Notion Of Spacetime Research Articles

The Positron Passport: An Essay-Poem in Quantum Poetics

This essay-poem develops the author's ongoing transdisciplinary examination of her integrated artistic practice and theory known as ‘quantum poetics’, investigating shared principles in poetry and science with the aim of reinventing common notions of spacetime, language, and reality. Topics touched upon include her research in particle physics at the European Organization for Nuclear Research (CERN) and Canfranc Underground Laboratory, the uncertainty principle in quantum theory and aesthetic ambiguity, Werner Heisenberg's essays on language and science, the reader of a literary text in relation to an observation in quantum theory, string theory and poetry, the asymmetry of matter and antimatter in the known universe in relation to the imagination, and the poethics of science. Using a cross-genre form that includes poetry, creative nonfiction, and academic scholarship identified as an essay-poem, the author writes in ‘windows’, justified text blocks that transition into and out of original poetry and quoted material by writers and scientists. One purpose of these windows is to treat the spacetime of the page as a literary device, one that visually foregrounds the material construct of literary language.

Relativistic Option Pricing

The change of information near light speed, advances in high-speed trading, spatial arbitrage strategies and foreseen space exploration, suggest the need to consider the effects of the theory of relativity in finance models. Time and space, under certain circumstances, are not dissociated and can no longer be interpreted as Euclidean. This paper provides an overview of the research made in this field while formally defining the key notions of spacetime, proper time and an understanding of how time dilation impacts financial models. We illustrate how special relativity modifies option pricing and hedging, under the Black–Scholes model, when market participants are in two different reference frames. In particular, we look into maturity and volatility relativistic effects.

Phase space of a test particle in the presence of natural cutoffs

Physics at very high energies (close to the Planck energy scale) is in the center of modern physics challenges. At the high energy scales, or equivalently very short distances, the very notion of spacetime acquires a complicated structure. In this scale, there are limitations on the complete resolution of adjacent points in spacetime manifold. While the effect of a minimal measurable length on algebraic structure of a free particle’s phase space has been studied in the literature, the simultaneous effects of minimal length and maximal momentum have not been explored in this subject so far. Here, we are going to fill this gap. We study some properties of the algebraic structure of quantum field theories in the presence of natural cutoffs as a minimal length and a maximal momentum in a free particle’s phase space. Especially, we pay attention on the phase space trajectories of systems in the presence of natural cutoffs.

Observers and Their Notion of Spacetime beyond Special Relativity

It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or a deformation of special relativity) are very different, both conceptually and phenomenologically. We discuss some of their implications on the description of events for different observers and the notion of spacetime.

The geometry of special relativity: a concise course by N. Dragon

This book arises from several years of the author’s teaching special relativity; it gives an interesting, if idiosyncratic, overview of the subject. The first chapter sets the scene for the subsequent development, introducing the notion of space-time, ideal clocks and measuring rods, and the invariant nature of the speed of light. This is used to give a pictorial explanation of simultaneity, and how observers in relativemotionwill therefore disagree not only about whether two distinct events take place at the same place, but also whether they take place at the same time. This geometric and pictorial approach is developed in the next chapter in a rather sophisticated version of Bondi’s k-calculus. Using only elementary geometrical ideas and symmetry assumptions the standard kinematical results of special relativity are obtained: composition of velocities, time dilation and length contraction, the Doppler effect, and the standard (non-)paradoxes of the twins and the pole-in-barn (here, carin-garage) are given a clear and careful development. The discussion is also extended to the full four dimensional space-time, not confined to the two dimensional case. Chapter three builds on this by finding the relationship between inertial coordinate systems: the Lorentz transformation. With the Lorentz transformation in hand, one can now consider what a moving object actually looks like to a stationary observer. A particularly nice example is the argument in terms of aberration that a moving sphere presents a circular appearance to a stationary observer. This chapter is rounded off by the introduction of the dynamical quantities of energy and momentum. Up to this point, the arguments have used little, if any, mathematics beyond what might be met in high school, or the early part of the undergraduate curriculum of a

