Gravitational Waves Theory

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Gravitational Waves Theory

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Copyright © 2020 Abdullah Al-Naddah All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. For permission requests, write to the publisher, addressed “Attention: Permissions Coordinator,” at the email below. Abdullah M. Al-Naddah [email protected]

SPARKLE This is a nonfiction book; it is scientific in nature and has nothing to do with literature other than the following quote from a poem by Walt Whitman. I found it suitable for use in commemorating Isaac Newton for his tremendous piece of work in the field of gravitational force. v “O Captain! my Captain! rise up and hear the bells; Rise up—for you the flag is flung—for you the bugle trills, For you bouquets and ribbon’d wreaths—for you the shores a-crowding, For you they call, the swaying mass, their eager faces turning”

Table of Contents FORWARD .............................................................................................................. 4 1. BRIEF HISTORY OF GRAVITY ........................................................................ 6 2. FOUNDATIONS OF GRAVITATIONAL WAVES THEORY .................. 11 3. EXTENSION TO NEWTON'S LAW OF UNIVERSAL GRAVITATION .................................................................................................... 18 4. THE TIME MEASURE, WHETHER ABSOLUTE OR RELATIVE ....... 25 5. THE INCONSTANCY OF THE SPEED OF LIGHT .................................. 29 6. FREQUENCY AND MASS-ENERGY EQUIVALENCE .......................... 32 7. THE DUAL BEHAVIOR OF CHARGED PARTICLES ............................ 39 8. WEATHER PHENOMENA AND THE CORIOLIS EFFECT .................. 42 9. PREDICTIONS AND RECOMMENDATIONS FOR UPCOMING GENERATIONS .................................................................................................. 45 10. SOURCES FOR THE CONTENT OF THE IMAGES ............................... 49

FORWARD The journey to discovering the fundamental laws of nature is endless. No matter how much we discover about these laws, we will continue being uncertain about what we found. Always, someone will be asking whether the discoveries are right or wrong, accurate or not. Even when we have practical and mathematical proofs, either there will be deviations from the standardized equations or they will be accurate only in ranges that are called “limits”. The simple example of that is the historical argument concerning GRAVITY. The latest claim was from Albert Einstein, who proposed different fundamentals for GRAVITY in his General Theory of Relativity, which was created over two hundred years after the proposed Theory of Gravitation by Isaac Newton. Although each of them supported his argument by using math and practical proofs, Newton’s proposal had deviations in some measures, while Einstein’s proposal works only in limits, as it does not yet work on a Quantum scale. However, regardless of who is right and who is wrong, GRAVITY IS NOT YET WELL KNOWN. So, the intention behind writing this manuscript is to shed light on GRAVITY by not only highlighting the contradictions in the previous theories but also by sharing a new proposal for the fundamentals of gravitational force. Throughout the journey to understand the previous philosophies about gravity, the Theory of Gravitational Waves was born from the identified similarities in addition to my own thoughts. It was necessary to add small modifications to the previous equations that explain Gravitational Force, the Momentum of Moving Objects, the Equivalence of Mass and Energy, and Time Measures. While the modified equations are very simple and not yet supported by practical results or advanced mathematics, the sounds of logic, the reasonable derivation, and the theoretical results should be found to be good enough to attract the attention of the physics community. Otherwise, due to the newly highlighted concerns along with the newly proposed ideas in this manuscript, the physics community would 4

probably have a hard time convincing the young generation of the validity of the current scientific concepts. Some of them would probably believe that the current generation regards dealing with nuclear energy as akin to cavemen dealing with fire.


1 BRIEF HISTORY OF GRAVITY The Newtonian apple was NOT the first attempt to answer the question of gravity. The first known attempt to answer this question was around 330 BCE, when Aristotle presented his argument that there is no effect or motion without a cause, and that air, earth, fire, and water have a place in which they travel. According to him, objects that contain more earth would fall to the ground faster than objects that contain less earth. In other words, heavy bodies tend toward the center of the universe (referring to the Earth) because of their heaviness and are not attracted to it by an external force. However, in the sixth century, John Philoponus proposed the theory of impetus (a modification of Aristotle's theory), in which, according to him, the continuity of motion depends on the continuity of the force acting upon it. Thus, to the discussion, he added a causative force that diminishes through time. Ibn Sina, in the 11th century, supported Philoponus’ theory while explaining projectile motion: "the moved object acquires an inclination from the mover". With this, Ibn Sina published his own theory of impetus in The Book of Healing. However, unlike Philoponus, Ibn Sina presented the impetus as a persistent one, requiring external forces such as air resistance to dissipate it. In the same century, Al-Biruni proposed that heavenly bodies have mass, weight, and gravity, just like the Earth. He criticized both Aristotle and Ibn Sina, who were not of the view that heavenly bodies have such properties and believed that only the Earth has mass, weight, and gravity.


BRIEF HISTORY OF GRAVITY In the 12th century, both Al-Biruni and Al-Khazini studied the theory of the center of gravity, which they generalized and applied to three-dimensional bodies. They also created the science of gravity and found experimental methods that were developed to determine the specific gravity or specific weight of objects. In the same century, Abu Al-Barakat Al-Baghdadi, who supported the view of Ibn Sina, came up with a modification of the theory of impetus for projectile motion, in which he stated that the mover imparts a violent inclination on the moving object and that this diminishes as the moving object distances itself from the mover. He also introduced the concept of the gravitational acceleration of falling bodies as an accumulation of successive increments of power with successive increments of velocity. Ibn Bajjah, in the same period, came up with a proposal that, for every force, there is always a reaction force, though he did not specify whether these reaction forces were equal. This could be recognized as the early version of the third law of motion; for every action, there is an equal and opposite reaction. Scientific conflicts raged in the 14th century when Jean Buridan, along with the Merton College of Oxford, rejected the Aristotelian concept of gravity. According to them, the motion of objects is attributed to an impetus (related to momentum) that varies according to velocity and mass. Along with Albert Saxony, Buridan adopted Al-Baghdadi’s theory that the acceleration of a falling body is a result of an increase in its impetus. Albert Saxony also developed the square law concerning the relationship between the speed of an object in free fall and either the time or space elapsed. The mean speed theorem was introduced in the same century by Merton College, and was used later in the gravitational equations. In the 16th century, Al-Birjandi introduced a hypothesis concerning the Earth's rotation. It was similar to Galileo’s 17th-century concept of circular inertia, which was an attempt to explain planetary orbits without gravity. Additionally, the contribution of Galileo Galilei in the studies that concern gravity is NOT limited to his concept of circular inertia. In addition to other fields, he 7

BRIEF HISTORY OF GRAVITY studied speed and velocity, gravity and free fall, the principle of relativity, and projectile motion, as well as worked in applied science and technology, describing the properties of pendulums, which are all linked to explain gravity. However, among all of his contributions, the experiment he conducted on gravity using the Tower of Pisa was a turning point in the history of gravity. Out of his experiment, the common belief that a heavier object falls faster than a lighter one was proven wrong, contradicting Aristotle's concept. Thus, according to Galileo, all objects in free fall tend to accelerate equally in relation to the duration of their fall. He accordingly hypothesized that the distance of a falling object is proportional to the square of the time elapsed. Thus, Galileo was the first to calculate the gravitational acceleration constant for Earth. Francesco Maria and Giovanni Battista confirmed, in the same century as Galileo, the relation of the distance of objects in free fall to the square of the time taken. They also calculated the gravitational constant by recording the oscillations of a pendulum. In the 17th century, after Galileo, the story of the Newtonian apple started. However, Newton did not ask the same question about the falling apple. Instead, he compared the apple to the Moon. Thus, his questions were different: Why doesn’t the Moon either fall on the Earth like the apple or fly off from its orbit around the Earth? Are they both under the same natural force? To answer these questions, Isaac Newton came up with his own theory of gravity, in which he introduced the law of universal gravitation, which stated that: every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Newton formulated this law in his famous equation:


M1 ∗ M2 r!


