T R U T O N
by Kalman Klim Brattman
"Give me matter, and I will construct a world out of it."
Immanuel Kant, Kant's Cosmology
("Universal Natural History and Theory Of Heavens ")
7. Motion Line Collisions

 
Under Construction

The dynamics of the primeval LOON, called the primeval dynamics of Nature (PRIDON), and representing the default dynamics of Nature, was introduced as consisting of randomly moving/gliding XB-blocks in the (limitless) xenovoid (XV) space --the HOS. That global primeval picture of Nature will be considerably enhanced when questions like --from where those gliding XB-blocks came from?, or from where they have acquired their speeds and directions of motion?-- will get their answers. For that enhanced grand cosmological picture of Nature to emerge, we need to do some more preparatory work --the subject that we begin in here.



Centerline (CELI) collision
.Regardless of their origin, the primal XB-blocks of Nature, in their linear translatory motions in the XV-space will generate various linear paths of motion called motion lines (MOLIs).
.Within such a MOLI, XB-blocks executing linear translatory motions will collide one into another. We call that type of linear MOLI collision a centerline (CELI) collision.

Because the MOLIs (motion lines) have a variety of directions, we could have 2-way XB-block collisions from two distinct MOLIs, called off-centerline (off-CELI) collisions, as outlined below:

Off-centerline collisions:



Angular (ANGU) collision

   

and
 

   .
 
 Parallel linear (PALI) collision

A MOLI, of course, could intersect its path with another MOLI and, as such, some of XB-blocks belonging to one MOLI could collide with a XB-block from another MOLI. We call that type of off-CELI collision an angular (ANGU) collision.

We also could have a MOLI whose linear path is parallel and close "enough" to another MOLI. Their respective XB-blocks, if they are large "enough," could therefore "hit each other" and therefore collide one into another generating a type of off-CELI collision called parallel linear (PALI) collision.

The two types of collisions just identified --the CELI and the off-CELI collisions are called collectively the MOLI (motion line) collisions.

The study of those MOLI collisions is the subject of this section. We are thus studying the impact of the XB-block collisions that take place within one particular MOLI (the CELI collisions) and from different MOLIs (the off-CELI collisions).

.2

The study of XB-block collisions --in all their varieties-- is of particular interest to us because of the monumental recognition posted in the Seventh Fundamental Principle of Nature (7th FUPON) where the Collision was identified as the primeval agent of creation in Nature.


A collision involves a hit/push and the transmission of that hit/push. Our ultimate goal in this study is in "dissecting" those
MOLI-collisions.

The XB-blocks of the primeval LOON by virtue of the status of their motion are endowed with inertial energy called hitoEnergy (hitE). When a hit/push takes place on a XB-mass, an inertial tendency of motion formalized by Newton in his First Law Of Motion (FLOM) will take place in all the points forming the respective XB-block receiving the respective hit/push. However, since a XB-mass is a non-stretchable mass, it follows that for most of the points of a XB-mass that have been hit/pushed, that inertial tendency will not be able to manifest its existence. The only XB-points that can obey their "inward" inertial tendency (and thus transmit their inertial energy) are those surface points that do not have "behind them" XB, but have XV. That surface points will generate a so-called inertial spill-surface that will be able to advance "inward" --by the inertial tendency created-- pressing, and thus compressing (as an open accordion advancing inward from one end) their respective colliding mass (resembling thus the XECO property). Thus, in a collision of two XB-masses, XB1 and XB2, their respective inertial-spill surfaces and (red outer contours), will impinge those masses inwards transforming them into compressed XB (cXB) masses. That process of conversion from XB into cXB, called the compressional inertial transmutation (CIT) process, can formally be written as a mathematical transformation, CIT:XB--->cXB.

In the inner part of the collisional formation, the point(s), line(s), or surface(s) of contact of the two colliding XB-masses, as they transform into the XF-state, will unite --by SUCO property-- transforming themselves into XF-point(s), XF-line(s), or XF-surface(s) called xenosealant(s). During that union, they could entrap pockets of environmental xenovoid (eXV) called holeon(s) (Ø).

Let us now study individually the two types of MOLI collisions introduced above.

We begin with the Centerline (CELI) collisions. They can be

(i) either head-on, or
(ii) rear-end, dorsal collisions.

