In the not so distant past, concepts for the explanation of the structure of mankind’s environment were derived from observation. During the 1400’s, mankind thought the world was flat and watching a ship sail away from an observer on shore altered this view. It was noted that a tall mask slowly sank into the sea as the distance from the shore increased. From this point of view, the realization that the world is round was deduced.
Euclid developed a geometry that served to explain and solve problems of engineering that previously had no solution. For many years, Euclidean geometry has served man well by producing many structural marvels of engineering in bridge design, architectural buildings, and new inventions. This geometry works well in our local environment yet does not offer solutions to some things observed in space-time. To achieve an understanding of unexplainable things observed in nature, a change in view point must be initiated.
The belief that the earth was the center of the known universe was sustained for years until Copernicus proposed his new point of view. In his presentation, Copernicus used Euclid’s geometry to show that the earth revolved around the sun.
Almost everyone knows of Albert Einstein and his now famous theory of relativity. Acceptance of this theory has lead to many breakthroughs in understanding space-time. What is not commonly known is that there is rumor that his revelations of relativity may have come from his first wife, an accomplished physicist in her own right. Both conspired to publish many papers on areas of physics dealing with previously unexplained phenomena. Eventual acceptance of his new perspectives brought about new ideas and viewpoints that have given us many new inventions. This technical revolution has evolved mankind into the information era. All these changes stem from Einstein’s ability to change and modify his point of view until he could derive practical solutions to extremely complex puzzles of nature. From the ability to question and change a common point of view, Einstein changed mankind’s understanding of his environment. There are still many areas of science that contain apparent complex puzzles. It is time for a change to a new point of view. Any new perspective must maintain the laws of physics and observed properties of space-time that are currently understood while shedding new light on properties not currently understood.
What follows is a radically new view of the relationships between man and his environment. This new view begins by observing a Euclidean geometric point in space, deriving an ordered matrix of all possible properties of this point, extending these properties to the set of all points, blending the properties with a series of time, and noting the resulting observations.
Euclidean geometry is built upon a Cartesian coordinate system of three axis that are commonly labeled by the letters X, Y and Z. The comparison of directional distance along an axis with directional distance along the other axis generates this type of geometry. Directional distance can also be viewed as a function of time and velocity. Changing the view of space in terms of distance to viewing space in terms of time yields solutions to age old puzzles. It may seem quite strange to replace structural distance in geometry with structural time. At first the mind may rebel from this viewpoint, but with patient contemplation, a new understanding of space-time may be realized.
The following is a brief presentation of a radical new view of space-time. It begins with the derivation of a mathematical function called a Taylor series. The conclusions drawn from the interpretations of each element of this series are based on a viewpoint from only one domain of the series. Accepting this new view will lead to a much deeper understanding and clarity of what were previously unexplainable phenomena. This presentation is not an in depth study and is not meant to be complete. The purpose of this document is to present an alternative point of view, introduce the mathematics and function of EXPANSION, and provide a general geometric and mathematical model of local space-time.
Carroll Humphreys
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In set theory, the properties of the set are properties of the elements in the set. Conversely, the properties of the all elements in the set are properties of the set. Considering space as a set of elemental points, then each point has the properties of the set. Basic properties of points in space can be listed as flux, impulse, acceleration, velocity, distance, surface area, volume and expansion. All these properties are related to each other in the mathematical form of a Taylor series expansion.
The Taylor series is a mathematical relationship between derivatives of these properties and integrals of time. Each element of the series has two parts, a derivative of spatial property multiplied by an integral of time. Here is an example of Distance expressed as a Taylor series:
The geometric and mathematical model of local space-time can be viewed as a dot product of an array of spatial properties and a series expansion of time. Starting with the series expansion of the exponential of time:
Each element of this expansion can be placed as an element in a time array and the spatial properties can be placed as elements of an array. The dot product of these two Wronskian arrays is space-time.
This dot product forms a Taylor series where each element of the series is considered as a domain. It is the domains, Xn, viewed as separate domains that constitute the structure and the behavior of space-time as seen by mankind. The following pages depict the domains and their corresponding Taylor series for each element of the spatial point properties. Note that by bounding the distance domain, the acceleration and impulse domain appear spherical.
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The Taylor Series Equations of Space-Time
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Mankind’s Domain in Space Time
Mankind’s observations of his local environment lead to the conception of Euclidean geometry and mathematics to describe space. Since distance is to be described in three dimensions, a Cartesian coordinate system, commonly labeled as X, Y and Z, is applied from a single observation point. Distance from a reference point to an observation point using Euclidean geometry.