BRIEF HISTORY OF GRAVITY * Where (F) is the force of gravity, (G) is the gravitational constant, which was first accurately measured by Henry Cavendish in 1797, M1 is the mass of object 1, M2 is the mass of object 2, and (r) is the distance between the two centers. It is worth mentioning that electricity, as a physical phenomenon associated with the presence and motion of matter that has the property of an electric charge, was known even before Newton. However, it was not heavily taken into consideration for gravity studies. In the 18th century, it was linked instead to a new field of study (magnetism). Many experimental results, as described by Maxwell's equations, indicated that electricity is part of the phenomenon called electromagnetism. The reason for mentioning this is that it highlights the similarities between Newton's law of universal gravitation and Coulomb's law of electrical forces, in 1785, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, but Coulomb's law has the product of two charges in place of the product of the masses in Newton’s law. The Coulomb constant is in place of the gravitational constant.

F = ke

q1 ∗ q2 r!

From the end of the 18th century until the early 20th century, there have been many attempts to unify gravity with electromagnetism. However, these attempts did not succeed in combining gravity and either wave or corpuscular theories of gravity until the landscape of physics was changed by the discovery of Lorentz transformations. Henri Poincare, Hermann Minkowski, and Arnold Sommerfeld tried using the principle of relativity to modify Newton's theory and to establish a Lorentz invariant gravitational law. On the other hand, Einstein had realized that Lorentz transformations are not generally applicable, but he retained them in his theory relativity. The theory states that the speed of light is constant in free space, but it varies in the presence of matter. The theory was only expected to hold when the source of the gravitational field is stationary. 9

BRIEF HISTORY OF GRAVITY In general relativity, the revolutionary ideas of gravity swept over the landscape of physics in the 20th century, and it is still leading the scene today. The reasons for its domination are that the proposed fundamental laws in general relativity are new and radically in contradiction to the previous philosophers. Unlike the others, Einstein sees the effects of gravitation as being attributed to a SPACETIME curvature instead of a force, referring to a fuse of the three dimensions of space and the time dimension as a single fourdimensional manifold. The other reason for the interest in this theory is linked to the appearing conflicts between two schools of physics (classical and modern). Thus, though there existed a lack of understanding of general relativity, it was not only the core of any scientific discussion between the two groups, but it attracted the attention of influential sponsors, who had different definitions of force, power, and energy than scientists. On the other hand, even with all supports to general relativity by physics community, it is still imperfect. One of the difficulties that general relatively faces is that free-falling objects can accelerate with respect to each other, which was a puzzle in terms of the principle of equivalence, which equalizes the free fall with inertial motion. To overcome such a challenge, Einstein proposed that matter curves spacetime and that free-falling objects move along locally straight paths in curved spacetime. Another, bigger difficulty that has been facing general relativity is that although there have been many attempts to synergize quantum mechanics with general relativity, the spacetime curvature diverges at the center of the black hole, at distances closer than Planck’s length. This challenge is the reason why theoretical physicists seek to describe gravity according to the principles of quantum mechanics in the field of study that is called quantum gravity.



The term “gravitational waves” has been around since the end of the 19th century, when Oliver Heaviside discussed the possibility of gravitational waves using the analogy between the inverse-square law in gravitation and electricity. Henri Poincare, in 1905, also proposed gravitational waves that are emanated and propagated from a body at the speed of light, to satisfy the requirement of Lorentz








electromagnetic waves due to an acceleration of electrical charge, gravitational waves should be produced due to accelerated masses in the relativistic field theory of gravity. Einstein also predicted gravitational waves in his general relativity. Recently, in 2017, the Nobel Prize was awarded to Rainer Weiss, Kip Thorne, and Barry Barish for their role in the direct detection by LIGO (Laser Interferometer Gravitational-Wave Observatory) of fourth gravitational waves from merging black holes and fifth gravitational waves from a binary neutron star merge. Nevertheless, unlike the current understanding, which attributes the production of gravitational waves to the existence of accelerated masses, ANY PARTICLE THAT ROTATES AROUND ITS OWN AXIS PRODUCES GRAVITATIONAL WAVES TOO, and what happens between the accelerated masses is NOT different from what happens with a single rotating object. The 11

FOUNDATIONS OF THE THEORY OF GRAVITATIONAL WAVES two accelerated masses create a third center of gravity at the center of the gravitational waves they produce, while the center of the gravitational waves that is produced by single rotating mass is at the center of its own axis. However, unlike the center of the gravitational waves that is produced by a single rotating mass, the center of the gravitational waves that are produced by accelerated masses is empty of masses. Thus, when the distance between the accelerated masses decreases, their acceleration increases to more than the speed of light. Thus, the force of the gravitational waves increases. When the produced gravitational waves become stronger than their centers of gravity, they will be decomposed at the weaker gravitational force surrounding their axes and recomposed around the axis of the third center of gravity. Referring to the detected gravitational waves by LIGO, the demonstration of the observation of the collision of two neutron stars in 2017 (Figure 2.0) supports the validity of this concept.

Figure 2.0

Gravitational waves detected from the collision of two neutron stars

Thus, from the biggest massive black hole to the smallest light unity of a photon, all objects produce gravitational force (in the form of waves), which varies depending on the cumulative MASS. So, obviously, the gravitational waves are the form of gravitational force that produces masses. Therefore, it is axiomatic to say: BIGGER GRAVITY PRODUCES BIGGER MASS AND BIGGER MASS PRODUCES BIGGER GRAVITY. This is not only logical and 12

FOUNDATIONS OF THE THEORY OF GRAVITATIONAL WAVES obvious, but also comes from a very strong foundation of facts in all previous and current theories, where rotation around the axis cannot be ignored as an effect on the proposed equations. However, it was not considered a main principle of gravity. The first example to highlight is within the dominant theory for gravity: general relativity. Although it has a strong mathematical basis, when it comes to explaining the effect of rotation around an axis, it has two ignored concerns (i.e., the constancy of the speed of light and explaining the structure of spacetime). Instead of being weaknesses, both concerns were mathematically turned into strengths supporting the foundations of general relativity. In contrast, if these concerns would be addressed correctly, the modified equations could go beyond the limits and reach infinity. As proof of this, rotation around an axis was considered in the gravitomagnetic frame-dragging effect (Lense–Thirring effect), which is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth, where it is also combined with de Sitter precession, which considered the presence of central mass, with the total precession obtained by combining both precessions. However, although the need for the Lense–Thirring effect is proof of the effect of rotation around an axis on the equations, it was not considered in the conceptual explanation for gravity. The prediction of the effects of rotation around an axis in general relativity does not mean that it was conceptually considered a cause of gravity at all. In general relativity, the gravitational force is attributed to SPACETIME curvature, which is structured in the common visualization as the fabric of space and time that is warped because of mass, just as the weight of a bowling ball placed on a rubber sheet would dent the sheet (Figure 2.1). On the other hand, rotation around an axis is considered only through frame-dragging as a prediction of an effect that explains the non-static stationary distributions of mass-energy. The common visualization of the structure of the frame-dragging effect on spacetime is shown in (Figure 2.2), which means that general relativity does not consider rotation around an axis to be a cause attributed conceptually to gravity. 13


