Quantum Mechanics and the Metrics of General Relativity (original) (raw)
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.
Quantum Mechanics as a Theory Based on the General Theory of Relativity
2022
In this paper, we obtain the quantum dynamics in the framework of the general theory of relativity, where a quantum particle is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spatial coordinates and of the momentum, called wave functions. For a free particle, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time dependent phases proportional to the relativistic lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the particle wave functions, we obtain lorentz's force and the maxwell equations. For a quantum particle in electromagnetic field, we obtain dynamic equations in the coordinate and momentum spaces, and the particle and antiparticle wave functions. We obtain the scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion.
The Project of the Quantum Relativity
The intrinsic unification of the quantum theory and relativity has been discussed here in the light of the last developments. Such development is possible only on the way of the serious deviation from traditional assumptions about a priori spacetime structure and the Yang-Mills generalization of the well known U (1) Abelian gauge symmetry of the classical electrodynamics. In fact, more general gauge theory should be constructed. Formally we deal with the quantum version of the gauge theory of the deformable bodies-the gauge theory of the deformable quantum state. More physically this means that the distance between quantum states is strictly defined value whereas the distance between bodies (particle) is an approximate value, at best. Thereby, all well known solid frames and clocks even with corrections of special relativity should be replaced by the flexible and anholo-nomic quantum setup. Then Yang-Mills arguments about the spacetime coordinate dependence of the gauge unitary rotations should be reversed on the dependence of the spacetime structure on the gauge transformations of the flexible quantum setup. One needs to build " inverse representation " of the unitary transformations by the intrinsic dynamical spacetime transformations. In order to achieve such generalization one needs the general footing for gauge fields and for " matter fields ". Only fundamental pure quantum degrees of freedom like spin, charge, hyper-charges, etc., obey this requirement. One may assume that they correspond some fundamental quantum motions in the manifold of the unlocated quantum states (UQS's). Then " elementary particles " will be represented as a dynamical process keeping non-linear coherent superposition of these fundamental quantum motions.
arXiv: General Relativity and Quantum Cosmology, 2005
The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function of the field strength tensor F^uv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric g_uv is not only a solution to the second-order Einstein equation based on T^uv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappa_u for each T^uv. The common appearance of F^uv in all of the T^uv and kappa_v makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.
Quantum Theory within the Framework of General Relativity
Eprint Arxiv Gr Qc 0009052, 2000
A local conception (in the sense of the equivalence principle) is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties-as e.g. vacuum catastrophe-of the global approach. All nonlocal aspects of quantum theory, including EPR paradox, remain intact. 1 A slghtly improved version of the paper arXiv:gr-qc0009052.
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.
Recent mathematical developments in quantum general relativity
Arxiv preprint gr-qc/9411055, 1994
After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's superspace; ii) a rigorous procedure leading to the general solution of the diffeomorphism constraint in quantum geometrodynamics as well as connection dynamics; and, iii) a scheme to incorporate the reality conditions in quantum connection dynamics. Furthermore, there is a new language to formulate the central questions and techniques to answer them. These developments put the program on a sounder footing and, in particular, address certain concerns and reservations about consistency of the overall scheme.
