Chapter 1: The Necessity for a Unified Physical Mechanism

The time has come to adopt a cohesive approach to physical mechanics, one that integrates matter with the concepts of space and gravity rather than treating them as isolated entities.

In his formulation of General Relativity, Einstein stated:

"We will differentiate between 'gravitational field' and 'matter' such that everything except for the gravitational field is termed 'matter.' Our terminology thus encompasses not only traditional matter but also the electromagnetic field."

This classification raises significant philosophical dilemmas reminiscent of those posed by Aristotle and other classical thinkers regarding atoms and the void. If matter occupies a defined volume, can the gravitational field and matter simultaneously occupy the same space? And what, exactly, is the gravitational field if its only observable effect is its influence on the motion of matter? The apparent irrelevance of absolute space led Newton's contemporary, Gottfried Leibniz, to humorously suggest that Newton perceived space as "an instrument through which God perceives existence." Had Leibniz witnessed the emergence of General Relativity, he might have quipped that in Einstein's framework, space merely serves as a mechanism for God to maneuver objects.

Nonetheless, this perspective is incomplete. We understand that space possesses dynamic qualities; it exists in various forms. The detection of gravitational waves indicates a medium through which these waves propagate, rather than merely an empty void. Discussions about the curvature and geometry of space often extend to its movement. NASA describes Earth's gravitational field as a space-time vortex, suggesting not only curvature but also motion and pressure.

For over a century, it has been evident that space functions as a dynamic medium capable of transmitting energy and facilitating the movement of matter. Concurrently, our understanding of matter has evolved, revealing that atoms and their constituent particles display wave-like behavior rather than acting as solid, indivisible entities traversing a vacuum. If space is indeed an energetic medium and particles are fundamentally waves, the stark division between vacuum and substance—a concept rooted in classical atomism—has become significantly blurred, if not entirely dismantled.

Current scientific consensus suggests that mass "informs space-time how to curve," or that matter constitutes "everything except for the gravitational field." Yet, if space is a dynamic medium and particles are waves, might it not be reasonable to propose that mass itself is a manifestation of space-time curvature or movement rather than merely inducing it? If particles are waves, they must exist as waves within something, which is space itself.

What implications does this conceptual shift hold?

Reconceiving mass as a distortion or fluctuation within space-time allows us to categorize mass and energy into distinct types—negative and positive. The mathematical framework of General Relativity accommodates the notion of negative mass, even while established doctrine asserts that energy density within a region of space-time cannot dip below zero. Energy conditions are not strict physical limitations, but rather mathematically imposed boundaries that reflect a belief that "energy ought to be positive." This perspective, however, is fundamentally flawed. As discussed in my article on Euler's formula and oscillating systems, we can envision energy as either negative or positive, or "real or imaginary," akin to potential versus kinetic energy. As long as the absolute magnitude remains consistent, the variables of positivity and negativity can shift without violating the principles of energy conservation.

This understanding is crucial for visualizing how space-time can be warped. Like a spring, if space-time can be compressed, it can also be expanded. If gravity can be conceptualized as a "sink-like" curvature within the space-time framework, then "hill-like" curvature must also exist, capable of repelling. The universe's inflation, often attributed to dark matter or dark energy, serves as compelling evidence that space not only facilitates attraction between objects but also their repulsion. Our current understanding of mass only accounts for the attraction, leaving the phenomenon of repulsion to be explained by the "cosmological constant," a term Einstein introduced into his equations as an arbitrary adjustment to prevent gravitational collapse. If mass is indeed a form of space-time distortion or fluctuation, then both attraction and repulsion can be elucidated as two facets of the same process—compression and expansion, influx and outflux—potentially providing a metaphysical basis for the cosmological constant without resorting to exotic new forms of matter.

Returning to the concept of universal oscillation through Euler's Formula, this revised understanding of space as a medium aligns well. At the moment of the Big Bang, space was infinitely compressed, akin to a spring poised to release from its pent-up pressure. This pressure induces accelerating expansion until reaching a balance point (pi/2 in the graph below), where space could be imagined as neither compressed nor expanded. Momentum carries it beyond this equilibrium, stretching the fabric of space until the momentum dissipates, reaching a state of infinite expansion (pi in the graph below), at which point space begins to retract towards its center. In this model, the compression or stretching of space symbolizes its potential energy or tension.

However, this explanation lacks a critical element. Why does the outward pressure from this compression overpower the inward pressure we associate with gravity? If gravitational attraction intensifies with increased mass and proximity of massive objects, shouldn't the Big Bang—when all matter was infinitely close together—represent the peak of gravitational attraction? Conversely, shouldn't the moment when all matter is dispersed across vast distances reflect the lowest gravitational attraction? The metaphor of compression and stretching contradicts our understanding of gravity's behavior, suggesting that gravity should be reinforced by compression rather than countered by it.

We are only observing one aspect of the equation—the potential energy. To enrich this metaphor of stretching and compression, we must introduce another concept: inward and outward flux, representing kinetic energy.