Figure 2.1

Common visualization of spacetime

Figure 2.2

Common visualization of frame-dragging effect

Moreover, in 2011, the OPERA experiment (Oscillation Project with Emulsion-tRacking Apparatus (OPERA)) observed that muon neutrinos travel faster than the speed of light. Although in 2012 it was announced that this result was incorrect due to equipment failures, the physicists who had worked on the experiment refrained from interpreting the result, stating in their paper: “Despite the large significance of the measurement reported here and the stability of the analysis, the potentially great impact of the result motivates the continuation of our studies in order to investigate possible still unknown systematic effects that 14

FOUNDATIONS OF THE THEORY OF GRAVITATIONAL WAVES could explain the observed anomaly. We deliberately do not attempt any theoretical or phenomenological interpretation of the results”. What is very odd and fishy in the announcement that contradicts the initial result is the tension that emerged in the OPERA collaboration in the months after the initial announcement, when a vote of no confidence failed among more than thirty group team leaders. Spokesperson Ereditato and Physics Coordinator Autiero resigned from their leadership positions on March 30, 2012, with Ereditato claiming in the resignation letter that their results were "excessively sensationalized and portrayed with not always justified simplification" and that "The OPERA Collaboration has always acted in full compliance with scientific rigor: both when it announced the results and when it provided an explanation for them." Despite the debates over the observed results, which show a violation of special relativity, there was another explanation that referred to the variance in how fast the muon neutrinos travel to the variance of motion between latitudinal lines, which is axiomatic for any rotating sphere, and also a foundation in the theory of gravitational waves. Nevertheless, it should have been clear that the constancy of the speed of light is debatable whether or not it is a postulate. According to the gravitational waves theory, it should not be the only absolute frame of reference for the concept of relativity. Theoretically, the principles of relativity come from classical mechanics. Simply, from the cases in which the velocities of moving objects are compared to each other, like comparing the velocities of two cars to each other considering their directions. However, in Einstein’s theories, the principles of relativity are limited to cases in which the velocities of moving objects are comparable to only the speed of light, considering that the speed of light is the only absolute value and a limit that cannot be exceeded. So, it was smart to limit comparison of other velocities to it as if it were the fastest reachable speed. In other hand, the base of measuring the speed of light refers to the prediction of Maxwell’s equations, and it was not refers to an experimental measurement. In addition, Einstein did not differentiate between linear and angular velocity. According to him, the speed of light is absolute and constant Therefore, the 15

FOUNDATIONS OF THE THEORY OF GRAVITATIONAL WAVES consideration of the speed of light as a speed that cannot be exceeded should remain a prediction rather than a fact. What if there is another velocity that is faster than the predicted speed of light? What if the invisible light is faster than visible light? Both classical and modern physics are aligned when it comes to the effect of rotation around an axis as an overall concept. However, none of them attributed this effect to gravitational force. In quantum mechanics, SPIN is one of two types of angular momentum. The other is orbital angular momentum, which is the counterpart to the classical angular momentum of orbital revolution and appears when there is a periodic structure to its wavefunction as the angle varies. When one compares this to Newton’s universal law of gravitational force, it becomes clear that the missing pace of foundation is not considering the other type of angular momentum as per quantum mechanics (the SPIN), which supports the foundation of the GRAVITATIONAL WAVES THEORY. The only remaining thing to do is to synergize between relativity concepts and both types of angular momentum in the law of universal gravitation considering the concept of the variance of the angle in quantum mechanics. To understand the variance of the angle that plays a critical role in orbital angular momentum, it is important to find answers to the following questions: If one drew a straight line from Earth to the Sun and from the Moon to Earth, where would the Earth be located in reference to the equator of the Sun? And where would the Moon be located in reference to the equator of Earth? To answer these questions, the following fundamentals should be found to satisfy the mechanics of both classical and modern physics and to explain the universal phenomena in addition to being aligned conceptually with quantum mechanics: 1) Due to the rotation around an axis (x, y, and z), gravitational waves are produced, which cumulate masses around the center of gravity


FOUNDATIONS OF THE THEORY OF GRAVITATIONAL WAVES (where the values of x, y, and z are all ZERO). The mass is cumulated as CONSERVED ENERGY around the center of gravity. 2) Due to the variance of the kinetic energy, attributed to the rotation, which depends on the value of z, where the ultimate angular velocity (highest kinetic energy) is at z=ZERO, the gravitational waves cumulate masses in the form of a sphere as non-static stationary distributions of mass-energy, which explains the frame-dragging as predicted in general relativity. 3) Depending on the quantity of cumulative mass, the produced gravitational waves will curve the space while propagating the creation of the SPACETIME curvature, which looks like a spherical balloon that bends from the top and bottom. Thus, the SPACETIME should be formed out of several layers of fabric of space and time that is alike to the magnetic field lines (Figure 2.3) (Oblate Spheroid). 4) From the theory of relativity, the free-falling objects move along locally straight paths in curved spacetime, which means that the paths of the free-falling objects are always linked to the sphere through the arc of a great circle. In other words, the warped spacetime will affect the path of the free-falling object to be warped too. Thus, the least value of z to the center of gravity has the least effect of warped spacetime.

Figure 2.3

Visualization of how spacetime propagates through space



To answer the question concerning Earth’s location in reference to the equator of the Sun, it is necessary to integrate the fundamentals of the theory of gravitational waves with Newton’s law of universal gravitation. The starting point for integrating the fundamentals of both theories is through first understanding the relationship between the time and distance traveled, which was determined through Galileo’s experiment. He found that the distance depended on the square of the time and that the velocity increases as the object moves down the incline. The explanation for this stems from the relativity concept based on the fundamentals of both the theory of relativity by Einstein and the gravitational waves theory; any object at a far distance from the center of gravity (at high altitude), due to the velocity of rotation around the axis (gravitational waves effect), moves faster than any other object at a shorter distance to the center of gravity, though to the observer, both objects have the same velocity relative to each other. For example, an object hanging on a very tall tower travels faster than an observer who is at the bottom of the tower; however, to the observer, the hanging object is static and not moving at all. In classical physics, the hanging object is described as having POTENTIAL ENERGY. Only when it starts moving down does the observer start noticing its previous velocity as if it were accelerating. So, from the perspective of gravitational waves theory, the free-fall acceleration can be perceived as a free18

EXTWNSION TO NEWTON’S LAW OF UNIVERSAL GRAVITATION fall deceleration. In addition, the free-falling object does NOT fall in a straight line; considering the fact that Earth rotates around its axis, it falls in a curved line (Figure 3.0), though the observer perceives it as a straight line because the observer is in motion him/herself. This explains why the Frame-Dragging effect cannot be observed. However, the mass and energy can only be transferred; neither can be created or destroyed. Therefore, as changing direction is considered momentum, the free-falling object would be simply carrying momentum to be transferred. This is what happens not only with the pendulum experiment but also with the planets while orbiting. The Earth, while orbiting the Sun, has a momentum that equals its mass times its orbiting velocity (p=m*v), and, as per Newton's mechanics, the momentum is a vector quantity, possessing a magnitude and a direction.

