I. The Definition of the Planck Scale is an Artificial Combination

The "Planck scale" is a dimensional combination constructed from three constants—gravitational constant (G), Planck constant (ℏ), and speed of light (c):

Planck length:l_P = sqrt(ℏG/c³) ≈ 1.6×10^-35 meters

Planck time:t_P = l_P/c

Planck mass:m_P = sqrt(ℏc/G)

These three quantities are called natural units, often interpreted as "the limit where spacetime fails" or "the scale where gravitational and quantum effects are equally significant."

However, this is merely a dimensional splicing, not derived from any physical process. It is an "algebraic product of constants" rather than a "natural physical limit."

In other words, the Planck scale is not obtained through observation but calculated through mathematical manipulation.

Any "limit scale" without a verifiable mechanism can only be a symbolic speculation.

II. The "Significance" of the Planck Scale Stems from Erroneous Presuppositions

It assumes point particles + local gravity + infinitely divisible spacetime.

The combination of quantum gravity and general relativity is believed to "break down" at this scale because:

• Treating matter as point particles leads to the divergence of gravitational self-energy;

• Assuming spacetime is continuously divisible, meaning infinite magnification remains meaningful;

• Regarding the gravitational field as a quantized object of spacetime geometry.

These three assumptions together construct a logical singularity:When energy is concentrated into an extremely small point, gravity causes it to collapse into a black hole—thus the "Planck scale" is defined as the boundary where "collapse balances quantum fluctuations."

But if particles are not points but possess a real spatial structure on the Compton wavelength scale:

• Energy density is finite;

• Spacetime does not require "quantization";

• There is no so-called "Planck limit."

Therefore, the Planck scale is merely a product of wrong premises, not a fundamental natural scale.

III. The Compton Scale is the Real Microscopic Limit

All observable particles in nature have a Compton wavelength:λ_C = h/(mc)

It reflects the spatial resolution limit of wave-particle unification:If one attempts to confine a particle to a region smaller than λ_C, the system's energy will trigger particle-antiparticle pair production.

Thus, λ_C is the verifiable, physical lower limit scale in nature.

The Planck length is 20 orders of magnitude smaller than the electron's Compton wavelength—No experiment, theoretical structure, or mathematical solution indicates that nature will "reach" that scale.

This shows that the Planck length corresponds not to a "limit" but to a "meaningless interval."

IV. The Philosophical Origin of the Planck Scale: Misguidance of Mathematical Formalism

The belief in "the existence of the Planck scale" is essentially a misinterpretation of physical reality by mathematical formalism.

It assumes:Mathematical relationships apply equally across all dimensions.

In contrast, Natural Quantum Theory holds:Mathematical relationships are only approximate descriptions, and physical structures at different levels do not need infinite extension.

The Planck scale confuses continuous mathematics with the infinite divisibility of real structures, and treats the dimensional extension of models as the existence of natural levels.

This is precisely a symptom of modern physics falling into "formalism replacing reality."

V. Conclusion: The Planck Scale is a Formal Limit, Not a Physical Limit

Concept	Origin	Physical Verifiability	Meaning
Compton Scale	Experimentally measurable wave-particle boundary	✅ Verifiable	Physical lower limit of the wave structure of particles
Planck Scale	Mathematical dimensional combination	❌ Unverifiable	Formal boundary where the model fails

Therefore, the Planck scale is not the "minimum length" of nature but the boundary of the point particle model and dimensional games.

Within the framework of Realistic Quantum Theory (or Natural Quantum Theory), the fundamental scale of nature is not the fictional "limit" of 10^-35 meters,but the Compton level around 10^-12 meters—where quantization truly occurs.

In short:The Planck scale is not a secret of nature but an illusion of mathematics.Only the Compton scale is a real trace left by nature.

Would you like me to further polish the academic rigor of this translation, such as adjusting the wording of key theoretical terms or optimizing the logical connection of sentences?