7.2.29 Communication 
Aether 7.2.27 
Created Dec 313, 2003 Stavropol, RU.
^{To Understand The Aether} 

We Need To Understand The Cosmos! 
The Cosmos!  

^{We Understand}  
28 The Cosmos Exists!  
_{To Understand The Cosmos} 

We Need Communication Skills. 
We Have Communication Skills.  
^{We Understand} 
What is the reality that we have to start with to reason on, to investigate and interpret our results to discover the true science of physical reality and discover the eternal unchanging laws.
When I say reason on I do not mean scientific babble, I mean the logical foundation of physical reality that can guide our investigation and discover mathematical, computerizied models that prdict outcomes in reality.founded on e if we reason on and with correctly we can dis
Space, Aether in Space and Motion of the Aether in Space.
Insights 




*Aether (From Wikipedia, the free encyclopedia) In Plato's Timaeus (St55c) Plato described aether as "that which God used in the delineation of the universe."Logos (pronounced /ˈloʊɡɒs/ or /ˈlɒgɒs/; Greek λόγος logos) is an important term. Heraclitus (ca. 535–475 BCE) established the term as meaning the source and fundamental order of the cosmos. John 1:15 In the beginning was the Logos, and the Logos was with God, and the Logos was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not. 
1 
Logos  the source and fundamental order of the cosmos.
Cosmos  the universe regarded as an orderly, harmonious whole.
Universe  All matter and energy, including the earth, the galaxies, and the contents of intergalactic space, regarded as a whole.
Chaos  The background random matter in transnational equilibrium (an ideal fluid in thermal equilibrium).
Figure 1.1 Random background motion of elements of matter in space.
The Physical Universe is the Space, Matter and Motion in which and from which our visible and invisible physical Universe is formed. Aether is the one and only formless substance of the Logos from which and in which all material (Matter) bodies are formed and exist. The background Aether is in constant motion with collisions from all directions transferring momentum in all directions uniformly.
2 
Postulate 1 (The Extensive Property).
The extensive property of the Logos exists and is called Space! Space is continuous in three linear, independent, infinite dimensions.
Note: a vector is an arrow going from a starting point to an end. A vector can be a location (given an arbitrary starting point) or displacement . An example of the use of terms would be the corner stone in a building as the origin. Locations are vectors from the origin to points. Displacements are vectors from one point to another. Displacements subtract out reference to the origin.
In the Figure below R_{i}_{i} and R_{f}_{f} are locations and r is a displacement. The vector r gives no information about the location of its beginning R_{i}_{i} or its end R_{f}_{f}.
Defining an arbitrary inertial, orthogonal Cartesian coordinate system starting point of R_{0}_{0} as the origin with three perpendicular directions (_{1},_{2},_{3}).
Figure 2.1 Location r in an orthogonal Cartesian coordinate system.
We define location R in physical space in terms of its components
Definition 1R_{0} ≡ R_{01}_{1} + R_{02}_{2} + R_{03}_{3}.
We define displacement r_{fi} in physical space in terms of its components
Definition 2r_{fi} ≡ R_{f}_{f }– R_{f}_{f}.
≡ R_{f1}_{f1} – R_{i1}_{i1} + R_{f2}_{f2} – R_{i2}_{i2} + R_{f3}_{f3} – R_{i3}_{i3}
≡ (R_{f1} – R_{i1})_{1} + (R_{f2} – R_{i2})2 + (R_{f3} – R_{i3})_{3}
≡ r_{fi1}_{1} + r_{fi2}_{2} + r_{fi3}_{3}
Notice that displacement subtracts out reference to R_{f}_{f} and R_{i}_{i} so r_{fi} has magnitude and direction but not location.
We define area A_{12} as the cross product
Definition 3A_{12}_{12} ≡ r_{1}_{1} x r_{2}_{2}.
We define volume V as the dot product of area and extension
Definition 4V_{123 }≡ A_{12}_{12} • r_{3}_{3},
= r_{1}_{1} x r_{2}_{2} • r_{3}_{3}.
Postulate 2 (The Inertial Property).