Figure 3.0 Visualizing the actual path of a free-falling object

Considering the fundamental element of the theory of relativity that freefalling objects move along locally straight paths in curved spacetime, which is also a fundamental in the theory of gravitational waves, the paths of free-falling objects are always linked to the sphere (greater center of gravity) through the arc of a great circle. Thus, the great circle, due to the gravitational waves, which is attributed to the rotation of the Sun around its axis, is at the equator of the Sun. Therefore, Newton’s law of universal gravitation (F = G

!" × !" !!

) is perfect

at any given point on the orbit path of Earth, but only when the Earth is located at z=ZERO at all times in reference to the center of gravity of the Sun (the least 19

EXTWNSION TO NEWTON’S LAW OF UNIVERSAL GRAVITATION warped spacetime). That means there would be no observed acceleration at all. However, if the Earth, while orbiting the Sun, got any value of z that is either less or higher than ZERO, then its orbital path around the Sun would be warped, fluctuating its momentum while moving between the value of z+ to z-. The warped orbit path will still present a great circle around the center of gravity, but this would be a warped circle. The deformation ratio of the orbit path depends on the value of z in reference to the center of the rotating axis of the Sun. It would be as per the following mechanics: a) Due to the rotation around its axis, the Sun produces gravitational waves that curve spacetime (refer to Figure 2.3), where the motion varies based on the z value from its rotating axis. b) When Earth maintains the coordinate z=ZERO all the time, in reference to the center of gravity of the Sun, its momentum will remain the same all the time (no observed acceleration). Thus, its orbit path will maintain the shape of a perfect circle all the time (refer to the path of point (C) in Figure 3.1) c) When Earth does NOT maintain the coordinate z=ZERO, its momentum will fluctuate (observed to be accelerating and decelerating) between z+ and z-, and its orbit path will be warped. The deformation ratio depends on the value of coordinate z (refer to the path of points (A) and (B) in Figure 3.1). The orbit path is always going to be between z+ and z- to satisfy the principle that the orbit path takes the arc of a great circle. d) The value of the fluctuating momentum depends on the angle Theta between the highest value of z in reference to the equator of the Sun (Figure 3.1).



Figure 3.1

Visualizing the possible orbit paths around the Sun

It is clear from the explained mechanics that the orbit paths around the center of the greatest gravitational force are symmetric only when maintaining the coordinate value of z at ZERO at all the time, in reference to the center of gravity. Otherwise, none of the orbit paths would be symmetric. From Figure 3.1, the angle Theta can be calculated if the longest and shortest distances are known, as from the TRIGONOMETRY, cos θ =

!"# !"#$%&'% !"#$%&'( !"# !"#$%&' !"#$%&'(

. For Earth,

!"# !"##"$% !"

cos θ = !"# !"##"$% !" = 0.96709. Accordingly, the Earth must be located at 14.74 degrees from the Equator of the Sun when it is at either 147 million kilometers or 152 million kilometers from the Sun. Also, this degree decreases and increases while the Earth is orbiting the Sun, though this angle is the maximum it can get, and the Earth does not change its tilt while orbiting, as it is always tilting to the Sun either North-to-North or South-to-South (Figure 3.2). This explains the change in seasons. When Theta is ZERO, the Earth also does not need to change its tilt; it reaches a stabilized level of motion as spacetime is not warped as per the gravitational wave mechanics.



Figure 3.2

Visualizing the Earth’s tilt with respect to its location from the equator of the Sun

The strongest proof of the validity of the explained mechanics should be through scientific tests, either lab experiments or astronomers’ observations, which is the objective of this book. However, for the simple person who knows little about physics, Newton’s equation for gravitational force is known as: M1 ∗ M2 r!


Where (F) is the force of gravity, (G) is the gravitational constant, M1 is the mass of object 1, M2 is the mass of object 2, and (r) is the distance between the two centers. Only the distance between the two centers is changeable in this equation, and the distance cannot be changed unless the direction or velocity is changed. In addition, this equation should have been valid at all times. Thus, it should have been true that: G

!" × !" !!


!" × !" !!

at all times, and because the

gravitational constant and the two masses are all constants, then the following !


equation should have been true too: !! = !! . Now, this is scientifically proven to be wrong; the distances between planets are not equal at all times, as observed by astronomers. Nevertheless, the change in momentum cannot happen without a cause, and as explained in the Theory of Gravitational Waves, the cause is the variance of the angle from the center of the rotating axis, where z ≠ ZERO, which Einstein refers to as the curvature of spacetime. Newton did not address 22

EXTWNSION TO NEWTON’S LAW OF UNIVERSAL GRAVITATION it properly. Therefore, it is clear that there is a need for a corrective factor that !


can explain the variance in Newton’s equation, where !! ≠ !! after 180 degrees. This can be recognized from the explained mechanics of the gravitational waves theory, as the variance in the path is attributed to the change in angle from the !


center of gravity; to make !! = !! , the equation for the corrective factor can be taken from the cosine of the angle in reference to the equator of the greatest !!

gravitational waves axis. Thus: (cos θ)! = !! , where the distance on the top is the shortest one, and the distances cannot be equal unless the angle is ZERO. The reason for stating that the effect happens 180 degrees later is to satisfy the gyroscopic effect, in which the effect happens on any rotating system at 90 degrees before and 90 degrees after. Thus, the change from z=ZERO will appear 90 degrees before as torque (shortest distance) that is used to reach a higher inertia at 90 degrees (longest distance), while to satisfy the law of physics, where neither matter nor energy can be created or destroyed, the total amount of force remains the SAME in the total length of the orbit path. This happens as Momentum Fluctuation (gaining maximum momentum at a point to reach a higher inertia at the opposite point). Now, the square of the corrective factor (cos 𝜃) also satisfies the concept of the relationship between the time and distance traveled, where Galileo determined that the distance depended on the square of the time. Thus, adding the corrective factor to Newton’s law of universal gravitation should be recognized as representing time in Newton’s equation, which explains what is stated at the beginning, i.e., that a free-falling object does not accelerate at all but, rather, experiences a change in the angle of its direction in reference to the center of gravity, due to the rotation around an axis. When the object is hanging still, it travels in the same direction of spacetime as the observer, who is at the bottom. However, when it is released, it will look like it is accelerating, though it is, in fact, neither accelerating nor decelerating; rather, it is experiencing a change in the direction of its motion. In addition, at a higher distance, the z 23

EXTWNSION TO NEWTON’S LAW OF UNIVERSAL GRAVITATION coordinate from the rotating axis of Earth is bigger. Thus, the angle Theta is bigger and, accordingly, the change in direction would be more excessive. This is why the force is observed to be increasing as perceived acceleration to the observer. However, as the momentum is a vector quantity, possessing a magnitude and a direction, the change in direction should be observed from the perspective of TIME-DISTANCE change instead of either acceleration or deceleration. So, Newton’s equation is not only an amazing equation that explains gravity. If it were linked to the foundations of the theory of gravitational waves, it could be the entrance to the THEORY OF EVERYTHING.



