The problem with force is it is non specific, even today. Newton defined a measure he called vis which was a differential form of Hooke's law. Hookes law is specific to springs, but force is a more general vector type.
The metaphysics of acceleration required a cause Newton called motive. This, like celerity entered a body to hasten it. But when Boyle et al. studied fluids they found a motive disbursed throughout the material they called pressure. The concept of pressure and motive are identical, but the measure of pressure was counterbalancing: a force against the area it acted upon against a pressure and the area it acted on.
It is clear that pressure is a more specific notion than force, being MULTI directional and appreciated by its action on a surface. This in fact closely matches Newtons description of an action on a body that produces a vectored acceleration. The notion of pressure is a better more satisfying notion than force. We can accommodate the so called four forces into it.
If we have a pressure, we really do not know the cause. It could be an electric motive, or a magnetic motive a mechanical motive( including gravity and gas pressures) , a nuclear weak or a nuclear strong motive, not forgetting a thermodynamic motive, that is heat pressure(temperature) and expansive contractive motive.
Since we do not know the distinguished motive we put them all in to the equations. Effectively they are weighted pressure terms, their proportional effect either guessed or discounted. In this way we determine a weight for the action of each motive by approximation and judgement of the observed behaviour.
What are we looking at in terms of pressure? It seems to be a kind of weighted mixture of motives,which we have distinguished into 4. They act radially , but seem to have a vectored maximal for the electric and magnetic motives. Others seem to be uni vectored but environmentally determined. Others seem to have their own innate vector action, and all are susceptible to scale, except the electromagnetic(fluid dynamic) descriptions.
Is Pressure a vector?
We find it difficult to apply the notion of a vector to a multioriented magnitude. We tend to call them scalar potential fields. Theirs is a theory of conservative fields that defines this precisely, but essentially it is simple. If something is everywhere and in every direction then it is a potential scalar field. We cannot vectorise it. our notion of vector as a line label does not apply and is misleading. However, in spaciometry i have called these types of fields compass multivector networks, and written a few posts on the topic. These are the basic or fundamental seemeioon algebra, that is a Grassmann point A;gebra.
So i am going to be looking at how a Grassmann point algebra compares with a conservative field theory. These types of fields rings or groups are looked at as topological spaces in which the usual way to measure is to use the real number measuring tape and pythagoras theorem. However more unusual "metrics", rules of measuring, can be invented to help by analogous reasoning in other areas of comparison or specification.
P = α pe + β pm + γps + δpw + ζ pl + θ pt + μ pi + ς pd
Which is electric, magnetic strong weak, lever, thermal inertial and deformation pressures weighted.
Now we are accustomed to thinking in terms of gravitational pressure, but i have deliberately left this out of the general pressure notion except in the sense of a balanced lever or a mechanical "force".
The fact that things fall with acceleration is unexplained. or inexplicable out of context, but within the context of a general pressure notion "gravity" may be interpreted.
Why do we include the others? Each one creates spatial motion of acceleration, some damped. Gravity therefore obscures the effects of each of these others. It also obscure the fact that at least 3 other pressures could be used to define relative density and so mass as a product concept of relative density and volume.
I seem able to characterise pressures by their internal source and external action. Some pressure self actuate by an internal source or potential which cannot be located no matter how narrowly we search: others are activated by an external system or medium directing these internal pressures by boundaries and passing between boundaries in the most curious ways.
We have to acknowledge, as in the case of boiling water, our environment feeds into our local measurements. Gravity as it is used is a catch all because all our science has been defined against an assumed global characterisitic, and so in universal contexts we need to account for it. It is merely an accounting correction which we may be able to eliminate by more strictly defining these others
The empirical data suggests that pressure acts radially and spherically.