The inertial property of the Logos called Matter exists! Matter is not created or destroyed. Each element of Matter is infinitely divisible. Each element of Matter occupies its own space uniquely. Basic Matter is a nonviscous, inelastic fluid. Out of the Logos Matter all material things formed and in the unformed chaos the move and have their being. The inertial property of Logos is called mass m.
Logos Matter is not just a medium in which electromagnetic radiation propagates and is effected (like the imagined Aether or Dark Matter). The radiation and all material objects are forms created of the Logos Matter and swimming in the Logos Matter.
Each point of Logos Matter m_{i} occupies it's own unique location R_{i}_{i} in space.
Equation 1R_{i}_{i} ≡ R_{i1}_{i1} + R_{i2}_{i2} + R_{i3}_{i3}.
We define density of a volume of space as the mass divided by the volume of space containing it.
Definition 5_{x} ≡ m_{x}/V_{x}
Postulate 3 (The Mobil Property).
Given two elements of Matter m_{a} and m_{b} the displacement between them r_{ab}_{ab}. Relative motion (velocity) v_{ab}_{ab} between them exists!
Given two elements of Matter in space separating at a constant velocity v_{ab}_{ab} and the associated displacement r_{ab}_{ab}
, we operationally define a clock with time t by
Definition 6t_{ab} ≡ r_{ab}_{ab} /
v_{ab}_{ab} ,
where r_{ab }≡ r_{ab}_{ab} and v_{ab} ≡ / v_{ab}_{ab}.
With a clock defined we can graph the position of an element of Matter as a function of time. Collisions in the Matter change the position of an element of Matter instantaneously so the graph is jagged as represented in one dimension below.
Figure 3.1 Position as a function of time.
This kind of graph has no well defined slope at the points of collision. In calculus terms r(t) is not a differentiable function of time.
3 
With a clock to measure time and a length standard to measure distance we operationally define the velocity vector in a given direction v_{a} for a period of time in space where there are not any collisions as
Definition 7v_{a} ≡ r_{a}_{a}/t_{a}.
In the inertial frame of reference the net flow in a given direction is equal to the net flow in the opposite direction because as with the one dimensional physics toy motion flow is possible simultaneously in all directions (meaning + and  directions along each axis).
The magnitude of velocity (speed v_{a}) of any element of matter m_{a }in space exists with an average speed v_{0}. The average speed v_{0} is uniform through out background matter. From this we conclude there exists an inertial frame of reference R_{0} where the average speed v_{0} is zero.
Given the random distribution of background matter, with a large enough volume V, we observe the effects of chaotic motion matter is in
equilibrium giving an average background density_{0} that is constant.
Observation 1 The average background density of matter _{c} is constant.
The dimensionless saturation is the ration of the volume of mass V_{m} in a volume of space V_{s}
Definition 8 ≡ V_{m} / V_{s}
By Observation 1 we define a universal constant the saturation of the chaos _{c} for the ratio of a volume of matter V_{mc} and the volume of confining space V_{sc}.
Equation 3.1_{c} ≡ V_{mc} / V_{sc}
With space, density, and motion we can define momentum passing through a given area or impinging on a given surface. The definition of momentum as mass m times its velocity v needs some insight when talking about a fluid like the Logos Matter. What mass are we talking about and what velocity are we talking about?
Figure 4.1 Source of basic Insight
Basic matter is not viscous and not compressible:
This means that if we had two pieces of pure basic matter with no internal motion, in a collision the momentum of one could be transmitted through the other without friction. For example see the diagram below showing a collision.
Figure 3.2 Basic matter is not viscous and not compressible.
In Figure 3.3 we observe the mechanism for keeping a form in the chaos.
Observation 2 In collision momentum is conserved but instantaneously transferred ahead with a space discontinuity in the path of the center of mass of momentum. In the chaos the shape depends on the shapes and mass distributions in the collision. Since the shape is chaotic so is the outcome.
Momentum can move in opposite directions at the same time in the same pure matter. Below is a model of a Physics Toy with hanging steel balls.
Figure 3.3 Physics Toy with hanging steel balls.