Perceiving time is also a historical argumentative topic, not only for physicists but for most people who might have little knowledge of physics. The reason for making this topic the core of any debate in the physics community, in addition to society in general, is the confusion involved in using time as a measurement of the rate of change in different frames of reference. The clock on the wall or the watch on your wrist is a human-manufactured frame of reference for time, and it cannot be used as a frame of reference in physics, unless through the concept of relativity. However, this is not entirely true in reality; in classical and quantum mechanics, time is absolute, while in the theory of relativity, time is also absolute, though only in comparison to the speed of light as a frame of reference for space and time. Thus, only the speed of light is absolute; everything else is relative as per the concept of Albert Einstein. In contrast, from the perspective of the theory of gravitational waves, time is neither absolute nor relative; it is absolute in every relativistic frame of reference. This means, for any multiple systems that share the same frame of reference for time relative to each other, time is absolute and the same in every single system. Thus, the time in every single atom is absolute and the same in every relative single atom. For example, the fans of a losing team perceive time the same way as their peers in the amphitheater (as if it were going fast), while the fans of the winning team perceive time the same way as their own peers (as 25

THE TIME MEASURE, WHETHER ABSOLUTE OR RELATIVE if it were going slow). Putting this philosophy in a standard mathematical frame of reference is somewhat complicated, but through explaining the angular frequency (𝜔). The angular frequency is the point at which the theory of gravitational waves meets classical and quantum physics. It is also called angular velocity. It refers to how fast an object rotates relative to another point, or, in other words, to how fast the angular position or orientation of an object changes with time. The scalar measure of the rotation rate for angular velocity is RADIANs per second, not as per the known used unit for velocity (m/s). Therefore, the concept of angular velocity supports the foundation of the gravitational waves theory by addressing the rate of change for the rotation around an axis, which is also the (Spin) in quantum mechanics. It seems that the dilemma in physics is to find a standardized frame of reference for time to calculate the rate of change of momentum. So, it is not limited to find a standardized frame of reference for time that is to calculate the rate of change of distance, but also to calculate the rate of change of mass times distance. This is why the angular frequency is to present the magnitude of the vector quantity angular velocity, where one revolution equals (2𝜋 𝑟𝑎𝑑𝑖𝑎𝑛). To simplify the meaning of radian, one radian in measure presents the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Thus, the velocity in radians measurement can be represented:

𝐥𝐞𝐧𝐠𝐭𝐡 (𝐦) 𝐭𝐢𝐦𝐞 (𝐬)


= 𝟐 ∗ 𝛑 ∗ 𝐫𝐚𝐝𝐢𝐮𝐬(𝐦) 𝟑𝟔𝟎 , and, because the traveled

distance equals the radius, then:

𝐥𝐞𝐧𝐠𝐭𝐡 (𝐦) 𝐫𝐚𝐝𝐢𝐮𝐬 (𝐦)


= 𝟐 ∗ 𝛑 ∗ 𝐭𝐢𝐦𝐞 (𝐬) 𝟑𝟔𝟎 . Therefore,


𝐓𝐈𝐌𝐄 𝐬 = 𝟐∗𝛑∗𝛉. Hence, the radian is 57.2957759 degrees per second. In other words, the distance is separated from the measurement of motion, where the velocity has a different unit of measure; instead of being measured by the rate of change for distance over time, for angular velocity, it is measured by radians over time. The conceptual dilemma in this is in using the manufactured 26

THE TIME MEASURE, WHETHER ABSOLUTE OR RELATIVE frame of reference for time without considering the relativity concept. The manufactured frame of reference for time is not spreadable from the rotation of Earth, where 24 hours is an absolute measurement of time representing one day, while the day is relative on Earth, whether through considering the variance in motion between latitudinal lines or through considering the variance between the periods from the sunrises and sunsets. Thus, on Earth, the angular velocity is equal at every latitudinal line, where every latitudinal line rotates 57.2957759 degrees per about 4 hours (0.262 radian per hour), though the actual velocity is different because the used radius for measuring angular velocity refers to a circle, not a sphere. Therefore, every latitudinal line represents a circle that is shorter than the greatest rotating circle on Earth (the equator), and as previously explained for the mechanics of the gravitational waves, the angle of which an object is located in reference to the center of gravity defines the relative velocity, and thus, it defines the relative momentum. For this, every latitudinal line presents a circle that has the same measure in terms of the length of the radian relative to any other latitudinal line, but a different measure in terms of the length of the meter, although all of them have the same frame of reference for time (24 hours). Therefore, TIME is absolute in every relativistic frame of reference such as the latitudinal lines on the surface of a rotating sphere. When this explanation is linked to the curvature of spacetime, the time is attributed to the static axis (z-axis), like the time axis in the light cone (Figure 4.0), which is the path of a flash of light, emanating from a single event (localized to a single point in space and a single moment in time). The view of both the light cone and the sphere (Figure 4.1) from the top is the same. However, the hypersurface of the present is NOT FLAT, but is a warped sphere that looks like a bent balloon from top and bottom. This goes along with the new perception of the structure of spacetime (Figure 2.3). In my personal view, the debate over the perception of the hypersurface of the present, whether it is flat or spherical, is like debating whether the surface of the Earth is flat or spherical. 27


Figure 4.2

Sphere from top views



In classical physics, light is described as a type of electromagnetic wave, and its speed is predicted by Maxwell's equations, which describe the propagation of electromagnetic waves through the vacuum as of the distributed capacitance and inductance of the vacuum by the equation: c=

1 ε0µ0

* Where ε0 is the electric constant and µ0 is the magnetic constant. Because of the special relativity, the Speed of Light (c) in a vacuum became one of the universal physics constants. Its exact value is defined as 299,792,458 meters per second. The reason for the existence of an exact value is that wavelengths are from frequency measurements, and a given value of the speed of light is found to be more reproducible than the previous standard. The definition of second was kept, but the cesium hyperfine frequency was used to determine both the second and the meter. Therefore, as per an international agreement, the meter was redefined as "the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second". However, light usually does not propagate at a speed equal to c. Also, supporting the inquiries raised concerning the constancy of the speed of light, different types of light waves travel at different speeds. Such a variance in the observed speed of light refers to what is called phase velocity, 29

THE INCONSTANCY OF THE SPEED OF LIGHT which determines how light waves travel through a material or from one material to another, i.e., the refractive index. In exotic materials, the effective speed of light may reach a few meters per second. However, there are situations in which it seems that matter, energy, or information travels faster than the speed of light. For example, the phase velocity of X-rays through most glasses can routinely exceed the speed of light, regardless of the explanation that the phase velocity does not determine the velocity at which waves convey information. As the nature of light is from the electromagnetic wave, the debate of concerning the constancy of its speed is somehow linked to the debate concerning the nature of the gravitational force. On the other hand, while electromagnetism is one of the most important aggregations of empirical facts in the history of physics, its masteries are still not yet solved from the principia perspective, where the current biggest challenge is to explain the behavioral duality of matter (electrons and photons). Therefore, the calculation of the speed of light from the electric and magnetic constants is an area for questions. According to the explained foundations, the propagation of the electromagnetic field and the propagation of the gravitational waves are the same. However, the wave propagates in accordance with the principle of relativity as per the explained spacetime, which should be found as an extension of spacetime described by Albert Einstein. Therefore, the speed of light should also be presenting a magnitude of a vector quantity as either angular or linear velocity. Not only the light, but also any particle (including the electro charge one), carries on a duality of both linear and angular velocity, according to the linear and angular momentum. The mass is defined based on the angular velocity, while the speed is defined based on the linear velocity. Both definitions are found in the explained angular frequency, where the meter was defined through the concept of radian in order to define the velocity. The angular frequency (𝜔) is presented by:


!! !

= 2𝜋𝑓


THE INCONSTANCY OF THE SPEED OF LIGHT where T is the period, which is measured in seconds, and f is the ordinary frequency, which is measured in Hertz. If one assumes that the work of angular velocity is in the same position (no linear velocity associated), then the frequency


will be undefined, as the wavelength would be ZERO. However, when the linear

velocity is associated, the wavelength will be > ZERO. Thus, the frequency will be defined, though in different velocity ranges, where some velocities would be faster than the speed of light.



