Scalar–Tensor Theories and Quantum Gravity (original) (raw)
Conformal Transformations and Quantum Gravity
Modern Physics Letters A, 1998
Recently,1 it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space–time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e. changing the metric), or by making a conformal transformation (i.e. changing all physical quantities). These two ways are investigated and compared. Also, it is argued that, the ultimate formulation of such a quantum gravity theory should be in the framework of the scalar–tensor theories.
Quantum Gravity from General Relativity
The Routledge Companion to Philosophy of Physics, 2021
Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a quantum theory of gravity suggest that such a theory may have radical consequences for the nature, and indeed the fate, of spacetime. The present article articulates what this problem of spacetime is and traces it three approaches to quantum gravity taking general relativity as their vantage point: semi-classical gravity, causal set theory, and loop quantum gravity.
Journal of High Energy Physics, Gravitation and Cosmology, 2022
We present a simple way to approach the hard problem of quantization of the gravitational field in four-dimensional space-time, due to non-linearity of the Einstein equations. The difficulty may be overcome when the cosmological constant is non-null. Treating the cosmological contribution as the energy-momentum of vacuum, and representing the metric tensor onto the tetrad of its eigenvectors, the corresponding energy-momentum and, consequently, the Hamiltonian are easily quantized assuming a correspondence rule according to which the eigenvectors are replaced by creation and annihilation operators for the gravitational field. So the geometric Einstein tensor, which is opposite in sign respect to the vacuum energy-momentum (plus the possible known matter one), is also quantized. Physical examples provided by Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter solutions are examined.
A pure geometric approach to derive quantum gravity from general relativity
viXra, 2013
In this paper scalar-tensor gravity is derived from the Schwarzschild solution of General Relativity. The solution is also extended to a maximal and complete manifold. A well-defined relationship between the scalar product of metric and the scalar field is revealed. A theoretical quantum test particle is constructed on the basis of Compton wavelength and General Relativity. It is also demonstrated how the rest mass of such particle depends on the background geometry of the space, which explains the correlation between the scalar field and the curvature. Finally we try to sum up and draw a conclusion of the paper as well as to make some recommendations, wherever it seems to be reasonable.
Gravity induced from quantum spacetime
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x, t] = λx drastically reduce the moduli of possible metrics g up to normalisation to a single real parameter which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study the suggested spherically symmetric classical geometry in n = 4 in detail, identifying two 1-parameter subcases where the Einstein tensor matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w Q = − 1 2 . The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a 'quantum Einstein tensor' which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(λ 2 ) correction to the classical Einstein tensor and an O(λ) correction to the classical metric.
Quantum Mechanics and General Relativity
Fundamental subjects of quantum mechanics and general relativity are presented in a unitary framework. A quantum particle is described by wave packets in the two conjugate spaces of the coordinates and momentum. With the time dependent phases proportional to the Lagrangian, the group velocities of these wave packets are in agreement with the fundamental Hamilton equations. When the relativistic Lagrangian, as a function of the metric tensor and the matter velocity field, is considered, the wave velocities are equal to the matter velocity. This means that these waves describe the matter propagation, and that the equality of the integrals of the matter densities over the spatial and the momentum spaces, with the mass in the Lagrangian of the time dependent phases, which describes the particle dynamics, represent a mass quantization rule. Describing the interaction of a quantum particle with the electromagnetic field by a modification of the particle dynamics, induced by additional terms in the time dependent phases, with an electric potential conjugated to time, and a vector potential conjugated to the coordinates, Lorentz’s force and Maxwell’s equations are obtained. With Dirac’s Hamiltonian, and operators satisfying the Clifford algebra, dynamic equations similar to those used in the quantum field theory and particle physics are obtained, but with an additional relativistic function, depending on the velocity, and the matter-field momentum. For particles and antiparticles, wavefunctions for finite matter distributions are obtained. The particle transitions, and Fermi’s golden rule, are described by the Lagrangian matrix elements over the Lagrangian eigenstates and densities of these states. Transition rates are obtained for the two possible processes, with the spin conservation or with the spin