Physical Space-time Research Articles

An extremely ultrathin flexible Huygens’s transformer

The current study aims to present the physical perception of a meta-surface energy harvester’s (MEH’s) design based on space-time physics of a traveling wave. Regarding the relation between the wave-velocity and field-impedance, the balance condition in Huygens’s meta-atoms is provided. Accordingly, it was demonstrated that MEH behaves as a transformer at far-field. It was observed that the location of the metallic-via is mimicked by the number of loop coils in the secondary of the transformer in the unit-cell. In addition, the impedance matching between the wave impedance in a lossless medium and MEH’s load was to be tuned by adjusting the size parameters of the unit-cell at a desired resonance frequency. For this purpose, the present study developed a simple design framework to achieve the resonance frequency at a more optimum pace based on surrogate modeling. The theoretical analyses are validated by the results of full-wave and circuit simulations. Finally, a recently developed flexible MEH was further extended to a multi-polarization structure using more compact cells. The fabricated flexible MEH has 10 × 10 number of deep subwavelength thick cells (≈0.004λ0), while traditional MEH was basically designed only to fit on the planar surface. The new design paves the way for the multi-polarized MEH to wrap around the cylindrical surface as a 2D-isotropic MEH. The results of the data analyses show that the simulation and experimental results enjoy an acceptable agreement.

Sensorimotor and interoceptive dimensions in concrete and abstract concepts.

Recent theories propose that abstract concepts, compared to concrete ones, might activate to a larger extent interoceptive, social and linguistic experiences. At the same time, recent research has underlined the importance of investigating how different sub-kinds of abstract concepts are represented. We report a pre-registered experiment, preceded by a pilot study, in which we asked participants to evaluate the difficulty of 3 kinds of concrete concepts (natural objects, tools, and food concepts) and abstract concepts (Philosophical and Spiritual concepts, PS, Physical Space Time and Quantity concepts, PSTQ, and Emotional, Mental State and Social concepts, EMSS). While rating the words, participants were assigned to different conditions designed to interfere with conceptual processing: they were required to squeeze a ball (hand motor system activation), to chew gum (mouth motor system activation), to self-estimate their heartbeats (interoception), and to perform a motor articulatory task (inner speech involvement). In a control condition they simply rated the difficulty of words. A possible interference should result in the increase of the difficulty ratings. Bayesian analyses reveal that, compared to concrete ones, abstract concepts are more grounded in interoceptive experience and concrete concepts less in linguistic experience (mouth motor system involvement), and that the experience on which different kinds of abstract and concrete concepts differs widely. For example, within abstract concepts interoception plays a major role for EMSS and PS concepts, while the ball squeezing condition interferes more for PSTQ concepts, confirming that PSTQ are the most concrete among abstract concepts, and tap into sensorimotor manual experience. Implications of the results for current theories of conceptual representation are discussed.

Improved existence for the characteristic initial value problem with the conformal Einstein field equations

We adapt Luk’s analysis of the characteristic initial value problem in general relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood of the set on which the data are given. In particular, we obtain existence of solutions along a narrow rectangle along null infinity which, in turn, corresponds to an infinite domain in the asymptotic region of the physical spacetime. This result generalises work by Kánnár on the local existence of solutions to the characteristic initial value problem by means of Rendall’s reduction strategy. In analysing the conformal Einstein equations we make use of the Newman–Penrose formalism and a gauge due to J. Stewart.

Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect

The main objective of this work is to present a theoretical proposal for an implementation of the $(2 + 1)$-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds; however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analogue of such a setting can in principle be implemented using the proposed waveguide setup.

K -essence emergent spacetime as a generalized Vaidya geometry

We establish a formal connection between the {\bf K}-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the {\bf K}-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the {\bf K}-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor derived from the emergent Einstein equation, restrictions are obtained on the functions characterizing the emergent metric for consistent identification with generalized Vaidya spacetimes. We discuss the possibility of dynamical horizons in the {\bf K-}essence emergent Vaidya spacetime. Admissible explicit black hole background metrics are discussed as examples.

Spinning gyroscope in an acoustic black hole: precession effects and observational aspects

The exact precession frequency of a freely-precessing test gyroscope is derived for a 2+1 dimensional rotating acoustic black hole analogue spacetime, without making the somewhat unrealistic assumption that the gyroscope is static. We show that, as a consequence, the gyroscope crosses the acoustic ergosphere of the black hole with a finite precession frequency, provided its angular velocity lies within a particular range determined by the stipulation that the Killing vector is timelike over the ergoregion. Specializing to the ‘Draining Sink’ acoustic black hole, the precession frequency is shown to diverge near the acoustic horizon, instead of the vicinity of the ergosphere. In the limit of an infinitesimally small rotation of the acoustic black hole, the gyroscope still precesses with a finite frequency, thus confirming a behaviour analogous to geodetic precession in a physical non-rotating spacetime like a Schwarzschild black hole. Possible experimental approaches to detect acoustic spin precession and measure the consequent precession frequency, are discussed.

