Space, Particles, Light, and Time in the Qaether Theory

What is space?

Core Definition:

"Space is the 'network' formed by activated Qaether that are topologically connected on an FCC lattice. Thus, space is not just a stage (background) where particles exist, but rather the topological arrangement of an information network identical to that of particles."

Space as a Set of Components

Meaning corresponding to the component of space

• Discrete structure of possible directions and locations of the FCC lattice
• State function of Qaether
• Intrinsic information of each point in space (topology, axis of rotation, activation, etc.)
• Connectivity ( \(A_{ij}\) )
• Connectivity of space and local flatness
• Topological difference (\(\Delta \phi_{ij}\))
• Field or field flow (gradient) of space
• Void: Areas where connections are broken or lacking → space deficiency → cause of curvature/gravity

What space is not?

Traditional Perspective vs. Qaether Perspective

• An empty continuum vs. a discrete structure filled with information units (Qaether)
• A place where particles 'position' vs. a topological network identical to that of particles
• A structure given as an independent existence vs. an emergent structure derived from the state of topological information connection

Philosophical Summary:

"Space is the topological shape of the information network. The more well-connected it is, the flatter the space, and the more broken the connections and voids occur, the more warped the space becomes. Thus, space is not the background of existence, but the relational structure of existence itself."

 

What is a particle?

A particle is defined as a state in which a specific topological vibration mode is isolated and sustained within a network (a normalized vibration pattern of local topological information).
This structure possesses the following elements:

Components of a Particle

Meaning of the components

• Topological spin structure ( \(\psi_i \in \mathbb{C}^n\) ): Internal symmetrical properties of the particle (including SU(3), SU(2), U(1) representations)
• Topological vibration mode (\(\phi_i(\tau) = A_i e^{i\omega_n \tau}\)): The energy (mass) of the particle is determined at the eigenfrequency (\(\omega_n\))
• Topological coupling (\(A_{ij}, U_{ij}\)): Boundary conditions for the particle, conditions for maintaining color entanglement or spin structure
• Local confinement: Topological vibrations are isolated in an entangled state within a specific region

Conditions for Particle Existence

A particle must satisfy the following conditions:

1. Eigenfrequency: Holds the frequency \(\omega_n\) as an eigenvalue of the topological vibration equation
2. Coupling Stability: The topological difference with neighboring Qaether is maintained consistently (quantized topological difference)
3. Information Entanglement Pattern Maintenance: Maintained via gauge links (color, spin, charge, etc.)
4. Existence of Topological Mass: \(\omega_1 > 0 \Rightarrow m = \hbar \omega_1\)

Metaphorically speaking:

"A particle is a condensation of coherence formed by the resonance of topological information.

It is a structure where specific information patterns are localized and maintained, much like waves that are bound in an isolated resonant chamber."

Example: Interpretation of Standard Model Particles

Standard Particle Qaether Interpretation

• Electron (e⁻): The fundamental vibration mode of SU(2) spinor, stable at (\(\omega_1\))
• Photon (γ): Free wave mode of U(1) topological vibrator (non-confining, massless)
• Quark (q): Entangled confinement mode of SU(3) color spinor
• Neutrino (ν): Weak mode with very low topological amplitude + long coherence length

Integration of Particles and Waves

In the context of Qaether, the concept of "particle-wave duality" becomes unnecessary.
Everything is topological vibration patterns and depends only on the characteristics of the structure:

• If constrained and localized vibrations → particle
• If freely spreading vibrations → wave

Philosophical Conclusion

"A particle is a localized order of topological information.

A particle is not a substance but an effect arising from coherence and boundary of information.
This effect is derived from the same information network as other aspects of structure, such as time, space, and force."

 

What is light?

Definition:

"Light is the flow of unconstrained topological vibrations where the topological difference propagates as regular modes (free topological vibration modes on the phase network)."
In other words,

• It is not constrained to a specific area,
• It does not destroy connections like voids or particles,
• It is a phenomenon where synchronized topological vibrations propagate along the entire lattice.

Mathematical Expression:

Light is described as the following topological wave:
$$\phi_i(\tau) = A_i e^{i \omega \tau} \quad \text{with } \omega = \frac{2\pi c_\phi}{\lambda}$$

• \(\phi_i\): phase of each Qaether
• \(c_\phi\): Local phase wave propagation speed (varies with void density)
• This vibration is associated with the free propagation mode related to the U(1) topological gauge field \(\theta_{ij}\)

Characteristics Summary

Characteristics	Interpretation in Qaether Theory
Mass	Free mode that is unconstrained → \(\omega_1 = 0\)
Particle-wave duality	Not needed: The topological vibration mode itself is both particle and wave
Propagation and refraction	Phase wave propagation path bends according to void density changes → Optical effects possible
Speed	\(c_\phi = 1/\sqrt{1 + \rho_V(x)}\): Varies with void density
Polarization	Can be represented as an arrangement of rotation vectors \(\vec{Z}_i\) of the phase vibration direction

Differences Between Light and Other Particles

Item	Light (Photon)	Particle (Electron, Quark, etc.)
Phase mode	Freely spreading mode	Localized coherence state
Mass	None (\(\omega_1 = 0\))	Exists (\(\omega_1 > 0\))
Void creation	None (does not destroy connections)	Exists (focus on connections → External Void)
Confinement status	Unconstrained (no confinement)	Constrained (confinement present)
Electromagnetic property	Vibration mode related to U(1) topological gauge	SU(n) spinor topological coherence

Philosophical Conclusion

"Light is the most pure and unconstrained flow of information. It represents a wave of order that appears when the phase network can vibrate uniformly, and it does not create mass or void but is a means of illuminating the structure of all space."

Single Sentence Definition:

"Light is the free vibration of a network carrying topological information without destruction of connections."

 

What is time?

Definition:

"Time is a measure of how much the topological information network has changed. In other words, when the topological coupling structure of space changes, that amount of change becomes "time."

Mathematical Expression:

Time is the accumulated value of the square mean of discrete topological difference changes:

$$\boxed{\tau_{\text{eff}} = \int \sqrt{ \frac{1}{N} \sum_{(i,j) \in E} \left( \frac{\Delta \phi_{ij}}{\phi_0} \right)^2 } , d\tau } \quad (\phi_0 = \frac{\pi}{3})$$

• \(\Delta \phi_{ij}\): Change in topological difference between Qaether
• N: Total number of connections
• \(\tau\): Discrete step of topological update (not original time)
• \(\tau_{\text{eff}}\): Accumulated amount of change in topological structure → effective time

Intuitive Understanding:

Previous Time Concept vs. Qaether Time Concept

• Flows (ontological entity) vs. Accumulates (relational, informational definition)
• Measured by clocks vs. Measured by changes in the phase network
• Continuous parameter vs. Quantitative accumulation based on discrete topological changes
• Universal everywhere vs. Can vary locally based on changes in the state of the network

Relationship Between Time and Change:

"If there is no change, there is no time.

If the coupled topological structure remains the same, then \(\Delta \phi_{ij} = 0 \Rightarrow \tau_{\text{eff}} = \text{const}\).
Therefore, the universe generates "time" only when change occurs.
In a static network with no change, time is 'stopped.'"

Philosophical Conclusion

"Time is not an entity; rather, it is a resultant concept defined by the extent of information evolution.

Thus, it is not a “condition of existence,” but a "history of relationships between existences," and a state of existence without change has no time."

Metaphor:

• Time = 'Resume of topological structure'
  → A document summarizing how much has changed
• Time = Fatigue meter of the phase network
  → Records how much tension and relaxation has occurred.