inversion. Dirac’s formalism of general relativity, with basic concepts of Christoffel symbols, covariant derivative, scalar density and matter conservation, the geodesic dynamics, curvature tensor, Bianci equations, Ricci tensor, Einstein’s gravitation law and the Schwarzschild matric elements, are presented in detail. From the action integrals for the gravitational field, matter, electromagnetic field, and electric charge, Lorentz’s force and Maxwell’s equations in the general relativity are obtained. It is also shown that the gravitational field is not modified by the electromagnetic field. For a black hole, the velocity and the acceleration of a particle are obtained. It is shown that, in the perfect spherical symmetry hypothesis, an outside particle is attracted only up to three times the Schwarzschild radius, between this distance and the Schwarzschild radius the particle being repelled, so that it reaches this boundary only in an infinite time, with null velocity and null acceleration. At the formation of a black hole, as a perfectly spherical object of matter gravitationally concentrated inside the Schwarzschild boundary, the central matter explodes, the inside matter being carried out towards this boundary, but reaching there only in an infinite time, with null velocity and null acceleration. In this way, our universe is conceived as a huge black hole. Based on this model, the essential properties, as big bang, inflation, the low large-scale density, the quasi-inertial behavior of the distant bodies, redshift, the dark matter and the dark energy, are unitarily explained. From the description of a gravitational wave by harmonically oscillating coordinates, the wave equation for the metric tensor is obtained, the propagation direction of such a wave being taken for reference. For a quantum particle as a distribution of matter interacting with a gravitational field, according to the proposed model, it is obtained that this field rotates with the angular momentum 2, called the graviton spin, as a rotation of the metric tensor which is correlated to the matter velocity, as the particle matter rotates with a half-integer spin for Fermions, and an integer spin for Bosons.
Proposal for a New Quantum Theory of Gravity
Zeitschrift für Naturforschung A, 2019
We 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 ...
Spacetime and the Philosophical Challenge of Quantum Gravity
1999
We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction, we briefly review the conceptual problems of the ingredient theories and introduce the enterprise of quantum gravity We then describe how three main research programmes in quantum gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called problem of time. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than t...
A Form of Quantum Gravity Unification with the General Theory of Relativity
A form of Quantum gravity unification with the General theory of Relativity, 2024
The problem still remains (in theoretical physics) of how gravity can be unified with quantum mechanics, in as much as it would be possible to explain a consistent theory of quantum gravity. Which, this unification theory should (to a sufficient extent) adhere to the Friedmann-Lemaitre-Robertson-Walker metric. In the preceding work, a universal model is formulated, considering the results of the theory of quantum gravity, as well as the General theory of relativity. The space-time continuum is modelled to arise from the gravity quanta. This is by allowing the universe to retain its homogeneous nature at scales near the plank scale in (relativistic) difference from the time of the Big Bang and treating the gravity particle as behaving, both as a wave and as a particle (as of the theory of wave-particle duality). Once space-time is modelled, the field equations of general relativity are considered, and briefly mentioned, in the modelling of repulsive gravity as being the cause of the expansion of the universe. The space-time metric is considered, as possibly moving at faster than the speed of light. This is considered as suggesting, an event (as of the Special theory of relativity) of which its occasion supersedes the symmetry of which the Special theory of relativity was modelled, this is considered with no changes to the frame of reference of the Special theory of relativity.
From general relativity to quantum gravity
Lecture Notes in Physics, 1982
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades. 1
Quantum Gravity:the axiomatic approach, a possible interpretation
Twenty years ago, by extending the Wightman axiom framework, it has been found possible to quantize only a conformal factor of the gravitational field. Gravitons being excluded from this quantum scalar field theory, numerous attempts were done to give a valuable description of what could be quantum gravity. In this talk we present a familly of Lorentz manifolds which can be foliated by isotropic hypersurfaces and pose severe restrictions on the form of the energy-momentum tensor in Einstein's equations. They can be associated to gravitational waves "without gravitons" in a vacuum described by two cosmological functions, but not to a massless particle flow. From this cross-checking with the previous remark, a "very" primordial quantum cosmological scenario is proposed.
2010
The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space–time literature.
