here we define a transformation design protocol that incorporates both spacetime transformations and dispersive material responses in a natural and rigorous way. We show how this methodology is applied to an event cloak designed to appear as a homogeneous and isotropic but dispersive medium. The consequences for spacetime transformation design in dispersive materials are discussed, and some parameter and bandwidth constraints identified.