Space-time Events Research Articles

Ghirardi-Rimini-Weber model with massive flashes

I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or collapse space-time events) source a classical gravitational field. The resulting semi-classical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the $1/r$ gravitational potential of Newtonian gravity is cut-off at short ($\lesssim 10^{-7}$m) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for \emph{all} values of its parameters.

A simple approach to temporal cloaking

In recent years a remarkable progress was made in the construction of spatial cloaks using the methods of transformation optics and metamaterials. The temporal cloaking, i.e. the cloaking of an event in spacetime, was also widely studied by using transformations on spacetime domains. We propose a simple and general method for the construction of temporal cloaking using the change of time variables only.

The Particle as a Statistical Ensemble of Events in Stueckelberg–Horwitz–Piron Electrodynamics

In classical Maxwell electrodynamics, charged particles following deterministic trajectories are described by currents that induce fields, mediating interactions with other particles. Statistical methods are used when needed to treat complex particle and/or field configurations. In Stueckelberg-Horwitz-Piron (SHP) electrodynamics, the classical trajectories are traced out dynamically, through the evolution of a 4D spacetime event $x^\mu (\tau)$ as $\tau$ grows monotonically. Stueckelberg proposed to formalize the distinction between coordinate time $x^0 = ct$ (measured by laboratory clocks) and chronology $\tau$ (the temporal ordering of event occurrence) in order to describe antiparticles and resolve problems of irreversibility such as grandfather paradoxes. Consequently, in SHP theory, the elementary object is not a particle (a 4D curve in spacetime) but rather an event (a single point along the dynamically evolving curve). Following standard deterministic methods in classical relativistic field theory, one is led to Maxwell-like field equations that are \hbox{$\tau$-dependent} and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the trajectory. The width $\lambda$ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons emitted by particles. As $\lambda$ becomes very large, the photon mass goes to zero and the field equations become $\tau$-independent Maxwell's equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which $\lambda$ is larger than any other relevant time scale. Thus, statistical mechanics is a fundamental ingredient in SHP electrodynamics, and its insights are required to give meaning to the concept of a particle.

Speeds of light in Stueckelberg-Horwitz-Piron electrodynamics

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events xμ as functions of an external evolution parameter τ. As τ grows monotonically, the spacetime evolution of classical events xμ (τ) trace out particle worldlines dynamically and induce the five U(1) gauge potentials through which events interact.In analogy with the constant c that associates a unit of length x0 with intervals of time t in standard relativity, we introduce a constant c5 associated with the external time τ. Whereas the nonrelativistic limit of special relativity can be found by taking c → ∞, we show that 5D SHP goes over to an equilibrium state of Maxwell theory in the limit c5 → 0. Thus, the dimensionless ratio c5/c parameterizes the deviation of SHP from standard electrodynamics, in particular the coupling of events. Put another way, Maxwell theory can be understood as currents and fields relaxing to an equilibrium independent of chronological time as c5τ slows to zero. We find that taking 0 < c5/c < 1 enables the resolution of several longstanding difficulties in SHP theory.

Cosmological Black Holes and the Direction of Time

Macroscopic irreversible processes emerge from fundamental physical laws of reversible character. The source of the local irreversibility seems to be not in the laws themselves but in the initial and boundary conditions of the equations that represent the laws. In this work we propose that the screening of currents by black hole event horizons determines, locally, a preferred direction for the flux of electromagnetic energy. We study the growth of black hole event horizons due to the cosmological expansion and accretion of cosmic microwave background radiation, for different cosmological models. We propose generalized McVittie co-moving metrics and integrate the rate of accretion of cosmic microwave background radiation onto a supermassive black hole over cosmic time. We find that for flat, open, and closed Friedmann cosmological models, the ratio of the total area of the black hole event horizons with respect to the area of a radial co-moving space-like hypersurface always increases. Since accretion of cosmic radiation sets an absolute lower limit to the total matter accreted by black holes, this implies that the causal past and future are not mirror symmetric for any spacetime event. The asymmetry causes a net Poynting flux in the global future direction; the latter is in turn related to the ever increasing thermodynamic entropy. Thus, we expose a connection between four different "time arrows": cosmological, electromagnetic, gravitational, and thermodynamic.

Observation of relativistic effects by a single observer: a geometric interpretation using Loedel diagrams

The apparent length of a relativistically moving rod and visualization of the Einstein time dilation are studied. The description of events in space-time is given geometrically as viewed from two different inertial frames that are in relative motion with one another. These relativistic phenomena are graphically illustrated using one-dimensional Loedel diagrams. The equations that describe these effects are then deduced using elementary geometry. The aim of this paper is to outline a procedure that complements the standard algebraic presentation of these effects, and show that the kinematic concepts of special relativity can be deduced from the geometry.