SPECIAL RELATIVITY WITH TWO INVARIANT SCALES: MOTIVATION, FERMIONS, BOSONS, LOCALITY, AND CRITIQUE

We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, [Formula: see text], (c and λP). We introduce canonically-conjugate variables (χ0,χ) to (∊,π) of Judes-Visser. Together, they bring in a formal element of linearity and locality in an otherwise non-linear and non-local theory. Special relativities with two invariant scales provide all corrections, say, to the standard model of the high energy physics, in terms of one fundamental constant, λP. It is emphasized that spacetime of special relativities with two invariant scales carries an intrinsic quantum-gravitational character. In an addenda, we also comment on the physical importance of a phase factor that the whole literature on the subject has missed and present a brief critique of [Formula: see text]. In addition, we remark that the most natural and physically viable [Formula: see text] shall require momentum-space and spacetime to be non-commutative with the non-commutativity determined by the spin content and C, P, and T properties of the examined representation space. Therefore, in a physically successful [Formula: see text], the notion of spacetime is expected to be deeply intertwined with specific properties of the test particle.

Again on relativistic semantics

This paper has two parts: Part I is a continuation of the work [10] and as well as this it deals mainly with the logic of an auxiliary (semantical) theory, ST , in effect generally considered (by textbooks) within the semantics for a typical theory T of general relativity; and especially the modal features of this auxiliary theory are studied. Part II deals with the influence had by relativistic theories and especially by the new notion of space-time on pragmatic languages (in Carnap’s sense), so that they include, e.g., „now” and „here”.

Spacetime structures from critical values in two-dimensional quantum gravity

A model for two-dimensional (2D) quantum gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,) generators) lose their dynamical content (they are no longer conjugated operators). The notion of spacetime itself in 2D gravity then arises as associated with this kinematical SL(2,) symmetry. An ensemble of different copies of AdS do co-exist in this model with different weights, depending on their curvature (which is proportional to 2) and they are connected by gravity operators. This model suggests that, in general, quantum diffeomorphisms should not be imposed as constraints to the theory, except for the classical limit.

Mathematics and Reality: Two Notions of Spacetime in the Analytic and Constructionist Views of Gauge Field Theories

This paper presents two interpretations of the fiber bundle fonnalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical fonnalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure fonnal arguments.

Changes in the Regionalisation of Transport and the New Orientation of Centrality in Europe

The emergence of the Se/Vice economy and the globalisationput an end io the theory of central places elaborated byChristaller and Losch at the end of the industrial period. Thegrowing mobility of persons and goods and the breakthrough oftechnologies favowing speed and information flows have giventhe main importance to the notion of space-time. The resultingmutation of transp01t, renders ever more emphasis to the networkconnection of relais stations and gives 1ise to network .systemsdevelopment, especially at large scale, that reduces considerablythe interest of old urban hierarchical pattems approp1iare10 a relatively static era which has now gone by in the developedcountries.

Conceptions of space-time: Problems and possible solutions

Abstract In this paper, the implications of quantum mechanics and general relativity for the understanding of space-time are discussed. There are strong indications that Classical notions of space-time are inadequate as a basis for these theories. A number of proposals for non-Classical space-time structures are reviewed. Bohm's framework for the description of natural phenomena based on the notion of process is described. Here, space-time is no longer taken as basic; rather it is a derived feature of the underlying process. This approach opens up the possibility of investigating space-time problems from a new angle, where the nature of space-time is determined by the system under study.