Is a Deterministic and Local Interpretation of Quantum Mechanics Possible?… First Steps

Quantum states in superposition cannot be observed, suggesting that they merely embody information on possible measurement results. Yet, we think of them as describing physical systems that evolve in time according to given mathematical equations. Furthermore, evolution takes place in physical space-time, and local causality is imposed on space-time by Special Relativity (a sequence of cause and effect that constitutes a fundamental principle by which we think about and do scientific work).It is therefore strange that there is non–locality and violation of causality embedded in Quantum Mechanics. We try to give here a first step to see whether a deterministic and local interpretation is possible. We will show that Bell’s inequality is not conclusive about the non–local nature of Quantum Mechanics, in that there exists an interpretation of reality (which we put forward) which is local and in which Bell’s inequality cannot be derived. Assuming determinism and locality a new Bell-like inequality is derived, which is always satisfied by Quantum Mechanics and which allows for local hidden variables [1].

Similarity Structure and Emergent Properties

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this similarity-structure-based account of emergence applies to any science that represents its possibilia with (mathematical) models.

Type D conformal initial data

For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data giving rise to an initial data set for the Friedrich vacuum conformal equations. When will the data development with respect to the conformal equations of this set be a conformal extension of a type D solution? In this work we provide a set of necessary and sufficient conditions on a set of initial data for the conformal equations that guarantees that the data development of the conformal equations has a subset that is conformal to a vacuum type D solution of the Einstein’s equations. In particular we find the conditions under which this vacuum solution corresponds to the Kerr solution. Using our results we are able to show that there are no obstructions to extend the Petrov type of the physical spacetime to the unphysical spacetime if the conformal data are hyperboloidal.

General expansion of time transfer functions in optical spacetime

When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric. Additionally, an accurate modeling of the geodesic evolution of observable quantities (e.g., the range and the Doppler) requires us to know the reception or the emission time transfer functions. In the physical spacetime, these functions can be derived to any post-Minkowskian orders through a recursive procedure. In this work, we show that the time transfer functions can be determined to any order in Gordon's optical spacetime as well. The exact integral forms of the gravitational, the refractive, and the coupling contributions are recursively derived. The expression of the time transfer function is given within the post-linear approximation assuming a stationary optical spacetime covered with geocentric celestial reference system coordinates. The light-dragging effect due to the steady rotation of the neutral atmosphere of the Earth is found to be at the threshold of visibility in many experiments involving accurate modeling of the time and frequency transfers.

A C*-algebraic Approach to Interacting Quantum Field Theories

A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag–Kastler axioms, with insights gained in the perturbative approach to quantum field theory. Key ingredients are an appropriate version of Bogolubov’s relative S-operators and a reformulation of the Schwinger–Dyson equations. These are used to define for any classical relativistic Lagrangean of a scalar field a non-trivial local net of C*-algebras, encoding the resulting interactions at the quantum level. The construction works in any number of space-time dimensions. It reduces the longstanding existence problem of interacting quantum field theories in physical spacetime to the question of whether the C*-algebras so constructed admit suitable states, such as stable ground and equilibrium states. The method is illustrated on the example of a non-interacting field and it is shown how to pass from it within the algebra to interacting theories by relying on a rigorous local version of the interaction picture.

New Foundations for Branching Space-Times

The theory of branching space-times, put forward by Belnap (Synthese 92, 1992), considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the (local) possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle.

Peeling property and asymptotic symmetries with a cosmological constant

This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient [Formula: see text] when expanded as inverse powers of [Formula: see text] (where [Formula: see text] is the usual spherical radial coordinate, and [Formula: see text] is null infinity, [Formula: see text]) has coefficient [Formula: see text]. (2) In the absence of gravitational radiation (a conformally flat [Formula: see text]), the group of asymptotic symmetries is trivial, with no room for supertranslations.

Quasi-local energy with respect to de Sitter/anti-de Sitter reference

This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of surface Hamiltonians. The ground state for the gravitational energy is taken to be a reference configuration in the de Sitter (dS) or Anti-de Sitter (AdS) spacetime. This defines the quasi-local energy with respect to the reference spacetime and generalizes our previous definition with respect to the Minkowski spacetime. Through an optimal isometric embedding into the reference spacetime, the Killing fields of the reference spacetime are transplanted back to the surface in the physical spacetime to complete the definitions of quasi-local conserved quantities. We also compute how the corresponding total conserved quantities evolve under the Einstein equation with a cosmological constant.