In Figure 3.3 we observe the mechanism for keeping a form in the chaos.
Observation 3 Matter deposited on one side of a stream is removed by collisions on the opposite side!
When we consider that the pure matter is not viscous and not compressible, we see that momentum freely moves in all directions at the same time.
Question: In background matter, what is the mass moving in a given direction?
Considering uniform random motion (similar to a gas) where half the matter has a component moving in any given direction and half the matter has a component
moving in the opposite direction.
Figure 3.4 Elements of matter moving through random collisions.
Answer: At any given time, half the mass has a motion component in any direction and the other half of the mass has a component of motion in the opposite direction. With the infinitesimal sizes in the Logos Matter, this is on a scale large enough that random fluctuations are averaged out.
The expression of the half of the mass m_{i}_{i+}
moving in a given direction _{i+} in terms of the density (by Observation 1) _{o} ≡ m_{x}/V_{x} is
Equation 2 m_{i+} = (1/2)m_{i}
=(1/2)_{0} V_{i+} , ( i+ is direction on the i axis.)
Question: What is the average component in any given direction at any given time of the average speed?
The average speed associated with any momentum is distributed in all directions equally, so we need to find the average component of the average speed in any
given direction (note only one direction along the axis, both ways average to zero).
Answer: The velocity v_{k+}_{k+} in a given direction associated with
the mass m_{ik+} is the average velocity component of the average speed in any given direction. This ranges from 0 to v_{o}. An
approximate average of this in any direction is half the average speed.
Equation 3 v_{k+}_{k+ } (1/2)v_{o}_{k+} (where k+ indicates the + direction on the k axis.)
The definition of momentum of a mass element m_{i} is m_{i} times its velocity v_{i}_{k+}
Definition 9 p_{i+}_{k+} ≡ m_{i+}v_{k+}_{k+}
For a component of momentum passing through a given area in a given direction, we use Equation 2 and Equation
3 in Definition 9 to get:
Equation 4 p_{i+}_{k+} m_{i+}(1/2)v_{o}_{k+} , Equation 3 in Definition 9
(1/2)_{0} V_{k} (1/2)v_{o}_{k+} , Equation 2 in Definition 9
(¼)_{0} V_{k} v_{o}_{k+}
4 
(The speed of a longitudinal wave as a function of density)
Matter transfers its momentum in collision. The collisions are of incompressible fluid matter. Consider a set of billiard balls in a row. An element of matter traveling with the average background speed *v_{o}=dl/dt (*one dimensional).
Figure 4.1 Billiard Balls.
From Figure 4.1, momentum is transmitted the distance L_{t} in time t_{t}.
Observable 4.1 L_{t} = the distance momentum is
transmitted.
Observable 4.2 n = the numver of elements in length L_{t}.
Observable 4.3 d = the diameter of an element.
The length of matter the momentum traveled through instantaneously was
Definition 4.1L_{m} ≡ nd.
The length of space the momentum traveled through at *v_{o}
Definition 4.2L_{f} ≡ L_{t}  L_{m} , or L_{m}=
L_{t} L_{f} .
The observed time t_{t} for the momentum to be transmitted distance L_{t} is
Observable 4.4t_{t} =observed time to transmit momentum distance L_{t}
.
Matter traveled the free space distance L_{f} in time t_{t}. By Definition 6 t_{t} ≡ L_{t}
/v_{t} , the speed of the free matter is
Equation 4.1 v_{f} = L_{f} /t_{t}.
From Observable 4.1 L_{t} and Observable 4.4 t_{t}
the speed of momentum v_{p} is
Equation 4.2 v_{p}=L_{t} /t_{t}
From Equation 4.1 v_{f} =L_{f} /t_{t} and Equation 4.2 v_{p}=L_{t} /t_{t} the ratio of the speed of momentum transmission v_{m} to the average background
free space speed v_{f} is
Equation 4.3 v_{p} /v_{f} =( L_{t} /t_{t})/(L_{f}
/t_{t})
= L_{t} /L_{f} .