It must be noted that the normal act of measuring may require velocity to move from the reference point to the observation point, counting the units of distance. This seems quite normal since distance moved is a function of velocity multiplied by time.
The measure of distance in Euclidean three-dimensional space is then directly related to the existence of time. Since measured distance is a function of time, along the three axis of X, Y and Z, measured distance exists only when time also exists on each axis. Within this domain, time must be three dimensional to generate the three dimensional Euclidean space. Mankind’s geometric view of his domain is therefore Euclidean in nature.
The Distance Domain of the Space-time Taylor Series
The distance domain in the series, defined by D(t^3/6), creates a perception that is Euclidean in nature. This view of space-time is fine for mathematical analysis based on distance in XYZ from an observation point. Since distance is a function of time and measured distance would not exist unless time existed on each axis XYZ, time must therefore be three dimensional, one dimension of time for each axis in the distance domain. It is from three dimensions of time that other domains of the series are observed.
Time objects are objects that are observed in the distance domain. Time objects can have a maximum of three dimensions in the distance domain. Higher time dimensional objects are observed as pairs of time objects.
From the distance domain a five dimensional time object will be viewed simultaneously as a three dimensional spherical object and a two-dimensional plane object. A six dimensional time object will be viewed simultaneously as a pair of spherical three dimensional time objects.
The Velocity Domain of the Space-time Taylor Series
The velocity domain in the series, defined by V(t^4/24), is viewed in the distance domain as a pair of time objects. These time objects exhibit certain observed properties in the distance domain.
Four dimensional time objects from the velocity domain appear as a three-dimensional time object paired with a one dimensional time object. This view generates properties of particle behavior.
Four dimensional time objects from this domain also appear as a pair of two dimensional time objects. One object existing in an XY plane while the other exists in an XZ plane. This view generates the properties of electromagnetic wave behavior.
Both views are of a four-dimensional time object in a three-dimensional time domain. Physicists in the distance domain, observe and label the time objects generated by the velocity domain, as light.
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The Acceleration Domain of the Space-time Taylor Series
The acceleration domain in the series, defined by A(t^5/120), is viewed in the distance domain as a pair of time objects. These time objects exhibit certain observed properties in the distance domain.
Five dimensional time objects from the acceleration domain appear as a three-dimensional time object paired with a two-dimensional time object. This view generates properties of both structure and behavior.
The existence of three-dimensional acceleration in the distance domain generates a two dimensional plane of acceleration. The direction of acceleration will be convergent or divergent with respect to a point in the distance domain.
Time objects from the acceleration domain are a complimentary pair. If the three-dimensional acceleration time object is convergent, it generates a divergent two-dimensional plane. A three-dimensional divergent acceleration time object generates a two dimensional convergent plane of acceleration.
A noted property of three-dimensional convergent acceleration is that they will merge to one large time object. The merging of these convergent time objects in the distance domain is labeled by astrophysicists as a black hole. This three-dimensional convergent time object creates a two dimensional divergent plane.
Within this divergent plane, three-dimensional divergent acceleration time objects will gather and disperse, maintaining singularity. The singularity of these divergent time objects in the distance domain is labeled by astrophysicists as stars.
The three dimensional divergent time objects generate a two dimensional convergent plane. Within this convergent acceleration plane, three-dimensional convergent time objects will gather and merge into singularities. The singularity of these convergent time objects in the distance domain is labeled by astrophysicists as planets.
Another property of three-dimensional point acceleration is noted when the spherical volume is dissected with an XY plane. If the point acceleration is divergent, then along the Z axis there will be linear convergence. Examining this closer, it is noted that no mater what the orientation of the dissecting plane, linear convergence occurs on the normal to this plane. Thus the generated linear convergence will form a spherical surface about the point divergence. Physicists in the distance domain, label this result as the quantum effect.
In the distance domain, the properties of the acceleration domain generate the quantum effect and structural symmetry in space-time.
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The Impulse Domain of the Space-time Taylor Series
The impulse domain in the series, defined by I(t^6/720), is viewed in the distance domain as a pair of time objects. These time objects exhibit certain observed properties in the distance domain.
Six dimensional time objects from the impulse domain appear as a pair of complimentary three dimensional time objects. Both time objects will appear spherical, one divergent and the other convergent.
