A Form of Quantum Gravity Unification with the General Theory of Relativity
ABSTRACT
The problem still remains (in theoretical physics) of how gravity can be unified with quantum mechanics, in as much as it would be possible to explain a consistent theory of quantum gravity. Which, this unification theory should (to a sufficient extent) adhere to the Friedmann-Lemaitre-Robertson-Walker metric. In the preceding work, a universal model is formulated, considering the results of the theory of quantum gravity, as well as the General theory of relativity. The space-time continuum is modelled to arise from the gravity quanta. This is by allowing the universe to retain its homogeneous nature at scales near the plank scale in (relativistic) difference from the time of the Big Bang and treating the gravity particle as behaving, both as a wave and as a particle (as of the theory of wave-particle duality). Once space-time is modelled, the field equations of general relativity are considered, and briefly mentioned, in the modelling of repulsive gravity as being the cause of the expansion of the universe. The space-time metric is considered, as possibly moving at faster than the speed of light. This is considered as suggesting, an event (as of the Special theory of relativity) of which its occasion supersedes the symmetry of which the Special theory of relativity was modelled, this is considered with no changes to the frame of reference of the Special theory of relativity.
Keywords: Physics Beyond the Standard Model, Cosmology, Theoretical Physics, General Relativity, Special Relativity
Introduction
In the late 1890s, physicist Max Planck proposed a set of units to simplify the expression of physics laws. Using just five constants in nature (including the speed of light and the gravitational constant), everything in the universe could arrive at these same Planck units. The basic Planck units are length, mass, temperature, time, and charge. The proton is about 100 million trillion times larger than the Planck length. To put this into perspective. The Planck scale’s purpose of invention was as a set of universal units, so it was a shock when those limits also turned out to be the limits to where the known laws of physics applied. Quantum gravity and superstrings are also possible phenomena that might dominate at the Planck energy scale. The Planck scale is the universal limit, beyond which the currently known laws of physics break.1 The discovery of the universe’s acceleration made a real sensation in the science world which led to the creation of the cosmological model 30/70. In astronomy (cosmology), Ω refers to the average density of the universe, also called the density parameter. In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.2–4 In Sir James Clerk Maxwell’s time, It was known that Maxwell’s electrodynamics—as they were usually understood at that “present time”—when they were applied to moving bodies, led to asymmetries that did not appear to be inherent
in the phenomena. “Take, for example, the reciprocal
electrodynamic action of a magnet and a conductor”. The
phenomenon that was observed depended only on the
relative motion of the conductor and the magnet, whereas
the customary view drew a sharp distinction between the
two cases in which either one or the other of those bodies
was in motion. For if the magnet was in motion and the
conductor at rest, there would arise in the neighborhood
of the magnet an electric field with a certain definite
energy, producing a current at those places where parts
of the conductor were situated. But if the magnet was
stationary and the conductor in motion, no electric field
would arise in the neighborhood of the magnet. In the
conductor, however, they found an electromotive force,
to which in itself there was no corresponding energy, but
which gave rise - assuming equality of relative motion in
those two cases discussed - to electric currents of the same
path and intensity as those produced by the electric forces
in the former case. Examples of that sort, together with
the unsuccessful attempts to discover any motion of the
earth relative to the “light medium,” suggested that the
phenomena of electrodynamics as well as of mechanics
possessed no properties corresponding to the idea of
absolute rest. They suggested rather that, as has already
been shown to the first order of small quantities, the same
laws of electrodynamics and optics would be valid for all
frames of reference for which the equations of mechanics
hold good. They rose that conjecture (the purport of which
was thereafter to be called the “Principle of Relativity”)
to the status of a postulate, and also introduced another
postulate. This was only apparently irreconcilable with the
former, namely, that light is always propagated in empty
space with a definite velocity -which is independent of the
state of motion of the emitting body. Those two postulates
sufficed for the attainment of a simple and consistent
theory of the electrodynamics of moving bodies based on
Maxwell’s theory for stationary bodies.5
Semi-Riemannian manifolds have applications, particularly
to modern gravitational theory and electrodynamics. Semi-
Riemannian geometry is a branch of differential geometry,
similar to Riemannian geometry. In fact, Riemannian
geometry is a special case of semi-Riemannian geometry
where the scalar product of nonzero vectors is only allowed
to be positive. From a mathematical perspective, Semi-
Riemannian manifolds proved theorems of geometry such
as the existence and uniqueness of the covariant derivative
of the Levi-Civita connection, and some properties of the
curvature tensor. The Einstein tensor:
is a symmetric, (0, 2) tensor field with vanishing divergence.