From Equation 4.3 v_{p} goes to infinity as L_{f} goes to zero. That is as the density increases the speed of transmission
of momentum increases while the speed of free motion is unchanged.
By Definition 5 _{i} ≡ m_{i}/V_{i}
the density of pure matter is its mass divided by its volume
Equation 4.4 _{0m} =m_{i}/V_{m}.
We have Observation 1 _{0} = m_{x}/V_{s}
but here we are varying the background volume to explore the effect on speed of momentum transmission in the Chaos
Equation 4.5 _{b} = m_{x}/V_{b}
By taking the ratio of Equation 4.4 _{0m}=m_{x}/V_{m}
and Equation 4.6 _{b} = m_{x}/V_{b}
Equation 4.6 _{0m}/_{b} = (m_{x}/V_{m})/(m_{x}/V_{b})
= V_{b} / V_{m} = L_{m}^{3}/L_{t}^{3}
Given the average background free space speed v_{o}, consider average speed as a function of density. We look at this system
for an arbitrary unit of distance (large enough that the averages are not invalidated). We use 1000 units of total space and very the free space 1000 to 0.01.
Figure 4.2 The Table uses a 1000 units total distance Lt and varies the free space Lf 1000 to 0.01.
The graph below represents the data table above.
Figure 4.3 Graph as the density approaches 100% the speed approaches infinity!
5 
Consider the improbable event of streams forming in the chaos.
Figure 5.1 A stream forming in the chaos.
Our ideal matter has its own characteristics. To have intuitive insight into behavior of a stream on the chaos we need to have the reality experiences that reflect these characteristics.
A stream is a group organization out of the chaotic matter. A steam travels with a group velocity with respect to the background which averages to zero.
Observation 4 From Observation 3 says that the stream shape will tend to be maintained while Observation 2 says there is a difference in the speed of any element and the external speed of momentum as the momentum advances through transfer. An unverified thought is that the average speed of an element of matter participating in the stream is the same as the ambient average speed. This would mean that there is a direct relationship between that average ambient speed and the speed of any stream.
The next level of organization is a stream forming a vortex. Consider the improbable event of a vortex forming from streams. Below we consider a section of a vortex about the axis of rotation.
Figure 5.2 A vortex forming in a stream.
What is the difference in effect of ambient chaos on the inner vortex boundary and the outer vortex boundary?
Observation 5 The need here is to discover the mechanics that give identity and multiplicity there is some condition (probably density dependent) that gives a size constraint. The spiral form of solar systems and galaxies may also be an outcome of the same mechanics on a larger scale. Here I am not talking about some abstract statistical formulation but a concrete visible mechanics. What is happening differently on the inside surface and the outside surface interaction with the chaos is a focus worth attention.
Figure 5.3 A vortex cross section.
Consider the improbable event of a vortex ring (toroid) forming from the vortices.
Figure 5.4 A toroid cut out.
With vortex rings and multiring objects formed from them in the Chaos, we can find objects and observe their position as a function of time. The position as a function of time is smoother than collisions in the Chaos. An example would be throwing a ball. up as shown below.
Figure 5.5 Position as a function of time.
Using the limit as t 0 in Definition 7 operationally defines the threedimensional velocity of and
object as the slope of the displacement time graphs.
Definition 10 v_{i}_{i }≡ Limit (r_{i}/t_{i})_{i}_{
}t 0
= Limit (r_{i1}/t)_{i1}+ (r_{i2}/t)_{i2 }+ (r_{i3}/t)_{i3 }t 0
= (dr_{i1}/dt)_{i1}+ (dr_{i2}/dt)_{i2 }+ (dr_{i3}/dt)_{i3}
= v_{i1}_{i1}+ v_{i2}_{i2 }+ v_{i3}_{i3}
Figure 5.6 Velocity as a function of time.
