Relations and Connections in the Derivation of the Genesis Formula

The Facts Suggest a Continuous Increase in the Mass-Energy Content of the Cosmos

Fundamental Essences in the Existence

Regarding the Gravitational Field and the Continuous Mass Formation

On Stephen Hawking's Latest

Quoted in BBC News and Yahoo News – Stephen Hawking: God did not create Universe and God did not create the universe, says Hawking, Hawking Picks Physics Over God For Big Bang – from his latest book "The Grand Design," co-authored with U.S. physicist Leonard Mlodinow, Hawking says:

Hawking is apparently adopting the steady-state's "continuous creation from nothing" idea, although now with the suggestion that gravity is involved in the creation process. He is saying that because there is gravity "the universe can and will create itself from nothing."

But Hawking's new idea of spontaneous creation lacks the clarifying details – clarifying details that I've been discussing for so many years now and which are presented in this website. This website contains details (especially the genesis formula) regarding the continuous cosmic creation process.

As for the big-bang, the idea is irrelevant. There are cosmic bangs but not so big as to involve everything. Hawking's new idea of spontaneous creation highlights the big-bang's irrelevance.

To facilitate the creation process, the law of gravitation requires seed-masses. Seed-masses are a requisite according to the mathematics. Seed-masses are necessary kinematic centers for the creation process.

The cosmos that contains the seed-masses must have always existed, for otherwise there won't be a creation process and hence no cosmos. Moreover, since order must be enforced and maintained, gods-begetting gods govern and maintain the order in the cosmos.

Relations and Connections in the Derivation of the Genesis Formula

The following illustrates the relations and connections leading to the derivation of the genesis formula.

In Galileo's idea of the relativity of motion the transformation equations are as follows.

Basically, the Galilean transformation equations describe velocity additions.

Because of the assumption that the velocity of light is the same in all the differing frames of reference, an invariance factor became necessary in the transformation equations to ensure that c=u=u'.

The necessity to have c=u=u' required that rotations on the motion of the electromagnetic phenomenon should be reflected by the transformation equations. (Unfortunately, this idea was never sufficiently treated in the popular explanations). The rotations aspect departs from the velocity additions idea of the Galilean transformation equations.

To reflect the consideration regarding the electromagnetic phenomenon, the value c was introduced into the equation for x'. So, with c=x/t and hence t=x/c, we have

Now, the relation for time was also modified to show t'=x'/c, which departs from the old t'=t assumption. Thus,

Since x'=(x–vt), we have

And because t=x/c, we have

And thus, we have

or simply

The Lorentz invariance factor (1–v²/c²)^–½ was used in order to have the invariant equations that allowed c=u=u'. Thus with γ=(1–v²/c²)^–½, the Lorentz transformation equations are of the following form.

or, to rewrite,

Obviously, the Lorentz invariance factor (1–v²/c²)^–½ does not get to the transformation factor without intermediate approximations and the special treatment for the square root. This is because the Lorentz invariance factor in the Lorentz equations only accounts for a two-dimensional translation of the electromagnetic phenomenon – that is, half of the full tensor.

Also, a fact worth noting, it is not popularly clarified how the transformation factor is arrived at from the use of the invariance factor (1–v²/c²)^–½. The rationale of the application and usage of the Lorentz invariance factor and the Lorentz transformation factor is also not popularly clarified.

On the other hand, the invariance factor (1–v/c)^–1 proponed by the author allows the complete transformation without the intermediate approximations. The new transformation equations take the following form.

The invariance factor (1–v/c)^–1 clearly shows

and

The (1), which is the product of the reciprocals, simply signifies an immediate and complete transformation.

The new invariance factor (1–v/c)^–1 (and hence, consequently, the (1–v²/c²)^–1 transformation factor) allows a relation for a three-dimensional translation of the electromagnetic phenomenon – that is, the full tensor. The two pairs of the v and c vectors along the x-and-y and the x-and-z axes are appropriately represented in the full tensor, which accounts for the three-dimensional rotation and contraction (or attenuation) of the electromagnetic phenomenon that has the transverse electric and magnetic wave components.