Quantum gravity: an introduction to some recent results
Reviews of Modern Physics, 1989
This article presents a general overview of the problems involved in the application of the quantum principle to a theory of gravitation. The ultraviolet divergences that appear in any perturbative computation are reviewed in some detail, and it is argued that it is unlikely that any theory based on local quantum fields could be consistent. This leads in a natural way to a supersymmetric theory of extended objects as the next candidate theory to study. An elementary introduction to superstrings closes the review, and some speculations about the most promising avenues of research are offered. CONTENTS Gravitational Fields III. Einstein Gravity as a Gauge Theory. Perturbative Results at One and Two Loops A. Gravity as a gauge theory B. The method of the background field C. The one-loop computation of 't Hooft and Veltman D. The two-loop computation of Goro6'and Sagnotti IV. Ultraviolet Divergences in a Quantum Field Theory of Gravity V. Canonical Formalism: The Wheeler-De%'itt Equation VI. The Semiclassical Approximation: Schrodinger s Equation VII. Some Specific Boundary Conditions. Toy Models in Quantum Cosmology A. The de Sitter model of Hartle and Hawking B. The effect of conformally invariant scalars in the toy model C. A cosmological model of Banks VIII. Quantum Gravity in the General Framework of Superstring Theories A. Gravity from strings B. Modular invariance C. Gravity in the long-wavelength limit D.
Brief Introduction to Quantum Gravity
Iconic Research and Engineering Journals, 2019
Quantum gravity is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, as almost compact astrophysical objects where gravity effects are strong. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the other three fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory, radically different formalisms for describing physical phenomena. It is sometimes argued that a description of quantum gravity is necessary based on the fact that a classical system cannot be consistently coupled with a quantum system. Although a quantum theory of gravity may be necessary to reconcile general relativity with the principles of quantum mechanics, difficulties arise when applying the usual prescriptions of quantum field theory to the force of gravity via gravitational bosons. Indexed Terms-gravity, quantum, and general relativity.
A theory's equations are designed to model physical behavior that reflects the nature of physical reality. Einstein's nonlinear gravity equation is 'linearized' in the 'weak field limit' by ignoring nonlinear terms. This can be misinterpreted as affecting the nature of the field. Linearization is a mathematical artifice making equations easier to solve, having zero effect on the physical nature of the field itself. Thus it is false to say that the weak gravitational field is not self-interacting. Nor is the weak gravitational field based on mass; the field equation is based on mass density. These aspects of gravity are investigated by replacing curved space-time with mass density in flat space. A novel quantum gravity relation is derived and related to quantum mechanics.
Quantum Gravity: A Heretical Vision
Springer Proceedings in Physics, 2014
The goal of this work is to contribute to the development of a background-independent, non-perturbative approach to quantization of the gravitational field based on the conformal and projective structures of space-time. But first I attempt to dissipate some mystifications about the meaning of quantization, and foster an ecumenical, non-competitive approach to the problem of quantum gravity (QG), stressing the search for relations between different approaches in any overlapping regions of validity. Then I discuss some problems raised by the approach we call unimodular conformal and projective relativity (UCPR).
Remarkable aspects and and unsolved problems in quantum gravity theory
Academia Letters, 2022
The search of a theory of quantum gravity (QG) which is consistent both with the principles of quantum mechanics as well as with the postulates of the classical Einstein theory of General Relativity (GR) has represented until recently one of the most challenging, long-standing debated and hard-to-solve conceptual problems of mathematical and theoretical physics alike. In fact, a basic crucial issue is about the possibility of achieving in the context of either classical or quantum relativistic theories, and in particular for a quantum theory of gravity, a truly coordinate-(i.e., frame-) independent representation, realized by 4-tensor notation of physical laws. This means that the latter theory must satisfy both the principles of general covariance and of manifest covariance with respect to the group of local point transformations (LPT-group), i.e., coordinate diffeomorphisms mutually mapping in each other different GR frames. These principles lie at the foundation of all relativistic theories and of the related physical laws. In fact, although the choice of special coordinate systems is always legitimate for all physical systems either discrete or continuous, including in particular classical and quantum gravity, the intrinsic objective nature of physical laws makes them frame-independent. For the same reason, since LPTs preserve the differential-manifold structure of space-time, these principles represent also a cornerstone of the standard formulation of GR, namely the Einstein field equations and the corresponding classical treatment of the gravitational field. The same principles should apply as well to the very foundations of quantum field theory