We operationally define the threedimensional acceleration of and object as the slope of the velocity time graphs
Definition 11 a_{i}_{i} ≡ Limit (v_{i}/t_{i})_{i
}t 0
= Limit (v_{i1}/t)_{i1}+ (v_{i2}/t)_{i2 }+ (v_{i3}/t)_{i3 }t 0
= (dv_{i1}/dt)_{i1}+ (dv_{i2}/dt)_{i2 }+ (dv_{i3}/dt)_{i3}._{
}= a_{i1}_{i1}+ a_{i2}_{i2 }+ a_{i3}_{i3}
We can define the three dimensional force F acting on an element of mass m_{i} with cross section area A_{i} in the Chaos by
time t rate of change matter r_{0} V_{i} in the impacting volume moving at average background speed v_{oi} .
Definition 12 F_{i}_{i} ≡ dp_{i}_{i}
/dt
= dp_{1}_{i1}
/dt + dp_{2}_{i2} /dt + dp_{3}_{i3} /dt
Now we need to recognize the infinite divisibility of the Chaos. This means that when two particles of matter collide the momentum of the contacting parts is
not lost like in the crash of to cars but as with the physics toy continues in exchange and jumps ahead into the forward element in both directions. Since Chaos
is ubiquitous (everywhere like a fog) this continuation of momentum and in fact jumping ahead was accounted for in the average speed in any given direction.
We have the net force F_{ir+} acting in the r+ direction on an element of mass m_{ir+}. The mass is in a volume
with cross section area A_{ir}. The average momentum p_{ir+}_{r+} of the ith element moving in a given direction (r+) is from Equation 4 p_{ir+}_{r+} (1/4)_{o}V_{ir+}v_{o}_{r+}. The ambient force F_{ir+} in any direction _{r+} on an arbitrary area of obstruction A_{ir} is
Equation 5F_{ir+}_{r+} ≡ d(p_{ir+}_{r+}) /dt ,
d((1/4)_{0} V_{ir+} v_{o})/dt_{r+ }, note (1/4)(_{0} A_{ir} v_{o}) is not a function of time
= (1/4)(_{0}
A_{ir} v_{o})dr_{i}/dt_{r+} , by Definition
7 dr_{i}/dt_{r+} = v_{ir+}_{r+}
= (1/4)(_{0}
A_{ir} v_{o}) v_{ir}_{+r+} , by Equation 3 v_{ir+}_{r+}= (1/2)v_{o}_{r+}
= (1/4)(_{0}
A_{ir} v_{o})(1/2)v_{o}_{r+} ,
= (1/8) _{0}
A_{ir} v^{2}_{o}_{r+} .
We can define the average pressure on an element of mass m_{i} in a given direction r_{r} by dividing the average force F_{i ave} over the area A_{r}
.
Definition 13 P ≡ F_{ir+ave}_{r+}●A_{ir}_{r+} / (A_{ir}_{r+} ● A_{ir}_{r+} )
= F_{ir+} / A_{ir} ,_{
}
Using Equation 5 F_{ir+}_{r+} = (1/8)_{o}A_{ir} v^{2}_{o}_{r+} or F_{ir+} = (1/8) _{o} A_{ir} v^{2}_{o} in Definition 13 P = F_{ir+}/A_{ir}
gives
Equation 6 P = (1/8) _{o}A_{ir} v^{2}_{o }/ A_{ir}
= (1/8) _{o}
v^{2}_{o} ,
Note that in the primitive (no vortexes) Chaos this is universal and for a vortex it is the external pressure.
6 
For uniform circular motion we study the diagram below.
Figure 6.1 A point in uniform circular motion.
We have a point moving at a constant speed v_{c}. At time t_{1} the point is at r_{1}. At time t_{2} the point is at r_{2}. In the change of time is dt, the change in position is dr and the change in velocity is dv.
We have similar triangles that give equal ratios for dr/r and dv/v
Observation 6 dr/r = dv/v.
Solving Definition 10 v=dr/dt for dt gives:
Equation 6.1 dt = dr/v
Rearranging Observation 6 dr/r = dv/v gives vdr/r = dv.
Then dividing both sides by Equation 6.1 dt = dr/v gives (vdr/r)/(dr/v)=dv/dt=a then reducing gives centripetal acceleration
Equation 6.2 a=v^{2}/r.
Consider a vortex section shown below.
Figure 6.2 A vortex cross section.