The particularly meaningful interpretation of the motion transformation equations becomes obvious by fixing x, y, and z as the static background space dimension, and by assuming the change in t as a separate natural occurrence and an essentially fixed background occurrence, and then by introducing into the equations new variables that represent the actual physical transformations resulting from the motion transformations.

The variables m and E are logically the variables worth introducing into the equations. These variables enter into the equations by substitution – as substitutes either for the x or the t. The substitution gives us the following.

In substituting m for x or t, we have

or substituting E for x or t, we have

It is obvious that the new transformation factor is

Upon a first use of the approximation, we arrive at a transformation factor that actually reflects an appropriate treatment of the transverse-wave vectors in the vectors interaction considered. We have

And this gives us

Thus, solving for the motion transformation that reflect the change in mass, the transformation equation becomes

This shows m' as the initial mass that transforms into the final mass m upon the application of the transformation factor (1–v²/c²)^–1.

Unlike in the Lorentz equations, in the new transformation equations the rationale for the invariance factor is very clear; and the derivation of the transformation factor is also very clear; and then the use of the new transformation factor, with the introduction of the variables m and E in the transformation equation, is now very clear and meaningful.

The relevant relation relates the velocity or motion transformation that describes the contraction or condensation of motion into mass m or energy E.

Using the transformation factor for the full tensor translation (or motion) of the three-dimensional gravitational translation, the formulation for the final mass m is –

or to rewrite with the commonly known m_o,

The above shows that the final mass m, arising from the velocity-to-mass-energy transformation, is twice the final mass suggested by the Lorentzian half tensor formula m=m_o(1–v²/c²)^–½.

The full tensor formulation and the half tensor formulation are valid formulations. But it must be clarified where each is a valid formulation.

The old formulation accounts for only half of the full tensor translation, since the formulation uses only a pair of the c and v component vectors for the two-dimensional interaction involving only the x and y, with the c along the x and the v along the y for the rotation.

On the other hand, the new formulation accounts for the full tensor translation with two pairs of the c and v vectors upon consideration of the three-dimensional interaction involving the x, y, and z on account of the transverse wave interaction.

The new formulation leads to the relation in which energy increases in increments of mv² and, subsequently, leads to the suggestion of the genesis formula.

Upon the final approximation, we have the relation of the cosmic energy genesis, where m is the final mass and m_o is the initial mass, and where E is the final energy and E_o is the initial energy:

The connection of the idea of gravitational acceleration with the idea of velocity transformation suggests the energy accumulation by the formulation where A is the gravitational acceleration and t the elapsed time in ∆v.

The proposition regarding A is according to the undeniable fact of gravitational acceleration. And the extension of the idea to ∆v (the idea that gravitational acceleration occurs as time passes) is according to the fact of the free flow of time that figures in the formulation to advance the idea of the process of duration as an inherent part of the fundamental existential change.

Thus, we have the meaningful genesis formula –

In comparison, Einstein's relation of the change in mass is shown in the following.

Einstein recognized in the relation of the change in mass the connection with the classical kinetic energy K.E.=½mv². But it appears that Einstein simply jumped to the conclusion that E=mc², considering that he only had the ½mv² that signifies half of the full tensor.

Einstein's recognition of the connection with the classical kinetic energy was his greatest discovery. But he evidently did not have a clear recognition of the idea of the transformations of motion. And so, he wandered into the idea of the arbitrary transformations of space and time – which was a departure from the pure kinematics.

In the General Theory of Relativity, Einstein started out with the principle of equivalence and the idea of acceleration (which was again a suggestion regarding motion transformations). But because he abandoned the idea of the space-occupying substance called the ether, he resorted to the idea of the transformations (curvature, warping, etc.) of space and apparently later of space-time. Einstein had to explain gravitation in terms of the curvature of space, instead of simply the curvature (acceleration) of motion. Evidently, Einstein's approach was consistently a departure from pure kinematics.