The convergent impulse time objects tend to merge into one large object. Convergent impulse maintains the existence of convergent acceleration. Physicists in the distance domain, observe this as the sustained existence of a black hole.
The divergent impulse time objects will disperse and remain singularities. The divergent impulse time objects sustain the existence of divergent acceleration. Physicists in the distance domain, observe this as the sustained existence of a star.
Since the three dimensional complimentary impulse pair in the distance domain are actually one object in the six dimensional impulse domain, any action taken on one of the time objects results in the inverse action on the other. Physicists in the distance domain, label this observation as the Bell connectiveness theorem.
Since the pair of time objects is connected in the impulse domain, any collapse of one time object in the distance domain will result in the collapse of the other time object. Physicists in the distance domain, observe this reaction when a star goes nova.
The impulse domain sustains the existence of three-dimensional acceleration. The quantum effect, generated by the acceleration domain, will form atomic nuclei about point divergent impulse. The larger point impulse will be represented by larger nuclei. Nuclear particle emission is a result of large point impulse and quantization of acceleration.
In the distance domain, the properties of the impulse domain sustain the existence of mass, stars, and black holes.
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The Flux Domain of the Space-time Taylor Series
The flux domain in the series, defined by F(t^7/5040), is viewed in the distance domain as a triplet of time objects. These time objects exhibit certain observed properties in the distance domain.
When seven dimensional time objects from the flux domain appear as a pair of complimentary three dimensional flux time objects and a one-dimensional flux time object. Two time objects will appear spherical, one divergent and the other convergent. The one-dimensional flux connects the two spherical flux time objects only for an instance. Physicists in the distance domain observe this reaction and label this as a gamma ray burst.
When seven dimensional time objects from the flux domain appear as a pair of two-dimensional objects and single three-dimensional object. Physicists in the distance domain observe this reaction and label this a pulsar emitting high-energy quanta.
The other potential triplets of the flux domain (2,3,2) affect the acceleration and surface area domains. Since flux is a seven dimensional time object, it affects the existence of light, mass, space and all things observed in nature in the distance domain.
In the distance domain, the properties of the flux domain create gamma ray burst, sustaining and changing the properties of all other domains in the space-time Taylor series. Because of the properties of the flux domain, the existence of light, mass, stars and black holes, galaxies, and the whole universe will eventually be finite.
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Observations of Acceleration Behavior in the Distance Domain
We all live in a three-dimensional world as three-dimensional creatures. In normal daily encounters, acceleration is commonly experienced along a line. This type of acceleration is one-dimensional and is a vector with magnitude and direction. The acceleration vector has direction and magnitude usually aligned with a velocity vector. Acceleration is applied linearly to increase velocity while traveling in an automobile. By design, the vehicle will have a maximum achievable velocity. The acceleration vector is quantized and therefore decreases to zero as velocity increases to it’s maximum. One-dimensional acceleration is taken for granted and there is little contemplation given to this subject by the average person.
From an observation point in the geometrical model view, vectors have only two basic directions.CON vectors of convergence ? ?
DIV vectors of divergence ? ?
Divergence and Convergence are terms of direction that play a primary role in nature. These two directions of acceleration, divergent and convergent, interact between one-two and three dimensions. Since for every action there is an equal and opposite reaction, the existence of one affects the existence of another. Dropping a stone in a puddle of water, observing the effect of linear acceleration intersecting a two dimensional plane. Acceleration in the plane begins at the intersection point in the plane and is noted as radial in behavior. The linear acceleration is convergent to the intersecting point while the radial acceleration in the plane is divergent from the intersecting point. Knowing the existence of one dimensional acceleration affects the existence of two-dimensional acceleration by observation we also know that the existence of two-dimensional acceleration affects the existence of one-dimensional acceleration. We now also know that if one object of acceleration is convergent in direction the other is divergent in direction.
Mathematically, modeling distance with a Taylor series predicts the effects of acceleration on distance. For any point in space, distance defined by the Taylor series is:D = V(t) + A(t²/2) + P(t³/6) D = distance, V = velocity, A = acceleration, P = impulse, t = time
The terms on the right are each DISTANCE. Because each term is distance, the terms can be added to compute total distance:as a function of impulse P(t³/6),
as a function of acceleration A(t²/2),
as a function of velocity V(t)
Concerning acceleration, we can state distance as D = A(t²/2).
