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2.6.13 Presumption of the Whole Inclusive Theory of Everything 2

2.6.13.1 Overview

Causal Dynamical Triangulation (CDT) shows a correct direction. However, it does not seem to accommodate all various findings in physics.
I hereby present the first half of my own hypothesis regarding a model capable of addressing these diverse physical insights—namely, the "Whole Inclusive Theory of Everything."

2.6.13.2 Details

2.6.13.2.1 Composition of 3D Space: The Tetrahedron

First, the tetrahedron is used as the small unit that constitutes three-dimensional space. The standard form is a regular tetrahedron.
When numerous tetrahedra are placed on a plane (2D), they appear as shown in the diagram below. The labels $ x^1, x^2 $, and $ x^3 $ correspond to the x, y, and z axes commonly used in elementary mathematics.

Furthermore, when stacking them in 3D space—for example, three layers deep—the result is shown in the figure below. However, even at only three layers, the diagram becomes practically difficult to comprehend.

These tetrahedra eventually fill the entire 3D space, arranged both horizontally and vertically. The diagram below illustrates the base of a tetrahedron as seen from above when a portion of 3D space is cut horizontally. Dark blue lines are used to represent these as the fabric of space.


2.6.13.2.2 Representation of Tetrahedra in Spacetime

Ideally, space and time should be represented using four-dimensional axes (3D space + time), but this results in an extremely complex diagram. Therefore, a 1D spatial axis have been set horizontally and a 1D time axis vertically.
The diagram shows the state of space at a specific moment in time—a state where the edges of numerous tetrahedra are spread out. The axis $x^0$ represents the time axis. While the $x^2$ and $x^3$ dimensions of 3D space are omitted here, the tetrahedra actually extend throughout the entire 3D space. As time elapses, the state is recorded by moving along the $x^0$ direction.



2.6.13.2.3 Representation of Waves and Particles

2.6.13.2.3.1 Massless Elementary Particles and Wave States

There are entities referred to as massless particles. A typical example is light—specifically, electromagnetic waves composed mainly of what we call photons. However, as mentioned previously, their true nature is merely a type of wave propagating through spacetime.
The diagram below shows the base of the tetrahedra from a bird's-eye view when a part of 3D space is cut horizontally. It illustrates a wave of distorted space, having received energy from the left, as it propagates. When viewed on the $x^1$ and $x_0$ axes, it appears as shown in the figure below. Energy is transmitted through the elongation and contraction of parts of space.


By appropriately setting the space and time axes, light or photons propagate along a 45-degree line.

Of course, as explained via path integrals, the wave accurately spreads in all directions from a single point; however, in most locations, the waves cancel out due to interference. Only the areas where the change is reinforced by interference move forward.
These are merely examples to grasp the general conceptual atmosphere.

2.6.13.2.3.2 Elementary Particles with Mass and Wave States

For elementary particles with mass, the diagrams shown in the section on the General Theory of Relativity serve as the foundation. In a Minkowski diagram, the closer one gets to the center of a black hole, the more space (spacetime) is distorted toward the past. Space itself moves toward the center of the black hole as time passes.

While some argue that physical properties diverge to infinity at the center of a black hole, making it incompatible with quantum theory, this problem does not arise if a minimum fundamental unit of spacetime is presumed.
Presuming the existence of a fundamental minimum unit, the state of a black hole can be detailed as shown in the diagram below.

The fundamental units of space in the central region become severely distorted, tilting to align toward the temporal direction. This schematic illustrates a situation where, as a result, the angles of adjacent spatial units shift, causing the surrounding space to also become slanted.
The formation process is straightforward: Initially, within normal space, immense pressure or force is applied from opposing sides—such as during the Big Bang. This pressure causes the fundamental spatial units caught in between to twist and curve toward the time dimension. Significant energy is stored within this distorted central space.
While a single twisted spatial unit cannot produce a large-scale black hole, the accumulation of many such units results in the formation of a black hole. Conversely, if a trigger allows this distorted space to be released, the stored energy is discharged, and the space returns to its normal state.