Generalized Klein–Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca–Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein–Gordon potential (KGP) and Klein–Gordon field (KGF) equations for massive dyons from the generalized Proca–Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein–Gordon equations.

Relativistic Localizing Processes Bespeak an Inevitable Projective Geometry of Spacetime

Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein’s relativity. Accordingly, a comparison between observational data and theoretical expectations might then be strongly compromised. In the present paper, we give the principles of relativistic localizing systems so as to bypass this issue. Such systems will allow locating users endowed with receivers and, in addition, localizing any spacetime event. These localizing systems are made up of relativistic autolocating positioning subsystems supplemented by an extra satellite. They indicate that spacetime must be supplied everywhere with an unexpected local four-dimensional projective structure besides the well-known three-dimensional relativistic projective one. As a result, the spacetime manifold can be seen as a generalized Cartan space modeled on a four-dimensional real projective space, that is, a spacetime with both a local four-dimensional projective structure and a compatible (pseudo-)Riemannian structure. Localization protocols are presented in detail, while possible applications to astrophysics are also considered.

Sparse coding-based space-time video representation for action recognition

Methods based on feature descriptors around local interest points are now widely used in action recognition. Feature points are detected using a number of measures, namely saliency, periodicity, motion activity etc. Each of these measures is usually intensity-based and provides a trade-off between density and informativeness. In this paper, we address the problem of action recognition by representing image sequences as a sparse collection of patch-level space-time events that are salient in both space and time domain. Our method uses a multi-scale volumetric representation of video and adaptively selects an optimal space-time scale under which the saliency of a patch is most significant. The input image sequences are first partitioned into non-overlapping patches. Then, each patch is represented by a vector of coefficients that can linearly reconstruct the patch from a learned dictionary of basis patches. The space-time saliency of patches is measured by Shannon's self-information entropy, where a patch's saliency is determined by information variation in the contents of the patch's spatiotemporal neighborhood. Experimental results on three benchmark datasets demonstrate the effectiveness of the proposed method.

Conformal Weyl-Euler-Lagrangian equations on 4-Walker manifolds

The main purpose of the present paper is to study almost complex structures conformal Weyl-Euler-Lagrangian equations on 4-dimensional Walker manifolds for (conservative) dynamical systems. In this study, routes of objects moving in space will be modeled mathematically on 4-dimensional Walker manifolds that these are time-dependent partial differential equations. A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r ≤ 2 . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex analogues of Lagrangian mechanical systems on 4-Walker manifold. Also, the geometrical-physical results related to complex mechanical systems are also discussed for conformal Weyl-EulerLagrangian equations for (conservative) dynamical systems and solution of the motion equations using Maple Algebra software will be made.

Gravitational properties of light—the gravitational field of a laser pulse

The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.

FIRST RESULTS ON THE DIRECTION STATISTICS OF PAIRS OF EPICENTERS OF NEIGHBOR EARTHQUAKES ON KAMCHATKA

FIRST RESULTS ON THE DIRECTION STATISTICS OF PAIRS OF EPICENTERS OF NEIGHBOR EARTHQUAKES ON KAMCHATKA

Hawking radiation of vector particles via tunneling from 4-dimensional and 5-dimensional black holes

Using Proca equation and WKB approximation, we investigate Hawking radiation of vector particles via tunneling from 4-dimensional Kerr-de Sitter black hole and 5-dimensional Schwarzschild-Tangherlini black hole. The results show that the tunneling rates and Hawking temperatures are depended on the properties of spacetime (event horizon, mass and angular momentum). Besides, our results are the same as scalars and fermions tunneling from 4-dimensional Kerr-de Sitter black hole and 5-dimensional Schwarzschild-Tangherlini black hole.

Adjusting for population shifts and covariates in space-time interaction tests.

Statistical tests for epidemic patterns use measures of space-time event clustering, and look for high levels of clustering that are unlikely to appear randomly if events are independent. Standard approaches, such as Knox's (1964, Applied Statistics 13, 25-29) test, are biased when the spatial distribution of population changes over time, or when there is space-time interaction in important background variables. In particular, the Knox test is too sensitive to coincidental event clusters in such circumstances, and too likely to raise false alarms. Kulldorff and Hjalmars (1999, Biometrics 55, 544-552) proposed a variant of Knox's test to control for bias caused by population shifts. In this article, I demonstrate that their test is also generally biased, in an unknown direction. I suggest an alternative approach that accounts for exposure shifts while also conditioning on the observed spatial and temporal margins of event counts, as in the original Knox test. The new approach uses Metropolis sampling of permutations, and is unbiased under more general conditions. I demonstrate how the new method can also include controls for the clustering effects of covariates.