On Discrete Models of Space-Time

Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. § 1. Discrete models of space-time without elementary length There is a common belief 1 ) that discrete models of space-time must suffer from at least three chronic diseases: i) They introduce the experimentally not found elementary length. ii) They violate experimentally verified relativistic invariance. iii) They legate their mathematics from the continuous models. In the present paper we shall show that this belief is not justified and in order to present our approach we should like to start from the very beginning, i.e., from the analysis of general properties of the experimental methods used to measure space­ time coordinates. The notion of space-time is a physical concept and if we want to be able to understand all its features we should take into account and understand the measure­ ment methods of any quantity used in the mathematical description of space-time. In particular, we must precisely define the method of measuring space-time coordinates the results of which, due to the principle of relativity, have a subjective character for each observer. We consider Einstein radiolocation method 2 ) as a starting point of our discussion. For the completeness of the paper we shall remind here its basic idea in spite of the fact that it is well-known. In this method in any inertial reference frame stiffly connected to a given observer we measure two quantities:

The relativistic theory of gravitation and new notions of space-time

The relativistic theory of gravitation and new notions of space-time

Bifurcate Space-Times

The notion of space-time is generalized in order to include the non-Hausdorff manifolds that do not admit any sort of pathological bifurcate curves. By means of these space-times, a geodesically complete extension of Taub and NUT space is constructed.

Non-Usual Topologies on Space-Time and High-Energy Scattering

Motivated by recently observed deviations from quantum electrodynamical theory, we study the possibility that our notions of space-time may need revision at small distances. In this work, we wish to call attention to certain techniques which are available for studying different space-time structures within the framework of topology. Our main effort is in the consideration of a non-usual topology on space-time in which is embedded an elementary length. By working separately in each n-particle subspace, the embedding is done in an inhomogeneous Lorentz invariant way, and we avoid any lattice structure in space-time. Particles in this topology are in general extended structures, and we find the surprising feature that, at high energies, the topology enhances backward and large-angle scattering. From these preliminary investigations, we are not as yet able to make more than qualitative comparison with experiment. Along the way, we have the opportunity to remark on ways of embedding an intrinsic breakdown of certain invariances (e.g., parity) in the topology of space-time.

A New Approach to God

If civilisation is to survive, if the emergent civilisation is to achieve the fulfilment of its potentialities, the coming age must be an age of spiritual as well as social integration.Today the human mind is torn and divided between positivism and irrationalism. The endeavours of pragmatism succeeded in making important discoveries concerning a number of basic attitudes in thought and morality, and in what might be called the sociology of knowledge. As a universal system of knowledge and life, as a philosophy, however, pragmatism has been a failure.What is essentially needed is a renewal of metaphysics. The conceptions of modern science—the unification of matter and energy, physical indeterminism, the notion of space-time, the new reality recognised both as to quality and duration—are invaluable means of deciphering material phenomena. A cosmos of electrons and stars in which the stars are the heavenly laboratories of elements, subjected everywhere to genesis and transmutation, a universe which is finite but whose limits cannot be attained because of the curvation of space, and which dynamically evolves in a definite direction, namely toward the highest forms of individuation and concentration and toward a simultaneous degradation of the quality of its total energy—all this is external description and scientific imagery rather than ontological insight. Such knowledge can never directly serve the purpose of any philosophical or metaphysical extrapolations. Yet all this constitutes at the same time a basic representation of the world incomparably more favourable to the edification of a philosophy of nature and more open to the deepening labour of metaphysical reason than the old Newtonian physics.

Societies and Academies

LONDON. Aristotelian Society, December 1.—J. A. Smith: Prof. Alexander's notion of “space-time.” The notion of space-time is equated by Alexander with that of pure motion. The elucidation of motion is a prime requisite for science. Alexander's aim is to help us to apprehend it immediately. Our difficulty in doing so is because we are sensitive and not purely intuitive beings. To remedy this we must endeavour to remount the stream of experience to its sources and reach a state of pure intuition. Pure motion is the simple intuition we then attain. We apprehend it not by definition but by a refinement of sensible motions and of mathematical motion. It is for science the surest and best hypothesis capable more than any other offered basis of supporting its structures.