The two colliding XB-masses, through the compressional inertial transmutation (CIT) will be compressed, and through the SUCO property will be united, transforming themselves into a new united mass called protodense (PD) mass. The specific characteristics of the newly born PD-mass is determined by the nature of the collision as described below.

(i) Head-on Linear Collisions
In a collision of type (i), the force of impact will be able to unite and transform the two XB-masses into a PD (protodense) mass as follows:
.The PD-block resulted from that kind of collision could be either a dense XF (xenofluid) and called xenodense (XD) with its extreme density limit xenogel (XG), or a xenorigid (XR) block --depending on the "power" of the collision.
Remark:
.If the two colliding XB-masses have the same speed, then the force of impact will be converted totally into a compressional force as the newly created object becomes stationary in the xenovoid (XV) space --the HOS.
.If, on the other hand, the two colliding XB-masses have different speeds, then upon collision, the newly created object will acquire a translatory linear motion whose speed equals the difference of speeds of the two colliding masses. In this case the force of impact will not be converted completely into a compressional force as part of it is being channelled for the newly created translatory motion of the newly created object.

.(a) If the result of the collision is the formation of a xenodense mass, then by the renormalization property of XF (RENO), the newly formed XF-mass will return back to its original default state --the XB-state, generating thus a duobase (DUB) formation. Thus in here, the PD-mass has been transformed into a DUB. That end result obtained is with no interest as we are revolving into a circle:
we begin with two XB-blocks that collide and in the end we get back the same two XB-blocks that touch each other as two independent entities and nothing else.

In the analysis provided, we considered that
holeons (Ø) were absent. Let us now consider the case when upon collision the two XB-masses entrap some environmental xenovoid (eXV) and thus, creating some holeons between them. Let us then examine what is going to happen with the holeons just born.
Well, as the two colliding masses will unite and their masses begin to be transformed into xenofluid (XF), the holeon(s) --by the XF-pressure exerted upon them-- will begin to shrink. That shrinkage will transform the XB-surface of the holeon into a XF-surface that is a COXI XF-surface. The transformed holeon that has acquired a COXI XF-surface is called a COXI gellyon. As the shrinkage of a gellyon continues, its COXI XF-surface density will increase. An important remark that needs to be made is that the increase of surface density is not even as it is greater in those surface parts that have the greatest (Gaussian) curvature. And as such, those parts of the surface with the highest curvature will advance inward faster than the rest of holeon's surface --and that is because the renormalization tendency of XF (RENO) is greater where its density has the highest value. (For instance, for visualization purposes only, if the holeon is in the shape, say, of a hot-dog, then the edges of that hot-dog shape "hole" --upon compression-- will have the highest density and, as such, those edges will advance inwards faster than in any other part of that hot-dog shape surface.)
.The remarkable consequence that follows is that if the compression of the gellyon can continue to proceed, then, regardless of the initial shape of the holeon (Ø), the gellyon will end up transforming into a spheroid. The fate of that spheroid is function of two initial conditions (ICs): the initial size of the holeon, and the initial force of collision generating the initial density of the XF PD-mass studied.

.

  

.i) One scenario that could take place, called the integrative scenario, is the one where the spheroid will shrink until its xenovoid interior vanishes completely transforming the shrinking spheroid into a "pod" of dense xenofluid that a COXI XF-mass called a COXI gellypod (GEP). By the renormalization property of XF (RENO) both the COXI gellypod and its surrounding PD XF -mass will begin to decompress in the XV-space until they reach the default material state of Nature --the XB-state. When that happens, such a PD-mass will transform into two disjoint XB-masses (DUB) that are now being united through their common COXI-gellypod that was transformed by BAXI into an indistinguishable XB-blob called baseblob (BB). Thus, such a BB (baseblob) can be viewed as the base union bridge (BUB) between two XB-masses.
   The formation created, two XB-blocks united by one or more baseblobs (BBs), is called a vagonbase (VAB). Through an accretionary process, the VABs (vagonbases) within a
MOLI could unite generating a linear formation of VABs called a trainobase (TRAB).
.ii) The other scenario that could take place, called the particle scenario, is the one where the spheroid could shrink until its surface becomes xenorigid (XR). In such a case, we say that the spheroid has transformed into a minitron (MIT).

