As we delve into the realm of physics, it’s crucial to adopt a more integrated view of physical mechanics, one that considers matter not as a separate entity from gravity and space, but as an intrinsic component of the same framework.

Einstein, in his development of General Relativity, stated:

We make a distinction hereafter between “gravitational field” and “matter” in this way, that we denote everything but the gravitational field as “matter.” Our use of the word therefore includes not only matter in the ordinary sense, but the electromagnetic field as well.

This characterization of matter as everything except the gravitational field presents a philosophical dilemma reminiscent of the inquiries posed by Aristotle and classical thinkers regarding atoms and voids. If matter occupies a specific volume, can it coexist with the gravitational field at the same point in space? What, then, is the gravitational field if its sole purpose is to govern the behavior of matter? The apparent irrelevance of absolute space led Newton's peer, Gottfried Leibniz, to quip that Newton perceived space as "an organ which God utilizes to perceive things." Had Leibniz witnessed the emergence of General Relativity, he might have similarly remarked that in Einstein’s framework, space serves merely as an organ through which God moves objects.

However, this perspective is not entirely comprehensive. We recognize that space possesses dynamic characteristics and manifests in various forms. The detection of gravitational waves indicates a medium through which these waves propagate rather than merely an empty void. We discuss not only the geometry and curvature of space but also its motion. NASA conceptualizes Earth's gravitational field as a vortex in space-time, implying movement and pressure beyond mere curvature.

For over a century, it has been evident that space acts as a dynamic medium capable of transmitting energy and facilitating the movement of matter. Concurrently, our understanding of matter has evolved; quantum physics reveals that, at a fundamental level, atoms and their subatomic particles behave as waves. They are no longer viewed as solid, indivisible spheres traversing a vacuum. If space functions as an energetic medium and particles are essentially waves, the clear-cut distinction between vacuum and substance—a dichotomy dating back to ancient Greek atomists—has been significantly blurred, if not entirely obliterated.

Currently, we perceive mass as the entity that "informs space-time how to curve," or as "everything except the gravitational field." But if space is indeed a dynamic medium and particles are waves, then it’s not unreasonable to propose that mass is not merely responsible for causing space-time curvature but actually constitutes it. If particles are waves, they must exist within something, and that something is space itself.

What implications arise from this perspective?

Reconceptualizing mass as a distortion or fluctuation in space-time allows for a clearer distinction between various forms of mass and energy, categorized as negative and positive. The mathematics underpinning General Relativity accommodates the existence of negative mass, despite conventional wisdom asserting that the energy density of a space-time region cannot be negative. Energy conditions serve not as physical restrictions but as mathematical boundaries that reflect a belief that "energy should be positive." This assumption, however, is flawed. In my previous discussion on Euler’s formula and oscillating systems, I illustrated that energy can be viewed as either negative or positive, or even as "real or imaginary," akin to potential or kinetic energy. As long as the total magnitude remains consistent, these values can fluctuate without violating energy conservation laws.

This insight is crucial for envisioning how space-time can be distorted. Just as a spring can be compressed, it can also be extended. If we visualize gravity as a "sink-like" curvature in space-time, it follows that "hill-like" curvatures must also exist, which produce repulsive forces. The universe's inflation, typically attributed to dark matter or dark energy, provides evidence that space mediates both the attraction and repulsion between objects. Our current understanding of mass primarily accounts for attraction, with repulsion relegated to the ambiguous "cosmological constant," a placeholder Einstein introduced into his equations to prevent gravitational collapse. If mass is indeed a form of space-time distortion, both attraction and repulsion can be explained as two facets of the same phenomenon—compression or extension, influx or outflux—allowing us to derive a metaphysical basis for the cosmological constant without resorting to exotic forms of matter.

Returning to the concept of universal oscillation proposed by Euler’s formula, this revised view of space as a medium aligns well. At the Big Bang, space was infinitely compressed, akin to a spring poised to release from pent-up pressure. This outward force leads to accelerated expansion until it reaches an equilibrium point (illustrated as pi/2 in the accompanying graph), where space is neither compressed nor extended. Momentum carries it past this equilibrium, stretching the fabric of space until it ultimately exhausts its momentum, reaching a point of infinite extension (illustrated as pi in the graph), at which space begins to retract towards its center. In this model, the compression or extension of space represents its potential energy or tension.