2.6.13.2.4 Quantum Entanglement

The diagram below is a Minkowski diagram of the Aspect experiment. The first photon is emitted from $S$ and travels to the left. After 5 nanoseconds, the second photon is emitted from $S$ and travels to the right.
The first photon passes through crystal $a$, its path to one of the two left detectors is determined randomly, and it enters a polarizing filter just before reaching the detector. The photon may or may not pass through. If it does, it is detected and simultaneously annihilated.
The second photon passes through the crystal and a polarizing filter on the right. According to the findings of the Aspect experiment, information regarding the vibration angle of the first photon is instantaneously transmitted to the second photon. The second photon then adopts the same vibration angle before hitting its filter.
This information transfer is much faster than the speed of light—estimated in subsequent experiments to be over 10,000 times faster.
From the standpoint that spacetime has no minimum unit, theories like the Holographic Universe are proposed to explain this mechanism, but they lack a rational basis.

From the standpoint that spacetime possesses a minimum fundamental unit, information may be considered as being transmitted through the fabric of spacetime itself.
For waves identified as photons or other elementary particles, the maximum speed is regarded as the speed of light, occurring when spacetime propagates as a wave. This is primarily a result of models being constructed to align with the observed phenomenon of the constancy of the speed of light. If there are phenomena (such as Quantum Entanglement) that cannot be explained by these models, a model capable of addressing such anomalies becomes necessary.
It is hypothesized that information is transmitted instantaneously—at speeds exceeding 10,000 times the speed of light—along the dark blue lines of space depicted here.
However, even with this mode of information transfer, it is understood that the signal attenuates as distance increases. In quantum entanglement experiments, the annihilation of photons occurs in regions throughout the universe, yet these events do not impact local experimental results. This suggests that information transfer via entanglement attenuates across vast intervals of time and space. Quantum entanglement is, in principle, a phenomenon in which information is transmitted to the immediate, neighboring spacetime.

2.6.13.2.5 The Big Bang and the Formation of Three-Dimensional Space

2.6.13.2.5.1 Background

According to Rael, small regions within this universe contain other universes (child universes), suggesting the existence of an immense number of such entities. In this view, our universe is merely one of many child universes generated from a "parent" universe. Conversely, established scientific knowledge suggests that this universe began with an explosion known as the Big Bang. Furthermore, Causal Dynamical Triangulation (CDT) theory posits that spacetime becomes two-dimensional at the microscopic level. This two-dimensionality likely implies one dimension of time and one dimension of space. By synthesizing these insights, a model for the Big Bang and the generation of a three-dimensional universe can be proposed as follows.

2.6.13.2.5.2 Large Blue Rods and Small Blue Rods

The short blue lines previously used to represent the fundamental units of space are hereafter referred to as "Large Blue Rods." A single Large Blue Rod is a rigid yet somewhat elastic, long cylindrical structure. It is assumed to be composed of an immense number of extremely minute components called "Small Blue Rods." Although these Small Blue Rods are not strictly bonded and can be separated individually, they originally cluster together like a bundle, held by a light mutual attraction to form a Large Blue Rod.
Small Blue Rods also possess a rigid yet elastic, long cylindrical structure. It is hypothesized that they contain internal crystal-like structures capable of simple information storage and transformation at an electronic circuit level. Such a mechanism is necessary to explain the varied phenomena exhibited by spacetime, such as spin.

2.6.13.2.5.3 Initiation of Child Universe Generation

When significant energy is applied to a narrow region of spacetime, a Large Blue Rod becomes distorted while storing that energy, creating a tilt toward the temporal direction as described previously. If even greater energy is applied, the Large Blue Rod collapses, releasing the Small Blue Rods. These Small Blue Rods, which were previously folded or bundled, begin to extend like spreading roots. This marks the beginning of child universe generation, corresponding to the Big Bang. Initially, this process starts with the formation of a one-dimensional space.


2.6.13.2.5.4 Extended Elastic Filaments

The term "rubber-thread-like Small Blue Rods" is used because each Small Blue Rod is envisioned as being attached at both ends to something resembling long, elastic threads. These threads connect one Small Blue Rod to the ends of others. The tips of the Small Blue Rods are referred to as "endpoints," and the elastic, long thread-like connections are called "Elastic Filaments." These Elastic Filaments serve as a conceptual tool to help visualize the manifold.