Commonly, we visualize space as being drawn into a gravitational center. The idea of a planet or star generating a "space-time vortex" is widely accepted. Inherent in the notion of a vortex and almost every three-dimensional representation of gravity is a kinetic flow of space itself, drawing objects towards the gravitational center. Some might dismiss this as a mixed metaphor, asserting that there is no actual movement of space, only curvature that instructs real matter on how to move. Nevertheless, for the sake of this argument—and the earlier discussions about the merging of our definitions of space and matter—let's operate under the premise that space is indeed in motion: the strength of the gravitational field is a manifestation of a current within space-time, the flux.

While this conceptualization is intriguing, it fails to clarify what occurs to the space that is "absorbed." If gravity is a mechanical result of space being drawn into the center of mass, why does it not accumulate there? How do mass and the gravitational field's strength remain constant even as space continually flows inward?

(For the next section, it may be helpful to refer to my earlier article on the double-slit experiment and four-dimensional space.)

Imagine reality as a two-dimensional plane. At its center lies a planet with a strong gravitational field. According to General Relativity, this planet cannot exhibit gravity without introducing an additional dimension to create the curvature responsible for gravity. However, for the sake of this discussion, let's assume our two-dimensional planet possesses gravity, and the surrounding space flows towards the center of mass like water entering a drain. This metaphor implies the existence of a third, vertical dimension, allowing for an outflow of that water into that dimension, rather than a mere disappearance as it reaches the center. Whether we apply General Relativity or the "flux" concept, a higher dimension remains necessary.

If we entertain the notion that gravity is an influx of space, this influx must necessitate a corresponding outflux, hidden from us because it occurs in a manner "perpendicular" to our perception in a fourth dimension. This perspective provides a potential explanation for how spatial "pressure" could surpass gravitational attraction at the moment of the Big Bang. Essentially, there is no space for the outflux to escape. When all of space-time is compressed to a singular point, with all "parallel universes" effectively superimposed, there can be no observable influx or outflux—therefore, no gravity. However, any influx of gravity immediately following the Big Bang would result in an outflux, pushing against neighboring matter. This is a struggle that gravity will ultimately lose, as we have reached the limit of contraction. Even disregarding the positive potential energy suggested by the compression metaphor, the inward and outward kinetic energies are equal, leaving only one direction for matter to progress: outward.

This influx/outflux model also elucidates how gravitational attraction could surpass spatial pressure at the opposite end of the spectrum, during the onset of the "Big Crunch." With space at its maximum expansion in four dimensions, the gravitational influx once again approaches zero, but so does the outflux. Any outflux directed into neighboring parallel universes would have a negligible impact on their matter due to the absence of adjacent matter. In the reverse of the Big Bang, all parallel universes become once more identical and superimposed, this time due to an infinitely low density, where any added pressure is akin to a droplet falling into an ocean. With the limit of expansion reached, gravity emerges victorious in this contest. Even if we disregard the negative potential energy implied by the stretching metaphor, the inward and outward kinetic energies remain equal, leaving only one direction for matter to navigate: inward.

Ultimately, our conventional models of gravity falter for two primary reasons: they inadvertently treat four-dimensional space as if it were three-dimensional due to our difficulty in visualizing four dimensions, and they fail to coherently incorporate the movement or momentum of space itself. The compression and stretching metaphor is not without its flaws, as it only addresses space's potential energy while neglecting its motion. Conversely, the influx and outflux metaphor, while insightful, only describes space's kinetic energy while overlooking its tension. Combined, they offer a somewhat comprehensive, though simplified, overview of the mechanics governing space.

Where does this leave our understanding of mass and matter? It may be beneficial to envision mass as a measure of the flux—the rate at which space is drawn into matter, with matter itself representing a four-dimensional vortex within the space-time fabric. This might be the most literal and accurate representation, yet it remains challenging to visualize or comprehend, as we require a dichotomy to conceptualize anything. What does it mean for space to traverse itself? What is moving in relation to what? It sounds paradoxical.

Ultimately, we can conceptualize the universe as a complex interaction between two or more mediums, but asserting it as a complex evolution of a singular substance is akin to the sound of one hand clapping—it defies understanding. In our pursuit of unification and simplicity, two interacting mediums represent the logical boundary.

In a forthcoming article, I will delve into the concepts of fractals and iterative equations, elucidating how these ideas may provide a fresh perspective on how space can simultaneously appear homogeneous and infinitely intricate.

Chapter 2: Exploring Dark Matter Theories

As we continue to question the traditional concepts of gravity and mass, we find ourselves delving into alternative theories that challenge the existing paradigms.

The first video titled "Gravity Without Mass Could Explain Dark Matter" discusses the potential implications of redefining gravity in the absence of mass. This concept opens new avenues for understanding dark matter and its effects on the universe.

The second video, "Physicists Dismiss Dark Matter and Develop a New Theory of Gravitation!" elaborates on emerging theories that reject the notion of dark matter, proposing innovative frameworks for understanding gravitational phenomena.