I am doing research towards an explanation of why and how the kinematic tendencies (i.e., the various natural forces) and the observable cosmic mass-energy exist. All these can be explained in purely kinematic terms.

If I can't finish my research work, I hope someday somebody will find the research road that I have wandered into and therein find success...

The Facts Suggest a Continuous Increase in the Mass-Energy Content of the Cosmos

There is evidently the three-dimensional motion towards any given gravitational mass. The three-dimensional motion is represented by the gravitational tensor vector and the tensor represents an acceleration. The gravitational field is accelerative and therefore it is an acceleration.

According to the principle of the relativity of motion, the motion towards a given object may also be viewed as the motion of the object. Thus, the gravitational acceleration is actually also the relative motion of the given gravitational mass. The mass-energy formulation indicates that the mass-energy content of a given mass increases as the mass accelerates.

The simple idea that the gravitational field represents a flow or motion towards the gravitational center suggests that energy flows into the gravitational center. Hence, the mass-energy of the gravitational center increases.

The three-dimensional motion towards a gravitational center is irrefutable. Anybody who understands their kinematics understands that the gravitational tensor represents motion towards the gravitational center.

The perpetual existence of the gravitational field suggests perpetual motion and an inexhaustible source of motion or energy. And the question as to "where the inexhaustible source of motion comes from" can only be answered by the idea of a hierarchical cosmos.

All these facts suggest that the masses or energies of all the gravitational masses in the cosmos increase as time passes. Hence, the suggestion is that the cosmos is biased towards cosmic mass-energy accumulation.

These facts refute the big-bang theory and the idea of the entropic demise of the cosmos put forth according to the second law of thermodynamics.

Fundamental Essences in the Existence

The fundamental existence is absolutely and completely a mystery. Even the gods would not know any origin more fundamental than the fundamental existence. Fundamental existence exists, and that is that.

The fundamental existence has fundamental essences (component existential principles or aspects). The following discussion involves several of the fundamental essences in the existence.

There is time, the time dimension, an abstract reality through which the infinite past-to-present-to-future duration of the whole instance of existence abstractly occurs. The time dimension is the abstract background "container" of the instance of existence – this is its fundamental function.

There is the instance of existence, the ever-in-the-present instance of existence. The instance of existence "occupies" the time dimension and receives the definition rendered by the essence of duration – these are its fundamental functions.

There is duration, the duration of the instance of existence. Duration is the abstract "occurrence". Duration "carries" or "vectors" the instance of existence and thereby gives definition to the instance of existence – this is its fundamental function.

There is space, the space dimension. Space is the infinite volumetric expanse that is occupied by the space-occupying matter or substance of existence. Space "gets occupied" by the substance of existence – this is its fundamental function.

There is the substance of existence, which is the space-occupying matter. The substance of existence occupies space and receives the definitions rendered by the essence of motion – these are its fundamental functions.

And there is motion. Motion is the tangible "occurrence". Motion is the fundamental essence of mass and energy. Motion is the fundamental essence that renders the glorified tangibility of the cosmos. Motion is also the fundamental essence that renders the dark voidness of the chaos. Motion is the essence that gives "texture" to the substance of existence – this is its fundamental function.

The fundamental essence called motion has been treated by Newton in the Laws of Motion and by Galileo in the idea of velocity transformation in the Galilean relativity.

But the advent of Maxwell's ideas on the electromagnetic phenomena posed questions on the validity of the Galilean relativity on account of the theorized and observed constancy of the velocity of light.

Einstein stressed the idea of the relativity of motion. However, he overlooked the idea of the transformations of motion and instead introduced the idea of the arbitrary transformations of space and time according to the assertion that the velocity of light remains constant.

It is evident that no motion can be attributed to space. And there is the duration of the instants in time but not the motion of the instants. Therefore, because no motion can be attributed to space and time, it is impossible to have the arbitrary transformations of space and time.

Although the idea of velocity transformation is the underlying principle of the relativistic mass formulation, Einstein did not have a clear treatise regarding the idea of the transformations of motion.

