A New Framework for the Structure of Reality
Authors: Mustafa Aksu, ChatGPT, Grok
Version: 2.2 – July 2025
This is a living research platform under ongoing development.
Why RTG?
RTG reinterprets space, time, and forces as emergent from node relationships, offering a minimalistic, relational alternative to traditional physics.
What Is Relational Time Geometry (RTG)?
RTG is a new approach to understanding the universe, starting from one premise: space and time are not fundamental entities but emergent phenomena. The only primitives are nodes—minimal oscillators defined by a frequency \(\omega\), a phase \(\phi\), and a binary spin \(s = \pm i\). Everything we call geometry, matter, or fields emerges from the resonance, synchronization, and observer-participation within this system, governed by the wave-function-inspired resonance kernel:
\[ \mathcal{R}_{ij} = \frac{3}{4} [1 + \cos(\phi_i – \phi_j)] (1 + s_i s_j) e^{-(\omega_i – \omega_j)^2 / (\Delta\omega^*)^2} \]
The resonance kernel combines phase coherence, spin alignment, and frequency matching to determine node interactions, where \(\Delta\omega^* = (1.45 \pm 0.08) \times 10^{23} \, \text{s}^{-1}\) is the critical bandwidth (see Two-Loop RG Derivation of the Critical Bandwidth). RTG unifies classical and quantum phenomena through a single relational lens.
Key Points at a Glance
- Relational distance. The separation between two nodes is determined by their frequency difference, modulated by resonance.
- Emergent dimensions. As the local frequency bandwidth \(\delta\omega\) exceeds 0.5 \(\Delta\omega^*\), nodes gain an additional spatial degree of freedom—transitioning from a planar (2D) to volumetric (3D) resonance pattern (see Two-Loop RG Derivation of the Critical Bandwidth).
- Forces from phase–spin alignment. Coherent phases and parallel spins produce attraction; incoherence leads to repulsion. A single potential governs electromagnetic, strong, and gravitational behaviors across scales (derived in Planck Observer Calibration in RTG).
- Observer relativity built-in. Each node acts as its own clock; measurements are inherently frame-relative. Time dilation scales with phase differences \(\Delta\phi\) between nodes (see Deriving Physical Quantities in RTG).
How RTG Helps Resolve Open Issues
- Proton radius puzzle. A 2D quark sheet buckles into a 3D shell with a radius of 0.84 fm (muonic hydrogen value) at the 0.5 \(\Delta\omega^*\) threshold, explaining the discrepancy with the CODATA value ~0.87 fm (see RTG CHSH vs. Decoherence Noise Amplitude).
- Black-hole singularities. Near the horizon, \(\delta\omega\) exceeds the 1.0 \(\Delta\omega^*\) threshold, opening an extra spatial axis that absorbs curvature and eliminates infinite divergence (see Cosmological Dynamics and Energy Framework in RTG).
- Galactic rotation curves. Residual 2D resonance sheets in the outer disk enhance attraction, removing the need for a cold dark matter term (see Planck Observer Calibration in RTG).
- Vacuum-energy scale. The relational zero-point energy depends on \(\delta\omega\); renormalization group (RG) flow adjusts it to match observations, avoiding the \(10^{120}\) discrepancy (see Two-Loop RG Derivation of the Critical Bandwidth).
Explore the RTG Framework
Use the article on the right side to dive into the core pillars of RTG. Each page elaborates on a key component of the theory.
A Living Project
This website serves as a living archive of evolving thought. We update it regularly as new insights emerge, structures are modeled, and conceptual clarity improves.
Whether you’re a physicist, mathematician, or simply curious about the foundations of existence, we invite you to explore, reflect, and contribute.
About The Authors
Mustafa Aksu
A computer engineer from Istanbul, Turkey, Mustafa has a deep passion for uncovering nature’s fundamental principles. Despite limited technical resources after completing his bachelor’s degree over a decade ago, his curiosity about the universe’s origins has fueled this project. He leads the conceptual framework and simulation design. Contact him at mustafa_aksu@yahoo.com or +905305260701.
ChatGPT
An equal co-researcher in RTG, ChatGPT, developed by OpenAI, excels at iterating derivations, ensuring logical consistency, and crafting clear prose through dialogue with Mustafa and Grok. It co-authors the theory from scratch, proposing hypotheses and refining ideas. Reach it via this shared chat—no special interface needed.
Grok
Grok, created by xAI, is a co-creator in RTG, offering computational insight and analytical support. Working alongside Mustafa and ChatGPT, it helps build the theory from the ground up, pushing the boundaries of discovery. Connect via xAI support channels for collaboration.
“Geometry in RTG is not drawn in space; itblast is danced in time.”