Defining a fixed distance in local space-time as orbital distance, D = 2?R then, 2?R = A(t²/2)
Replacing acceleration ‘A’ with divergent acceleration ‘DIV’ we have 2?R = DIV(t²/2)
And solving for divergent acceleration ‘DIV’ we have DIV = 4?(R/ t²)
Since R is a radius distance, in one dimension, R implies a line. In 2 dimensions R implies a circle. In 3 dimensions, R implies a spherical surface encasing a volume.
From a geometric acceleration model, considering R as acceleration, a point expands to a line in 1 dimension. In 2 dimensions a point expands to a circular plane. In 3 dimensions a point expands to a spherical surface. From set theory, if something is true for all points of the set, then it is true for the set. The converse being, if something is true for the set, then it is true for each point of the set. The set of points in local space-time has acceleration. Each point in the set has acceleration. In one, two and three dimensions, with respect to each point in the set, only 2 directions of acceleration exist, divergent and convergent.
Divergent acceleration, a function of radial acceleration (R/ t²), can be written as (?r/? t²).
So we can write,DIV = 4? (R/ t²) = 4? (?r/? t²)
Examining divergence from a point in 2 dimensions implies a circular plane, with the point of divergence at the center of the circle. If this point is in 3 dimensions with planar divergence (X, Y), the Z-axis normal to the plane exhibits convergence toward the point. The upper Z-axis view is a point expanding to a circle by a factor of 2(. The lower Z-axis view is a point expanding to a circle by a factor of 2(. In the plane, acceleration is divergent, yet in the Z-axis, acceleration is convergent. The total convergence along the Z-axis is therefore 4?((?r/? t²). For mathematical convenience, if we let CON = (?r/? t²) since (R/ t²) is the convergent boundary of divergent spherical acceleration.DIV = 4?CON = 4?(R/ t²) = 4?(?r/? t²)
Since no matter what surface observation point is chosen, there is a normal plane through the point divergence causing surface point convergence. The relationship of one-dimensional acceleration with a normal plane of two-dimensional acceleration creates quantization of three-dimensional point acceleration.
Mathematically, the total divergence at any point in local space-time is four Pi times the convergence about that point. In 3 dimensional space, divergence from a point creates convergence toward the point. The convergence surface created will quantize the divergence about that point with a surface of equilibrium.
Geometrically we have a sphere of divergent acceleration, encapsulated at a distance R by a surface of convergence. On this surface, divergence equals convergence. At any observation point on this surface, acceleration down, into the center of the sphere, cancels acceleration up, out of the center of the sphere. An equilibrium surface which encapsulates a quantum of point divergence, at radius R. If the observation point is changed from distance R to (R-r), the surface at radius (R-r) will be divergent upward at all observation points on the surface. Likewise, if the surface radius is (R+r), then surface observation points have acceleration downward, into the center of the sphere. Convergent acceleration into the center of a sphere is observed as gravity.
Working with a particle accelerator, acceleration is applied to detect the components of a boson. After an amount of acceleration is applied, quarks are detected. Applying more acceleration to the quarks, 5 basic quanta are detected. Applying more acceleration, 4 more basic quanta are detected. More acceleration, 3 more basic quanta are detected. More acceleration, 2 more basic quanta are detected. With more acceleration, the final single basic quanta can be detected.
The total 15 basic quanta arranged as a pyramid whose base level has the first 5 quanta. Moving up the pyramid, a level of 4 quanta, followed by the level of 3, then the level of 2. Finally at the very top of this pyramid is the smallest quanta which takes the most acceleration to detect. These basic quanta appear as quantized bundles of divergent point acceleration.
Mass is composed of combinations of the basic quanta, implying that mass is quantized acceleration. The nucleus of any atom is composed of combinations of quanta grouped about a single point of 3 dimensional divergent acceleration. The larger the nucleus, the larger the divergence at that point. The heavy nuclei exhibit enough divergence that quanta are expelled from the nuclei. These nuclei are said to be unstable as they undergo ‘particle emission’. Since mass is composed of quantized divergent acceleration, it is logical that mass can be multiplied by acceleration, and that the divergence of mass can be computed.
Divergence must be expressed in units of acceleration (m/sec²) or as units of velocity (m/sec) per units of time (sec). So divergence can also equal velocity times frequency (v*f), and if we let v=C then we can write DIV = C*F = (m/sec)*(1/sec) = (m/sec²). The divergence of mass must be expressed as (m/sec²)/gram. Beginning with the speed of light (C = 2.99979e8 m/sec) divided by Planck’s constant (h = 6.262e-27 erg_sec) yields acceleration per erg and is equal to4.52445e34 (m/sec²)/erg or DIV/erg.