The class of stable particles that have their surfaces made of xenorigid (XR) and their interior of xenovoid (XV) are said to form the rigidtron or the hardtron family of the primeval particles of Nature (PPONs).

.(b) In a powerful collision, as noted, the generated PD-mass will be xenorigid (XR). Thus in here, the XR-protodense is a permanent XR-block.
.(c) In a most extreme powerful collision, the two colliding XB-masses upon becoming a XR-block will disintegrate and pulverize transforming into a heavy xenodust (hXD). (The heavy xenodust, as noted, could be called and referred to as the heavy dark matter.)


(ii) Dorsal, rear-end linear collisions
In this case, only an infinitesimally minute portion of the force of impact will be converted into a compressional force. As a result of this infinitesimal contribution, the united
PD (protodense) mass created is a thin xenofluid (or xenothin). As in the case (i) above, the created PD-block will transform into a DUB. If holeons are being formed at the creation of tXF (thin xenofluid) PD-mass, then as in the case a(i) above, a vagonbase (VAB) will be born.

Aside from the center linear collisions, head-on or dorsal, forming the centerline (CELI) type of MOLI-collisions, two XB-blocks, as noted above, could be involved in a different type of collision --the off-center linear collisions called the off-centerline (off-CELI) collisions that can
a) take place on an angle --the angular (ANGU) collisions; or
b) take place through close parallel motion line (MOLI) paths --the
parallel linear (PALI) collisions.

Those collisions are dramatically different in their outcome from the CELI collisions as the off-CELI collisions bring with them a qualitatively different type of motion --the Spin. The appearance of a new type of motion --the Spin-- at the primeval LOON (level of organization of Nature) is in itself most remarkable as it represents, as stated, a new qualitatively primeval motion. It is qualitatively different because it cannot be reduced into anything else, i.e., because the Spin cannot be reduced --through any transformation-- into a linear, translatory motion.

Now since the Spin was generated through and by Collision --the master agent of evolution in Nature, it follows that the Spin is the primeval "tool" of evolution in Nature. That means that the Spin, by being the "primeval" tool of creation, must be responsible for the creations of all primeval formations in Nature including our own Universe. We mark that monumental recognition with

.

The Eleventh Fundamental Universal Principle Of Nature (11th FUPON):

In Nature, the Spin is the primeval material tool of evolution.   

That recognition of the crucial role of the Spin in Nature is trully monumental. As we look around, up into the cosmos or down into the atom and below, we see that everything spins! Wow!

It is as somehow all objects of Nature would tell us:
We are here because of the Spin!
We are, in the way that we are, because of the Spin!

.Remark:
The primary generator of evolution, the (material)
Collision, will generate a number of "tools" that can, when implemented, make new evolutionary classes of material objects. In here, we have identified the (material) Spin as being the primeval material tool of evolution in Nature.
.

.

.The Fundamental Theorem of the Spin (FUTOS)
.In the primeval LOON, a spin of an object can never decrease in its magnitude.


Proof:
In the primeval LOON, the spin can be generated only through collisions. And through collisions, the colliding bodies in the
XV-space can only increase their spin. That is because
 i) the axis of spin (AOS) of a spinning object in the
XV-space is not fixed and thus it can rotate freely without constrains and,
ii) because a rotation of 180º of AOS amounts to a reversal of the direction of the Spin.

QED.


The appearance of the Spin in
off-CELI collisions is by far the most important addition in studying those type of collisions. As in the case of dorsal collisions, in here, only a minute portion of the force of impact will be converted into a compressional force. That is because as soon as the combined mass resulted from collision --the protodense (PD) mass, becomes xenothin (or thin xenofluid) it will acquire a (minute) resistivity towards further compression. And, as a result of that, by being embedded in the XV-space, it follows that the remaining portion of the force of impact (that is almost the entire original force) will be converted into a force propelling the new motion created --a motion that now has two components: one, of translation; the other, of Spin. We call such a spinning object a spinolon (SL). Let us now take a closer look at that newly born object to see how its PD-mass develops and transforms.

A Study of a spinolon upon its formation in the XV-space

Let SLV be a spinolon of a volume V whose PD-mass is xenothin (thin xenofluid) that has acquired a spin. We want to see how that spin is going to shape up spinolon's stated mass.

