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(t2/6) 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(t2/6),
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 = 2Ï€R then, 2Ï€R = A(t2/2)

Replacing acceleration 'A' with divergent acceleration 'DIV' we have 2Ï€R = DIV(t2/2)

And solving for divergent acceleration 'DIV' we have DIV = 4Ï€(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 (λr/λ t2).

So we can write,

DIV = 4π (R/ t2) = 4π (λr/λ 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((λr/λ t2). For mathematical convenience, if we let CON = (λr/λ t2) since (R/ t2) is the convergent boundary of divergent spherical acceleration.

DIV = 4πCON = 4π(R/ t2) = 4π(λr/λ 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 acceleration within a 'particle' of mass can be computed.

Divergence/Cnvergence must be expressed in units of acceleration (m/sec2) or as units of velocity (m/sec) per units of time (sec). So acceleration can also equal velocity times frequency (v*f), Computing the 'divegence' 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 to

4.52445e34 (m/sec2)/erg or DIV/erg.

Since one electron volt is equal to 1.602e-12 ergs, then divergence per electron volt is equal to

7.24817e22 (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 = DIV

Divergence 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 = DIV

Divergence 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 0.01474624176227%. 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 = 4Ï€CON

and one of Maxwell's equations states that the gradient of the electric field equals four pi times the charge density,

∇*E = 4πQ