And let us agree that momentum is the observed self sustaining motion of space.
Let us propose that momentum when experienced is relative to all other experiences and distinguishes itself by magnitudes of speed and extent of region and rotation of region and change of path; bald observable experiences should we not be blind. However, should we be blind , then let us also experience the intensity of impact and the extent of the surface area of our sensory mesh that is impacted and also the penetration into the cavity of our sensory network also as distinctions of momentum. We may colloquially refer to such attributes of momentum as the "force of momentum".Yet again, suppose we are unfortunately blind and without proprioception or any Kinaesthesia, then we may also experience the changes in intensity of loudness and pitch as well as the stereophonic changes as further distinctions of momentum.
Let us now observe that universally such force of momentum inheres with it a change in the momentum of the object and the momentum of the sensory mesh. Let us further observe that be this cahnge ever so smsll or ever so large yet the change is sequential in its essential nature as experienced by the sensory mesh.
Thus let us agree that the force of momentum is the cause of such changes, and that an interchange exists between the sensory mesh and the momentum as colliding spatial regions in which the sensory mesh mommentum is altered in precisely contra ways to the alteration of the momenum of the region we initially supposed, and that this alteration is sequential in precisely contra ways.
Further, let us observe hat the momentum of a region , as an observed or experience distinction is relative to the subjective process of the observer. Thus for every observer there is a unique distinction of an agreed region that is called momeentum, a unique distinction of the force of momentum and a unique distinction of the sequence of the force of momentum, and finally that the contra momentum exactly matches the momentum in the sequence of change in the force of momentum.
Let us now understand that the sensory mesh in a collision with a region of space in motion is analogous to 2 regions of space in collision. Thus let us freely inhere the sensory mesh to one or other of the regions or to both. We may then come to understand that the relative description of the force of momentum issues from whichever region "describes " its distinctions, and that for the same collision observed by both regions in the collision we may receive a report that is the ame, but with eacj distinction relative to the region, or different but again each sistinction relative to the region, and that those differences may corespondinglyy be greater or lesser by some common measure that both regions have agreed upon.
We may further observe that should the "parties" to the collision be not agreed on measure that does not invalidate the honest reports of both, but requires a third independent observer able to measure the 2 regions relative to itself to provide a description of the distinctions which by a common measure makes sense of both the parties description.
Thus have i laid out the grounds upon which any description of a collision of 2 bodies may be described and calibrated by some third independent observer , and in which i am forced to inhere the notions of measurement for all the distinctions described, and the notions of inherent relativity and the notions of contra relative experience, which by some third independent observer mut also be taken into account.
Finally it is also not to be dismissed that such force of momentum has a sequential observed change that is essentially "wave like" in characterisation. and such a "wave" refers to the change in momentum in all its observable distinctions. By analysing such distinctions and there changes relationships may be expressed that describe the "wave" like changes. The introduction of ratios and proportions to compare these distinctions is the fundamental role of the measurement scheme established by the third independent observer, who being independent nevertheless must adopt the position of both parties to the collision to give a satisfactory description, and must not fail to account for each detail of the observations of both parties to the collission in his ]her own determination.
Should a supposition be made or some lemma so as to begin the account and to recommend it to the 2 parties in the collision as to whether it satisfactorilly explains their experience and distinctions, it is not thereby to be assumed that the supposition is "the Truth" of a matter should it be deemed satisfactory. Rather it ought alwys to be remembered that it is one of many possible lemmas which may satisfactorilly account for the experiences. However, if over may such investigations the lemma proposed is the best one then it in fact confers upon it not certainty but probability, and so may it continue as the most probable explanation.
Thus into any analysis or explanation of any collision involving momentum we must introduce the notion of probability, and should we further seek a "cause " of any action we must accept the notion of probable cause.
And so to rest. For if momentum is self sustaining when will space ever be at rest? One may say never, except in a relative sense. Thus a region which relative to my observation is at rest may nevertheless be in motion relative to some other regions, which necessarily will be in relative motion to myself. Now. Also should a region be in contact with another and appears at rest relative to itthen we may suppose that this rest is inertial. That is a contra momenum stops or puts at rest the regions momentum through contact. In this way we may define rest as the resultant of momentum and inertia.
The resultant of momentum and inertia works out in whatever scheme we establish to measure such or any distinctions as being equivalent to rest in hat scheme. Moreover inertia may be seen or considered as the contra scheme to the observed momentum. Also , the structure of momentum may be such that it consists of momenta and similarly the structure of inertia will consist of contra momenta.
Without here giving too great an ellaboration i may summarily say that we may describe all manner of interaction observed in these "momental" terms. Such a greek use of the term momental is to be distinguished from the use of the term in relation to instances of a dubious ratio called time.
The forces of momentum called friction contribute therefore to the overal forces of inertia which counter the forces of momentum. And such systems of momental change may be called equilibria, that is systems based on the notion that momentum and inertia result in "rest", which we have seen is a relative experience. Since rest is a relaive experience we only really can expect dynamic equilibrium in which he resultant is at rest to some given observer, but the whole system with that observer is in relative motion to some " other" independent observer. To this observer we may attribue the ability to discriminate uniform relative momentum and non uniform relative momentum, paricularly in collisions, but also in other situations of variable momentum.
If the notion of the force of momentum is utilised to describe these non colliding variations in momentum, we ae at once bereft of a cause for momentum variation if we attribute it to collision alne. However, if we attribute it to inerta then we may expect the inertial balance to be so constructed as to explain the ariation in the momentum.
To date the only inertial momenta we regularly explore are "frictional" ones (one might almost say fictional ones, on account of how very small thet may be!), and these are routinely casr in the fractal framework of very small collisions.
We have only one extant theory of matter and that is corpuscular, in which both particle and wave phenomena sit as complementary descriptions of different statistical complexity. The attempt has been made to move to a probabilistic description of the momentum inertia resultant, but this necessarily is by way of statistical experimentation. Thus any continuous theory of matter , per force is an abstraction derived by a process of approximation, or an assumption of continuity. Such an assumption is foundering on the rocks of experience becuase we can never get to that level of abstraction in our measuremen schemes.
It is better to found the theory not on corpuscles as irreducible regions of space, but as bounded regions of fractally related spaces with a fractal entrainment cause that crosses the boundary, which cause as i say is inherent motion in multipolar space . This motion is rotational, translational and expansionable(expanding and contracting), and of course there s the inertia equivalent which is contra to it(reflection through a centre of rotation)
Reflection through centre of rotation only exists if the motion change is collinear with the diameter through the centre of rotation. Any other motion is described by a complex rotation and translation. Therefore inertia only appears as a motion that is a reflection of another through a centre of rotation.
In attempting to simplify the metrical description of these magnitusinal relationships, different magnitudinal models have been constructed and their algebras prescribed so as to provide safe conduct to well known results. Such models are called "number systems" of which the chief one nowadays is the vecto tensor sysems, although they are built on older systems such as the complex and quaternion ones.
Such models are not to be believed as giving insights about reality. They in fact only give structure to our metrication and statistical frameworks, formalism for the procedures of calculation and terminology that hopefully simplifies the complex relationships. At the end of the day, what is to be perceived will be perceived without such complex machinery. The only justification for the machinery is that it makes the analysis of these observations more accessible to aanalytical and synthetical thought. However it fails in that score because of the abstractions of some, and the intellectual snobbery of others.