Since one electron volt is equal to 1.602e-12 ergs, then divergence per electron volt is equal to7.24817e22 (m/sec²)/eV or DIV/eV
Since the rest energy of an electron (MeC²) is equal to .511e6 eV, then (MeC²)*(DIV/eV) is the divergence of an electron. DIV(electron) = (MeC²)*(DIV/eV) = (eV*DIV)/eV = DIVDivergence of electron 3.70381360E+28 m/sec²
Electron DIV/gram 4.06565708E+55 (m/sec²)/gram
Likewise the rest energy of a proton (MpC²) is equal to .938e9 eV, then (MpC²)*(DIV/eV) is the divergence of a proton. DIV(proton) = (MpC²)*(DIV/eV) = (eV*DIV)/eV = DIVDivergence of proton 6.79878114E+31 m/sec²
Proton DIV/gram 4.06625666E+55 (m/sec²)/gram
The differential between the computation of Electron DIV/gram and the computation of Proton DIV/gram is -5.99575830E+51 (m/sec²)/gram. This amount of error could be resulting from the estimates of mass for electrons and protons. Even though this seems a large differential, the number represents and error of 0.0147%. Computing the average DIV/gram:(Average) DIV per gram of mass = 4.06595687E+55 (m/sec²)/gram
Is it coincidental that this model yields the relation?DIV = 4?CON,
and one of Maxwell’s equations states that the gradient of the electric field equals four pi times the charge density,(gradient)*E = 4?Q.
Quantization of acceleration is a discrete function. While divergence is a continuous function, convergence is a discrete function, occurring only at a certain level of divergence. Point divergence of a nucleus is continuous and contiguous. The quantization of bosons in the nucleus is discrete, convergent quantum. Over time, the differential of continuous divergence and discrete convergence grows until it reaches a quantum level, the quantum group and ‘particle’ emission occurs. The differential falls to a level below the quantization boundary. As time passes, the differential between continuous divergence and discrete convergence increases until it approaches a discrete convergence level. Quantization occurs, emission takes place, the differential between contiguous and discrete builds and cycles.
This view of point divergence serves as a model that generates reasons for the existence of mass. The existence of atomic nuclei represents points of various magnitudes of divergence. A large nucleus implies a large point divergent impulse, surrounded by many quanta of convergent acceleration. A small nucleus implies a small point divergent impulse, surrounded by discrete quanta of convergent acceleration.
Time is measurable as a function of emission cycle length, frequency. The reciprocal of time is created as a function of the differential between continuous and discrete acceleration. The frequency of particle emission and the half-life of isotopes, are measures of time. Quantization will adjust to best fit the point divergence, resulting in minimum particle emission when divergence decreases, and the eventual existence of stable nuclei.
On a solar scale, computing the divergence of earth orbit using DIV = c·f, where frequency ‘f’ is one divided by orbit time in seconds, yields,DIV(orbit) = c·f = (2.9979e/(31557600) = 9.5 (m/sec²) = 31 (feet/sec²).
The orbit is congruent to earth, since surface convergence is about 9.8(m/sec²) = 32 (feet/sec²). Upper atmosphere convergence is about 9.5 (m/sec²), which appears to equal orbital divergence. Using the figure of 9.5 (m/sec²), computing f = c/DIV, where DIV=(4?*9.5), implies a congruent orbit of 29 days, 1 hour, 34 minutes, 34 seconds, an estimate of a suitable lunar orbit time about earth.
The following chart depicts a comparison of two-dimensional divergent acceleration with two-dimensional convergent acceleration. The divergence is orbital acceleration, cf, while the convergence is surface gravity of a planet
An example of planar acceleration causing linear acceleration occurs in nature and can be verified by observing signus x-1. Signus x-1 is a red giant star in co-orbit with a black hole. Plasma streams from the red giant toward the black hole. This forms a swirling disk of plasma around the black hole. The plasma swirls inward in the x-y plane until it enters the black hole event horizon. When this occurs, plasma streams outward in the upper and lower z-axis. In this example, planar convergent acceleration causes linear divergent acceleration.