From the Einstein tensor, it can be defined as a set of
nonlinear partial differential equations solved for the
geometry of the semi-Riemannian manifold M called the
Einstein field equations, given by
Where T is the stress-energy tensor, which represents
the energy-momentum content of the universe in the
physical model.6 Space is generally considered to be a
three-dimensional continuum. This means that it is possible
to describe the position of a point (at rest) by means of
three numbers (coordinates) x, y. Also, there is an indefinite
number of points in the neighbourhood of this one, the
position of which can be described by co-ordinates such as
x1, y1, z1, t1 which may be as near as chosen to the respective
values of the coordinates x, y, z of the first point. In virtue
of the latter property we speak of a “continuum,” owing
to the fact that there are three coordinates to speak of
it as being “three-dimensional.” Similarly, the world of
physical phenomena, which was briefly called “world”
by Minkowski is naturally four dimensional in the spacetime
sense. It is composed of individual events, each of
which is described by four numbers, namely, three space
coordinates x, y, z and a time coordinate, the time value
t. The “world” is in this sense also a continuum. For every
event there are as many “neighboring” events (realised
or at least thinkable) as it can be cared for to choose, the
coordinates x1, y1, z1, t1 of which differ by an indefinitely
small amount from those of the event x, y, z, t originally
considered. To have not been accustomed to regard the
world in this sense as a four-dimensional continuum is due
to the fact that in physics, before the advent of the theory
of relativity, time played a different and more independent
role, as compared with the space coordinates. It is for this
reason that it has been in the habit of treating time as an
independent continuum. In fact, according to classical
mechanics, time is absolute, i.e. it is independent of the
position and the condition of motion of the system of coordinates.
It can be seen expressed in the last equation
of the Galilean transformation t1 = t the four-dimensional
mode of consideration of the “world” is natural in the theory
of Relativity.7 What are the values: x1, y1, z1, t1 of an event
with respect to K¹ (a reference frame in motion), when the
magnitudes x1, y1, z1, t1 of the same event with respect to
K (a reference frame at rest) are given? The relations must
be so chosen that the law of the transmission of light in a
vacuum is satisfied for one and the same ray of light (and
of course for every ray) with respect to K and K1. For the
relative orientation in space of the co-ordinate systems,
this problem is solved by means of the equations:
This system of equations is known as the “Lorentz
transformation.8 If a stone was picked up and then let go
of, why does it fall to the ground?” The usual answer to this
question is: “Because it is attracted by the earth.” As a result
of the more careful study of electromagnetic phenomena,
it has come to be regarded that action at a distance is
rather a process impossible without the intervention of
some intermediary medium. The effects of gravitation
also are regarded in an analogous manner. The action of
the earth on the stone takes place indirectly. The earth
produces in its surroundings a gravitational field, which
acts on the stone and produces its motion of fall. As it is
known from experience, the intensity of the action on a
body diminishes according to a quite definite law, as a
body proceeds farther and farther away from the earth.
From a point of view, this means that the law governing
the properties of the gravitational field in space must be a
perfectly definite one, in order correctly to represent the
diminution of gravitational action with the distance from
operative bodies. It is something like this: The body (e.g.
the earth) produces a field in its immediate neighbourhood
directly; the intensity and direction of the field at points
farther removed from the body are thence determined
by the law which governs the properties in space of the
gravitational fields themselves. In contrast to electric and
magnetic fields, the gravitational field exhibits a most
remarkable property.