As we know, the spin will generate an axis of spin (AOS) and, each point of a spinning mass that is not located on AOS is impelled or forced to execute a circular motion around AOS.

By Newton's First Law of Motion (FLOM), each point of a spinning mass that is not on its axis of spin (AOS), by executing a circular motion, will have the tendency, called the inertial centrifugal tendency TCF, to return to its default motion i.e., to its linear translatory motion away from AOS. So, all points of a spinning mass that are not on AOS are subjected, simultaneously, to the "influence" of TCF. The "strength" of that TCF varies with the distance from AOS increasing linearly with that distance as seen from the variation of the centrifugal acceleration aCF derived below.

For a rotation point P around AOS of speed v at distance r from AOS, we have the angular velocity (in radians per unit time) as
=d/dt, with v=r d/dt=r

In a uniform circular motion, v is constant so in one period T
we have for the distance s of a circumference
s=2r=vT so T=2r/r=2/

The magnitude of centrifugal acceleration is aCF=v=r  
So the linear proportionality of the magnitude of the inertial centrifugal tendency TCF with distance r from the center is given by this relation obtained for its acceleration:
aCF=r       (1)


The TCF's variation of strength with the distance from AOS will imply that TCF, if left unopposed, will impinge each point of a spinning mass that is not on AOS with a force whose strength increases with the distance from AOS. That, in turn, will generate a particular speed of impingement proportional to the TCF's strength.

For a point (that is not on AOS of a spinning mass) to be able therefore to continue with its circular motion, a force must exist capable of annihilating that inertial TCF tendency. That counterbalancing force required to exist for a circular motion to take place is thus an inward center-seeking force that is called the centripetal force FCP.

From where then such a required, inward, center-seeking force could come from or originate, in the primeval LOON?

Well, looking around, the only place that such force could come from is from the material of that object itself as there is nothing else out there... So in order for a mass to continue to spin, that mass must be able to provide, for all its points, a resistance --called the material resistance-- that is able to annihilate the outward centrifugal tendency TCF. The points of the spinning mass that are not provided with that material resistance will therefore fly-off from the respective spinning mass.

For a spinning XB-mass, by its non-stretch property, the material resistivity needed to confront and annihilate the inertial centrifugal tendency TCF is provided by the ability of XB to sustain a stress (up to its critical breakup limit). A gradal tensioned XB (tXB) mass is being created as a result of the spin as that tension is not uniform throughout its body. The magnitude of tension increases proportionally with the distance from AOS as derived above from the variation of the centrifugal acceleration aCF with the distance from AOS.
For a spinolon (SL), because it is made not of xenobase (XB) but of thin xenofluid (XFT), the situation is quite different.
!

W
R
O
N
G

  

On a superficial analysis, one may say that, in fact, the situation is not that different following that ill-rationale:

The renormalization property (RENO) of the thin xenofluid coupled with the inertial centrifugal tendency (TCF) will undoubtedly force the spinolon to transform into a spinning XB-mass and, as such, there is little difference that exist between the two cases. The thin xenofluid XFT mass must in the end transform into a XB-mass as both RXF and TCF act in the same direction --that of "flattening" down the XFT-mass to the XB-state.

Well, as we are going to see below, that "raw" reasoning is WRONG, WRONG, WRONG.


For starters, let us note that the two tendencies that the thin xenofluid is subjected to --the xenofluid's renormalization tendency RXF and the inertial centrifugal tendency TCF are quite different in nature:

.

 .

The RXF tendency is a dispersing tendency while the TCF tendency is a directional tendency --a direction that is perpendicular to AOS running away from it.

Also, another fundamental characteristic of those two tendencies --that when combined will generate a Net Tendency (NT)-- is that NT is not instantaneous:

.For the inertial centrifugal tendency TCF, its speed of propagation is being governed by its "strength" increasing thus with the increase of the distance from AOS. The place first affected by the presence of TCF is thus in the surface point or points that is/are furthest away from AOS, the so-called distant surface (dS) points.
.For the RXF tendency, we know that XF has the natural tendency to "spread" towards regions of lower XF density and the difference between the two densities (the one from where the XF exists to the region towards it is spreading) will determine the speed of that "spread" and thus of the tendency. Those "spreads" generated by the renormalization property of the xenofluid (RENO) are called xenofields and, as we shall see, they play the pivotal role in understanding all interactions of the primeval particles of Nature (PPONs).