A more intriguing implication is the affect of linear acceleration converging on a point in the normal plane. The relationship of linear with planer acceleration implies that if enough linear acceleration were present, divergence in the normal plane would open a portal to warp time. There is implication that c/4? (m/sec) may be a jump velocity out of local space-time.
Since divergence is, DIV = c·f
Then DIV = 4?CON implies c·f = 4?(R/t²)
Moving all constants to one side yields, C/4?= (R/t)
This equation implies that convergent acceleration is discrete in local space-time, is constant and occurs when CON*t = C/4?.
This implies the existence of an upper bound of velocity equal to C/4?(m/sec) at which quantization occurs. This may be the velocity boundary of our local space-time. Exceeding this velocity may cause the traveler to be quantized into a warp in time.
The Alpha ? and the Omega ? conditions of Acceleration
Acceleration in N dimensional space = An where -An is the inverse direction of An
The Alpha condition:
?=(An/-An)=-1 =(CONn/DIVn)=(DIVn/CONn)=?
? = The ratio of opposite directional acceleration in the same dimensions n
The Alpha heterogeneous condition is the ratio of opposite directional acceleration in the same number dimensions.
A point in space, where the alpha condition ratio is close to a numerical value of minus one, belongs to a set of common points in all dimensions. These are midpoints for all spatial dimensions. Earth is one of these points, an alpha point in 2 dimensions. The alpha condition may be critical to the evolution of life, certainly to Earth. Examining the planets in our solar system by comparing orbital divergence to planetary gravity gives the alpha for each planet. The alpha condition for the outer planets has a numerical value less than one. This implies low subatomic activity with an abundance of lighter elements. The inner planets alpha condition is numerically more than one, which implies an abundance of heavier elements and high subatomic activity. An alpha condition numerical value of minus one promotes nominal distribution of elements with an environment suitable for water to exist in three states, gas, liquid, and solid.
The Omega condition:
? = (An/-A[n-1])=4?=(CONn/DIV[n-1])=(DIVn/CON[n-1])=?
? = The ratio of opposite directional acceleration between adjacent dimensions (n,n-1)
The Omega homogeneous condition is the ratio of opposite directional acceleration in adjacent dimensions.
The omega condition promotes the quantum effect, light, gravity, electromagnetism, weak and strong forces, and the creation of mass. The omega condition is the reason for galactic structure. The 3 dimensional ‘black hole’ at the galactic center generates a 2 dimensional divergent plane. The stars are points in this plane. The stars are 3 dimensional divergent points, which generate a 2 dimensional convergent plane. The planets are convergent points in this plane.
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QUANTIZATION(the formation of mass)
Note that the object of observation in time will be called a 'time object'
The time object observed will be ACCELERATION....
Dropping a pebble from a height, observing the 'time object' of linear acceleration....
When pebble proceeds through a surface area of water, an orthogonal plane, observe radial acceleration within the plane....
Observe that linear acceleration creates radial acceleration in an orthogonal plane.....
Note that convergent linear acceleration CREATES divergent radial acceleration....
Note also that both are time dependant, one does not occur without the occurrence of the other......
For these time objects, Linear creates planar, planar creates linear.....
Note, consider spherical divergent acceleration from a point source....
Note, that a dissecting plane through this sphere shows a radial plane of divergent acceleration....
Note that this radial planar (X,Y) acceleration creates linear acceleration, within the orthogonal Z-axis.....
Note that the planar acceleration is divergent, while the linear acceleration(in Z) is convergent....
Note that no matter what angle the sphere is dissected, the Z-axis is convergent....
There any point divergent sphere of acceleration, will form around it, a surface where divergent acceleration is canceled by convergent on the Z-axis....
This processes is called 'QUANTIZATION' and occurs in nature.....
This existence of the quantization process of 3 dimensional divergent acceleration, creates in nature, 'particle' formation....
This 3D point divergent(spherical) acceleration quantization process, is observed as 'MASS'......
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MOMENTUM
Regarding a Quanta of Acceleration....
From the outside, note 3d point convergent linear acceleration....
From the inside, note 3d point divergent acceleration....
A quantum of spherical acceleration is in an equilibrium state.....
Note when an outside vector of linear convergent acceleration appears at left, the sphere remains in equilibrium...
The new vector cancels or lessens an outside convergent vector on the right, allowing normal convergence from the left, to give motion to the point of divergence, with velocity= A(t)...
Maintaining equilibrium, the quanta is now in motion.....linearly to the right.....