Bodies, which are moving under the sole influence of a
gravitational field, receive an acceleration, which does
not; in the least depend either on the material or on the
physical state of the body. For instance, a piece of lead
and a piece of wood fall in exactly the same manner in
a gravitational field (in a vacuum), when they start from
rest or with the same initial velocity. This law, which would
hold most accurately, can be expressed in a different form
in the light of the following considerations. According
to Newton’s law of motion: (Force) = (inertial mass) x
(acceleration), where the “inertial mass” is a characteristic
constant of the accelerated body. If now gravitation is
the cause of the acceleration, it then had that (Force) =
(gravitational mass) x (intensity of the gravitational field),
where the “gravitational mass” is likewise a characteristic
constant for the body. From these two relations follows: If
now, it’s found from experience, the acceleration is to be
independent of the nature and the condition of the body
and always the same for a given gravitational field, then the
ratio of the gravitational to the inertial mass must likewise
be the same for all bodies. By a suitable choice of units, it
can thus make this ratio equal to unity. The following law
is the present: The gravitational mass of a body is equal
to its inertial law. It is true that this important law had
hitherto been recorded in mechanics, but it had not been
interpreted. A satisfactory interpretation can be obtained
only if it’s recognized that: The same quality of a body
manifests itself according to circumstances as “inertia” or
as “weight” (lit. “heaviness”).9
Formulation of Theory
In some other analogous, space-time itself becomes a direct
solution to Sir Isaac Newton’s action at a distance. When
coming to think that all the mass in a Galaxy, e.g. the Milky
Way Galaxy must be connected by the action at a distance
that pulls all the mass in the Galaxy towards a specific
gravitational centre within the Galaxy. All other galaxies
in the same Galaxy cluster are moving towards the Great
attractor, and thus, connected by the action at a distance
field force. When this action at a distance is caused by some
kind of quantum particle (gravity particle) accelerating a
certain mass, and with the addition of the cold dark matter,
the whole universe becomes interconnected by gravity.
The gravity becomes so great, that from the field equations
of general relativity, it could become repulsive when a
universal metric is introduced into the frame. The series
of mathematics, later on, modelled the gravity particle as
the makings of the space-time metric, and repulsive gravity
resulting from this. The natural positioning of the cold dark
matter and ordinary matter in the universe would allow
for the flow of the gravity particles in a circular motion, or
spin from here on. The spin is of the gravity particle along
the matter in the universe without the particles being
directed towards a specific great mass in the universe. As
mass in the universe is accelerated by the gravity particle,
the speeding gravity particle could as very well become the
inertial frame of acceleration by which mass must deform
as it’s accelerated by the inertial frame. In this frame of
acceleration, gravity by Sir Isaac Newton’s action at a
distance becomes so great that it can become negligible.
When the mass in the universe is positioned so that the
net force is equal at all points in this frame of acceleration,
when these gravity particles are moving, the space-time spin
arises and unifying geometrical curvature of space-time as
a force of gravity with Newtonian (quantum) gravity. This
universal model would not break down at the small-scale
observations of Newtonian net gravitational field force when
the net field force is zero. This is through the insight that
the inertial frame of acceleration is a quantum system, thus
exhibiting the properties of quantum mechanics, such as the
“wave-particle duality”; in which the inertial frame behaves
like a particle and a wave at the same time. From the inertial
frame of acceleration behaving like a particle point of view,
at the observable small scale, the net gravitational field
force between masses can be calculated to be at zero and
the masses attract each other at the same rate and with
the same intensity. Although, not necessarily contradicting
the spin of the inertial frame of acceleration. The quantum
particles/ waves causing the acceleration of the masses
must flow along the masses in such a way that the spinspin
(the intrinsic form of angular momentum carried by
particles) of gravity particles from multiple masses do not
pull a certain mass in multiple directions. Instead, the mass
is accelerated in a single direction, which can be said as
an interference between the gravity particles, resulting in
the mass being accelerated in a single direction. Although
the net gravitational field force of gravitational masses
is calculated to be at zero, this same gravitational field
force is increased by the factor equal to the gravitational
sphere of influence between the masses. In this way the
gravitational force behaves like a wave; the amplitude of
the gravitational field force is increased by the addition
of a mass although causing a net gravitational field force
of zero between the masses. In this way, the spin of the
inertial frame of acceleration can occur at the grandest
scale of universal interconnected gravity, with the natural
positioning of matter that would allow for the spin. More
on how this inertial frame of acceleration could cause the
observed expansion of the universe: space-time in this
universal model becomes the direct consequence of a
large gravitational field. One such candidate, which could
be causing the expansion of the universe is gravity itself,
or repulsive gravity to be more exact. Repulsive gravity
as it is a suspected candidate, that caused the inertial
universal expansion, could be modelled to be the cause of
universal expansion in the inertial frame of acceleration,
where gravitational fields are the makings of space-time.
The notion that space-time as gravitational field forces
can be modelled to have existed when repulsive gravity
came into effect from the Big Bang. An expansion of the
universe in this inertial frame of acceleration becomes
eminent. The recent observed increase in the acceleration
of the expansion of the universe, could as very well be
caused by an increase in the mass density in the universe,
such as the formation of stars from their nebulae, causing
an increase in the gravitational field force, in a system
with a great enough gravitational field that it’s repulsive.