Yet, this narrative presents a gap. Why does the outward pressure of this supposed compression surpass the inward pull we associate with gravity? Shouldn’t the Big Bang—when all the universe's "matter" was in close proximity—have maximized gravitational attraction? Conversely, shouldn’t the moment when all matter is dispersed be characterized by the least gravitational pull? The compression and extension metaphor contradicts our understanding of gravity; typically, gravity should be enhanced by compression rather than resisted.

We are only examining one aspect of the situation—the potential energy. A more comprehensive view requires integrating the concepts of stretching and compression with inward and outward flux, which relates to kinetic energy.

It is increasingly common to visualize space being drawn into a gravitational center. The idea of a planet or star creating a "space-time vortex" is widely accepted. This concept inherently involves the kinetic movement of space, suggesting a current directed toward the gravitational center that carries objects along. Some might argue that this is a mixed metaphor, contending that there is no genuine motion of space, only curvature that directs real matter. However, for the sake of this discussion—and considering the fading boundaries between our notions of space and matter—let’s entertain the idea that space is indeed in motion; the gravitational field's strength reflects the current within space-time.

While this model is intriguing, it doesn’t clarify the fate of the space that is "sucked in." If gravity results from space being drawn toward a mass center, why isn’t it accumulating there? How do mass and the gravitational field's strength remain stable while space continually flows inward?

(For further insights, reviewing my prior article on the double-slit experiment and four-dimensional space may be helpful.)

Let us envision reality as a two-dimensional plane. At its center lies a planet with a robust gravitational field. According to General Relativity, this planet cannot possess gravity, as an additional dimension is required to create the curvature that generates gravity. Nevertheless, for argument's sake, let’s assume our two-dimensional planet does have gravity, and surrounding space is moving toward it like a whirlpool or water draining from a sink. This imagery implies a third, vertical dimension and an outflow of water into that dimension, rather than a simple disappearance at the center. Whether we consider General Relativity or the "flux" concept, a higher dimension is necessary.

If we entertain the notion of gravity as an influx of space, necessitating a complementary outflow, we may account for why spatial "pressure" could exceed gravitational attraction at the moment of the Big Bang. Essentially, there is nowhere for the outflow to go. With all of space-time compressed to a singular point, with all "parallel universes" indistinguishably superimposed, no influx or outflux can be discerned—resulting in a lack of gravity. However, any gravitational influx in the moments following the Big Bang must incite an outflux that pushes against surrounding matter. Gravity is destined to lose this battle because we have reached the maximum of contraction. Even ignoring the positive potential energy suggested by the compression metaphor, the inward and outward kinetic energies balance, leaving only one possible direction for matter: outward.

This influx/outflux model also elucidates how gravitational attraction could surpass spatial pressure during the impending "Big Crunch." When space is at its maximum expansion in four dimensions, gravitational influx becomes minimal, virtually zero, yet so does the outflux. Any outflux directed into neighboring parallel universes would have a negligible effect due to the absence of neighboring matter. In the reversal of the Big Bang, all parallel universes are once again identical and superimposed, this time resulting from a density that is infinitely low—making any added pressure inconsequential. With expansion at its limit, gravity is poised to win this contest. Even disregarding the negative potential energy implied by the stretching metaphor, inward and outward kinetic energies again balance, leaving only one direction for matter to move: inward.

In conclusion, our conventional models of gravity falter for two reasons: they inadvertently treat four-dimensional space as three-dimensional, as we struggle to visualize four dimensions; and they fail to adequately incorporate the movement or momentum of space itself. The compression and stretching metaphor is incomplete, as it solely addresses space’s potential energy while neglecting its motion. Conversely, the influx and outflux metaphor also falls short, as it only captures space's kinetic energy while disregarding its tension. When combined, they provide a reasonably comprehensive, albeit simplified, account of the dynamics of space.

Where does this leave our understanding of mass and matter? It may be insightful to view mass as a measure of flux, the rate at which space converges into matter, with matter itself acting as a four-dimensional vortex within the fabric of space-time. While this is perhaps the most literal and precise expression, it remains challenging to visualize or grasp, as we require a dichotomy to conceptualize anything. What does it entail for space to traverse itself? What moves in relation to what? This concept appears paradoxical.

Ultimately, we can conceive of the universe as a complex interplay between two or more mediums, yet to assert that it evolves from a singular substance is akin to describing the sound of one hand clapping; it lacks coherence. In our pursuit of unity and simplicity, the interaction of two mediums emerges as the logical boundary.

In a forthcoming article, I will explore fractals and reiterative equations, offering insights into how they may provide a fresh understanding of how space can simultaneously appear both homogeneous and infinitely intricate.