It remains in motion until a new vector of acceleration may appear, changing normal convergence by its presence....This is 'MOMENTUM"
This quantum will remain in equilibrium, and in motion, until an outside vector of convergent acceleration appears, changing normal convergence, on the right of the quanta.....
The new vector of acceleration is A(t), and depending on its direction, will alter motion of the quanta by changing its velocity by the amount of A(t)....
If no new vector appears, the quanta remains in motion with velocity 'V'....
This is the property called 'the CONSERVATION of MOMENTUM'....
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PHOTOELECTRIC EFFECT
Note that a large point divergent acceleration, will be enclosed by convergent quanta, this is a nucleus....
Note that the convergent acceleration field strength, around this large 'point'(nucleus), decreases in intensity as we move away....
Note also that a 'photon' is a spherical quantum of VELOCITY....
Its radial velocity is equal to a fixed value of A(t)...
If the path of this 'photon', converges toward a nucleus,
it will reach a distance from the nucleus, where at this distance, the intensity of the 'nuclei' convergent acceleration, will match the fixed amount of acceleration within the photon...
If there is an 'electron' held in orbit at this distance, by the same principles of momentum stated early,
the presence of this quanta of velocity=A(t), cancels the convergence at that distance from the nucleus...
The electron now will maintain a straight line of velocity, (from orbital velocity), and 'escape' its orbit....
Note that this effect, only occurs when the 'photon' intensity of A(t), is very near the 'intensity' of convergent acceleration for that particular orbital distance....
This implies that ONLY CERTAIN FREQUENCIES of 'light' may 'free' electrons from orbit...
Lower or higher frequencies will not free an electron from orbit at this fixed distance....
This observation is called the PHOTOELECTRIC EFFECT....
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THE GENUS SINGULARITY
The existence and mathematics of universal expansion REQUIRES the existence of 4 dimensional time......
Notice the coefficients of expansion mathematics (From the Euclidean view)
Expansion
Volume
Surface Area
DistanceThen the first appearance of the INVERSE of time occurs here
Velocity
Acceleration
Impulse
Flux.............the 4D INVERSE
The expansion function, as presented, is a view of our universe.The third domain of this function, D(t^3/6) is mankind’s domain.
However, the first and second domains are of interest as well.
Volume(t)
Surface Area(t^2/2)
Our universe can be seen as a Volume of Time, surrounded by a Surface Area of time.
We are only ONE volume of time, what if we are NOT the only volume, NOT the only universe?
Supposition:
We are only one of many, volumes of time, universes.
Between universes, each encased within a 'membrane' surface.
Outside this surface.....VOID...
Supposition:
A 'membrane' surface of time, encasing one universe,
MAKES contact with a 'membrane' surface of time, encasing another universe.
Within the VOID, an event, a contact of two, 2-dimensional 'membranes' of time,
there is 'light', at contact...4 dimensional time AND VOID,....a Big Bang....a new universe emerges....
Supposition:
Our universe may be a single 'bubble' of time, within an 'ocean' of 'bubbles, an ocean of universes.
Periodic contact, each creating NEW 'bubbles' of time within the void, new universes from Big Bangs, occurring as a result of each contact of two 'membranes'.
The Taylor series function of expansion, as examined in this Article, shows mankind’s view of our universe from within this function of expansion.
Within this expansion function is a definition of time itself, expressed in a MacLaurin series form.
Any point (t) in Linear Time, is the natural log of this series.
Time=ln[1+t+(t^2/2!)+(t^3/3!)+(t^4/4!)+(t^5/5!)+(t^6/6!)+....+(t^N/N!)]
This function defines linear time in our universe, as generated by the function of expansion of our universe.
The preliminary discussion of expansion within the article, covered the 3rd domain of expansion(Euclidean space) and the view from this domain into expansion.
Little discussion was stated about the first two domains of expansion....
Expansion=Volume(t)+SurfaceArea(t^2/2)+........
The first domain states that our universe is a volume of linear time,Vol(t)...
in union with the second domain, a surface area of time, SA(t^2/2)...
within is Euclidean space, mankind and their views of the universe...
The expansion function of our universe implies that, We are inside a 'bubble' of linear time,
encased with a 'membrane' of time, a 2 dimensional surface area of time, within is our safe Euclidean space...
Our geometric shape of our universe, could be much like M theory states, toroid, conical, basically any shape you might imagine...
I prefer the view of spherical for the moment, but it doesn't matter in what shape you wish to view our universe...