Similarly, the moving away of certain galaxies from other
galaxies could very well be the cause of cold dark matter
outside of galaxies.
Predictions of Theory
The curvature caused by the inertial frame of acceleration
as it accelerates matter can be said as
c < c’(c’ is the known speed of light that is 299 792 458 m/s)
because light has to travel a longer distance between the
two points that can be said as
k = 0 Between,
where the curvature:
k < 0
can be observed.
c < c’
Becomes an outcome of gravitational time dilation. tanθ
represents the path that the gravitational field force wave/
particle must take as it accelerates a mass. This path can
be said as:
λ Is the wavelength of the interconnected gravitational
field force of the universe, where the wavelength is
directly proportional to its amplitude. The momentum in
the equation
of a wavelength, when it’s that at this scale, it becomes
the proportionality resultant by which the inertial frame
of acceleration is causing acceleration to the matter in the
universe and multiplied by the mass in the universe (as
all the mass in the universe is now connected). With the
natural positioning of the matter in the universe causing
a net gravitational field force between the matter in the
universe, all the gravitational force must be directed
towards the centre within space-time; it has a greater
Newtonian gravitational field force activity in that direction.
R is the repulsive intensity of spacetime. It’s c ≥ because
the gravitational field force waves/ particles might be
moving faster than the speed of light, as Newtonian action
at a distance happens faster than the speed of light. The
speed of the gravitational field force waves/ particles is
included in the equation because the waves/ particles are
the inertial frames of acceleration. The equation also shows
that Newtonian gravity might make for a small correction
that the geometrical curvature wouldn’t be able to account
for, with total net zero influence of Newtonian gravitational
field force, due to the direction of acceleration of the inertial
frame of acceleration. Factors such as the angle at which
a mass hanging in space must fall, inside the gravitational
field. This is when the repulsive nature of gravity is less
than its attractive nature in a region with mass density. At
the plank scale, all the energy in the universe was repelled
(this is the understanding of Big Bang cosmology). The
inertial frame of acceleration is from Plank time, from the
plank scale, this acceleration reduced over time and is
now increasing. Although, there is a tremendous amount
of gravity present, the mass in this universal wouldn’t
necessarily collapse under gravitational field stresses from
the plank scale due to repulsive gravity.
Modelling Mathematics of Gravity/ Repulsive
Gravity
The intensity by which the universe repels matter, by a
form of repulsive gravity can be modelled as
Where is the region compactness of matter in a region
in space-time, is the region compactness of cold dark
matter in a region in space-time and g is gravity. In this
model, gravity is limited by the amount of energy and cold
dark matter in a region in space-time, as it is shown below.
When the gravity in a region in space-time is repulsive, and
when the gravity in a region in space-time is attractive. > g
Is a resultant of repulsive gravity adding a negative value to
gravity, as it acts in the opposite direction of gravity. The
Einstein field equations can support the claim of gravity
being repulsive at the Plank scale, as being part of an
observable universe. This can also be the case, by saying
When the Plank scale is the inertial frame of observation,
in the driving force of repulsive gravity, when the amount
of gravity in the universe is acting at the Plank scale; in a
proportionality difference. When the frame of difference is
that of the amount of gravity in the universe and the distance
by which it is acting. At the Plank scale gravity becomes
repulsive, this being a solution in the field equations of
General relativity. Repulsive gravity is a suspected candidate
for causing the initial expansion of the universe. This can
be modelled as
In order to yield real-world observations. The gravitational
repulsive intensity of this model is constant when the
amount of gravity in the universe and the scale of frame
of reference- the Plank scale, are constant. The repulsive
intensity of repulsive gravity reduces with the increase in
size of the scale factor, so repulsive gravity and the scale
factor are inversely proportional. Using the plank scale as
a reference, from the time when all the mass and energy
in the universe is from this point (from Plank time), it can
also be modelled as a transformation that is;
Both gravity and repulsive gravity are acting in opposite
linear directions.
Extra Gravity Within Galaxies
More on the extra gravity within galaxies. The virtual
particles (quantum fluctuations) in space are a form of
energy with momentum, from general relativity they will
have the ability to constitute gravity. Also from General
relativity, events happening for a large mass are happening
at a relatively slower rate than for another relatively less
compact mass. This can be seen from the two relativistic
clocks which are t = 0 (which is a clock at rest) and the one in
a space-time curvature at t = -1. From this, once a quantum
fluctuation is created in the frame of t = -1, the time that the
quantum fluctuation could take to decompose could as very
well be much less than for an event of a quantum fluctuation
in the t = 0 frame. If the time the quantum fluctuation is
created is independent of the events of the curvature. As
the quantum fluctuation is not affected by gravity when it
is not created, this could constitute a relative gravitational
field contribution of the quantum fluctuation from the time
after the virtual particles are created to the time they are
destroyed, and the relativity of which corresponding to
the amount by which the time in the curvature is slowed.