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 Geometrization of Spacetime in General Relativity
The primary aim of this study is to establish a unified criterion for obtaining the gravity developed by quantum mass densities within spacetime. This is achieved by extending the principle of equivalence between inertial and gravitational mass, a fundamental aspect of General Relativity, to the covariance of equations of motion. In the classical scenario, we obtain the gravity of spacetime with classical characteristics, whereas in the quantum scenario, we obtain the gravity of spacetime with quantum mechanical properties. In both cases, the principle of least action is employed to define the geometry of spacetime. The gravity resulting from the quantum geometrization of spacetime can be seen as the quantum mechanical counterpart of General Relativity, where the fields of quantum physics are integrated into the theory of gravitation. In this study, we derive the gravity generated by boson and fermion fields. The outcomes of the theory have been utilized to derive antimatter gravity, resolve black hole singularities, and understand the origin of small-valued cosmological constants. The work also derives the fluctuations of the black hole quantum potential in the presence of the gravitational wave background and evaluates the resultant repulsive gravity at large distances. Furthermore, it examines the breaking of the matter-antimatter symmetry caused by the gravitational coupling of the fermions field. The significance of matter-antimatter asymmetry in pre-big bang black hole is described: This behavior implies that the matter-antimatter asymmetry might have played a crucial role in the highly energetic vacuum states of the pre-big bang black hole. When surpassing the Planck mass, the high-energy fermion state in the pre-big bang black hole's comprised fermion and antifermion black holes. The annihilation of these black holes emitted lighter fermions, accounting for the mass difference between the black hole and anti-black hole. The theory shows that as we approach the Minkowskian limit, the matter-antimatter symmetry becomes asymptotically established, and the mass disparity between particles and antiparticles diminishes as we transition from heavier to lighter particles within each particle family. The theory also shows that if antimatter symmetry were upheld, the vacuum would have collapsed into the polymer branched phase because there would have been no residual mass (resulting from the matter-antimatter difference) to stabilize the vacuum and confer a nonzero cosmological constant. Thus, the matter-antimatter symmetry in a quantum mechanical covariant gravity is incongruent with the formation of a physically stable vacuum with non-zero mean cosmological constant value. The process of quantum geometrization of spacetime provides a comprehensive framework for understanding the evolution of our universe, from the Pre-big bang black hole to the current quantum-decoherent classical reality. The theory posits that the ubiquitous presence of supermassive black holes (SMBHs) at the centers of galaxies is a direct consequence of the big-bang, from which SMBHs are generated without mass accretion, and that it plays a pivotal role in cosmological expansion, driven by their repulsive interactions. Finally, the system of field equations for Quantum Electrodynamics (QED) in curved spacetime (containing the fields back-reaction), along with an introductory section on the Standard Model in self-generated gravity is presented. The problem of second quantization of fields in spacetime with the coupled gravity of is also introduced. This has the potential to extend the standard Quantum Field Theory (QFT) to high energies. Experimental tests examining the disparities in magnetic moments between leptons and antileptons, as well as investigations involving entangled photons, are proposed as potential avenues for empirically validating the theory.
To the Issue of Reconciling Quantum Mechanics and General Relativity
The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 10 42 G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. If the numerical values of K 5.110 31 Nm 2 kg-2 and =4.410 29 m-2 , there is a spectrum of stationary states of the electron in its own gravitational field (0.511 MeV ... 0.681 MeV).Adjusting according to the known mechanisms of broadening does not disclose the broadening of the registered portion of the emission spectrum of the micropinch. It indicates the presence of an additional mechanism of broadening the registered portion of the spectrum of the characteristic radiation due to the contribution of the excited states of electrons in their own gravitational field. The energy spectrum of the electron in its own gravitational field and the energy spectra of multielectron atoms are such that there is a resonance of these spectra. As obvious, the consequence of such resonant interaction is appearance, including new lines, of electromagnetic transitions not associated with atomic transitions. The manuscript is the review of previously published papers cited in the references.
Classical and quantum general relativity: A new paradigm
General Relativity and Gravitation, 2005
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.
Quantum gravity as the unification of general relativity and quantum mechanics
2020
A nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg's matrix mechanics and Schrödinger's wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the invariance "within-out of" of the same system.
On the Integration of General Relativity with Quantum Theory and the Standard Model
2018
We propose (1) that the flat space-time metric that defines the traditional covariant Heisenberg algebra commutation rules of quantum theory between the four-vector position and momentum, be generalized to be the space-time dependent Riemann metric satisfying Einstein’s equations for general relativity (GR), which determine the metric from the energy-momentum tensor. The metric is then a function of the four-vector position operators which are to be expressed in the position representation. This then allows one (2) to recast the Christoffel symbols, and the Riemann and Ricci tensors in Einstein’s GR differential equations for the metric, as an algebra of commutation relations among the four-vector position and momentum operators (a generalized Lie algebra). This then (3) defines the structure constants of the rest of the Poincare algebra with the space-time dependent metric of general relativity tightly integrating it with quantum theory. (4) We propose that the four momentumoperat...
