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.
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.