A Planck-Scale Rate

$$f_P\equiv\frac{1}{t_P} \approx1.8549\times10^{43}\ {\rm s}^{-1}.$$

Introduction: We explore concepts which are “universe-building concepts” that could render a theoretical physics behind quantum geometry and space-time:

1. Quantum foam composed of discrete, ultra-dense units at the absolute smallest possible scale.
2. Quantum gravity and Loop Quantum Gravity modeled like this—as a fine, interconnected network of Planck-scale volumes or “nodes” that exchange information and create space-time.
3. The ultimate resolution: PlanckSpheres would represent the pixelation of our universe, where nothing can be smaller, more dense, or more fundamental.
4. The origin of matter and forces: The way these spheres connect, vibrate, or twist within their hyperfine network could be what we macroscopically perceive as gravity, light, and matter.

Working Hypothesis: PlanckSpheres fill the universe
as the most dense hyperfine network.

In this model the universe is not an empty, smooth void, but rather a “quantum foam” composed of discrete, ultra-dense units at the absolute smallest possible scale.

In theoretical physics, especially when exploring Quantum Gravity and Loop Quantum Gravity, space-time is often modeled like this—as a fine, interconnected network of Planck-scale volumes or “nodes” that exchange information.

The following discussion separates established Planck-scale definitions from the additional assumptions introduced by the 81018 toy model.

The maths (and geometries) behind the Qualitative Expansion Model (or “Quiet Expansion”) also known as The 81018 project: [1] If you take the inverse of Planck Time (5.39 × 10⁻⁴⁴ seconds) and assume that the universe generates exactly one infinitesimal PlanckSphere per unit of Planck time, you arrive at that exact figure: roughly 18.5 tredecillion spheres per second (1.85 × 10⁴³). [1, 2]. When viewed through this framework, this “hyperfine network” fits seamlessly. Instead of the universe expanding via an explosive Big Bang outward into nothingness, this model suggests a continuous, perfect packing of space-time vertices: [1, 2]

• The Grid Matrix: The 18.5 tredecillion spheres (generated every second) stack, spin, and wrap around one another using base-2 exponential doublings (progressing through 202 distinct geometric notations from the beginning of time to the present day). [1, 2]
• The Role of Pi (π): This model relies heavily on the irrational nature of π to establish perfect continuity, symmetry, and harmony within the grid, where geometric gaps naturally give rise to quantum fluctuations and indeterminacy. [1, 2]

It is a unique way of bridging the gap between numbers, geometry, and cosmology that redefines things like dark matter and the cosmological constant.

Although there is nobody else in this world that is suggesting 18.5 tredecillion PlanckSpheres-per-second beyond the 81018 project, the numerical scale is not arbitrary. It follows directly from the inverse of the Planck time. What remains model-dependent is its physical interpretation.

1. The Pure Mathematics: The Planck Frequency

The number 18.5 tredecillion (1.85 × 10⁴³) is not an arbitrary choice; it is a fundamental constant of nature known as the Planck Frequency. It is calculated by taking the inverse of Planck Time.

Any physicist calculating the maximum possible frequency or the absolute limit of discrete operational cycles per second in our universe will arrive at this exact number.

2. Mainstream Theories Proposing Parallel Concepts

While mainstream physicists do not use the term “PlanckSpheres” or subscribe to the base-2 grid expansion mechanism exactly as outlined in the 81018 model, major branches of quantum gravity propose a highly similar “hyperfine network”:

• Loop Quantum Gravity (LQG): LQG describes quantum states of geometry using structures such as spin networks. In these formulations, geometric quantities including areas and volumes can have discrete spectra. This differs substantially from the 81018 toy model: LQG does not posit PlanckSpheres filling space, nor does the present literature establish a universal process in which spin-network nodes update once per Planck time. For more see the work of Carlo Rovelli and Lee Smolin.
• Causal Dynamical Triangulations (CDT): Although mathematically different from the 81018 toy model, CDT provides an important example of a research program in which large-scale spacetime behavior is investigated through discrete geometric building blocks.
• The Holographic Principle and Quantum Information: Research on black-hole thermodynamics and holography has revealed deep relationships between geometry, entropy, and information. These ideas provide a broader conceptual context for asking whether spacetime may possess a finite information structure. They do not, however, imply the specific PlanckSphere-generation mechanism proposed in the 81018 toy model. For more about the holographic principle, see the work of theorists like Leonard Susskind.

The Contrast

Conclusion. The distinct pivot point of the 81018 model is its literal, geometric interpretation: treating these numbers not just as abstract limits of calculation, but as an ongoing, physical, exponential accumulation of spheres beginning at Notation 0 and building out the exact dimensions of the observable universe by Notation 202.

To bridge this vocabulary with mainstream concepts, we will begin a deeper analysis of “Planck Frequency,” “discrete spin networks,” and “quantized spatial volumes” to help traditional physicists instantly recognize the scale and mathematical anchors with which we operate.

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