# LIGO: Gravitational Waves or Gravitational Tidal Effect?

General relativity correctly predicted the precession of the perihelion of Mercury and the correct angle of deflection of starlight by the sun both of which Newton’s theory of universal gravitation apparently had failed to correctly predict.

Newton’s theory of universal gravity also fails to describe the orbital decay of binary systems such as the Hulse-Taylor binary system which observation was consistent with general relativity. Favoring general relativity as the theory that correctly describes gravity is a clear cut decision considering its successes. General relativity succeeded where Newton’s theory of gravity had failed. But is the matter really settled? Let’s take a closer look at how Newton’s theory of gravity has been applied to the observations cited above.

In order to describe the evolution of two gravitationally interacting bodies  $a$  and  $b$  , the magnitude of the gravitational force is calculated using Newton’s equation for gravity  $\vec{F}={{G}_{N}}\frac{{{m}_{a}}{{m}_{b}}}{{{d}^{2}}}\vec{x}$  where  ${{m}_{a}}$  and  ${{m}_{b}}$  are the masses of the bodies, then substituted in the equation for Newton’s second law of motion; the familiar  $\vec{F}={{m}_{a}}\frac{\Delta {{{\vec{v}}}_{a}}}{\Delta t}$  where  $\frac{{{{\vec{v}}}_{a}}}{\Delta t}$  is the acceleration of $a$ . This is as straightforward a calculation as can be but there lays the problem.

Gravity, according to Newton’s law, is instantaneous. It follows that if gravity is instantaneous, so must the action of gravity be instantaneous. So applying the second law of motion (which is time dependent) to describe the effect of Newtonian gravity introduces a lag in the action that is incompatible with instantaneous gravity. This lag of the action of gravity introduced by using the second law of motion is precisely what caused predictive errors in Newtonian mechanical description of the precession of the perihelion of Mercury, of the bending of star light and of the orbital decay of binary systems. In fact, once the time dependency and consequently the time lag are eliminated from the gravitational action, we find that Newtonian gravity is in perfect agreement with observations (see Special and General Relativity Axiomatic Derivations).

The fact is that Newtonian gravity (when correctly applied) and general relativity can and with equal precision predict the behaviour of gravitationally interacting bodies for the above phenomena is problematic. This forces us to find other ways to answer the question as to whether gravity is a force that acts instantaneously between bodies or if is the effect of curvature of space due to the presence of matter. Clearly, the two explanations of the nature of gravity are foundationally incompatible.

It follows from QGD’s equation for gravity  $G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right)$  that gravity becomes repulsive when bodies separated by distances such that  $k\le \frac{{{d}^{2}}+d}{2}$ . That is, there is a threshold distance   ${{d}_{\Lambda }}\approx 10Mpc$  (from observations) beyond which gravity becomes repulsive and increases proportionally to the square of the distance.  The effect of repulsive gravity as described by QGD is consistent with the observed expansion of the universe which is currently attributed to dark energy. This allows for new predictions that are distinct from those of general relativity.

If QGD is correct, the magnitude of the gravitational repulsion between the Earth and the black holes that caused the GW150914 event must be  $2*{{10}^{3}}$  greater than the magnitude of the attractive gravitational force in close proximity to the binary system that caused the event. Such gravitational effect is astronomically greater than the signal detected by LIGO in 2015. In fact, the repulsive force would be enough to tear our galaxy apart from the gravitational tidal force and accelerate it to speed approaching the speed of light. And the repulsive force between the Earth and the recently observed GW170104 event, presumed to be a twice the distance, would be four times as great. The reason our galaxy (and others) is not torn apart is that the distribution of matter in the universe is nearly homogenous so that the repulsive gravitational forces from distant massive systems acting on each individual particle that compose our galaxy are nearly cancelled out by the repulsions from systems in the opposite directions; resulting in a weak net gravitational effect. So, if the GW150914 and GW170104 events are gravitational, the detected signals would be tidal effects of the net gravitational forces acting on the detectors . That is, the signals are not gravitational waves but the measurement of the instantaneous gravitational tidal effect  $\sum\limits_{i=1}^{n}{\vec{G}\left( a;{{b}_{i}} \right)}$  where  $a$   is the detector and  ${{b}_{i}}$  is one of a total of  $n$  massive structures forming the universe. So, LIGO may be thought as measuring the fluctuations of the gravitational tidal effect of the universe on its instruments.

Some Distinctive Predictions of QGD that Are Now Being Tested (or will be in the near Future)

If gravity is instantaneous as predicted by QGD and Newton’s law of universal gravity, then

• we will never detect multi-messengers signals from events predicted to simultaneously generate gravitational and electromagnetic signals.  Electromagnetic signal from the merging, for example, of neutron stars, would arrive up to billions of years after the gravitational signal.
• Gravitational signal from the merging of massive objects at distance close the threshold distance ${{d}_{\Lambda }}\approx 10Mpc$ would be undetectable.
• No loss in mass of the merging massive objects in the form of gravitational waves (in fact, there is no mechanism that may account for the conversion of mass into gravitational waves). The mass of the object resulting from the merging will be equal to the sum of the masses of the merged objects.
• Angular radius of the shadow of Sagittarius A* should be 10 times larger than predicted by general relativity

(more can be found in different section of this blog and in Introduction to Quantum-Geometry Dynamics)