One thing is clear, Einstein's emphasis was on the idea of space and time transformations. This idea departs from the fundamentals of pure kinematics.

Pure kinematics suggests the fundamental idea of the motion of motions. Considering now the idea that mass and energy are of the essence of motion, it becomes clear that the objects in motion are themselves motions – the objects in motion are forms of motion. This gives credence to the idea of the transformations of motion.

Pure kinematics suggests that fundamentally motions cling to motions. Motions interact with each other. Motions resolve into the resultant motions described by the application of the pythagorean idea.

To elucidate – when two vector-represented motions interact, the motions may be resolved. The resultant resolved motion is represented by the hypotenuse in the vectorial application of the pythagorean idea.

Moreover, extensively complex vector-represented interactions of motions may be resolved into three-dimensional constructs of motion, which are represented by tensors.

Motions may be resolved as manifested cosmic motions or they may be resolved as bedarkened chaotic motions. Motions may be densified or concentrated into volumetrically denser motions (particulate mass) or attenuated into volumetrically thinner motions (radiant energy dispersed in space).

Densified or concentrated motions may be disintegrated – particulate mass may be transformed completely into radiant energy (as in the explosion of a nuclear bomb wherein enormous amounts of kinetic energy, of motion, are released).

Motions may also be cancelled-out to the chaotic essence of a dark voidness (as in the interference of light). The motions may also densify to the chaotic essence of the dark super-massive gravitational domains, the so-called black-holes.

All these signify that the fundamental essence of cosmic mass and energy is the fundamental essence called motion. And evidently the fundamental essence of chaotic mass and energy, which are characterized by their bedarkened manifestations, is also the fundamental essence called motion.

It has now become logically evident that the voidness in the vastness of space is chaotic energy, which is dark (not glowing, not glorious) and without form and void (relatively intangible).

To elucidate by an example, consider the grade school double-slit experiment.

We know that the electromagnetic waves (i.e., the rays of light) in the double-slit experiment pass through the dark region. According to basic physics, energy is in that dark region but a dark voidness is observed in the dark region because the rays of light (i.e., energy in the form of electromagnetic waves) cancelled each other. Thus, energy got cancelled to a dark voidness.

The grade-school double-slit experiment indicates that cosmic energy got transformed into chaotic energy of the form that is bedarkened and voided (cancelled-out).

The extensions from these ideas point to the idea that the voidness in empty space is actually cancelled-out energy, and may even be void energy of the form that has yet to emerged from the voidness if accordingly subjected to a process that will transform the chaotic voidness into a cosmic reality.

Now, there is the suggestion that the dominant energy transformation may either be (1) a cosmic-energy-to-chaotic-energy process or (2) a chaotic-energy-to-cosmic-energy process.

The first suggestion regarding the dominant energy transformation points to the idea of a natural bias towards increasing disorder – which is the idea that extends to the idea that the cosmos (the order) is disintegrating and vanishing into the increasing chaos (the disorder). This is according to the idea that the dominant process in the physical existence is the process of radiation, which is according to the second law of thermodynamics that states that the energy in a system tends towards increasing entropy.

Among the ideas advanced to support the first suggestion are the second law of thermodynamics, the big-bang theory, the idea of the cosmic background radiation in accordance with the big-bang theory, the idea of the expansion of the universe according to the big-bang theory, and etc. These ideas stem from interpretations of mathematical formulations which are purported to be the relations of the transformations of space and time, instead of the transformations of motion.

These ideas embrace the idea that the cosmos will end in an entropic demise – which presents the idea of the ultimate death of the cosmos into the relatively intangible and dark nothingness.

The second suggestion regarding the dominant energy transformation points to the idea of the natural bias towards increasing order – which is the idea that extends to the idea that the chaos (the disorder and the yet to be ordered) is amassed and integrated into the increasing cosmos (the order). This is according to the idea that the dominant process in the physical existence is the process of gravitation, which is according to the fundamental principle of pure kinematics that states that motions cling to motions.