In physics, mass has an equivalent amount of energy and vice versa. The same principle applies to the theory of gravitational waves. The kinetic energy (as of rotation around a static axis) is conserved as momentum in a specified measure of space and time. Accordingly, mass, as per the new foundations, can be defined as conserved kinetic energy in a specified measure of spacetime. The current famous equation describing this equivalence is from Albert Einstein: E = mc ! * where E is the energy, m is the mass, and c is the speed of light in a vacuum. However, Einstein’s equation addresses the linear momentum only, where a moving object gains momentum and energy, but when traveling near the speed of light, it cannot move much faster. This implies that, in relativity, with the narrow perspective, the momentum of an object cannot be a constant times the velocity, nor can the kinetic energy be a constant times the square of the velocity. Thus, Einstein’s equation does not consider the angular velocity and the curvature of the light’s path. On the other hand, this is not the case in Max Planck’s equation: E=h∗f * where E is the energy, h is Planck’s constant, and f is the frequency.


FREQUANCY AND MASS-ENERGY EQUIVALENCE The mystique of the equation of mass-energy equivalence lies in involving the speed of light as a constant value in measuring the frequency. Unlike the speed of light, frequency carries the duality of both linear and angular velocity. However, by definition, the current measurement for frequency addresses its flow through time only, while its measurement through distance is addressed in the concept of relativity to the speed of light, which is measured through predictions and by other constants, not through the usual technical measures for velocity. On the other hand, as per the explained foundations of the gravitational waves along with the concept of angular frequency, the rotation is between the x- and y-axes, while the z-axis is static and represents time. Accordingly, frequency 𝒇 depends on the space in which the particle acts. For example, if we assume that there is a closed box and that a ball is hitting one of the walls, then bounces back to the opposite wall at a constant speed, assuming that the velocity is constant and that the two walls are close to each other, the frequency of the ball from one wall to another will appear to be greater than the frequency when the walls are far apart. The speed of the ball will also appear to be the same. This example explains the concern in synergizing the frequency and the speed of light. The frequency measures the number of occurrences of a repeating event per unit of time. From the highlighted example, one can see that the occurrence of repeated events per unit of time increases as the space in which the ball acts decreases. Considering the concept of relativity, the particle that moves in small distances appears to be faster than the speed of light, like Gamma rays, or the velocity of the electrons at a closer distance to the nuclei of an atom. Therefore, consider Louis de Broglie’s equation for electron wavelength (λ):

𝒎𝒆 ∗ 𝑽𝒆 = * where

𝒎𝒆 is

𝒉 𝝀


the electron’s mass, 𝑽𝒆 is the electron’s velocity, 𝒉 is Planck’s

constant, λ is the wavelength, and 𝒑 is the momentum. 33

FREQUANCY AND MASS-ENERGY EQUIVALENCE and Albert Einstein’s equation for energy and momentum:

𝒎𝒑𝒉 ∗ 𝑪 =

𝒉 𝝀


* where 𝒎𝒑𝒉 is the photon’s mass and 𝑪 is the speed of light. Thus, the following equation for MASS-ENERGY EQUIVALENCE should be true, too:

𝒎𝒑𝒉 ∗ 𝑪 = 𝒎𝒆 ∗ 𝑽𝒆 The last equation should be true in every frame of reference as explained in the time measurement and the inconstancy of the speed of light, considering the involvement of angular momentum. Therefore, the concept of relativity should be applied and exceed the current limitation of the speed of light, where the mass of the photon at the speed of light can be figured out from the following equation:

𝒎𝒑𝒉 =

𝒎𝒆 ∗ 𝑽𝒆 𝑪

considering that the speed of the electron in the relativistic frame of reference to the photon (in a vacuum) equals the electron’s velocity circling the hydrogen atom, which is 2.18 ∗ 10! m/s, then:

𝒎𝒑𝒉 =



∗ 2.18∗10



= 6.62406796 ∗ 10−33 Kg

Due to the similarity between this result and Planck’s constant, along with the similarities between the equations, if one regards Planck’s constant as if it were not a constant, and using this result with Einstein’s equation and Louis de Broglie’s equation, with the upper and lower ranges of wavelength for the visible light, the result would be as shown in the table:



𝒎𝒆 ∗ 𝑽𝒆 = 𝒎𝒑𝒉 ∗ 𝑪 = Table 6.0

𝒉 𝝀 𝒉

Wavelength (λ) in meter 400 ∗ 10!! 700 ∗ 10!!


400 ∗ 10!! 700 ∗ 10!!

Planck’s new value in Kg 7.943382463 ∗ 10!!" 1.390091931 ∗ 10!!" 7.943382463 ∗ 10!!" 1.390091931 ∗ 10!!"

The electron’s mass should not be considered as if it were coincidentally falling in between these results, but the vice versa. The utilization of multiple constants, which didn’t come from strong logical base, to describe the electromagnetism turned the science wheel to the wrong direction. This is the reason for the existence of scattered research in quantum mechanics. Surprisingly, the equation of Compton wavelength, which is a quantum mechanical property of a particle, is exactly like the equations of Einstein and Louis de Broglie: 𝝀=

𝒉 𝒎∗𝑪

* where 𝒎 is the particle’s mass, 𝑪 is the speed of light, 𝒉 is Planck’s constant, and λ is the Compton wavelength. Therefore, and depending on all the results above, equations, explanations, and the foundations of the gravitational waves, TIME and DISTANCE are to be chosen. Thus, one meter equals one second, and the frequency of the number of events occurring in one second equals the number of events occurring in one meter. Accordingly, the inversion of the wavelength should be considered velocity when one is calculating momentum. Based on this: The conserved angular momentum as mass can be converted to linear momentum as energy and vice versa. Also, the new quantum constant Pc (1.985845615 ∗ 10!!" 𝐾𝑔 ∗ 𝑚/𝑠) should be considered the constant momentum, which can be set as the maximum value for conservable momentum in a form of mass in a single particle.


FREQUANCY AND MASS-ENERGY EQUIVALENCE From the proposal of Gottfried Leibniz for the vis-viva, which describes the kinetic energy in an early formulation of the principle of the conservation of energy, Leibniz noticed, in many mechanical systems (of several masses, 𝑚𝑖 each with velocity 𝑣𝑖), the quantity:

𝒎 𝒊 ∗ 𝒗 𝒊𝟐 𝒊

If this is compared to Einstein’s equation E=mc^2, considering the new quantum constant Pc, then the following equation should be true too:


𝑷𝒄 𝝀

The theories of Louis de Broglie and Arthur Compton were very important discoveries in terms of wave-particle duality. Both equations are the same in terms of momentum equilibrium to Planck’s constant divided on the wavelength. However, the reason that de Broglie and Compton looked at the same equation from different conceptual angle is attributed to the first deviations in the electromagnetism field of study from the beginning. It was clear that Planck’s constant and the speed of light are NOT constants, but the combination of them as of conserved linear momentum is the constant. For example: let us assume a conservation of a specific amount of momentum in a space as big as a basketball, and a conservation of an equal amount of momentum in a space as big as a tennis ball, then the volume of the tennis ball would contain more mass than the volume of the basketball. This should be obvious from the density equation: 𝒎