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Symmetry of Space-Time
Aspects of the 4 dimensions overlapping in such a way,
that the tesseract folds inward (and the 1 dimension of
time that adds an extra dimension to the 3 dimensions is
overlapped by the 3 dimensions), that the 1 dimension is
the one carrying the negative value on the linear line of
space-time. This aspect will allow for the 4 dimensions
of space-time to exist. Operations of the Hilbert vector
space arise from this factor; this is a Hilbert space given
by the vectors
This operation then also generalises the dot product in
Euclidean vacuum space, as a product moving towards the
vacuum, or as a decomposing string in the vacuum. When
this operation is present; the dot product in Euclidean
space becomes a vector towards the dimension carrying the
negative value on the linear line. Generalising this operation
in Euclidean space, when the first 3 vectors are that of a
vibrating string, the 4th vector becomes the vacuum that
would allow for the decomposition of the vibrating string.
In 3 space the 4th vector also can be the null set, as it is
carrying a negative value. A manifold of space-time folding
in this way would mean that, although not directly observed
in the special 3 world as being so, the 1 dimension of time
could very well be a physical entity that is experienced in
more ways than through the interaction of mass and energy.
The below diagram is a representation of a relativistic frame
of reference known as a light cone, in which space-time is
represented in causal terms.
where the inertial frame of acceleration for the universe
is moving faster than the speed of light. Allowing for the
addition in the angle of the slope of the light cone’s gradient
would allow for the accommodation of events happening
for the inertial frame of acceleration, as it is moving faster
than the speed of light. In this case, the inertial frame of
acceleration when the events are happening in a frame,
where faster-than-light (or ct > frame) becomes a causal
event, the faster-than-light body accelerating the universe
changes from being the inertial frame to being a causal
event in this frame, as indicated in the diagram below.
Figure 1.Relativistic Light Cone in the CT Frame,
Where Nothing can Travel Faster than the
Speed of Light
Figure 2.Relativistic Frame of Reference of the Light
Cone with a CT > Interval Reference. In this frame,
an event that would have been paradoxical in the CT
frame becomes a casual event.
By observational means, when to say the vacuum that would
allow for causality to be, within the inertial frame. When the
inertial frame is moving faster than light (c >). This would
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allow for the modification of the Lorentz transformations
and adjusting of the world lines of the light cone, in order to
compensate for a relativistic frame of reference, where the
modification is by the gradient of the slop of the world lines,
In Figure 1, the dot at 0, 0 cannot proceed with the dot
at 4, 5 as this would cause violations in causality in the ct
frame of reference. In Figure 2, this dot is able to proceed
to the corresponding dot without any causal violations
and this is possible by adjusting the speed of light limit,
in the event were the space-time Metric is moving faster
than the speed of light. Both frames can be observed
simultaneously, in which the events occurring in the ct >
frame are observed as a paradox for an observer in the ct
frame. Such paradoxes that an observer in the ct frame
would observe would include the space-time continuum,
in which the space-time Metric is moving faster than the
speed of light, another paradox would be the vacuum
that facilitates events in the ct frame, and allowing for
the inertial frame to be an event in the ct > frame, now
facilitating events as causality in both the ct and ct > frames.
In this way, the vacuum facilitating both events becomes
of higher-order symmetry and can be said to be of higher
dimensions, depending on the geometrical displacement
observed on the Lorentz transformations caused by the
paradoxes in which it’s facilitating 2 frames of reference,
in which one is paradoxical for the other. From the field
equations of general relativity, it can be determined that
both the inertial frame of acceleration and matter occupying
space-time, as being in relative motion to one another. By
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mass curving space-time the time interval of the mass is
also slowed so all processes move slower for this mass.
When both the inertial frame of acceleration and matter
curving space-time are in relative motion to one another,
it becomes a possibility that a paradox can be within the
ct frame. This paradox could explain why the space-time
Metric is not visible. If the relativity in motion between a
light ray and the inertial frame of acceleration was sufficient.
