We take note of the material offered in [1] as to Geometrodynamics as a way to quantify an inter relationship between a quantum style Heisenberg uncertainty principle for a metric tensor and conditions postulated as t...We take note of the material offered in [1] as to Geometrodynamics as a way to quantify an inter relationship between a quantum style Heisenberg uncertainty principle for a metric tensor and conditions postulated as to a barotropic fluid, i.e. dust for early universe conditions. By looking at the onset of processes at/shorter than a Planck Length, in terms of initial expansion of the universe, we use inputs from the metric tensor as a starting point for the variables used in Geometrodynamics.展开更多
Classical mechanics and quantum mechanics are the two cornerstones of science. As is well known, classical mechanics, the theory that describes the macrophysical world, has grown and flowered both in experimentation a...Classical mechanics and quantum mechanics are the two cornerstones of science. As is well known, classical mechanics, the theory that describes the macrophysical world, has grown and flowered both in experimentation and theorization. The same is not true of quantum mechanics, the theory that describes the microphysical world. While experimentation has shown giant strides, theorization has been essentially static, having not moved appreciably beyond the great achievements of the 1920s. The reason is not difficult to fathom: while theoretical progress in classical mechanics has been intellect-driven, that in quantum mechanics, on the other hand, has been machine-driven! In this paper we describe both classical and quantum systems in an absolute and a common language (geometry). Indeed, we construct the whole of science on the basis of just three numbers, namely, 1, 2, and 3.展开更多
Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures...Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures which are preserved. We apply the resulting construction to convert the BTZ black hole metric to ITQG framework. We then modify the BTZ black hole in order to investigate the existence of the P-V criticality in ITQG theory.展开更多
In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi met...In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.展开更多
文摘We take note of the material offered in [1] as to Geometrodynamics as a way to quantify an inter relationship between a quantum style Heisenberg uncertainty principle for a metric tensor and conditions postulated as to a barotropic fluid, i.e. dust for early universe conditions. By looking at the onset of processes at/shorter than a Planck Length, in terms of initial expansion of the universe, we use inputs from the metric tensor as a starting point for the variables used in Geometrodynamics.
文摘Classical mechanics and quantum mechanics are the two cornerstones of science. As is well known, classical mechanics, the theory that describes the macrophysical world, has grown and flowered both in experimentation and theorization. The same is not true of quantum mechanics, the theory that describes the microphysical world. While experimentation has shown giant strides, theorization has been essentially static, having not moved appreciably beyond the great achievements of the 1920s. The reason is not difficult to fathom: while theoretical progress in classical mechanics has been intellect-driven, that in quantum mechanics, on the other hand, has been machine-driven! In this paper we describe both classical and quantum systems in an absolute and a common language (geometry). Indeed, we construct the whole of science on the basis of just three numbers, namely, 1, 2, and 3.
文摘Intrinsic time quantum geometrodynamics is a formulation of quantum gravity naturally adapted to 3 + 1 dimensions. In this paper we construct its analogous 2 + 1 formulation, taking note of the mathematical structures which are preserved. We apply the resulting construction to convert the BTZ black hole metric to ITQG framework. We then modify the BTZ black hole in order to investigate the existence of the P-V criticality in ITQG theory.
文摘In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.
