An Neogeometry for Universal Gravitation

Spacetime at the Center of the Discussion

Geometric gravity is already a scientific fact, but there is still a gap to be unraveled, namely, the divergence of the explanation of the gravity of massive bodies when it enters its mechanism in the microscopic world governed by quantum physics. There is, therefore, a possibility of redrawing this question that will be presented here. Our approach is based on the thought experiment procedure, bringing a new paradigm of approach to this subject, which we hope will conquer the reader's point of view. We assume that explaining the Universe can have a version to be understood by anyone, not necessarily a physicist or an aerospace engineer.

What we propose here is not to establish a new particle or entity integrating the space-time algebras or to decompose new subparticles of the periodic table of gravitation-friendly physical particles. The purpose of this text is not to garner applause, which is not expendable, of course, but to form a deconstruction and at the same time provide an opportunity for reflection.

Thus, we will here only present conjectures with the aim of founding a new category or philosophical basis about the interpretation of gravitational interaction.

I — First, let’s address an idea about the mass of bodies

It is already established by formal science that the interaction of particles with the Higgs field is what would give mass to these particles, and not only to them, but also to the intermediaries of the forces. Even so, the question does not end there because it remains unknown what the mass of the Higgs boson would be made of? The mass of the Higgs boson is stated to be equal to 125.2 GeV/c². Since it is expressed in units of energy, we can say that the mass of the Higgs boson is equivalently energy. However, there is another aspect to highlight: a photon carries inertia, despite having no mass.

To comment on a possible answer to this questions, we will base ourselves on the results of Einstein’s experiment on the gravitational deflection of light, that is, the gravitational lens effect. So what we will put forward would not be a hypothesis, but a plausible possibility.

According to the General Theory of Relativity (GTR), mass warps spacetime, and this warping affects the motion of other nearby objects that move along the curves and depressions created in the fabric of spacetime. Einstein claims that light rays that do not propagate along the axis are deflected by the gravitational field of an astronomical object, which in turn provides the potential that influences the angle of deflection. So a light ray is deflected as it interacts with a strong gravitational field.

My idea: the matter (particles or bodies) is the continuity of space-time

Let us now make an analogy with the lens in optics. In such a lens, light is deflected from its direction due to the change of medium. But in the case of gravitational deflection there is no such change of medium, especially since it is outer space. But we may infer, without prejudice, that if there were such a change of medium, it might be suggested that this would be associated with space-time itself, which would be subject to change as if it were a propagation medium. How?

Let us take as a basis the figure below an abstract geometric structure consisting of an infinite extensible mesh.

Let’s suppose that the polygon ABCD is deformed, for example under the effect of a vibratory (oscillatory) motion, then as the mesh is extensible this would result in a deformation of its surroundings suggested in the drawing below.

So if spacetime itself were the oscillating medium then any elementary physical particle defined as having an associated energy wave could be such a wave resulting from the vibration of spacetime itself. Such vibration would induce a deformation in its surroundings with the appearance of a figure converging towards the source of oscillation. This would correspond to a potential. This leads to the suggestion that a corpuscular “volume” of spacetime trapped in a stationary vibrational mode, and because it simulates a potential, could be associated with an inertia and concomitantly with a mass. Such a vibrational mode could be called a graviton. So a particle of mass would be the “wrinkled” spacetime.

Any particle, even without mass, could be contained in this representation model. Thus, a body as a source of gravitational potential could be represented as the result of the simultaneous contribution of an infinity of oscillation modes of spacetime. This immediately provides, without prejudice to current theories, an additional explanation for the gravitational deflection of light around a gravitational field, since it, as a propagating wave, and as a traveling vibration mode of spacetime, would have its trajectory adjusted precisely according to what results from its passage through the deformed medium (spacetime).

One problem would be that for this to be true, the oscillations could not be dissipated to the rest of the mesh. Since the mesh is considered infinite, its response time is very high and the local oscillations would be stationary in this condition. In other words, our hypothetical mesh offers a very high propagation impedance to the “mass” type vibration mode and we would have compatibility with quantum effects.

So, in the surroundings of a body with mass, this would provide an electromagnetic wave associated with a passing photon with a resulting path where it could follow in its propagation. An idea associated with this offers a supervenient explanation for the emission of a photon by an electron during its transition of quantum levels, since in order to stabilize the excited bound electron it transmits inertia to spacetime in the amount sufficient for its stabilization and this makes a lot of sense and seems to be something expected. Also, since the photon does not have mass, but it does have inertia, then in a collision between a photon and an electron, for example, what delivers the inertia is spacetime itself.

