scholarly journals CLASSICAL AND QUANTUM GENERAL RELATIVITY: A NEW PARADIGM

2005 ◽  
Vol 14 (12) ◽  
pp. 2355-2360 ◽  
Author(s):  
RODOLFO GAMBINI ◽  
JORGE PULLIN
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Numerical Simulations ◽  
New Paradigm ◽  
Recent Developments ◽  
Conceptual Problems ◽  
Discrete Theory ◽  
New Framework

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.

scholarly journals QUANTUM GRAVITY BY THE COMPLEX CANONICAL FORMULATION

1992 ◽  
Vol 01 (03n04) ◽  
pp. 439-523 ◽  
Author(s):  
HIDEO KODAMA
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Conventional Treatment ◽  
Quantum States ◽  
Hamiltonian Constraint ◽  
Canonical Formulation ◽  
Recent Developments ◽  
Canonical Approach ◽  
New Formulation ◽  
Basic Features

The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles already available and some original arguments are included. In particular the conventional treatment of the Hamiltonian constraint and quantum states in the canonical approach to quantum gravity is criticized and a new formulation is proposed.

scholarly journals Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

Transforming Historical Objectivism into Historical Hermeneutics: From “Historical Illness” to Properly Lived Historicality

2019 ◽  
Vol 61 (4) ◽  
pp. 490-515
Author(s):  
Thomas Tops
Keyword(s):  
Reception History ◽  
Biblical Studies ◽  
Historical Study ◽  
Necessary Condition ◽  
New Paradigm ◽  
History Of Interpretation ◽  
Critical Methodology ◽  
Recent Developments ◽  
History Of ◽  
Biblical Texts

Summary The present study analyses recent criticisms against the use of modern-historical methodologies in Biblical Studies. These methodologies abstract from the historical horizon of the researcher. In order to relate properly to the historicality of the researcher, historical objectivism needs to be transformed into historical hermeneutics. Recent developments in the historical methodology of biblical scholars are unable to reckon with the historicality of the researcher due to the partial or incorrect implementation of Gadamer’s views on reception history. I analyse the views of Nietzsche, Kierkegaard, and Gadamer on historicality and contend that the study of reception history is a necessary condition for conducting historical study from within the limits of our historicality. Reception history should not be a distinct methodological step to study the “Nachleben” of biblical texts, but needs to clarify how the understanding of these texts is already effected by their history of interpretation. The awareness of the presuppositions that have guided previous interpretations of biblical texts enables us to be confronted by their alterity. This confrontation calls for a synthesis between reception-historical and historical-critical methodology that introduces a new paradigm for conducting historical study in Biblical Studies in dialogue with other theological disciplines.

GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1678-1685 ◽  
Author(s):  
REZA TAVAKOL
Keyword(s):  
General Relativity ◽  
String Theory ◽  
Riemannian Geometry ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Spacetime Geometry ◽  
Test Particles ◽  
Light Rays ◽  
Recent Developments ◽  
Underlying Geometry

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more recent developments such as those in String theory, whereby Lorentz invariance is partially broken.

Compressed wavefield extrapolation

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM77-SM93 ◽  
Author(s):  
Tim T. Lin ◽  
Felix J. Herrmann
Keyword(s):  
Wave Propagation ◽  
Compressed Sensing ◽  
Signal Recovery ◽  
New Paradigm ◽  
New Approach ◽  
Measurement Basis ◽  
Recent Developments ◽  
Data Volume ◽  
Extrapolation Problem ◽  
Wavefield Extrapolation

An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation.

A NEW FORMULATION OF QUANTUM FIELD THEORY ON S4

1994 ◽  
Vol 09 (18) ◽  
pp. 3245-3282 ◽  
Author(s):  
B.A. HARRIS ◽  
G.C. JOSHI
Keyword(s):  
Field Theory ◽  
Angular Momentum ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Space Representation ◽  
Fundamental Constants ◽  
Spherical Space ◽  
Recent Developments ◽  
New Formulation ◽  
Constants Of Nature

Recent developments in quantum gravity suggest that wormholes may influence the observed values of the constants of nature. The Euclidean formulation of quantum gravity predicts that wormholes induce a probability distribution in the space of possible fundamental constants. In particular, the effective action on a large spherical space may lead to the vanishing of the cosmological constant and possibly determine the values of other constants of nature. The ability to perform calculations involving interacting quantum fields, particularly non-Abelian models, on a four-sphere is vital if one is to investigate this possibility. In this paper we present a new formulation of field theory on a four-sphere using the angular momentum space representation of SO(5). We give a review of field theory on a sphere and then show how a matrix element prescription in angular momentum space and a new summation technique based on the complex l plane, overcome previous limitations in calculational techniques. The standard one-loop graphs of QED are given as examples.

scholarly journals A First Approach to Loop Quantum Gravity in the Momentum Representation

2019 ◽  
pp. 1-8
Author(s):  
W. F. Chagas-Filho
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Classical System ◽  
Momentum Representation ◽  
First Order

We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations that can be interpreted as describing quantum gravity in the momentum representation.

scholarly journals From General Relativity to Quantum Gravity

2015 ◽  
pp. 553-611 ◽  
Author(s):  
Abhay Ashtekar ◽  
Martin Reuter ◽  
Carlo Rovelli
Keyword(s):  
General Relativity ◽  
Quantum Gravity

“Prehistoric” Quantum Gravity

2020 ◽  
pp. 41-70
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Philosophical Nature

In this chapter we examine the very earliest work on the problem of quantum gravity (understood very liberally). We show that, even before the concept of the quantization of the gravitational field in 1929, there was a fairly lively investigation of the relationships between gravity and quantum stretching as far back as 1916, and certainly no suggestion that such a theory would not be forthcoming. Indeed, there are, rather, many suggestions explicitly advocating that an integration of quantum theory and general relativity (or gravitation, at least) is essential for future physics, in order to construct a satisfactory foundation. We also see how this belief was guided by a diverse family of underlying agendas and constraints, often of a highly philosophical nature.

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