It is not possible to isolate a spherical action from a radial one, nor should we fall into that mistake. Therefore , using newtons resolution of his reference frame, my model must contain radial vectors and circular arc vectors or twistors acting in the surface of an expanding sphere. This is the fundamental structure from which I can resolve a tangential vector! In fact in 3d it will be a tangentially expanding circular plane which provides tangential vectors to the spherical surface relative to a given point, but also arc twistors in that circular plane. These can be resolved into tangential vectors to the circular plane in the plane
A spherical pressure thereby exhibits a fractal functional relationship in detailing its likely vector structure. However this vector structure is not realised until a test particle is placed in a pressure surface, so the description is Potential! Because it is not a vector it is called a scalar potential, but this is not explained clearly, rather it is obscured behind symbolic relationships. Probably because no one really understood what it meant rhetorically, they could just give examples in definition.
For a scalar potently to be useful it must be measurable. So a scalar potential exists in a topological space.
A simple topological space is an inelastic line. Now if I have another line that is elastic, I can compare the 2 and consequently recognise deformation. The elastic line is a topological space, but it is dynamic, which means I cannot describe its measured behaviour except relative to an Inelastic line. This means my visual sense is relying on my kinaesthetic sense to describe and distinguish an observed behaviour. If I did not make this comparison I would not be able to measure reliably, because I would be unaware of the elastic nature of my Metron.
Given this, I may now define a scalar potential for the elastic Metron. By making points on the elastic topological space I can refer to the extension of the Metron under different kinaesthetic pressures by noting the displacement of the distinguished points on to the inelastic space as a ratio. The inelastic ratio data is a scalar potential. It is a "measurement" associated with a point. Given the elastic Metron, and the correct kinaesthetic pressure I can read off a scalar definition by comparing distinguished points against the inelastic scale and noting the assigned ratio. We forget that all measurements are in fact ratios normalised.
Of course the inelastic line has its own orientation and so I have turned a potential reading into a representational vector in the elastic line. The vector is in the elastic line because I can orient this extended piece of elastic in any orientation on the surface of a sphere with the radius given by the topology of the in elastic line. It is the elastic line that has realised the vector potential of the topology.
For a pressure we realise the vector potential of a topological space by placing a surface that is translatable and orient able in it. The topological measure in the space is given by some function of the coordinate frame established appropriately in the space to provide a Metron, and in addition a Pythagoras rule for trianglesl
The Pythagoras rule is fundamental to our apprehension of how straight lines behave in space. It is not so much that it gives us a metric as it gives us a relationship between 3 points in a plane that is universally true for straight lines. The Euclidean notion of a good line goes beyond it bing straight. It defines a difficult but supporting concept that is a plane. While points can be defined by the first 2 given, a plane can be defined only by dual points and only then can a straight line of dual points be defined. Thus a straight line implies some plane and 3 dual points connected by straight lines specify it.
Of course dual points imply intersecting spherical surfaces, which is the fundamental superstructure or Hupostasis of Eudoxian and Euclidean ideas/ forms.
So now these forms or spaces can be specified by some reference frame. And some function based on this reference frame can specify a scalar potential in that space.
I have just used an example of Hookes law, let me now use an example of an inverse square law.
Specifying in polar coordinates makes this relatively simple. The scalar potential is (1/r^2 ,€) if the reference points are ( r,€). This is in the plane.
How do we now turn this circular potential into a vector field? We use newtons reference frame and resolve into vectors using newtons parallelogram rule, avoiding the mistake of giving primacy to the tangent. The tangent is a resolved vector in Newtons framework..
So now let us apply it to a spherical pressure potential.
The nature of potential is spherical so I can expect to see changes in potential radially therefore I can draw a vector radially to indicate a direction of potential change. Now I have a choice ofndrawingnanvector whose magnitude is the potential at the point or a vector which indicates the potential difference.