Being that the inertial frame of acceleration was moving
faster than light, it becomes apparent that even if the inertial
frame was able to emit a form of light ray, an observer in
the ct frame would not observe the light ray, firsthand, as
the light ray would be sent into the observer’s future. The
vacuum in which causality is facilitated for the 2 frames of
reference represented in the figures, this vacuum can be
said to be of higher-order symmetry. Evidently, because
causality is different in the 2 frames of reference. In the ct
frame of reference, nothing can travel faster than the speed
of light, while in the ct > frame of reference, faster than light
becomes a casual event. This could very well be evidence
of higher special symmetry, in which both the frames of
reference are part of a high-order special symmetry. Like
how the 2 dimensions are part of the 3 dimensions, but
are special geometrically restricted.
Relativistic Aether
It then becomes clear that adjustment to the Lorentz
transformations by the world lines will imply an addition
to the number of translatory relativistic frames in order
for spacetime to remain relative in all these frames, with
increasing velocity. By the introduction of the present
unknown candidate to the symmetry of the vacuum
facilitating the relativistic frames, it could very well be
translated to be that the axis of the relativistic frames are
simultaneously present in this vacuum, in which they are
translatory measurable by light velocity reflected at points
with resting clocks present, in all present frames, due to
length restrictions-that a light wave has superposition
because of its quantum size. A light ray propagated through
space has a constant velocity
c2
It then follows that the present unknown candidate:
can be introduced in the number of relativity frames and
complimenting the order of symmetry of this vacuum, it
then follows that
In which case this symmetry translates to a Hilbert vector
space, so that the translatory motion of light, allows for the
measurements of (relativistic) clocks that are synchronous
in their own respective frames. In which case for this to
be observational, the light waves are propagated in a
translatory motion perpendicular to the frames, it then
follows that
This series would now allow for length contractions
of a wave of length propagated through space. Given
that the speed of light in vacuum remains constant in
each frame, as it superimposes in/ on the frame. With
decreasing frame space in each axis direction as observed
in the 3 or 4 dimensions. The propagating wave must
travel perpendicular to the present frames. With increasing
frames, the more perpendicular the wave has to traverse
and the more its length contracts, so that with much space
the wave takes on a spherical shape with decreasing length,
as the number of frames increases. The mechanics of
relativistic length contraction translate to this wave given
the increasing symmetrical spaces of the vacuum act as if
(it was/ they were) a sort of Aether for the propagating
wave. With increasing frames-meaning increase in the
velocity of the additional frames these frames are a sort
of medium through which this wave must traverse. This
could as very well result in a waveform of the light ray
propagating through this Aether, due to the quantum size
of the propagating wave, and the symmetrical positioning
of the frames in the vacuum. This wave is propagated
in spherical form parallel to the observer in the 3 or 4
dimensions. With the addition of a continuity factor to
the propagation of the spherical wave, a number of them
are emitted in sequence from the emitting body and the
emitted spherical waves have wave energy as well as angular
momentum. The absence of the Aether for a body at rest
in the 3 dimensions remains true as this body is unable to
access the high symmetrical spaces (frames) due to “length
restrictions”.
On the note of black body radiation: It can be stated that as
two of the spherical waves approach, the present unknown
candidate can be introduced, in which case the two waves
either translate their spaces to each other due to at present
unknown relativistic mechanics, as they merge, increasing
angular momentum, or they don’t and the interference is
angular, in which case when the interference causes an
increase in wave frequency it very well causes an increase in
angular momentum and thus relatively translating the two
spherical wave frames. In this case, when the spherical wave
passes through a medium, the translatory consequence
can either be a loss in angular momentum relative to a
decrease in the frames traversed by the spherical wave at
the same time. As the spherical wave transverses through
the particles also, or the spherical wave breaks down into
the individual spherical waves by means of the equation
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in which n is the number of spherical waves adding up in
the same waveform and
dt
representing the frames traversed by the spherical wave,
so much that the clocks in the frames remain at rest when
measured relativistically.
is on the left-hand side of the equation because it’s only
known whether the spherical wave momentum will
decrease, or whether it will split into individual spherical
waves after the values on the righthand side of the equation
are found.
It’s now established that light rays can result from the
relativistic Aether. It then becomes consistent in this article
that space-time can exist in a vacuum where all bodies
present are in free fall (in which case both relativity and
Newtonian mechanics complement each other) on the
note that the number of spherical waves are squared, so
that it’s represented as n2.
So that a traversing spherical wave is capable of producing
a secondary spherical wave outside its traversable space.
