## GR's Two-Timing Versus An Optical Theory of Gravitation

Weber's force has played a dominant role in electrodynamics since its discovery by Weber in 1845. It can be considered as an amalgamation of Ampere's law and Coulomb's law in the time domain.

Weber's force has played a dominant role in electrodynamics since its discovery by Weber in 1845. It can be considered as an amalgamation of Ampere's law and Coulomb's law in the time domain.

Newton proved, save claims to the contrary, that under an inverse square law force every orbit is a conic section. And the reverse is also true that every orbit which is a conic section corresponds to and inverse square law for the force. Newton showed this by using uniform circular motion in which the radius of curvature is constant. The radius of the Schwarzschild metric is not constant, but, rather $$\kappa=-\frac{\mathcal{R}}{r^3}\left(1-\frac{3\mathcal{R}}{4r}\right),$$ and so the Schwarzschild metric does not, nor cannot, lead to conical orbits.

An equivalent question would be: Does $\Gamma^{\mu}_{\alpha\beta}dx^{\alpha}/d\tau\cdot dx^{\beta}/d\tau\neq0$ represent gravitation in the geodesic equation

$$\frac{d^2x^{\mu}}{d\tau^2}+\Gamma^{\mu}_{\alpha\beta}\frac{dx^{\alpha}}{d\tau}\frac{dx^{\beta}}{d\tau}=0?$$

where the connection coefficients, or the Christoffel symbols, are

Much ado has been made about the classical tests of general relativity. There was nothing before Einstein, and, after, all was light, and gravity for that matter. What to do about Soldner's analysis of the deflection of light by a massive body that preceded Einstein by a century? Or Gerber's calculation of the perihelion shift of Mercury, which again preceded Einstein by almost a decade?

Numerical relativity is purported to be a numerical aid to general relativity that can tackle problems which general relativity can only formulate. One example is black hole merger which LIGO has said to have witnessed. In their article "Properties of Binary Black Hole Merger GW 1509+14, B. P. Abbott, *et. al.* claim

LIGO amounts to a Michelson interferometer with a time-varying index of refraction. Since the index of refraction is everywhere the same, there can be no change in wavelength, and, hence, there is no difference between the optical and geometrical path length. In an interferometer of length L there are $N_1=2L/\lambda_1$ wavelengths, since the laser beam makes (at least) two passes. With movable mirrors there will be other factors involved: e.g. radiation pressure, action-reaction, Doppler effect, etc. which neither LIGO no we will take into account.

Suppose that $v_g$ is the speed of propagation of the gravitational force, and $a_0$ be the initial semi-major at the initial time $t_0$ of an orbiting system. Celestial mechanics derives the following formula to compute the semi-major axis at any other time $t$,

$$a=\surd\left(a_0+4GM(t-t_0)/v_g\right),$$

It rate of change can be related to the rate of change of the angular velocity by the constraint placed by Kepler's law, $a^3\omega^2=\mbox{const}.$ Again, perturbation theory gives the rate of change of the period as

The original "Observation of Gravitational Waves from a Binary Black Hole Merger", that appeared in the February 2016 issue of *Phys. Rev. Lett.* is fraught with grave mistakes in the mathematical formulation, if it could be called that. In their paper, the LIGO team presents a single equation for the so-called 'chirp mass', and another equation in a caption for the "effective relative velocity given by the post-Newtonian parameter"

$$ (v/c)^3=GM\omega/c^3,$$

The LIGO team used the gravitational wave luminosity,

$$L=\frac{2}{5}\frac{G}{c^5}M^2a^4\omega^6,$$

Until the recent 'sightings' of the collision of pairs of binary black holes, the only evidence for gravitational radiation came from the application of Einstein's formula for gravitational wave luminosity and the change in the rate of the orbit of the pulsar PSR 1913+16 at a rate $dP/dt<10^{-12}$, equivalent to $<10\mu s/yr$ When Hulse first discovered PSR 1913+16, he found that the pulsar's period decreased by as much as $80 \mu s$ in one day.