Gravitational Fields and Gravitational Waves

For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

A Unified Theory of All the Fields in Elementary Particle Physics Derived Solely from the Zero-Point Energy in Quantized Spacetime

We propose a new theory beyond the standard model of elementary-particle physics. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. No serious undetermined parameters are assumed. Furthermore, the relations between the forces at the quantum-mechanics level is made clear. Using these relations, we quantize Einstein’s gravitational equation and explain the Dark Energy in our universe. Beginning with the zero-point energy of the vacuum, and after quantizing Newtonian gravity, we combine the energies of a static electromagnetic field and gravity in a quantum spacetime. Applying these results to the Einstein gravity equation, we substitute the energy density derived from the zero-point energy in addition to redefining differentials in a quantized spacetime. We thus derive the quantized Einstein gravitational equation without assuming the existence of macroscopic masses. This also explains the existence of the Dark Energy in the universe. For the weak interaction, by considering plane-wave electron and the zero-point energy, we obtain a wavefunction that represents a β collapse. In this process, from a different point of view than Weinberg-Salam theory, we derive the masses of the W and Z bosons and the neutrino, and we calculate the radius of the neutron. For the strong interaction, we previously reported an analytical theory for calculating the mass of a proton by considering a specific linear attractive potential obtained from the zero-point energy, which agrees well with the measurements. In the present study, we calculate the strong interaction between two nucleons, i.e., the mass of the pi-meson. The resulting calculated quantities agree with the measurements, which verifies our proposed theory.

Entropy Generation Due to the Heat Transfer for Evolving Spherical Objects

Heat transfer accompanying entropy generation for the evolving mini and microbubbles in solution is discussed based on the explicit solutions for the hydrodynamic equations related to the bubble motion. Even though the pressure difference between the gas inside the bubble and liquid outside the bubble is a major driving force for bubble evolution, the heat transfer by conduction at the bubble-liquid interface affects the delicate evolution of the bubble, especially for sonoluminescing the gas bubble in sulfuric acid solution. On the other hand, our explicit solutions for the continuity, Euler equation, and Newtonian gravitational equation reveal that supernovae evolve by the gravitational force radiating heat in space during the expanding or collapsing phase. In this article, how the entropy generation due to heat transfer affects the bubble motion delicately and how heat transfer is generated by gravitational energy and evolving speed for the supernovae will be discussed. The heat transfer experienced by the bubble and supernovae during their evolution produces a positive entropy generation rate.

The Modern Induced Matter Approach of General Relativity for Quantum Mechanics

Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which fits Hubble expansion in a ”microscopic” cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory.

Klein-Gordon-Fock equation from Einstein general relativity

A time-space symmetry based cylindrical model of geometrical dynamics was proposed. Accordingly, the solution of Einstein gravitational equation in vacuum has a duality: an exponential solution and a wave-like one. The former leads to a "microscopic" cosmological model with Hubble expansion. Due to interaction of a Higgs-like cosmological potential, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve. In the result, the wave-like solution leads to Klein-Gordon-Fock equation which would serve an explicit approach to the problem of consistency between quantum mechanics and general relativity.

Icosahedral Symmetry: A Review

This Review covers over 40 years of research on using the algebras of Quarternions E6;E8to model Elementary Particle physics. In particular the Binary Icosahedral group is isomorphic to theExceptional Lie algebra E8 by the MacKay correspondence. And the toric graph of E8 in Fig.2 with240 vertices on 4 binary Riemann surfaces each carrying 60 vertices, models a solution of the Ernstequation for the stationary symmetric Einstein gravitational equation. Furthermore the 15 synthemesof E8, consisting of 5 sets of 3,can be identified with algebraic representations of the nucleon,supersymmetric particles,W bosons and Dark Matter.

Icosahedral Symmetry and Quantum Gravity

In this note we will show that Theta functions are a solution of the icosahedron equation and also a solution of the Ernst equation for the stationary axisymmetric case of Einstein’s gravitational equation.