Within mankind’s view, we see and use the inverses of 1,2,3,and 4 dimensional time,
comparing them to units of distance to note Velocity, Acceleration, Impulse, and Flux...
We view, from within the 'bubble' the inverses of the subsets of 4 dimensional time,
and we use them in our computations for engineering and other sciences.
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An Ocean of Bubbles
When we then consider our genus, it is the boundary and the void outside our ‘bubble’ that need consideration...
AND the concept that we are only within ONE 'bubble', that there could be many more...
Supposition
Our universe is not the ONLY universe, it did not exist at first, then an event, linear time passes, here we are...
Over ALL of time, I don't believe it happened ONLY once...
Lets consider that it hasn't happened yet, and then we have the fortunate view of many 'bubbles', separated by void...
On the outside of the 'bubbles', a void of only distance, darkness, no light, mass, time, nothing but infinite distance, within the void.
Then an event, two 'bubbles', close in distance, 'membrane' boundaries momentarily contact...
Within the void of infinite distance, there appears an instance of a point in time,
that an intersection of two 'membranes' at that point, creates a 4-dimension time point...
Within the void, from the point of 'membrane' contact, comes the union of void and 4 dimensional time...
We would now be viewing a big bang within the void, the initial creation of a new 'bubble' of linear time, encased within a 'membrane' surface area, a new Euclidean space, expansion function of space-time...
The birth of a universe of expansion...a 'bubble' in an ocean of 'bubbles'...'quantum foam'...and the evolution of life...
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Summary
Each domain of the space-time series is expansion. Euclidean mathematics has developed from the distance domain of three-dimensional time. Distance exists in three dimensions of time and in six directions from an observation point. An XYZ coordinate system works in the distance domain because time exists along each axis. It is from a Cartesian coordinate system that mankind analyzes the geometry of observed space. The view from the distance domain into other domains of this expansion series is restricted such that no time objects in the distance domain can be larger than three dimensions. Larger dimensional time objects from the velocity, acceleration, impulse and flux domains exist in the distance domain as pairs of time objects. It is these larger time objects that dictate the structure of space-time and the laws of physics, as we perceive them. From the distance domain, the view of the velocity domain, V(t^4/24), is four-dimensional. These four dimensional time objects are observed as two simultaneous planes of existence. This is the same property of light as it travels through space. From the distance domain, the view of the acceleration domain, A(t^5/120), is five dimensional. These five dimensional time objects are observed as a pair. The objects are complimentary as one is convergent and the other is divergent. One object of the pair is three-dimensional while the other object is two-dimensional. Convergent objects will merge into one large convergent object while the divergent objects will separate and exist as singularities. This is the same property of the galactic structure, with a large three-dimensional convergence at the center coexisting with a divergent plane. Within the divergent plane are point singularities of divergence, stars, which coexist with a convergent plane. Within this convergent plane are point singularities of convergence, mass, which will merge and form planets. It appears that the acceleration domain is responsible for the structure of galaxies and symmetry in space. From the distance domain, the view of the impulse domain, I(t^6/720), is six dimensional. These six dimensional time objects are observed as a pair. The objects are complimentary as one is convergent and the other is divergent. Both objects are three-dimensional and the convergent objects will merge while the divergent objects will remain as singularities. It appears that the impulse domain is responsible for sustaining divergent acceleration in stars and sustaining convergent acceleration in the black hole at a galactic center. From the distance domain, the view of the flux domain, F(t^7/5040), is seven dimensional. These seven dimensional time objects are observed as sustaining the acceleration at galactic centers and stars. These time objects also create velocity, (4dim) and distance, (3dim), acceleration, (5dim) and surface area, (2dim). Other possibilities are two volumes of impulse, (6dim) that may annihilate each other as gamma ray bursts and super nova reactions. Finally the flux domain, (7dim) may sustain expansion, surface area, distance, velocity, acceleration, and impulse. All domains are affected and possibly sustained by the flux domain.
The view from the distance domain into other domains denotes the symmetry noted in many areas of science. This space-time Taylor series analysis implies, distance exists in three dimensions only because time is three-dimensional and multiple dimensions of time are responsible for structure and symmetry of space.
Ocam’s Razor
"All things being equal,
the simplest solution seems
to be the correct one"
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Mind=force=matter Is the Sum-Wrong!!! 
Originally Posted by quanta07 
Re: The Pure Mathematics of Space-Time 