Chapter 40: Gravity: An Exact Solution

We're talking about actual gravity. Not the movie everyone buzzed about.

We’re talking about actual gravity. Not the movie everyone buzzed about.

Gravity. It is, if you listen to conventional wisdom, the force that holds the entire universe together.  It is the glue that binds us to the cosmos, the force that makes a structure out of ‘empty’ space, holding us down to the surface of our planet, keeping the planets of our solar system spinning around our sun. Gravity was the first of the fundamental forces to be recognized, and yet, it is still an enigma to those who study it.

For just what is, and what causes gravity? Or for that matter, how is it transmitted from one collection of mass to another? These are questions that, although we’ve created grand theories of how it affects the matter that we observe, we have no answers for.

Gravity just is.

But it’s worse than that, because we don’t even have a good explanation for why it does what it does. When Newton formulated  his famous equation that codified gravity’s inverse squared relationship with distance, he did so based on empirical evidence, not theory. Dear Dr. Einstein did this as well, choosing to offer us a much better understanding of the ways in which gravity affects our universe and the interactions that we observe without improving our fundamental understanding of the ways that it might be created, or why it behaves the ways that it does.

You see, electromagnetic energy has the photon, the mysterious ‘particle’ that transmits that force through space and can affect some of the smallest bits of matter known (electrons); and the strong force is transmitted by the gluons. The weak nuclear force has the intermediate vector bosons to move it from place to place, but gravity? Not so much.

Some will say that the graviton is the force ‘particle’ that transmits the energy of gravitation from one body to another, but that is pure conjecture since no such particle has been found. And the theories behind the famed Higgs Boson, whose ‘discovery’ (if it really is a discovery) heralds it as the force carrier that gives matter its mass, do not delve into any reasoning that imparts wisdom into the nature of the force that the mass it creates engenders, either.

Many of these questions will not be answered here, for while the author has some working theories about this, they are, shall we say, ‘half baked’ and not yet ready to face the light and introspection that comes with the publication of those thoughts.

However, he is able to offer a new explanation and a new formula for gravity.

Gravity you see, is not necessarily a force. Gravity is a characteristic of the space surrounding an object that has mass and that creates an acceleration toward that object. This much, Dr. Einstein got right. But the force of gravity can be seen as being created as a result of that acceleration, instead of the force creating the acceleration.

In our new system, it is the velocity, and its first derivative with respect to time, acceleration, that is the primary measurement, the foundation if you will, from which that force is created.

This is in direct opposition to Newton’s position that it takes a force to create an acceleration. The trick here is that, as we’ll show below, an acceleration can be created by an expanding velocity.

This might seem to be a ’chicken and egg’ sort of sort of question, and indeed it is, because, of course, it had to be the egg that came first. For although it is possible for a dinosaur, a lizard, a duck or even a platypus to lay an egg that has altered (mutated) DNA and that grows up to be a chicken, it is totally impossible for that lizard, duck or platypus to suddenly grow chicken feathers and go: “cluck, cluck, cluck”. Without that first egg, there could be no chicken. And so it is with the force created by gravity. Without the acceleration field surrounding the mass, there would be no force, and in fact, when one is in a state of free fall in a gravitational field, there is no force evident, only acceleration.

Which just goes to show that there can be acceleration without evident force.

This is a fact, the author is quite sure, that will be widely denied, decried and disputed, since we, as a scientific community, are so accustomed to referring to the four fundamental forces, and the ‘force’ of gravity (being the ‘flat earth’ sort of species that we are, used to being stuck to a small and rather innocuous planet in the backwaters of the Milky Way galaxy).

But let’s suspend disbelief for a few moments and follow this different logic.

Let us suppose that every mass, whether it is as large as a phantasmal mega monster super-duper black hole with the mass of two billion suns, or as small as a proton, creates a velocity field in the space that surrounds it.

We’ve already shown, many chapters back, that we are insensitive to velocity. We have no way to measure, much less experience even the rotation of the Earth, much less the incredible velocity at which we’re traveling through space in general, so it’s not that much of a stretch to assume that we are within the boundaries of a velocity field in space that is created by our beloved planet and have no awareness of it. Furthermore, the author would argue that it’s at least as credible to assume that there is a velocity filed created by the Earth’s cumulative mass as it is to assume that there is some invisible force that is created by it, that permeates its local space and is transmitted without an energy carrier; that acts upon objects within its relevant field seemingly instantaneously.

Newton called it “action at a distance” and never offered an explanation as to how that could be. Einstein transmogrified it into a Metric Tensor that ‘bends space’, but the only analogy used to explain it in physical terms relies on the very gravity that it hopes to explain. (Note: Check out any of the explanations for General Relativity and the ‘bending’ of space; they all use a model of a space as a flat sheet bent or dented by the presence of the gravitational force, in which the affected object moves basically downward toward the ‘pit’ created by the mass under consideration. Clearly, they use gravity to describe, um, gravity. Somehow, this is OK, and not circular logic.)

This velocity field is homogeneous (neglecting for small aberrations) across the entire surface of the object, which, for our purposes, we’ll assume is a sphere. Again, based on Chapter 24, The General Roundness of Being, this is not such a stretch.

And let us also assume that this velocity has some total value or amount at the surface of that object, a value that represents the sum total of the velocity created by the summed total mass of the object, and for that object, we’ll give that total summed velocity, the velocity tensor if you will, some constant value, ‘Cm’ for that particular object which is a volumetric vector, directed outward, radially. And we’ll sum up the statements above with the following equation:

VdA = Cm

This equation represents a surface integral that says; the sum of the velocity over the surface of a specific equipotential surface (generally, a sphere) is equal to some constant vector velocity quantity (Cm) related to the mass of the object. The quantity Cm must be vectoral since it is the result of the integration of a vector over the area of the sphere, A, which is a scalar (magnitude) quantity.