𝝆 = 𝑽 , where 𝝆 is the density, 𝑽 is the volume, and 𝒎 is the mass. The same should be considered for the density of conserved energy. Therefore, the angular momentum and mass can represent one another, with the momentum representing the density of energy times the volume. Accordingly, the following should also be correct: 36

FREQUANCY AND MASS-ENERGY EQUIVALENCE 𝝆 ∗ 𝑽 = 𝒎𝒐𝒎𝒆𝒏𝒕𝒖𝒎 = 𝒎 ∗ 𝒗 = 𝑷𝒄 where 𝝆 is the density, 𝑽 is the volume, 𝒎 is the mass, 𝒗 is the velocity, and Pc is the new quantum constant for the maximum conservable energy. This equation can be rearranged considering the new quantum constant for the maximum conservable momentum Pc to be: 𝝆=

𝑷𝒄 𝑽

This equation also explains mass-energy equivalence through Avogadro’s number by synergizing it with pressure as a constant momentum of force, where the inverted Avogadro’s number equals pressure, and it almost equals the new quantum constant Pc. The derivation for the formula is as follows: From Avogadro’s law, “equal volumes of all gases, at the same temperature and pressure, have the same number of molecules”, the same should be applied to an atom. Therefore, as the law was mathematically written as: V V = k thus = n n k where n is the amount of substance in moles, V is the volume, and k is a constant for a given temperature and pressure; it should be a constant value representative of the temperature and volume of the system. This is from Boyle’s law, which states that the absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system. Therefore, Boyle’s law was mathematically written as: P∗V=k * From the equations of Avogadro and Boyle, the following equation should be correct:


= n thus !∗!


= n also !


! !


FREQUANCY AND MASS-ENERGY EQUIVALENCE From this equation, one mole contains Avogadro’s number (6.02214086 ∗ 10!" per mole). Inverting this amount produces the value of ( 1.66053904 ∗ 10!!" ). Regarding the unit, the pressure is the force over the unit area; thus: m F (Kg ∗ s ! ) Kg ∗ m !! !! P= = = Momentum( )m s ! A m s When one compares this unit to the unit of Planck’s constant (Kg m! s !! ), it is clear that the vector of the momentum as pressure is going in the opposite direction with respect to the same time, which satisfies the third law of motion: For every action, there is an equal and opposite reaction.



The wave-particle duality goes back to the fifth century, when Democritus argued that all things in the universe, including light, are composed of indivisible sub-components. This was followed by Ibn Al-Haytham who, in the 11th century, described reflection, refraction, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He asserted that these rays are composed of particles of light. In 1630, Rene Descartes showed that the behavior of light could be recreated by modeling wave-like disturbances in a universal medium luminiferous aether (ather). However, Isaac Newton developed an argument that the perfectly straight lines of reflection demonstrated light's particle nature, as only particles could travel in such straight lines. He explained refraction by positing that particles of light accelerated laterally upon entering a denser medium. Newton's contemporaries, Robert Hooke, Christiaan Huygens, and Augustin-Jean Fresnel, mathematically refined the wave viewpoint, showing that if light traveled at different speeds in different media, refraction could be easily explained as the medium-dependent propagation of light waves. The principle of Huygens–Fresnel was supported by Thomas Young's discovery of wave interference of light through the double-slit experiment in 1801. The wave view did not immediately displace the ray and particle view but it did begin to dominate scientific thinking about light in the mid-19th century, as it could explain polarization phenomena that the alternatives could not.


THE DUAL BEHAVIOR OF CHARGED PARTICLES James Clerk Maxwell discovered that he could apply his previously discovered equations, with a slight modification, to describe self-propagating waves of oscillating electric and magnetic fields. It quickly became apparent that visible light, ultraviolet light, and infrared light were all electromagnetic waves of differing frequencies. Max Planck, in 1901, published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object; he had to make a mathematical assumption about the quantized energy of the oscillator atoms of the black body that emits radiation. From Max Planck’s analysis, Einstein proposed that electromagnetic radiation itself is quantized, and not the energy of radiating atoms. For this, Albert Einstein stated, “It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do”. However, the equations of Louis de Broglie and Arthur Compton, which are both inherent in the equations of Max Planck and Einstein, support the proposed equation in the theory of gravitational waves where: 𝑚1 ∗ 𝑉1 = 𝑚2 ∗ 𝑉2, which is also supported by Boyle’s law, which is: 𝑃1 ∗ 𝑉1 = 𝑃2 ∗ 𝑉2 , where the V in the equation from the theory of gravitational waves refers to velocity, while in Boyle’s equation it refers to volume. The theoretical result that shows the mass of the electron in between the predicted masses of visible light range for the upper and lower wavelengths is very strong evidence that the wave-particle duality cannot be explained except for through the concept of momentum fluctuation, where some of the angular momentum, as of mass, can be converted as linear momentum, as of motion, which is one of the main foundations of the theory of gravitational waves. Therefore, the theory of gravitational waves should be found satisfying, in addition to the classical mechanics and all the previous mechanics of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Werner Heisenberg, and many others. 40

THE DUAL BEHAVIOR OF CHARGED PARTICLES However, although the theory of gravitational waves can be found suitable for explaining quantum gravity, it should not be adopted without modifying many of the current equations, especially Schrodinger’s equation. In addition, the Somerfield model for the elliptical shape for the orbits’ pattern should be synergized with the explained angle from the center of gravity, which, as it is the foundation of the gravitational waves theory, is predictable in classical mechanics through the Vis-Viva, which is also referred to as orbital-energy-invariance law. In elliptical orbit (and, hence, also a circular orbit), the velocity and radius vectors are perpendicular at apoapsis and periapsis; conservation of angular momentum requires specific angular momentum:


𝒉 = 𝒓𝒑 ∗ 𝑽𝒑 = 𝒓𝒂 ∗ 𝑽𝒂 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕, thus 𝑽𝒑 = 𝒓𝒑 𝑽𝒂, This supports the above equations, and it is comparable to the equation !!

(cos 𝜃)! = ! ! , which is used to describe the Earth’s elliptical orbit around the Sun. The cos 𝜃 is to correct the momentum versus inertia in the relativistic frame of reference as velocity. However, it goes with the concept of momentum fluctuation and not acceleration. For this reason, the root of the square was taken into consideration.



As in the theory of gravitational waves, where the rotation around the static axis (z) produces gravitational waves, Gaspard-Gustave de Coriolis predicted the same, though, unfortunately, he did not extend it to the concept of gravity. Coriolis force was introduced as an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. Comparing this to the new concept of time in the gravitational waves, where it is considered to be absolute in every relativistic frame of reference, Coriolis considered the same, but not with the same concept of time. As per Coriolis, in a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. The deflection of an object due to the Coriolis force is called the Coriolis effect. However, as per the concept of relativity in the gravitational waves theory, which explains the confusion in the previous concepts regarding the free-falling of an object, the Coriolis effect is just another way to explain it, along with Claude Francois Milliet Dechales, who described, in his Cursus seu Mundus Mathematicus, how the rotation of the Earth should cause a deflection in the trajectories of both falling bodies and projectiles aimed toward one of the planet's poles. However, unlike the gravitational waves theory, neither Coriolis nor Claude 42

