ENTROPY DENSITY OF SPACE–TIME AND GRAVITY: A CONCEPTUAL SYNTHESIS

2009 ◽  
Vol 18 (14) ◽  
pp. 2189-2193 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Invariant Theory ◽  
Entropy Density ◽  
Space Time ◽  
General Covariance ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Accelerated Observers ◽  
Thermodynamic Interpretation

I show that combining the principle of equivalence and the principle of general covariance with the known properties of local Rindler horizons, perceived by accelerated observers, leads to the following inescapable conclusion: The field equations describing gravity in any diffeomorphism-invariant theory must have a thermodynamic interpretation. This synthesis of quantum theory, thermodynamics and gravity shows that the gravitational dynamics can be interpreted completely in terms of entropy balance between matter and space–time. This idea has far-reaching implications for the microstructure of space–time and quantum gravity.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

ON THE GEOMETRIZATION OF BOHMIAN MECHANICS: A NEW APPROACH TO QUANTUM GRAVITY

1998 ◽  
Vol 13 (04) ◽  
pp. 677-693 ◽  
Author(s):  
FATIMAH SHOJAI ◽  
MEHDI GOLSHANI
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Classical Limit ◽  
Bohmian Mechanics ◽  
Present Theory ◽  
Space Time ◽  
New Approach ◽  
Theory Of Motion ◽  
Quantum Theory Of Motion ◽  
De Broglie Bohm

In this paper, a new approach to quantum gravity is presented in which the de-Broglie–Bohm quantum theory of motion is geometrized. This way of considering quantum gravity leads automatically to the fact that the quantum effects are contained in the conformal degree of freedom of the space–time metric. The present theory is then applied to the maximally symmetric space–time of cosmology, and it is observed that it is possible to avoid the initial singularity, while at large times the correct classical limit emerges.

scholarly journals On the emergence of the structure of physics

2018 ◽  
Vol 376 (2118) ◽  
pp. 20170231 ◽  
Author(s):  
S. Majid
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Recent Work ◽  
Space Time ◽  
Quantum Space ◽  
Conceptual Level ◽  
Theme Issue ◽  
Self Duality ◽  
Born Reciprocity

We consider Hilbert’s problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space–time as motivated by this non-standard philosophy, including a new toy model of gravity on a space–time consisting of four points forming a square. This article is part of the theme issue ‘Hilbert’s sixth problem’.

scholarly journals Space–Time Physics in Background-Independent Theories of Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 251
Author(s):  
Martin Bojowald
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Riemannian Geometry ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Time Analysis ◽  
Complete Space ◽  
Background Independence ◽  
Starting Point

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.

scholarly journals Quantum Theory of Gravitation

1998 ◽  
Vol 51 (3) ◽  
pp. 459
Author(s):  
H. S. Green
Keyword(s):  
Quantum Theory ◽  
Wave Equations ◽  
Algebraic Method ◽  
Empty Space ◽  
Space Time ◽  
Field Equations ◽  
Gauge Groups ◽  
Gravitational Field Equations ◽  
Non Euclidean Geometry ◽  
Curvature Tensors

It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.

scholarly journals Black-Hole Models in Loop Quantum Gravity

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 125
Author(s):  
Martin Bojowald
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Classical Solutions ◽  
General Covariance ◽  
White Hole ◽  
Signature Change ◽  
Generalized Covariance ◽  
Line Elements

Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line elements with metric components that differ from the classical solutions of general relativity, motivated by modified equations of motion and constraints. However, recent results have shown by explicit calculations that most of these constructions violate general covariance and slicing independence. The proposed line elements and black-hole models are therefore ruled out. The only known possibility to escape this sentence is to derive not only modified metric components but also a new space-time structure which is covariant in a generalized sense. Formally, such a derivation is made available by an analysis of the constraints of canonical gravity, which generate deformations of hypersurfaces in space-time, or generalized versions if the constraints are consistently modified. A generic consequence of consistent modifications in effective theories suggested by loop quantum gravity is signature change at high density. Signature change is an important ingredient in long-term models of black holes that aim to determine what might happen after a black hole has evaporated. Because this effect changes the causal structure of space-time, it has crucial implications for black-hole models that have been missed in several older constructions, for instance in models based on bouncing black-hole interiors. Such models are ruled out by signature change even if their underlying space-times are made consistent using generalized covariance. The causal nature of signature change brings in a new internal consistency condition, given by the requirement of deterministic behavior at low curvature. Even a causally disconnected interior transition, opening back up into the former exterior as some kind of astrophysical white hole, is then ruled out. New versions consistent with both generalized covariance and low-curvature determinism are introduced here, showing a remarkable similarity with models developed in other approaches, such as the final-state proposal or the no-transition principle obtained from the gauge-gravity correspondence.

scholarly journals Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Proper Time ◽  
Theoretical Background ◽  
Space Time ◽  
Einstein Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

scholarly journals Revisiting the Black Hole Entropy and the Information Paradox

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Ovidiu Cristinel Stoica
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Black Hole Entropy ◽  
Principle Of Equivalence ◽  
Information Paradox ◽  
Related Research ◽  
Black Hole Information

The black hole information paradox and the black hole entropy are currently extensively researched. The consensus about the solution of the information paradox is not yet reached, and it is not yet clear what can we learn about quantum gravity from these and the related research. It seems that the apparently irreducible paradoxes force us to give up on at least one well-established principle or another. Since we are talking about a choice between the principle of equivalence from general relativity and some essential principles from quantum theory, both being the most reliable theories we have, it is recommended to proceed with caution and search more conservative solutions. These paradoxes are revisited here, as well as the black hole complementarity and the firewall proposals, with an emphasis on the less obvious assumptions. Some arguments from the literature are reviewed, and new counterarguments are presented. Some less considered less radical possibilities are discussed, and a conservative solution, which is more consistent with both the principle of equivalence from general relativity and the unitarity from quantum theory, is discussed.

scholarly journals ON THE GENERAL COVARIANCE IN BOHMIAN QUANTUM GRAVITY

1998 ◽  
Vol 13 (13) ◽  
pp. 2135-2144 ◽  
Author(s):  
FATIMAH SHOJAI ◽  
MEHDI GOLSHANI
Keyword(s):  
Quantum Gravity ◽  
Equations Of Motion ◽  
Space Time ◽  
Quantum Corrections ◽  
General Covariance ◽  
Einstein's Equations ◽  
Individual Level ◽  
Statistical Level ◽  
Covariance Principle ◽  
The Individual

It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space–time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant, so that in the framework of Bohmian quantum gravity the general covariance principle breaks down at the individual level. This principle is restored at the statistical level.

scholarly journals Proposal for a New Quantum Theory of Gravity

2019 ◽  
Vol 74 (7) ◽  
pp. 617-633 ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Noncommutative Geometry ◽  
Measurement Problem ◽  
Black Hole Entropy ◽  
Space Time ◽  
Classical General Relativity ◽  
Field Equations ◽  
Symmetry Principle ◽  
Theory Of Gravity

AbstractWe recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

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