Resuming now with the spinolon study, we note that both those two tendencies RXF and TCF are omnipresent in the entire mass of the spinolon (SL):

.

RXF tendency being present because of the intrinsic property of XF to return to its default XB-state, and
TCF tendency being present because of the Spin.


Combining those two tendencies, we can talk about a
Net Tendency (NT) and its speed of impingement (propagation) for any given point. That speed of propagation is most essential in determining where NT will land first, second, etc. We can talk thus about the 1st Transformation (TR1), the 2nd Transformation (TR2), and so on, of NT.

As TCF begins to "work" in the spinning mass of a spinolon (SL), the place first affected by the presence TCF is, as noted, at the surface points of SL that are the furthest away from AOS. There, those surface points will be transformed into XB points that will further pull the entire surface of SL transforming that surface into a tensioned XB (tXB) surface. That is the 1st Transformation (TR1) that will take place in a newly born spinolon (SL).

The 2nd Transformation (TR2) will take place in the layer (L) beneath the spinolon's XB-surface just formed at the point or points furthest away from AOS. Those furthest points, by the "influence" of TCF, will be squished first into the non-stretchable XB-surface of the spinolon before the rest of the points of layer L will "absorb" the influence of TCF. Through that push of TCF, the layer L will transform into a xenofluid (XF) layer whose uneven density is characterized by the property that each of its points satisfy the relation that the magnitude of their XF-resistivity towards further compression RXF equals the magnitude of TCF. We write this property of characterization of the formed layer L just beneath the spinolon's XB-surface as RXF(L)=TCF(L).

Let us "dissect" and "see" in detail the dynamics of the XF-motion that takes place in L:

the points furthest away from AOS, called the distant surface (dS) points, will acquire the maximum XF-density for L due to the force of impingement of TCF on those dPs into the non-stretchable xenobase surface of the spinolon just born. Due to the renormalization property RXF of XF (RENO) that (those) dP(s) will begin loosing the acquired density due to the XF-spread (dictated by RXF) that will overpower the influence of TCF. As that happens, TCF will generate for that/those endP points(s) a new same point-density so to continue to have RXF(dP)=TCF(dP). A cyclical XF-spread dispersed in the layer L, forming a perpetual whirl, will take place beneath the spinolon's surface where each of the points P of L will be engaged in maintaining the equilibrium RXF(P)=TCF(P).

So unlike the spinolon's surface, the layer beneath it is a dynamic surface whose "activity," in a form of whirl, is being fueled by the continuous process of maintaining the equilibrium RXF=TCF.

Remark: Let us note that the magnitude of TCF is function of two initial conditions (ICs) of the spinolon: the magnitude of its spin, and the magnitude of its size. The combination of those two ICs will give the net "strength" for the TCF. For a spinolon (SL) that is "big enough," because of its great size, the magnitude of the TCF towards the edges of SL will be greater than the resistivity of the xenorigid (XR) towards further compression. In such a situation TCF will be able to transform those end-points of L into XR-points. In that type of spinolons, the XR-points generated by TCF are the heavy xenodust (hXD) points. Thus in a "big enough" spinolon, the balance RXF=TCF will follow and not precede the formation of XR-points. We call spinoloverses (SLVs) those "big enough" spinolons.
(Let us note that spinoloverses are the end result of the linear head-on collisions of spinolons from one and the same MOLI, thus they from CELI collisions of spinolons within one MOLI.)

The distinctive features of the spinoloverses (SLVs) is therefore that they contain heavy xenodust (hXD) matter called also heavy dark matter.

With the creation of the layer L just beneath the spinolon's XB-surface, the end-result of the spinolon's formation is complete as its interior mass has transformed into a tensioned XB-mass in accordance to the pressure exerted by TCF. So, a spinolon that was born out of its spin has its surface made of a tensioned XB followed by XF- layer of uneven density with the rest of its mass being tensioned xenobase (tXB).

