The Contribution of the Gravitational Propagation Delay to Orbital and Center of Mass Motions

Recent measurements have shown that gravitational waves and thus the gravitational interaction propagate with the speed of light. The propagation delay of the gravitational interaction in orbiting systems couples the orbital and center of mass motions. This causes the orbits to spiral out and the center of mass to accelerate. It is one of a number of small effects modifying the Kepler orbits. The calculations show that the analytical describable expansion of the semimajor axis started at a time that is less than the age of the systems. This could be caused by a collision of a system component in the past. The effect of this propagation delay on the motion of the Earth Moon and the Brown Dwarf 569Bab binary star system is analyzed. These systems were chosen because a considerable amount of measured astronomical data is available. The calculated results are in excellent agreement with the measured data. In galaxies, too, the energy transfer from the orbit of the star cloud to the center of mass motion causes the galaxies to ac-celerate. If galaxies are considered to be molecules of the universe, then the acceleration of the galaxies will cause the molecular gas to heat and expand. Alternatively, the loss in orbital internal energy of the galaxies should be included in the mass and energy in the calculation of the expanding Universe.

Reaction Mechanics for Point Objects

The least action principle is used to derive a general mathematical model of the motion of point objects subject to non-instantaneous interactions. A Lagrangian Equation of Motion, a Hamiltonian Formalism, a Poisson Bracket and the Relation of Reaction Mechanics and the General Theory of Relativity are derived here. In the limit of no delay, the equation of motion reverts to Newtonian Mechanics. In the limit of infinitesimal delay, the equation of motion takes the form of the Geodesic Equation of Motion of the General Theory of Relativity. For two objects, the single instantaneous interaction splits into two interactions when the propagation delay is considered. Object ONE experiences the following interactions at the present: it senses an interaction radiated by object TWO in the past. It also radiates an interaction that other objects might or might not sense in the future. It experiences a Recoil interaction equal in magnitude and opposed to the direction of the interaction it radiated. The Recoil interaction is independent of the radiated interaction reaching its target or not reaching its target. The Recoil interaction is causal.

Energy Conservation and Gravitational Wavelength Effect of the Gravitational Propagation Delay Analysis

The motion of objects where the interaction propagated with a finite velocity was analyzed in my previous paper “The Contribution of the Gravitational Propagation Delay to Orbital and Center of Mass Motions”. It is shown here that this analysis is valid for the case when the wavelength of the gravitational wave excited by the motion of the masses is much larger than the system of masses. It is also proven here that the conclusion reached in my previous paper conserves energy. Since this interaction is conservative, the energy is equal to the Hamiltonian. Therefore, the Hamiltonian is calculated and it is shown that the time derivative of the Hamiltonian is equal to zero. Thus, the Hamiltonian and therefore, the energy, are constants.

The Propagation Delay Effect of the Expansion and Inflation of the Universe

The effect of the propagation delay of gravitational interactions results in a singularity of the normalized acceleration of the radius of a sphere representing the Universe. Stephen Hawking in his Inflation Model also discusses a delay type interaction. This term can be used to model the inflationary rapid expansion of the early Universe. Since the Universe is thought to occupy all of space-time, one cannot define a boundary or radius of the Universe. Therefore, the properties of a sphere in the Universe are analyzed. It is assumed that the Universe will behave similarly to this sphere. This analysis is performed by including the effect of the propagation delay of gravitational interactions in Einstein’s equation.

Delay Harmonic Oscillator

The motion of two point objects at the end of a spring is analyzed. The objects interact by an elastic wave propagating through the spring. A new comprehensive method, Reaction Mechanics, for the analysis of this motion is used.? This analysis is valid when the propagation of the interaction through the spring wire takes less time than the period of the oscillating frequency. The propagation delay couples the oscillating and center of mass motions. If the masses are equal, the center of mass velocity is a constant, and the objects oscillate with a frequency which is a modification of the oscillation frequency with no delay. If the masses are not equal, the center of mass also oscillates. In the case of zero delay, the motion of the objects reverts to the motion of a Simple Harmonic Oscillator.

Light Induced Gravity Phonons

Einstein theorized that a mass travels towards another mass, not because it is attracted by a force acting across a distance, but because it travels through space and time that is warped by masses and energy. Einstein postulated that this space-time fabric can have wave-like modes which have been measured by the LIGO experiment. A consistent model of the generation of space-time-fabric-modes by a light Photon is derived for slight space-time deformations. Each Photon generates a shower of very small amplitude space-time fabric modes. Each mode can have a number of energy quanta. The probability of a Photon generating a shower of space-time modes is much larger than the probability of all the space-time modes collecting and generating a Photon. Therefore, this process has a unique Arrow of Time. Similar to the energy quanta of displacement modes in an elastic medium which is called Phonons, the energy quanta of the space-time fabric modes are called gravity Phonons. Both are tensor waves. Gravity Phonons have spin angular momentum of 2 and propagate with the speed of light. At every step of these calculations, equations derived from the General Relativity Theory by scientists and verified by Astronomical observations or experiments are employed.

Space-Time Curvature Mode Quanta

Einstein theorized that Gravity is not a force derived from a potential that acts across a distance. It is a distortion of space and time in which we live by masses and energy. Consistent with Einstein’s theory, a model of space-time curvature modes and associated curvature quanta in slightly warped space-time generated by a light Photon is derived. Both a Schr?dinger and a Second Quantized representation of the space-time curvature mode quanta are calculated and are fourth rank tensors. The eigenvalues of these equations are radii of curvature, not energy. The Eigenfunctions are linear functions of the components of the tensor that describes the curvature of space-time.

Information Theory Model for Radiation

Information based models for radiation emitted by a Black Body which passes through a scattering medium are analyzed. In the limit, when there is no scattering this model reverts to the Black Body Radiation Law. The advantage of this mathematical model is that it includes the effect of the scattering of the radiation between source and detector. In the case when the exact form of the scattering mechanism is not known a model using a single scattering parameter is derived. A simple version of this model is derived which is useful for analyzing large data.