Hyperbolic statics in space-time

Based on the concept of a material event as an elementary material source that is concentrated on a metric sphere of zero radius—a light cone of Minkowski space-time, we deduce an analog of Coulomb’s law for a hyperbolic space-time field universally acting between space-time events. The collective field that provides interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb part and a logarithmic addition. We find that the Coulomb part depends on a fine balance between the causal and geometric space-time characteristics (a concordance of two regularizations).

Recurrence of Space-Time Events

A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. The “same colored paths and subgraphs” in the classical Ramsey theorem are interpreted as identical or semi-identical causal chains. In the framework of the model, Poincare recurrence and the cosmological recurrence arise naturally. We use Ramsey theorem to prove that there’s always a possibility of predictability no matter how chaotic the system is.

Topological defect with nonzero Hopf invariant in Yang–Mills–Higgs model

We propose a topological defect or instanton solution with nonzero Hopf invariant to the 3+1D non-Abelian gauge theory coupled with scalar fields. This solution, which we call Hopf defect, represents a spacetime event that makes a 2π rotation of vacuum manifold of the monopole. Although the action of this Hopf defect is logarithmically divergent, it may still give relevant contributions in a finite-sized system. Since the Chern–Simons term for the unbroken U(1) gauge field may appear in the low energy effective theory, the Hopf defect may possibly generate a phase factor change for the monopoles.

Genesis and evolution of the cultural landscape in central Mediterranean: the ‘where, when and how’ through the palynological approach

Cultural landscapes are priority research themes addressed in many fields of knowledge. Botanists can explore the ecological, formal and cognitive level of cultural landscapes with different approaches. Palynologists study both palaeoenvironmental (off-site) and archaeological (on-site) records and are, therefore, in a privileged corner to observe the origin and history of present landscapes, what is their true nature and vocation, what must be preserved or transformed for the future. The study of an archaeological site shows short space–time events and the behaviour of a few people. In order, though, to attain a regional and cross-area cultural landscape reconstruction, many sites must be studied as part of a regional multi-point site and with an interdisciplinary approach. The likelihood to observe human-induced environments in pollen diagrams depends on the nature and productivity of human-related plant species. In the Mediterranean area, many Palaeolithic, Mesolithic and Neolithic sites point to the long-term action on the environment. However, the pollen signal of pre-Holocene and early Holocene human impact is ambiguous or weak. The effects of culture became evident, and possibly irreversible, as a consequence of human permanence in a certain land. In the Bronze age, the establishment of human-induced environments was evident from the combination of decrease of forest cover and increase of cereal and synanthropic pollen types in pollen records.

Digital Image Forgery Detection by Contrast Enhancement

For decades, photographs have been used to document space-time events and they have often served as evidence in courts. Today, powerful digital image editing software makes image modifications straightforward. This undermines our trust in photographs and, in particular, questions pictures as evidence for real-world events. Contrast enhancement is mainly to adjust the brightness globally. Users may also perform local contrast enhancement for creating a realistic composite image. Most latest technology in the literature uses two algorithms to find the contrast enhancement for the manipulation of digital imagees. First algorithm focus on the detection of global contrast enhancement applied to previously JPEG compressed images. Here images are converted to non-overlapping blocks ie histogram of images, then gap/peak detection of blocks are performed. Locate the gap and peak bins. Pixel value mappings are analyzed theoretically, and difference between the pictures are obtained by identifying the zero-height gap fingerprints. Second method is used to identify the composite image created by enforcing contrast adjustment on any of the source regions/over the entire region of the image. This is followed by finding out the positions of the peak/gap bins, and clustering them for identifying the contrast enhancement applied to different source regions. Finally check for the similarity between peak/gap bins reference vectors calculated for both forged region and unforged region.If it is found to be dissimilar then the image is treated as a forged one. Index Terms: Contrast enhancement, image forgery.

Minimal length and small scale structure of spacetime

Many generic arguments support the existence of a minimum spacetime interval $L_0$. Such a "zero-point" length can be naturally introduced in a locally Lorentz invariant manner via Synge's world function bi-scalar $\Omega(p,P)$ which measures squared geodesic interval between spacetime events $p$ and $P$. I show that there exists a \emph{non-local} deformation of spacetime geometry given by a \emph{disformal} coupling of metric to the bi-scalar $\Omega(p,P)$, which yields a geodesic interval of $L_0$ in the limit $p \rightarrow P$. Locality is recovered when $\Omega(p,P) >> L_0^2/2$. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.