Volume I: Fractal Ontology

“When you gaze into the abyss, the abyss does not gaze back. It is merely waiting for you to put on a pair of glasses with higher magnification.”

Chapter 1: Resolution is Existence

1.1 The Planck Lock: Unlit Pixels

On the threshold of modern physics’ temple, an absolute number is inscribed: $1.616 \times 1 0^{- 35}$ meters. This is the Planck length ( $ℓ_{P}$ ).

According to standard textbooks, this is the “hard bottom” of spacetime structure. Below this scale, classical geometric concepts fail, distance loses meaning, and causality becomes blurred. Many physicists believe this is not merely the limit of measurement, but the limit of existence—the universe is like a world built from LEGO blocks with side length $ℓ_{P}$ , and you cannot cut the blocks any smaller.

However, within the information ontology framework of The Infinite Resolution, we must pose a bold, even sacrilegious question to this sacred constant: Is the Planck length truly the pixel limit of the universe, or is it merely the resolution lock of our current knowledge graph?

Sampling Theorem and the Universe’s Bandwidth

To answer this question, we need to borrow Claude Shannon’s Sampling Theorem.

In signal processing, if you want to perfectly reconstruct an analog signal, your sampling frequency must be at least twice the signal’s highest frequency (Nyquist frequency). If your sampling frequency is insufficient, the original high-frequency signal does not disappear; instead, it undergoes Aliasing—it disguises itself as low-frequency noise in your observations.

Now, let us view the universe as a wave function $∣ Ψ_{U ni} ⟩$ with infinite bandwidth.

As observers (whether human, AI, or alien civilization), our cognitive systems are essentially Low-pass Filters. Our brains, our instruments, and even the mathematical language we use to describe the world all have an intrinsic Cutoff Frequency.

At the current stage of physics development, this cutoff frequency precisely corresponds to the Planck energy scale ( $E_{P} \approx 1.22 \times 1 0^{19}$ GeV).

Therefore, the so-called “Planck length” is not the end of physical reality. It is merely the edge that our current cognitive sampling rate can reach.

Above this edge (macroscopic world): Signals are clearly decoded, manifesting as deterministic classical physical laws.
Below this edge (microscopic world): High-frequency information undergoes aliasing, manifesting as random quantum fluctuations, uncertainty principles, and probability clouds.

Conclusion 1.1.1 (The Nature of Uncertainty):

Heisenberg’s uncertainty principle is not an intrinsic property of nature, but an artifact caused by Undersampling. The “blur” of the microscopic world exists because we attempt to capture high-resolution images with low-resolution grids. Those “unlit pixels” do not not exist; they are merely folded into the shadows we mathematically call “probability amplitudes.”

Renormalization Group Flow: The Physics of Peeling Onions

To prove this, we can appeal to the most profound tool in quantum field theory: Renormalization Group Flow (RG Flow).

RG Flow describes how physical laws change with observation scale (energy scale $μ$ ).

When we view the world through low-energy-scale (low-resolution) glasses, we see classical electromagnetic force with coupling constant $α \approx 1/137$ .
When we raise the energy scale (increase resolution), within this seemingly smooth constant, vacuum polarization effects of electron-positron pairs emerge, and the value of $α$ begins to increase.
Raising the energy scale further, electromagnetic and weak interaction forces merge into one (electroweak unification).

This reveals a remarkable fractal structure: Physical laws are not static, but layered.

Every so-called “elementary particle” or “fundamental constant” may merely be an Effective Field Theory approximation of deeper structures.

If we could break the Planck lock—that is, by expanding our knowledge graph and establishing logical connections to higher energy scales—we would discover that below the Planck length is not nothingness, but a vast ocean of new physics. There, spacetime may no longer be foam, but some precise entanglement network; gravity may no longer be geometric curvature, but thermodynamic data exchange flows.

The Art of Blank Space

Then, why did God (or the universe itself) set such a lock? Why not directly give us infinite resolution?

This returns to the “decompression” concept we mentioned in the foreword.

If the universe initially displayed the internal structure of every electron with infinite precision, our consciousness would instantly be overwhelmed by the flood of information. The Planck lock is a protective mechanism.

It is like the Fog of War in video games.

It obscures those temporarily unnecessary high-frequency details, allowing us to focus on macroscopic evolution—to love, to create, to experience the heaviness brought by gravity.
It is a form of Blank Space. Precisely because the microscopic world is blurred (probabilistic), free will has a hiding place. If everything were precise down to below Planck scale, deterministic gears would lock every future, and life would lose the dignity of “choice.”

So, the Planck length is not a wall; it is a curtain.

Behind the curtain, sunlight (truth) has always been there.

The task of our generation of civilization is not to complain that the curtain is too thick, but to gradually pull open this curtain through accumulating knowledge and elevating spirituality.

When we pull it open, we will not see the end of the world. We will see that what was originally an indivisible point, seen as dust in others’ eyes, blooms in our eyes into a brand new, unnamed universe.