Assuming that this area-integral quantity, Cm, is a conserved ‘energy’, then as the surface areas of the progressive (virtual) equipotential spheres increase as one leaves the surface of the object, the magnitude of the velocity at each successive outer ‘layer’ must be less. By Conservation of Energy, there must be a deceleration of this velocity of space as the size of the virtual sphere increases (mass remaining constant), and therefore, creates an acceleration in the opposite direction (inward), toward the object under study.

By this logic, if the magnitude of the velocity is inversely proportional to the surface area of the ever expanding virtual spheres as described in the above equation, and the surface in the most common and general case is a sphere, whose area is proportional to its radius squared (Asphere = 4πr2), then magnitude of the acceleration must be inversely proportional to the square of the radius as well.

By making the these assumptions, the inverse proportionality of the force associated with gravity to the distance squared has been derived, rather than assumed.

Let’s dwell on that for a moment.

This is a fundamental strength of this new theory. By making the assumption that a mass can create a velocity field, rather than a ‘force field’ as is generally assumed, we can logically conclude that the strength of the ‘field’ created MUST be proportional to the inverse of the square of the distance from it. Newton could not demonstrate this. Neither could Dr. Einstein. But here we have it, plain as day, and rather easy to describe and comprehend.

Gravity must be inversely proportional to the square of the distance from the object due to the conservation of the energy of the velocity field.

The reason that we, as a society in general and a scientific community in particular, have not been able to come to this conclusion is that, as we pointed out much earlier in this book, we have always considered gravity to be a force that acts only in a linear fashion, completely ignoring the fact that one of the major characteristics of the phenomenon is that it expands as it reaches outward from the mass in question.

And this is why this formulation can be considered as an exact solution, while the Newtonian equation is only an approximation: the Newtonian solution is a point-wise construction, not a volumetric construction. Just as one cannot use Euclidean geometry to completely and fully describe a rudimentary form such as a circle, so too is it impossible for a point-wise equation to describe the effects that the ‘force’ of gravity has on the surrounding space. Newton’s, and hence, Dr. Einstein’s formulation of gravity is flawed because it does not account for the fact that gravity must have volume, and that it spreads as one gets farther and farther from the source.

Just as RΘ provides an exact equation for a circle, and includes every ‘point’ and arc within that construct, unlike the Euclidean X2 + Y2 = C, so too is this new construct an exact solution for the situation, rather than an approximate description.

If V is defined as dV/dt ≡ g, (or in the more general case, dV/dt ≡ (G*M1/r2) then all of the previously derived linear equations for gravitational attraction and acceleration can still hold true and be valid, except one. The complete expression for the gravitational velocity involves a direct association with the integral of the surface involved (∮VdA = Cm), and is thus dependent on that surface for its definition, expression and existence.

This means that if there is no surface, there is no integral and there is no gravitational acceleration.

Therefore, this formulation is not susceptible to ‘blowing up’ and becoming a singularity as is the classical Newtonian equation. Once the object under study becomes miniscule enough as to have no discernible boundary, the equation loses all value and becomes nonexistent (essentially zero).  (Note: this does not necessarily rob the quantity of its inertia).

In this interpretation there is an omnipresent acceleration vector surrounding any mass, created by the conserved energy of the velocity field, that interacts with any other mass that happens to be within range. No ‘communication’ (action at a distance) between masses is required although the velocity is omnipresent and will potentially transmit ripples or gravitational fluctuations. The acceleration created by the slowing of the velocity field creates the force when combined with an additional inertial mass (m2) and that force is defined as gravitational attraction.

So is this Quantum gravity? Not exactly. It is compatible with the subatomic metric because it has limits and therefore, will never tend toward infinity and/or require renormalization. This gravitational description is defined by a bounded, finite surface area that can be interpreted as a discrete energy level. These levels must have some minimum separation to be distinct, and therefore it is also implied that there must be some minimum quantum layering involved. But this expression does not contain or require a force carrier like a photon or a gluon, because it is essentially a field equation with a fixed definition for the velocity at every level, and neither requires nor conforms to any probability formulation. It is an exact, continuous solution to gravity rather than bound entity of discretes.

This formulation is based on the existing measurements and classical equations; all of the values derived by utilizing this expression will be the same as those calculated historically. It is, however, a model that is not subject to the same inconsistencies and shortcomings as modern Relativistic theories, and not nearly as fanciful or as hard to comprehend as current the String and Brane (dimensional) Theories (which do manage to include gravity in their formulations). Is there a true velocity pushing out from all massive objects into the vast reaches of space? The concept has some merit due to the fact that we know that there is a lot more energy concentrated in a planet or a star than in some section of interstellar space, so the idea that an emanating velocity from such, projecting out and dissipating (but never quite extinguishing) seems fundamentally acceptable. Showing that the inverse squared law is a result of the conservation of energy is probably this interpretation’s greatest strength.

Since mass does not seem to be affected by or interact directly with velocity, it will be difficult to provide an independent test of this model. It is certainly less cumbersome and more flexible than the presently accepted formulation.

It is very clear, that we do not fully understand gravity, charge, or energy at a fundamental level, and until we do, the hope for the synthesis of a Grand Unification Theory of any meaningful substance is slim. This proposition offers a new interpretation of the existing empirical data, one that incorporates classical thinking, without its theoretical limitations. It is based on the premise that velocity is the fundamental, non-reducible measurement, rather than the Euclidean system of discrete locations with independent time, and it is compatible with a ‘positives only’ measurement system. In so doing, one can theoretically unite the forms of acceleration and gravity into a comprehensive mathematical structure and answer several of the ‘why?’ questions that have plagued physics theory.

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