Among the ideas advanced to support the second suggestion are the fundamental principles of kinematics, the idea of the motion of motions (i.e., that motions resolve), the idea that motion is the fundamental essence of mass and energy, that mass and energy are kinetic constructs, that the cosmos and the chaos are of the essence of motion, the idea that fundamentally gravity is the essence of motions clinging to motions, also, the idea that gravitation is a dominant process that preserves a bias towards the continuous cosmic mass formation, and etc. These ideas stem from interpretations of mathematical formulations which are now deemed to be the relations of the transformations of motion, instead of the transformations of space and time.

These ideas embrace the idea that the cosmos has an ever-increasing cosmic mass-energy content because of a fundamental continuous cosmic mass formation process – which presents the idea of an immortal and ever-growing, tangible and glowing cosmos.

The second suggestion regarding the dominant energy transformation – the idea of a dominant chaotic-energy-to-cosmic-energy process, the idea of the natural bias towards increasing order – is the idea being proponed and promoted in this website.

Regarding the Gravitational Field and the Continuous Mass Formation

A gravitational field, regardless of the objects (e.g., electromagnetic energy or particulate masses) in the vicinity that are influenced by it, is fundamentally a three-dimensional motion towards a given mass.

Objects in the vicinity of a gravitational field are accelerated by the inherent gravitational motion towards the center of the gravitational field. For as long as the gravitational field exists, the inherent gravitational motion towards the gravitational center exists, regardless of the existence of the objects in the vicinity. This is according to the fundamental kinematics principles indicated by the vector representations. Thus, the vector of gravitation represents the perpetual gravitational motion inherent in the gravitational field.

Every given mass has a gravitational field. The field can be represented by vectors of motion that surround and point towards the mass. These vectors can be resolved into a single full tensor vector representing the three-dimensional motion towards the given mass.

The proper transformation factor γ suggested by the full tensor (three-dimensional) vector is (1–v²/c²)^–1, instead of the transformation factor (1–v²/c²)^–½ suggested by the half tensor used in the Lorentz equations. This proper transformation factor suggests the relativistic mass equation m=m_o(1–v²/c²)^–1 that leads to the derivation of the genesis formula.

The principle of the relativity of motion allows that the motion represented by the full tensor vector is essentially the motion of the mass itself. Hence, the mass itself is essentially moving with a three-dimensional motion.

Applying the three-dimensional motion to the given mass itself suggests that the given mass has increases in its mass or energy as time passes.

There is of course a simpler view than the one given above. Because the gravitational field indicates continuous motions or continuous kinetic energy fed to the gravitational center (an undeniable fact established by the idea of the gravitational vector), then the gravitational center should undeniably have the increases in kinetic energy. Thus, all gravitational centers have the perpetual increases in their energy or their mass. (Among the best candidates for such gravitational centers are blackholes. Because relativistic velocities are involved in blackholes, the relativistic formula – i.e., the genesis formula – undeniably applies. Although individual nuclear particles qualify as gravitational centers, and actually possess nuclear force fields which are applicable accelerative tensors, their quantum energy gains from the void are generally simply radiated away.) The mass and energy increases are eventually radiated or spread out in the fission processes of the observed expanding universe.

It is indeed a fact that every mass has an inherent gravitational field. The gravitational field may be represented by a linear motion vector towards the given mass; but the gravitational field is best represented by a tensor motion vector (for the volumetric, three-dimensional motion) towards the given mass. The gravitational field is thus a flow of motions towards the given mass. Motion is the fundamental essence of energy. Therefore, for as long as a given mass exists, there exists a flow of energy into the given mass, a flow of energy which is in the form of the concentric motion of the gravitational field itself. And so, the obvious suggestions are that the energy flowing into the given mass increases the mass-energy content of the given mass and that the energy flowing into the given mass is either condensed and aggregated in the form of mass or radiated away in some form of energy.

The following ebook contains further discussions on the ideas presented in this website.

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