The Unified Equation of Gravity and QM: The Case of Non-Relativistic Motion (original) (raw)
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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.
EXTENSION OF NEWTONIAN MECHANICS TO THE QUANTUM WORLD
This article describes a model of Unitary Quantum Field theory where the particle is represented as a wave packet. The frequency dispersion equation is chosen so that the packet periodically appears and disappears without form changings. The envelope of the process is identified with a conventional wave function. Equation of such a field is nonlinear and relativistically invariant. With proper adjustments, they are reduced to Dirac, Schrödinger and Hamilton-Jacobi equations. A number of new experimental effects have been predicted both for high and low energies. Fine structure constant (1/137) was determined in 1988, masses of numerous elementary particles starting from electron were evaluated in 2007 with accuracy less than 1%. 2 pentaquarks, θ^+barion, Higgs boson and particle 28 GeV were discovered 11 years later, all of them were evaluated with high accuracy before. The overall picture of the world is based on a unify field. These Equations allow for the beginning of a universe without a Big Bang. Gravity ceases to be a mystery. In principle, a completely new type of "green" energy is possible for mankind.
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It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution. The measurement apparatus itself can impose non-redundant boundary conditions. Measurements of such an object would fail to satisfy the distributive law of classical physics. This model reconciles General Relativity and Quantum Mechanics without the need for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it is not universal; classical particles and waves could exist and there is no graviton.
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.
arXiv (Cornell University), 2010
When a mountaineer is ascending one of the great peaks of the Himalayas she knows that an entirely new vista awaits her at the top, whose ramifications will be known only after she gets there. Her immediate goal though, is to tackle the obstacles on the way up, and reach the summit. In a similar vein, one of the immediate goals of contemporary theoretical physics is to build a quantum, unified description of general relativity and the standard model of particle physics. Once that peak has been reached, a new (yet unknown) vista will open up. In this essay I propose a novel approach towards this goal. One must address and resolve a fundamental unsolved problem in the presently known formulation of quantum theory : the unsatisfactory presence of an external classical time in the formulation. Solving this problem takes us to the very edge of theoretical physics as we know it today!
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AIP Conference Proceedings, 2007
The unity of classical mechanics and electromagnetism is proposed to be established through putting both on equal footing. The special-relativistic equations of motion for the particles and fields, the Maxwell-Lorentz force, and the Yukawa potential are derived exploiting Newton's and Euler's (stationary-)state descriptions, Newton's decomposition of forces into body-and position-dependent factors, and Helmholtz's analysis of the relationships between forces and energies. For instance, the magnetic Maxwell-Lorentz force is a special case of the Lipschitz force being a general class of forces that leave the kinetic energy constant. Adding this force to Newton's force of gravity leads to self-standing fields representing the mediating agent of interaction sought by Newton. Thus, equal footing is realized through a foundation on common principles, but not through a reduction to mechanical models.
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The present approach, which we named as "Quantal Theory of Gravity" (QTG), is based on the law of energy conservation and remains in full symbiosis with quantum mechanics (QM). Despite being built on different foundations, QTG and the General Theory of Relativity (GTR) yield practically identical results for the majority of classical problems historically considered to validate GTR. All the same, QTG successfully combines metric and dynamical methodologies, and, in the quantal case, delivers a new motional equation in the presence of gravity and a novel metric expression of space-time wherefrom one can independently derive all of the classical findings of the past century. What is more, QTG separately explains the propagation of projectile-like entities, such as high-energy gamma-quanta, in which case it predicts a drastic decrease of gravitational bending. This latter result falls outside the scope of GTR, as well as other purely metric theories of gravity, and constitutes an important aspect with regards to the experimental test of QTG.
Unitary theory of quantum mechanics and general relativity
Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.
Quantum Mechanics as a Classical Theory II: Relativistic Theory
2008
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic’s relativistic equations are obtained in the presence of electromagnetic fields for both the density function and the probability amplitude. It is shown that, within the present theory’s scope, Dirac’s second order equation should be considered the fundamental one in spite of the first order equation. A relativistic expression is obtained for the statistical potential. Axioms are again altered and made compatible with the general theory of relativity. These postulates, together with the idea of the statistical potential, allow us to obtain a general relativistic quantum theory for ensembles composed of single particle systems. 1