2.6.13.2.5.5 Formation of One-Dimensional Joints in a One-Dimensional Manifold

As these components begin to extend like elastic threads, it is assumed that their endpoints possess an attractive property. This assumption is necessary for the coherent construction of the model. Eventually, the endpoints of the Small Blue Rods are drawn together, forming a state called a "joint," which maintains a close proximity while allowing for free angular rotation. Specifically, when the endpoints of two Small Blue Rods approach each other along the aforementioned "Elastic Filaments" and exhibit "perfectly smooth motion" upon contact, a joint is established. Perfectly smooth motion is defined here as a deformation that is infinitely differentiable at every point.

Driven by a vast quantity of Small Blue Rods and immense energy, this elastic structure extends toward near-infinity. In this context, the Elastic Filament can be regarded as a one-dimensional manifold, analogous to a one-dimensional Euclidean space. The model envisions a scenario where the one-dimensional manifold (the Elastic Filament) undergoes perfectly smooth deformation to transition into a slightly different one-dimensional manifold. As previously noted, in a one-dimensional manifold, any continuous deformation (Homeomorphism) is simultaneously equivalent to a perfectly smooth deformation (Diffeomorphism). Therefore, if endpoints approach one another through continuous deformation, a joint is formed. This results in a one-dimensional joint formed by two endpoints (indicated in the diagram in light green), creating a robust, one-dimensional string. Multiple strings of this nature may be formed.


2.6.13.2.5.6 Formation of Massive Particles (Waves) in Space

During this process, if intense force is applied to certain Small Blue Rods from opposing directions, the distortion can only be diverted toward the temporal dimension. Consequently, these rods become warped in the direction of time. (Rather than the central portion moving into the past, it can be described as the center becoming temporally stationary while time progresses for the surrounding parts.) As explained regarding massive particles and waves, the Big Bang is considered a primary cause for the generation of these distorted Small Blue Rods.

2.6.13.2.5.7 Formation of Two-Dimensional Joints in a Two-Dimensional Manifold

As the Small Blue Rods extend into nearly infinite elastic threads, a joint or endpoint may approach another joint. If they exhibit perfectly smooth motion upon proximity, a two-dimensional joint is formed. A two-dimensional joint consists of three or more endpoints. Since this structure of Small Blue Rods can be viewed as extending infinitely, the formation of two-dimensional joints is modeled using a two-dimensional manifold, similar to a rubber sheet containing winding one-dimensional Elastic Filaments. If other endpoints or joints gradually approach a specific joint within this two-dimensional manifold and move with perfect smoothness, a two-dimensional joint is established. In a two-dimensional manifold, continuous deformation (Homeomorphism) is equivalent to perfectly smooth deformation(Diffeomorphism); thus, the proximity of endpoints via continuous deformation results in the formation of a two-dimensional joint. This process creates a two-dimensional surface that continues to expand nearly infinitely due to the vast number of Small Blue Rods and high energy levels.





2.6.13.2.5.8 Formation of Three-Dimensional Joints in a Three-Dimensional Manifold

Within this two-dimensional surface, other endpoints or joints approach an existing joint to form a three-dimensional joint, thereby creating three-dimensional space. To conceptualize three-dimensional joint formation, a three-dimensional manifold—akin to a sponge containing two-dimensional rubber sheets—is envisioned. If endpoints or joints approach one another within this three-dimensional manifold with perfectly smooth motion, a three-dimensional joint is formed. As with lower dimensions, continuous deformation (Homeomorphism) in a three-dimensional manifold is equivalent to perfectly smooth deformation (Diffeomorphism). Consequently, the proximity of endpoints through continuous deformation leads to the formation of a three-dimensional joint, resulting in a three-dimensional space that expands nearly infinitely.

2.6.13.2.5.9 Impediments to Four-Dimensional Joint Formation in a Four-Dimensional Manifold

It might appear that endpoints or joints within a three-dimensional structure would continue to approach one another to form a four-dimensional joint, creating four-dimensional space. Modeling this requires a four-dimensional manifold containing the three-dimensional "sponge." A four-dimensional joint would be established if the motion upon proximity were perfectly smooth.

However, as previously stated, the existence of exotic differentiable structures in four-dimensional Euclidean space applies to the four-dimensional manifold. In a four-dimensional manifold, a merely continuous deformation (Homeomorphism) does not, in principle, constitute a perfectly smooth deformation (Diffeomorphism). Because endpoints approaching one another solely through their natural attraction constitutes mere continuous deformation rather than perfectly smooth motion, a four-dimensional joint cannot be formed.

Consequently, the physical space of the universe is formed and maintained as a three-dimensional space.






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