WEATHER PHENOMENA AND THE CORIOLIS EFFECT Francois went further to explain the concept of gravity and the relativity of time in the frame of reference. The Coriolis and centrifugal accelerations appeared when Newton's laws were transformed into a rotating frame of reference. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to the square of the rotation rate, which acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame. It is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). When this is compared to the concept of gravitational waves, the centrifugal force represents the gravitational force. This should be clear from the proportional to the square of the rotation rate, while the Coriolis force explains the change in momentum’s vector relative to the rotation rate On the other hand, as per the relativity concept, objects accelerate and decelerate with respect to the time in the frame of reference. Therefore, they first move while maintaining the same distance from the center of gravity; thus, they tend to move toward the greatest circle of rotation (the equator). When gaining more energy, they will also start distancing from the center of gravity. Therefore, if assuming three Objects Bn (at the north of the equator), Bs (at the south of the equator), and A (at the equator), all of which are on the same longitudinal line (Figure 8.0), when objects Bn and Bs are accelerating, they will start approaching object A, maintaining the same momentum but changing the momentum vector relative to time. The opposite will be true for deceleration. This explains the weather phenomenon of the direction of hurricanes’ rotation, whether clockwise or counterclockwise (Figure 8.1). Not only the phenomenon of the direction of hurricanes’ rotation, but also the phenomenon of different observations of the color of the sunset, sunrise, and aurora can be explained through the foundation of the gravitational waves. Sunrise is brighter than the sunset due to the vector of Earth’s rotation around its axis. The momentum’s vector of Earth’s rotation is going in the opposite direction of the vector of light of the Sun, while at sunset the momentum vector of Earth’s rotation 43

WEATHER PHENOMENA AND THE CORIOLIS EFFECT is going in the same direction as the light of the Sun. For the aurora, the momentum at the poles is the lowest; thus, the interaction with the light coming from the Sun is reflecting the green color due to the variance between momentums and vectors. In addition, ice is formed at the poles not because of a lack of sunrays but because of the lower momentum, with, accordingly, the lowest kinetic energy. The sunrays also play a role in melting the ice, though the main concept of ice formation is attributed to the variance in momentum relative to the rotation velocity of the Earth around its axis.

Figure 8.0

Figure 8.1

2D visualization the direction of hurricanes’ rotation

Satellite view to visualize the direction of hurricanes’ rotation



No doubt, the theory of gravitational waves is going to be a breakthrough. However, living within its ultimate values requires understanding its simple meanings and how it touches different aspects of human lives. For example, how could it be helpful for those who are working in the field of study of medicine? The same question, I bet, would be asked by investors who seek profitability through industries, and even by the simple people with empty hands. They most likely would ask the same question, hoping to fill their hands with something that helps them to have humble lives. As support and prediction, I will simplify the theory and provide some tips and guidelines for looking at the challenges from different angles, where these tips and guidelines will most likely be found helpful to accelerate in inventions and discoveries. Simply, the theory of gravitational waves explains the existence of everything from different foundations. Mass, energy, motion, momentum, time, vectors, pressure, and temperature are all connected, and they are all connected through the foundations that explain gravitational force. Even the human body, which is heavily studied in the field of biology, is linked to the terminologies of blood pressure, body temperature, heaviness (mass), fastslow metabolism, age (time), and energy to move muscles (electric charge 45

PREDICTIONS AND RECOMMENDATION FOR UPCOMING GENERATONS particles). All these terms work in a natural system that is connected by the gravitational force. Every single particle is attracted to another single particle by gravity, and the combination of multiple particles is distributed and interacts with each other according to gravitational wave mechanics, where, accordingly, many shapes of formed masses can exist. The freewill limitation is what distinguishes a creature from another one. Based on this theory, it is all about momentum fluctuation in relative spacetime. Therefore, light, from the perspective of the gravitational waves theory, is simply a particle that moves in fluctuation patterns between angular and linear momentums that are transformed by the photoreceptors in retina, where it is then transferred to the brain for information processing. The ability of the photoreceptors is limited to interacting only with a specific range of momentums of light (the range of visible light). Thus, I recommend addressing the photoreceptors from the concepts of gravitational waves in order to extend the ability to receive all wavelengths of visible light and transform them into the momentums that the nerves carry to the brain. My prediction for the near future is that we will extend in knowledge, such that healing total and color blindness would be done through a one-day surgery. In addition, I predict that there will be technology in the near future for changing one’s eye color as per the patient’s preference. Today, there are lenses to change eye color, but my prediction involves an actual physiological change. If these seem to be extreme predictions, note that LASIK technologies for correcting vision in a one-day surgery represented an extreme ideology a long time ago. We should be thankful for the person who made it an achievable idea. Exposure to radioactive materials, X-rays, gamma rays, or other high frequencies is harmful to the human body, where it can cause cancer. On the other hand, radiotherapy is used to treat cancer. Through the gravitational waves theory, understanding the interactions between a particle’s momentum and its behavioral effects can lead to technologies capable of defeating cancer as if it were the seasonal flu. This is another prediction for the future generation. In addition, predictions in the medical field are endless; wave functions can be used 46

PREDICTIONS AND RECOMMENDATION FOR UPCOMING GENERATONS in a very wide range of clinical treatments for many diseases; preventing heart attacks, healing brain injuries, enhancing the fast healing of broken bones..etc., and no doubts that the upcoming generation will witness a revolutionary age in the technologies for clinical diagnostics. Currently, lots of energy is consumed in the manufacturing industry. Transforming feedstocks from one chemical characteristic to another is not an easy job without technologies that reduce the consumable energy as low as possible. Simplification is necessary to solve all industrial challenges, and this simplification is achieved by returning things to their roots. Heat, pressure, and catalysts are the keywords in manufacturing. For heat, there are heat exchangers, while for pressure, there are pressure safety valves (PSV). Meanwhile, catalysts are used to change the spacetime of the chemical reaction, where different characteristics of chemicals can meet at a closer distance to react at a lower energy level. However, as far I know, the heat is applied from the outside in and not from the inside out. This means the heat changes molecules’ momentum from the outside, where a lot of energy is required, but it would be smart to change the molecules’ momentum from the inside, where utilizing wave function, such as in a microwave, can save a lot of consumable energy. Microwave technologies are used in almost every kitchen, and I’m surprised that they have not yet been introduced to chemical manufacturers. Thus, I predict that, for the upcoming generation, factories—with no changes to the plants’ capacity and performance— are going to shrink in size. What now occupies an area of several square kilometers will fill an area equal to the size of an employee’s office, with microwave technologies making the chemical reactions efficient, reliable, and more accurate. Therefore, the people, who have empty hands, should be optimistic and utilize the foundations of gravitational waves, not only to start their own businesses by finding new technologies, but also through looking around for resources. From the concept of gravitational waves, a lot of resources can be utilized, and they exist around every person.


PREDICTIONS AND RECOMMENDATION FOR UPCOMING GENERATONS The last prediction to highlight concerns the technologies that support renewable or clean energy. The concepts in the theory of gravitational waves explain the current work in renewable energy from different perspectives. The process of transforming sunlight to electricity through sun-cells could be clearly seen through momentum fluctuation, similar to the process of transforming visible light within the eye retina. The process is conceptually the same, but the key is in knowing how—which can be found in the theory of gravitational waves.


Sources for the Content of the Images Figure 2.0 Figure 2.1 By NASA, Public Domain,

Figure 2.2 Figure 2.3

Image credit: Stanford University By Bdushaw - Own work, CC BY-SA 4.0,

Figure 4.0 By SVG version: K. Aainsqatsi at en.wikipediaOriginal PNG

version: Stib at en.wikipedia - Transferred from en.wikipedia to Commons. (Original text: self-made), CC BY-SA 3.0, Figure 8.1


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