Understanding the QPDE---continuing mediations... NOTE: THE MATRIX DOES NOT PROVIDE GEOMETRIES. The sub-tensors are specifically shaped and can be evolved into a geometry easily enough (not fully explored), but none of the dimensions actually describes a geometry. As such, do not confuse this method of mapping dimensional values with the actual resulting geometries derived from those values. The QPDE is so-named because it is a partial differential equation in quadratic form. Dimensions on the Matrix are multi-purposive, meaning they do several things at the same time, making both the value and the perspective of interpretation variable. As a rule the changes in values are independent of each other, and all changes are not exhibited by a singular function because some changes have simultaneous results not relevant to what is being observed. Until a holistic geometry for the Matrix can be established, we are temporarily stuck in traditional systems that do not accommodate these complexities. The QPDE on the surface appears as a quadratic equation of the form 0=a²–A²ab+b², where A is a constant scalar quotient, ab is called the absolute, and a²+b² is called the transitive. This is often shown as just a² +b²=►ab or as u=√ab. The last is consistent with a derived Matrix evaluation not showing any modifiers or quotients like m=√νμ. The transitive describes a circle with a radius of A²ab. In other words, consistent with the Pythagorean theorem and fundamental theorem of trigonometry, this describes a simple process of change from a to b or b to a (a↔b). Traditional trigonometry describes the circular functions in linear terms instead of polar terms. This system works well for us because the baseline (horizontal x-axis) fits the radian quality defined by the transitive. We see the absolute as the variable polar value in A²ab, which describes fluctuations in the radius (the vertical y-axis). It is absolute because √ab=►u describes a relative boundary condition (u) that is itself all or part of a limit. In the case of forces this limit is a spacetime identity of c². The boundary condition contains and limits the rate and ability to change in a↔b. This results in multiple concentric circles, with the outermost being the limit u, the next being the functional ab, and the inner being the variable (a²+b²)/A². To understand this merely consider boiling or freezing water. To boil water you use cold water, shrinking ab down toward (a²+b²)/A² leaving u open to rapidly absorb heat. To freeze water you use hot water for the opposite reason: (a²+b²)/A² approaching u will discharge excess heat rapidly to get below ab and normalize. Generally our only QPDE concerns are with forces and entropies. Everything else between is reactive to these. We can even arguably reduce the Matrix to just these nine dimensions, but if we did we would miss all the subtleties and conveniences of identifying the intermediate dimensions. The quotient A²=2 for equivalent but opposite dimensions like gravity and heat (r’ and r) or the entropies. If we only work from these two perspective then apply those results to intermediary dimensions, we don’t have to argue with other quotients. Forces are provided in fractions of their permittivity, which gives them generic and familiar units of measure. When unlike forces are applied to each other, they must be put in common spacetime terms using their permeabilities. This of course means the result must be reduced by a common permeability to arrive at a common unit (e.g. magnetism deriving from complex charge interactions). I want to discuss entropy in slightly different terms (e.g. tangibility, smoothing, solidity, and mass), so we will hold on them for the moment. For now the easiest example we can explore is the thermal one already mentioned. The most accessible example is the weak interaction (√gT). We aren’t concerned with the charge quality at this moment. Just the pressurized temperate field created by this interaction. We could do something similar with the strong interaction but it becomes ambiguous due to the creation of secondary vectors that emulate the pressurized gravi-thermal field. Noting the interaction in question is defined by its vectors, we simply switch to forces thusly: gT=r’r/ij. Now we can look at the forces independent of the temporal entropy parts. We will use R for the boundary condition that is limited to RZ=c² where Z is a function of the strong interaction. This gives us: (r’²+r²)/2=r’r=►R². The only problem with this is that forces alone have NO GEOMETRY. To illustrate we need to put these elements into shaped sub-tensor manifolds. Fortunately this isn’t as hard as it appears. Because the elements are both linear we can just apply the Inverse Square Law to find the concentric geometric radii (a, v, u) of the sub-tensors: absolute a² = r’rG/F transitive inner v² = (r’²+r²)G/2F upper boundary u² = R²G/F where R=c²/Z There are also the boundary conditions of WXYZ/ij=c²=e√gC’CT/m that we aren’t going to worry about in this elementary of an examination. Nor will we concern ourselves with relative proportionality of c² itself. They seem a hassle, but without them changes accelerate out of control and the whole system breaks down. As the local to LQG gravity discussion reveals, things are never quite as simple as we are about to depict, but for baby-steps let us keep it simple. Anything exceeding an upper boundary must quantize and have its own identity. Otherwise, containment results in extraordinary pressures illustrating concepts of susceptibility and conductivity of force transfer. The sub-Z and super-W sub-tensors apply directly to these forces. These are presumable spheres, though material shape will affect the exact shape of that space until smoothed (hence being manifolds=able to change their shape). Their natures reveal they are open spaces, which doesn’t mean they are without end, just that they are not self-contained. They are contained by their boundary limitations as a function of the main tensor (normal W and Z). The vectors g and T simply direct their respective forces toward the origin of the geometric without regard to the tensor shapes, but confined to their tensor spaces. We see this in near-Earth orbit where there are still some thermal affects but negligible to no gravity. As the field equations article shows, this function simplifies down to Einstein’s field equation for gravity. In some ways we are making the problem much more ambiguous. On the plus side we are making it compatible with EVERYTHING. Since we are dealing with these fields anyway, we should take a moment to look at r’/i (g-oblation) and r/j (T-attraction) in LQG. The Entropy document describes j as a logical OR with a positive presumed predisposition and i as a logical AND with a negative presumed predisposition. By themselves the intrinsic positive of r’ and negative of r is pretty meaningless. When these become part of intrinsic operations the assumption is that they will be mated with their respective entropies, not the opposing entropies of LQG conditions. Oblation means to flatten at the poles or make elliptical. Instead of just attracting, r’/i also repels, so the force is being applied in opposite directions on opposite sides of the body. A malleable body like Earth’s crust and particularly the oceans shows this notable with the Moon’s orbit. Because the T vector is being shaped initially by the gravitational field, oblation affects it, while T-attraction has no affect on the g field.
Posted on: Wed, 15 Oct 2014 23:22:12 +0000
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