II — Another aspect: a geometry

Another aspect of our approach has to do with a basic scheme that brings together the two entities sufficient to perceive the scope of gravity, point and line.

The entire meaning of three-dimensional space with 4π steradians can be interpreted by a meaning of a continuum as if it were a single dimension or pseudodimension, that is, an observer (not necessarily using vision) can consider his perception of three-dimensional space as a single dimension. For example: when walking down a street, changing sides does not change the way we walk, as long as we are restricted to the boundaries of the street. We will call this thought experiment omnipolar vision, or ϕ vision.

For the purpose of our demonstration, we will show a schematic drawing where, on one side, there is a three-dimensional space represented by the three Cartesian axes and on the other side the hypothetical omnipolar system.

next we will include a physical object such as a solid:

At the same time, we assign a point on the right side corresponding to the object on the left side,

and then we transfer the solid in space, changing its position in the drawing to correspond to the origin of the axis system:

Furthermore, on the right side (omnipolar system) the transferred object will still correspond to the same point on the drawing.

Let’s now suppose that we have another object in the scene and we move it “outside the drawing”, this object will correspond to a second point on the right side:

Let us now establish a line segment on the right side connecting the points drawn there, we will call this segment the restriction line.

This line has the meaning of a restriction line in the drawing, that is, every object on the left side of the drawing will necessarily be represented on it. The line becomes the natural container regardless of any transfer of objects within the right side of the drawing:

So the object represented by point “p”, even though, for example, it is supposedly in a predefined orbital motion, will still be static on the line on the right side.

In the event of a transfer of this same object towards the origin where the first one already resides in the sense of a fusion, then this is represented on the right side by the point “m”:

Before we continue, let us make a brief comment about what may be disturbing in our conclusion. So we are talking about things that may occur on the left side of our representation from the point of view of the physical effects related to motion, and in this case, we are certainly talking about the relativity of motion and its connection with the property of curvature of spacetime in the presence of physical objects (bodies with mass).

Without delving into complex theories usually accompanied by voluminous equations, what we have in mind is to describe it in words. Firstly, a fundamental aspect is about acceleration, which the primary bodies induce on the secondary bodies, supervening on the effect of curvature of spacetime. This is quite plausible to perceive in the effect of free fall (vertical fall). So now when a secondary body approaches a primary body, via spacetime, its gravitational effects will be combined by relativity of motion involving the speed of light as an intermediary in a conjugate relationship resulting in a natural product of geometric factors, as said before, already well defined by abundant differential equations — gravity is a symptom of the way the universe organizes itself as it expands.

So, these natural conditions are also represented in the drawing on the right side, as the continuous line allows us to represent a real-world object by highlighting a point on it, and the continuity of the line as a definition allows us to represent, therefore, the concept of gravity as a natural and intrinsic condition involving bodies, as the point (“m”) being on the line indicates that it itself has its gravity on itself (in the condition of being a body or a system) and that which arises through relativistic interaction with another (“p”), including with objects outside the drawing, which are represented by the point “n”. All bodies are connected by gravity.

III — The status quo is the motion

Thus the Universe, both at the level of cosmos and microcosm (elementary particles), is characteristically the result of the union of everything that is in motion, and beyond the boundaries of the Universe there is no motion. We are always seeking to explain the laws of motion and their implications, but in my understanding, motion is something intrinsic, which suggests that it is a property of the “Universes” and is more fundamental than particles, talking about the Universe is talking about motion. In the omnipolar scheme this can be represented by the continuation of the restriction line from point “n”, making it clear that the domain of motion would be between points “m” and “n”:

in short, all these points on the “nm” segment are images of spacetime itself, whether in the form of an object, particle or gravity. It is also possible to explore cosmological dynamics in the drawing, considering the future of the Universe, so we have: given the hypothesis of its expansion ad infinitum, then point “m” will overlap point “n”, and in the case of contraction (collapse) then point “n” will overlap point “m”.

This theory does not seek to oppose formal theories, as well as contemporary ones. We can even bet that it is compatible with any of them. The idea is that this theory can be shown as a receptive epistemological description for the theories of physics that today are in conflict or in gaps regarding the physics of gravitation.