   

  

Remark: Let us note that the magnitude of TCF is function of two initial conditions (ICs) of the spinolon: the magnitude of its spin, and the magnitude of its size. The combination of those two ICs will give the net "strength" for the TCF. Arguably there are spinolons in the primeval LOON, whose TCF towards the edge of the spinolon are stronger that than the resistivity of the xenobase (XB) towards further stretch. Thus, in those situation the newly born spinolons will disintegrate.

!

.Let us note the interior mass of a spinolon is a DUB-formation, and thus upon disintegration, the two XB-masses forming the DUB formation will fly apart.
.The grand cycle of Nature begins to show up its existence --a cycle that represents the backbone of Nature.


Let us now prove that the spinolons once born and formed cannot continue to increase their spin indefinitely through

The 1st Primary Theorem of Nature (1st PRITON):

In the primeval LOON, no formation that spins can increase its spin indefinitely.

Proof:

As the magnitude of the spin increases with each collision (FUTOS) so will the global inertial centrifugal tendency TCF. The points of the spinning formation that are the furthest away from AOS will be the first most affected by the spin as there the magnitude of the TCF will be maximum. The increase of TCF cannot continue indefinitely as there is a limit, called critical limit, beyond which the resistivity of the spinning formation will no longer be able to contain the force or the magnitude of TCF. The result is the disintegration of the respective formation.

QED.

The 2nd Primary Theorem of Nature (2nd PRITON):

All spinning objects in Nature have a finite existence and a finite size.

Proof:

We shall prove this theorem using the well-known reductio ad absurdum method where we assume that the contrary is true and using deductive reasoning we reach an impossibility.

Let us then first assume that there is in Nature a spinning object of infinite existence. Then, that object would have encountered a limitless number of collisions --each time with each collision its spin would have increased (FUTOS) reaching a spin of infinite magnitude that is in direct conflict with the 1st PRITON and the 4th FUPON. Thus, no spinning object can exist forever in Nature.

Let us now assume that there is in Nature a spinning object of an infinite size. But that is not possible because as we have seen above, the magnitude of the inertial centrifugal tendency TCF increases with the distance from AOS and thus, it will exist a distance from AOS that the magnitude of TCF becomes so big that it will break-up the material resistivity of the spinning object.

QED.

Corollary:

The Fundamental Characteristic Of Nature (FUCON)
All (material) objects of Nature have a finite existence.

Proof:
Again to prove this result, we use the reductio ad absurdum method. Let us then assume that in the primeval LOON, we have an object of infinite existence in violation of the 4th FUPON. Then, such an object will encounter an infinite number of collisions, with each collision --by FUTOS-- increasing continuously the magnitude of its spin. The end result obtained is therefore a spinning object acquiring a spin of infinite magnitude --an absurdity.


Spinolons, so far, were considered to contain no "holes" in them, i.e., no holeons (Ø). However those are singular situations. In general at their formation, spinolons will contain holeons.

We call simple spinolons (siSL) those spinolons that, upon their formation, contain no holeons and, call complex spinolons (coSL) those spinolons that do contain holeons. We no specification is provided, we use the generic name spinolons (SL). As we shall see, siSLs and coSLs are markedly different with respect to their ultimate fate in Nature.

..

  .

The holeons, as we already began to recognize, must represent the primeval seeds of all particles of Nature and thus, their evolution and development is key in deciphering the foundational elements of Nature. We already were able to see how the evolution and the transformations of holeons generated minitrons from head-on XB-colisions that do not generate spin. So far, their study did not contain the contribution of the Spin --the master primeval tool of creation in Nature.

The role of the Spin, as the primeval tool of creation (the 11th FUPON), must lead us to the discovery of the entire variety of primeval particles produced in Nature --and that recognition, in itself, is most exciting indeed. However, before entering into the study of holeons in the spinning formations of Nature, a most basic question pops out and needs to be entertained first, as follows:

The spinning formations that we were able to derive, so far, in the primeval LOON were the spinolons (SL) that are made of thin xenofluid (xenothin). Before proceeding further, the question that comes up is whether in the primeval LOON there are stable spinning formations that are not born having thin xenofluid, but are made of dense xenofluid (xenodense). If such formations do exist, we call them spinons (SPs), and the first order of business is to look for their existence --the subject of the next section.

 

      

Kalman Klim Brattman