Of which the secondary spherical wave effects are linearly
opposite to the effects of the producing spherical wave; as
of Newtonian mechanics. It then follows that the effects
of gravity; being caused by quantum particles, the gravity
quanta would then produce a secondary spherical wave of
which its effects are linearly opposite and outside its sphere
of influence. What then is to stop the proposed spherical
wave from producing a third one, and so on?
becomes a candidate for this case; for which the definite
number of the produced spherical waves is unknown. In
this case, it becomes the same as saying that the number
of produced spherical waves is proportional to the present
frames in the vacuum; for one quanta. On the note of
the gravitational quanta communicating faster than the
speed of light! This can be translated from the Newtonian
vacuum being infinite to the spaces or frames present in
the vacuum. The capability of which becomes that when
the length of the spherical wave reaches zero and it can
no longer traverse perpendicular to any more additional
spaces, its angular momentum can be translated linearly
and the spherical wave can then be relativistic observed
as travelling faster than light. In this case, it must remain
parallel in its own frame. The spherical wave can no longer
produce any more quantum waves at this point and this
is inherent in Newtonian mechanics. Because there are
no other spin-spin possibilities for any more produced
spherical waves it’s no longer able to traverse any more
spaces. In this case, the spin-spin nature of a spherical wave
can be a possibility following in all its traversable spaces.
With different spherical waves having different spin-spin
potentials, it then becomes a possibility that two spherical
waves superimposing at the same point in space may not
interfere that their wavelengths shorten or grow longer.
This means that the wave path of the two waves can be
drawn that-their superpositioning becomes asymmetric
and nonlinear. That an angle of
or
can be drawn from a point of intersection (the centre of
the spherical waves) between the two waves and the angle
of the waves is found to be unequal. In which the spherical
wave has angular momentum so may be able to alter the
direction of another spherical wave, as it approaches. It
can then be that
producing relativistic length contraction at faster-than-light
speeds; in which the spherical wave splits in two. So that
the spin-spin of the produced spherical waves are linearly
opposite.
Applications for the Formulation of an Equation
for Gravity
The applications of gravity can be transformed from the
mathematics of the theory of Relativity (since gravity in
this case results from relativistic effects). The going about
transforming the equations of the theory of relativity into
an equation for gravity is as follows. The series
translates the symmetry of space-time that the point x
appears elongated as the length of the propagated wave
contracts. For deriving a mathematical form for gravity-in
this case, only the 3 relativistic (linear) frames are needed
for the mathematics to remain partially linear throughout
the formulation. To start off, a wave propagating through
space appears to be linear in direction when the 2 frames K’
and k are neglected. By Newtonian mechanics, it becomes
almost an impossibility for this wave to propagate in the
y-axis of the stationary system when the second frame
is introduced that ct is now transformed into c2t2. The
impossibility becomes possible when the 3rd frame is
now introduced and (like the second frame) is not at all
empty. So that c2t2 now becomes a linear function, in which
the wave is propagated in a linear direction through the
frames k, K + 1 and K′ + 1 to a point x’ or x in the stationary
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systems. For applications where the wave is observed in
the axis x, y, and z for an observer at x, the linear function
is transformed. In which case the velocity of the observer
at x is increased to that for K′ so that K′ + 1, and -v is the
observer stationary in the K′ frame; that the observer now
takes the position of a point in K′ + 1 and the observer’s
position in the stationary system is at x + 1, −y. In this case,
this observer is now enclosed in a space where the 3 frames
are linear to the observer. In this case, the observer can be
seen as the one in motion and the frame k being stationary.
In this case, the motions of the observer in the K′ + 1 frame
can be relativistically translated to the k frame in order to
avoid the addition of any more frames. So that c2 = v2 can
now be said as
c2 = c
,
v2 = v − u
u − v is the initial and final velocities of the moving observer
in the K′ + 1 frame. In which case when a second body in
the K′ + 1 frame gets close enough to the observer in the,
it is then represented as
(c2)2 = c2,
(v2)2 = v2 − u2
following the equation for gravity is now obtained from
length contraction, where the contraction of the x-axis in
the second frame influences the length of a point in the K′
+ 1 frame relative to the other frames. So that when
(c2)2 = c2,
(v2)2 = v2 − u2
is obtained, the equation for length contraction becomes
proportional to
= m/m
for each of the gravitating masses. So that for 2 gravitating
masses, it becomes
and the smaller mass is observed as relatively gravitating
towards the larger mass with a certain force at a point on
the x-axis. These implications require a stationary system
moving with the observer and the body in K’ + 1 (the second
frame) so that with sufficient distance
(c2)2 = c2,
(v2)2 = v2 − u2
is transformed into
c2 = c,
v2 = v − u
and gravitation doesn’t necessarily occur. The equations
of gravitation measure gravity by the gravitating potential
of one mass towards the other. Since the observer and the
second body can’t move at the speed of K′ + 1, their position
in K′ + 1 is translated to their corresponding gravity wave
that is capable of superimposing into the K′ + 1 frame and
represented in the equation for gravitation as M1 and M2.