The pressure on the surface area exerts the force that is equal to the centripetal (inward) force of rotation. Note that momentum in a stable vortex behaves
like an element of matter m_{i} and momentum is associated with the same element as it moves.
We apply Newton's second law to a segment of the vortex cut out
Equation 6.3 F_{i}=m_{i}a_{i}.
=
Using Equation 6.2 a_{i}=v_{i}^{2}/r_{i} in Equation 6.3 F=ma gives
Equation 6.4 F_{i} =m_{i}v_{i}^{2}/r_{i}.
Using Equation 4.5 m_{i} = m_{i}/V_{mi} in Equation 6.4 F_{i} =m_{i}v_{i}^{2}/r_{i} gives
Equation 6.5 F_{i} =_{mi}V_{mi} v_{i}^{2}/r_{i}.
Looking at the segment in the diagram above we have the volume V_{i}
Equation 6.6 V_{i} = d_{l}A_{i}
Using Equation 6.6 V_{i}=d_{l}A_{i} in Equation 6.5 F_{i}
=_{mi}V_{mi} v_{i}^{2}/r_{i} gives
Equation 6.7 F_{i} =_{m}d_{l}A_{i} v_{i}^{2}/r_{i}.
We have the pressure from the Chaos by Equation 5.2 P_{i} = (1/8) _{0} v^{2}_{o} .
Using this in Definition 13 P_{i} = F_{i }/A_{i} gives the external force as
Equation 6. 8 F_{ext} = PA =(1/8)_{0}v^{2}_{o}A
We apply Newton's third law (to every force there is an equal and opposite force)
Equation 6.9 F_{r}= F_{r+} .
Using Definition 5 Density _{x}
≡ m_{x}/V_{x}^{ }in^{ }Equation 6.4 F_{c} =mv^{2}/r gives
Equation 6.10F_{c} = _{m}d_{l}A_{i}v_{i}^{2} /r_{i}
Using Equation 6.8 F_{ext} =PA =(1/8)_{o}v^{2}_{o}A
and Equation 6.10 F_{c} = _{m}d_{l}A_{i}v_{i}^{2}
/r_{i} in Equation 6.9 Fr=Fr+ gives
Equation 6.11 _{m}d_{l}A_{i}v_{i}^{2} /r_{i} = (1/8)_{0}v_{o}^{2}A_{i} ,
_{m}d_{l} v_{i}^{2} /r_{i} = (1/8)_{0}v_{o}^{2} ,
d_{l}v_{i}^{2} /r = (1/8)(_{0}/_{m})v_{o}^{2
}.
If we assume that the driving speed of the Chaos v_{o}^{2} is the same as the tangential speed of the vortex v_{i}^{2}
we have d_{l}/r =(1/8)( _{o}/_{m}), or:
Equation 6.12 r =8d_{l}(_{m}/_{o})
This Equation 6.12 r =8d_{l}(_{m}/_{o}) would mean that the ratio of the wall radius and the wall thickness would be a
constant. Since vortex rings are the building blocks of magnetic fields, this could explain how they can range so much in major radius. That is that as the
major radius expands conservation of energy is accomplished by the shrinking the minor radius and wall thickness.
The question remains, what limits the decrease in the radius of the vortex ring? We could speculate on the ratio of the densities, say if
the pure density is equal that of the chaos the ratio of r = 8d_{l}.
If the pure density _{m} was twice that of the chaos the ratio of r = 16d_{l}.
This is a limit. the minor radius r (the minor radius of the vortex must be smaller than 8d_{l} (the thickness of the vortex wall). We have:
Equation 6.13 r > 8d_{l} .
The internal energy is kinetic. The energy of a segment is (1/2)mv^{2}, m= 2rd_{l}_{m} ,
Equation 6.14 K.E._{R}/z =rd_{l}_{m}v^{2}.
7 
We start with a toroid cut out shown below. We assume this is a closed system in the sense the the mass is constant and the internal energy is constant.
Figure 7.1 A toroid cut out.
The total length of z (the axis of the toroid segments) is the center circumference 2R
Equation 7.1 z = 2R.