Placing an object in such a field of Vectors allows us to use the resolution of vectors . Thus we find that circular twistors counteract but tangent vectors do not for a spherical curved object. The material resists by Twistorque forces that cancel, leaving the tangent force( derived) to combine with the normal forces to push the shape or attract the shape. The force vectors for the potential field act as if the body was enclosing or embedding the field within its volume. Thus we have to calculate the overall effect of a pressure field on a body from all the pressure effects, not just from the surface pressure effects.
Because of the spherical potential field the pressure vectors will act on a spherical surface differently to a flat planar surface.mthe resolution of the vector fields will be different.
Now, so far I have only considered the lever effect of a pressure field. There are other pressures within a pressure field. I need to know the potential field for the electric and magnetic pressures within a general pressure field. In addition the resistive or reaction pressures themselves differentiate the electric and magnetic pressure effects. Triboelectric and tribomagnetic pressures are resultants of a general pressure field. The other contributory pressures also require their potential idles so thir effect cn be considered.
Anyone of these many component pressures acting through a body surface, and throughout its volume could compound to effect the dynamic stability of the combined system. The potential to rotate a body is therefore always present, and overwhelmingly so. The naturally resultant motion on any object under pressure would therefore be to follow an arbitrary trochoidal path. "Damping" of rotation or forcing of rotation may lead to a smaller or larger radius of curvature to the resultant motion.
The ballistic description of motion often incorrectly identifies the resultant motion of a missile as parabolic. It is in fact elliptic, because the object would return to its starting point if not impeded. A missile would have to exceed the escape velocity of the earth to get anywhere near being parabolic. However, it is the collective experience of these elliptical paths, more generally trochoidal paths, that we call gravity.
As I have hinted at, these general trochoidal paths are the resultants of a spherical potential pressure field consisting in many components.
The notion of a potential field from which we compose a vector field should not obscure the fact that these are topological models of a dynamic experience! In this the very topology is dynamic. It is exactly saying that Hookes law is dependent on the substance in which it is applied, and for how long that substance remains stable in its configuration, and in its position!
A pressure field varies dynamically. In fact from studying weather we know that we have to conceive of a system of pressure fields in dynamic relationships, and at different scales and levels all fractally entrained. The most energetic of these systems we call turbulence.
Turbulence is a matter of energy driving rotational regional motions a at all scales with fractal damping mechanisms back feeding through the complex system resulting in diffusion, dissipation and transformation.
The deformation of space matter involved in these turbulent conditions reveal the application of fractal damping, or inertia in maintaining some form of regionalised structure at each scale. We can only account for this by means of conservative actions. Conservative actions allow forces to react, dynamic situations to be in static equilibrium, inertial actions to be proposed, momenta to be maintained and opposite or contra actions in general to be expected?
How we frame our conservation laws defines our models of spacematter interactions, but in general it is reasonable to divide any magnitude into 2 contra magnitudes thus for any pressure field there is an anti pressure field. How that exhibits itself to our senses is not defined by conservation laws, but by experience.
When a spherical pressure potential acts on an area or in a volume it produces twistorque vectors as well as radial vectors. The acceleration radially is a(r)r, the acceleration vorticularly is @(r)r which indicates that the combined motion is a funcyion which is dependent on the vectors and the radial distance from the source of the pressure potential .
The resultant force for a given volume with crossesction A will be RAm+TAm where R is the radial accelerative motive. and T i the twistor accelerative motive when resolved and summed. This is for a given radial with a surface neighbourhood on the sphere with Area A, small enough to be approximated by the tangent circle at that radial.
The twistorque forces are usually not accounted for. If they are they are set to zero, implying perfectly elastic materials circilarly but perfectly rigid radially and tangentially! Since this can hardly be the general case, we should expect twistor vectors to be non zero and there to be net twistorque related to the viscosity of the medium under pressure and the wave propogation properties of the medium as a function of that viscosity as a tensile medium.
Finally the torque of the vorticular forces must be a function of the energy required to conserve matter in that action with that viscosity. The model is therefore fractally complex
PAm = RAm + TAm