A general theory of quantum relativity
Physics Letters B, 2004
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics. 1
An Integration of General Relativity and Relativistic Quantum Theory
Cornell University - arXiv, 2016
We propose (1) that the flat space-time metric that defines the traditional covariant Heisenberg algebra commutation rules of quantum theory between the four-vector position and momentum, be generalized to be the space-time dependent Riemann metric following Einstein's equations for general relativity, which determine the metric from the energy-momentum tensor. The metric is then a function of the four-vector position operators which are to be expressed in the position representation. This then allows one (2) to recast the Christoffel, Riemann, and Ricci tensors and Einstein's GR differential equations for the metric as an algebra of commutation relations among the four-vector position and momentum operators (a generalized Lie algebra). This then allows one (3) to generalize the structure constants of the rest of the Poincare algebra with the space-time dependent metric of general relativity tightly integrating it with quantum theory. Finally, (4) we propose that the four-mometumoperator be generalized (to be gauge covariant) to include the intermediate vector bosons of the standard model further generalizing this algebra of observables to include gauge observables. Then the generalized Poincare algebra, extended with a four-vector position operator, and the phenomenological operators of the non-Abelian gauge transformations of the standard model form a larger algebra of observables thus tightly integrating all three domains. Ways in which this may lead to observable effects are discussed.
Understanding of Quantum Mechanics as a Theory Based on General Relativity
Current Research Progress in Physical Science Vol. 4, 2024
In this paper, the quantum dynamics was obtained in the framework of the general theory of relativity, where a quantum particle is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spatial coordinates and of the momentum, called wave functions. For a free particle, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time-dependent phases proportional to the relativistic Lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the particle wave functions, Lorentz’s force and the Maxwell equations were obtained. From the wave/group equation in the momentum space describing the Lorentz force, the expressions of the electric and magnetic fields as functions of the electric potential conjugated to time and of the vector potential conjugated to the coordinates in the particle-field Lagrangian were obtained. With these expressions, the electric and magnetic fields that satisfy the Faraday-Maxwell law of electromagnetic induction and the two Gauss-Maxwell laws of these fields were obtained. The Ampère-Maxwell law is obtained only by taking into account the physical consistency of the matterfield interaction of the equality of the propagation field velocity with the maximum relativistic velocity c. For a quantum particle in the electromagnetic field, dynamic equations in the coordinate and momentum spaces and the particle and antiparticle wave functions were obtained. It was shown that the electromagnetic potentials as functions of the coordinates describing the matter distribution of the quantum particle do not alter this distribution – under the action of an electromagnetic a quantum particle moves as a whole. The scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion, were obtained. This description of a quantum particle as a distribution of matter with a density amplitude/wavefunction of the form of a wave packet, with the time-dependent phase proportional to the relativistic Lagrangian as a function of the metric tensor including also the gravitational field, enables the application of this theory in quantum gravity and quantum field theory in agreement with general relativity.
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.
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...
Spacetime Based Foundation of Quantum Mechanics and General Relativity 1
This work makes the case that everything in the universe (all particles, fields and forces) is derived from the single building block of 4 dimensional spacetime. The tremendously large impedance of spacetime (c 3 /G) permits small amplitude waves in spacetime to be the universal building block. The spacetime wave-based fermion model is shown to plausibly possess the correct spin, energy and the ability to appear to be point particles in experiments. This model also generates the weak gravity curvature of spacetime and the gravitational force between particles. The electrostatic force between fundamental particles is also derived and shown to be related to the gravitational force through a simple difference in exponents. A new constant of nature is proposed which converts electrical charge into a strain of space. The distortion of spacetime produced by photons is also analyzed.