Using Equation 7.1 z = 2R in Equation 6.14 K.E._{R}/z =rd_{l}_{m}v^{2}, the total energy K.E._{R} would be
Equation 7.2 K.E._{R} = rd_{l}_{m}v^{2}(z) ,solving Equation 6.14 for K.E._{R },
= rd_{l}_{m}v^{2}(2R)
= 2^{2}Rrd_{l}_{m}v^{2}.
Using Equation 6.12 r =8d_{l}(_{m}/_{o}) in Equation 7.2 K.E = 2^{2}Rrd_{l}_{m}v^{2}
gives
Equation 7.3K.E=2^{2}R {8d_{l}(_{m}/_{o})} d_{l}_{m}v^{2}
= 16^{2}Rd^{2}_{l}v^{2}^{2}_{m} /_{o}
This show us the variables while energy is conserved is such large change as the major diameter changes in magnetic fields.
8 
Consider two groups of vortex rings (making up visible matter) as depicted in the diagram below. The center and top spots represents the cross sectional area of a spherical object.
Figure8.1 Two groups (center and top) of vortex rings (making up visible matter).
The idea here is that the pressure of the chaos is ubiquitous but clusters of vortex rings deflect the incoming momentum causing a shadow effect. This shadow effect causes the shadowed surface to experience decrease in momentum impacting on the shadowed side. This decrease in pressure between the objects causes them to experience a net external force toward each other. Groups of rings (objects) are forced toward each other rather than the false concept of "action at a distance" mediated by some imaginary thing called a field.
Given the average cross section area of a single vortex ring is a_{o}. The average cross sectional area for the n center rings is
Equation 8.1 A_{center} = n a_{o} .
We assume that the chaos is fine enough that the cross section area of every ring is seen.
The free vortex rings at the center experience pressure from the momentum of the chaos impacting giving a force F_{center} from all
directions. We use Equation 8.1 A_{center} = n a_{o} to multiply the pressure in Equation
6 P_{i} = (1/8) _{o} v^{2}_{o} get the force
impinging on the surface of the center group from any direction. The ambient force on the center object is
Equation 8.2 F_{o center} = P A_{center}
= (1/8) _{o} v^{2}_{o} n_{center }a_{o}
What part of that force is missing due to the shielding or shadow effect of the object at the top?
Given the shielding and its shadow the decrease in force in that direction is proportional to the ration of the area of the obstruction divided by the area of the sphere on which it lies with the shadowed object at the center of the sphere and the shadowing object at the top of the sphere.
When object at the top has k vortex rings it casts a shadow of
Equation 8.3 A_{top} = ka_{o} .
For a sphere of projection with radius R_{s} we have the projected spherical surface area of 4R^{2}_{s} or
Equation 7 A_{sphere} = 4R^{2}.
Where the center object has n rings of crosssectional area of a_{o}. The shadow effect causes reduction in pressure from that direction. The net force pushing the two groups together is proportional to the ratio of the area of the cross section of a single ring a_{o} times the number k of rings and the area of the sphere of projection radius R_{s} and projected surface area of 4R^{2}_{s} or
Equation 8.4 A_{top} / A_{sphere} or ka_{o} /(4R^{2} ) .
Given the mass m_{o} of a single ring (constant mass of a single ring). The mass of the top object with n rings is
Equation 8.5 m_{center }= nm_{o} .
The mass of the center object with k rings is
Equation 8.6 m_{top}= km_{o} .
So the net force from the shielding imbalance is
Equation 8.7 F_{center net} = F_{o center} A_{top} / A_{sphere} , shielding from Equation 8.4
= (1/8) _{o} v^{2}_{o} A_{center} A_{top} / A_{sphere} , using Equation 8.2
= (1/8) _{o} v^{2}_{o }ka_{o }na_{o} /(4R^{2} ) , using Equation 7 ,8.5 , and 8.6
= (1/32) _{o} v^{2}_{o }a^{2}_{o }k_{ }n / R^{2} , simplifying
= (1/32) _{o} v^{2}_{o }a^{2}_{o }(m_{top}/m_{o}) (m_{center}/m_{o}) / R^{2} ,
= (1/32^{} m^{2}_{o}) _{o} v^{2}_{o} a^{2}_{o} m_{top} m_{center} / R^{2} , using Definition 14
= G m_{top} m_{center} / R^{2} .