О ненаблюдаемой онтологии

Two narratives – natural science and religious, intersect in the area of ​​unobserv­able ontology – an immaterial, transcendental, but real area that paradoxically exists outside and inside ordinary physical space-time. It is assumed that mathe­matical constructs, physical laws, physical constants, quantum objects, and even biological laws can be associated with this area. It is argued that physical laws are not invented by man, but are discovered, since they contain physical con­stants measured in special experimental works. Universal constants were not invented for reasons of convenience – physics accepts them as an inevitable con­sequence of the coincidence of the results of all special measurements. Observa­tional data are presented that indicate an extremely small change in fundamental constants or even their constancy over the entire time of the existence of the Uni­verse, although this interesting problem cannot be considered finally solved. The ontology of quantum objects is considered within the framework of Seval­nikov's polyiontic paradigm, according to which two modes are distinguished – potential and actual. The potential existence of quantum objects is described by the Schrödinger wave function, and the actual one appears during the transition from the spectrum of possible states to the only observable one. It is emphasized that potential being does not belong to the classical space, but is in an unobserv­able ontology. The observed state, on the contrary, is already in ordinary space – time and can be recorded by the device. This determines the existence of a spe­cial transcendental layer of reality, along with the material, which may indicate a certain duality in the structure of the Universe. Then it should be assumed that our Universe is not a universal, but a multiverse – a set of different worlds onto­logically having a different nature. In addition, the polyiontic paradigm leads to the idea that, at the quantum level, matter can be derived from information hid­den in an unobservable ontology.

Large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow

A numerical study is conducted to unveil the large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow at M∞ = 0.7. The numerical simulation allows us to acquire a high rate sampled unsteady volumetric dataset. This huge amount of spatial and temporal information is exploited in the Fourier space to visualize for the first time in physical space and at such a high Reynolds number (ReD = 1.2 × 106) the statistical signature of the helical structure related to the antisymmetric mode (m = 1) at StD = 0.18. The main hydrodynamic mechanisms are identified through the spatial distribution of the most energetic frequencies, i.e., StD = 0.18 and StD ≥ 3.0 corresponding to the vortex-shedding and Kelvin-Helmholtz instability phenomena, respectively. In particular, the dynamics related to the dimensionless shedding frequency is shown to become dominant for 0.35 ≤ x/D ≤ 0.75 in the whole radial direction as it passes through the shear layer. The spatial distribution of the coherence function for the most significant modes as well as a three-dimensional Fourier decomposition suggests the global features of the flow mechanisms. More specifically, the novelty of this study lies in the evidence of the flow dynamics through the use of cross-correlation maps plotted with a frequency selection guided by the characteristic Strouhal number formerly identified in a local manner in the flow field or at the wall. Moreover and for the first time, the understanding of the scales at stake is supported both by a Fourier analysis and a dynamic mode decomposition in the complete three-dimensional space surrounding the afterbody zone.

The Sagnac and Hafele–Keating experiments: Two keys to the understanding of space–time physics in the vicinity of the Earth

The role of preferred frames for light propagation and time dilation in the region of a massive, spherical, gravitating bodies, where according to general relativity, space–time curvature is described by the Schwarzschild metric equation, is discussed in the context of the Sagnac effect (for light propagation) and the Hafele–Keating experiment (for time dilation). Predictions for both translational and rotational motion relative to the preferred frame are calculated up to order [Formula: see text]. Different published theoretical calculations of the Sagnac effect are critically reviewed. The conflation in the literature of measured time differences in Sagnac experiments (a classical order [Formula: see text] effect) and time dilation (a relativistic order [Formula: see text] effect) are also discussed.

Towards an Observable Test of Noncommutative Quantum Mechanics

The conceptual incompatibility of spacetime in gravity and quantum physics implies the existence of noncommutative spacetime and geometry on the Planck scale. We present the formulation of a noncommutative quantum mechanics based on the Seiberg–Witten map, and we study the Aharonov–Bohm effect induced by the noncommutative phase space. We investigate the existence of the persistent current in a nanoscale ring with an external magnetic field along the ring axis, and we introduce two observables to probe the signal coming from the noncommutative phase space. Based on this formulation, we give a value-independent criterion to demonstrate the existence of the noncommutative phase space.

Finsler spacetime geometry in physics

Finsler geometry naturally appears in the description of various physical systems. In this review, I divide the emergence of Finsler geometry in physics into three categories: dual description of dispersion relations, most general geometric clock and geometry being compatible with the relevant Ehlers–Pirani–Schild axioms. As Finsler geometry is a straightforward generalization of Riemannian geometry there are many attempts to use it as generalized geometry of spacetime in physics. However, this generalization is subtle due to the existence of non-trivial null directions. I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically. The construction of such Finsler spacetimes lays the foundation for comparing their predictions with observations, in astrophysics as well as in laboratory experiments.

The Fractal Structure of Space Entails Origin of Pauli’s Equation

This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world entities, this condition acquires the precise form of the Pauli equation describing mechanics of the quantum electron with spin.