In this case, the force of gravity can be viewed as caused
by a spherical wave influencing the other frames where a
force of attraction occurs between 2 masses.
For a more accurate estimation of the valid distance, the
contraction of length for 2 masses is capable of supporting
a gravitating effect of 2 masses, this distance can be limited
within the space of an emitted light ray. Where there’s
energy there’s gravity. The going about limiting this distance
is as follows. The shortening of wavelength evokes the
shortening length of the mass emitting the light ray so
as for the principle of relativity to remain true for all the
observers. The shortening of the emitting mass follows the
compression or the stretching of the other frames and the
principle of relativity is once again valid for all observers.
The established fact that gravitation can result from the
aforementioned relativistic effects is enough to establish
that with reducing distance from the emitting mass the
weaker that the gravitational force gets as the wavelength
increases in size. Furthermore, all present relativistic frames
add that the symmetry of space-time remains simultaneous
in all its postulates. For all the symmetric spaces introduced
herein to remain simultaneous with those based on the
theory of relativity, the cosmological constant is introduced
and increased by a factor so much as with the increasing
symmetry of the light ray-the principal of the constancy of
the velocity of light in vacuum remains true, but the principle
of relativity is momentarily broken as the light ray contracts
faster than the emitting mass. This asymmetry is corrected
by the introduction of that the length of the emitting
mass isn’t contracting linearly but in a quadratic manner.
The emitting mass and the mass absorbing or reflecting the
light ray both contract in length towards each other. In this
way, the principle of relativity approaches towards being
true for both gravitating masses. Yet no claim has been
made as to how the k frame remains relative to the others.
In this instance, the k frame is viewed as contracting with
the present mass, in as much as the cosmological constant
remains true for the contracting light ray. So to prevent
any infinities caused by the cosmological constant and the
contraction of the light ray; the k frame contracts in such a
way that the approaching light ray is slowed by a factor that
the contraction of the k frame remains relative to the other
frames. In other words, it’s said that an increase in energy
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would cause an increase in the curvature and matter must
follow this curvature in order for the principle of relativity
to remain for all observers. And it has been established that
the presence of energy constitutes gravitation.
And now it can be deduced as action at a distance having
a postulate. This postulate is anchored to the principle
of relativity. For a practical approach to how the other
frames are able to pose negative mass as the symmetry
of space-time increases; the velocities in the equations of
relativity are transformed into the distance the deliberations
of an observer at rest are the same when the body in
so-called motion has velocity. While the speed of light
“c” is transformed to be p (the perceivable limit of the
observer) which is the point beyond which the observer
can’t perceive anything. With increasing distance of the
so-called body in motion, the more that the observer at
rest views the size of the body to reduce. With sufficient
distance, the body vanishes to the observer at rest but
appears to grow larger in size to a second observer far from
the first observer, and the body approaching the second
observer is being moved closer to the second observer as
it moves further from the first. It then emphasised that the
decreasing of length as velocity increases only has to do
with the principle of relativity and because a certain body
vanishes as it approaches the speed of light and faster,
this does not necessarily mean that this body also ceases
to exist as it can still be observed elsewhere. Then exists
the observation that with increasing distance the less there
would be a sort of linear interaction between the observer
at rest and the body with increasing distance. That with
sufficient distance the body even ceases to be perceived.
So now the distance in the practical approach is relative
to the velocity, and the interaction with distance is the
same with velocity. There then exists a limit between the
interaction of the observer at rest and the body in motion,
and this limit is within the energy of the two. More energy
would constitute faster velocity. As the speed of light is
approached the interaction with a body moving faster than
light becomes more observable. Now the light wave would
have a medium of negative mass to travel through. Also
there now exists a medium mediating length contraction.
Conclusion
The universal model described above tries to unify gravity
with quantum mechanics, in order to derive a universal
theory in which gravity is quantised. The results of the
theory were attained by unifying General relativity with
Quantum gravity.
Conflict of Interest: None
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