We define the Universal Gravitational Constant
Definition 14G ≡ (1/32^{} m^{2}_{o}) _{o} v^{2}_{o} a^{2}_{o} then = G (mkmn /R2)
This is then a derivation Newton's general law of gravitation!
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Figure List  Foundation Items 
Figure 1.1 Random background motion of Matter in space. Figure 2.1 Location r in an orthogonal Cartesian coordinate system. Figure 3.1 Position as a function of time. Figure 3.2 Basic Matter is not viscous and not compressible. Figure 3.3 Physics Toy with hanging steel balls Figure 3.4 Elements of Matter moving through random collisions. Figure 4.1 Billiard Balls Figure 4.2 As the density approaches 100% speed approaches infinity! Figure 5.1 A stream forming in the chaos. Figure 5.2 A vortex forming in a stream. Figure 5.3 A vortex cross section. Figure 5.4 A toroid cut out. Figure 5.5 Position as a function of time. Figure 5.6 Velocity as a function of time. Figure 6.1 A point in uniform circular motion. Figure 6.2 A vortex cross section. Figure 7.1 A toroid cut out. Figure 8.1 Two groups of vortex rings (making up visible Matter) 
Postulate 1 Space R_{0} Exists! Definition 1 Location R_{0} Postulate 2 Matter m Exists! Definition 5 Density_{x} Postulate 3 Motion v of Matter Exists! Definition 6 Time t 
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Postulate 1 Space R_{0} Exists! 
Equation 1 R_{i}_{i}
≡ R_{i1}_{i1} + R_{i2}_{i2} + R_{i3}_{i3}. Equation 2 m_{i+} =(1/2)_{0} V_{i+} , ( i+ is direction on the i axis.) Equation 3 v_{k+}_{k+}=(1/2)v_{o}_{k+} (where k+ indicates +direction on k axis.) Equation 3.1 saturation _{c} ≡ V_{mc} / V_{sc} Equation 4 p_{i+}_{k+} = (¼)_{0} V_{k} v_{o}_{k+} Equation 4.1 velocity in free space v_{f} = L_{f} /t_{t}. Equation 4.2 velocity of momentum in the chaos v_{p}=L_{t} /t_{t} Equation 4.3 speed of momentum / speed in free space v_{p} /v_{f} = L_{t} /L_{f} . Equation 4.4 density of pure matter _{0m} =m_{i}/V_{m}. Equation 4.5 varying the background volume _{b} = m_{x}/V_{b} Equation 4.6 ratio of constant and varied density _{0m}/_{b} = L_{m}^{3}/L_{t}^{3} Observation 4 difference in speed of element and speed of momentum Observation 5 What's happening differently inside surface and outside Equation 5 Force F_{ir+}_{r+} ≡ (1/8) _{0} A_{ir} v^{2}_{o}_{r+} . Equation 6 Pressure P_{i} = (1/8) _{0} v^{2}_{o} , Observation 6 similar triangles dr/r = dv/v. Equation 6.1 dt = dr/v Equation 6.2 centripetal acceleration a=v^{2}/r. Equation 6.3 Newton's second law F_{i}=m_{i}a_{i}. Equation 7 surface area of a sphere of radius R A_{sphere} = 4R^{2}. Equation 7.1 Major diameter of ring z_{total} = 2R. Equation 8.1 A_{center} = n a_{o} . Equation 8.2 F_{o center} = P A_{center}= (1/8) _{o} v^{2}_{o} n_{center }a_{o} Equation 8.3 A_{top} = ka_{o} . Equation 8.4 Ratio of view obstruction A_{top} / A_{sphere} or ka_{o} /(4R^{2} ) . Equation 8.5 center object m_{center }= nm_{o} . Equation 8.6 top object m_{top}= km_{o} . Equation 8.7 Force F_{center net} = G m_{top} m_{center} / R^{2} 