1. Introduction

The Planck units ($\ell_P$, $t_P$, $m_P$, etc.) are traditionally regarded as the most fundamental scales of physics, constructed from $c$, $G$ and $\hbar$. They appear to mark the boundary between classical and quantum gravity.

In the Panvitalistic Theory (PVT) this boundary is revealed as an artefact. They exist only because standard physics uses the wrong dimension for Planck’s constant h. The equation $E = hf$ was set up assuming an external, one-dimensional time. This forces h to have dimension $L^6/T^4$ to make it compatible with $E = mc^2$.

Once h is given its correct dimension $T^4/L^4$, the entire Planck scale dissolves and the path to the 12D volume comparison of PVT opens.

2. The Wrong Dimension of h and Its Consequences

In standard physics Planck’s constant has dimension

$h_{\rm std} = \frac{L^6}{T^4}$

This dimension was chosen so that $E = hf$ (with $f = 1/T$) has the same dimension as $E = mc^2$ (with $c = L/T$ and $m = L^4/T^3$). The assumption of an external, independent time parameter t forces this artificial dimension.

In PVT time is internal angular curvature, so the correct Planck constant is

$h_{\rm PVT} = \frac{T^4}{L^4}$

The relation between the two is

$h_{\rm std} = \frac{L^2}{h_{\rm PVT}}$

The extra factor $L^2$ is the projection correction caused by the external-time assumption.

3. Epistemological Foundations: Planck Units as Geometric Ratios

Planck’s quest for “natural units” — independent of specific bodies or substances — implicitly points to a profound insight: fundamental constants cannot be absolute magnitudes but must be invariant ratios.

Max Planck wrote in 1900 in “On irreversible radiation processes”: “Conversely, it might be of some interest to note that […] the possibility exists to establish units […] which, independent of specific bodies or substances, necessarily retain their meaning for all times and for all, including extraterrestrial and non-human cultures, and which can therefore be described as ‘natural units of measurement’.”

As Planck noted, such units “retain their meaning for all times and for all, including extraterrestrial and non-human cultures”. This epistemological stance demands that physics reduces to relations devoid of arbitrary scales, leaving only geometric invariants as candidates.

Consider the logic: Any measurement is a comparison, requiring a reference unit. If constants like c, G, and h are to be truly universal, their absolute sizes are unmeasurable — only their ratios can be invariant. For example, the ratio Sun diameter / Earth diameter ≈ 109 is constant over time, as repeated measurements confirm. Extending this to natural units eliminates all real objects (e.g., Earth as meter base), forcing a reliance on pure relations.

What relations remain? Arithmetic ratios (e.g., 1:1) are trivial and non-descriptive. Geometry provides the only consistent framework: ratios like circumference / radius = 2π, area / radius² = π, volume / radius³ = 4/3π. These involve length, area, and volume — the building blocks of any dimensional system.

Planck units embody this: $\ell_P = \sqrt{\hbar G / c^3}$ (length), $t_P = \sqrt{\hbar G / c^5}$ (time), $m_P = \sqrt{\hbar c / G}$ (mass). Stripped of specifics, they express invariants involving L, L², L³ — geometric scales.

The sole geometric constant is $\pi$ (curvature ratio), dimensioned as $T/L$ in PVT. Thus, h must align with this: Standard h = ML²/T assumes external time, forcing artificial compatibility (e.g., $E = hf = mc^2$). PVT corrects to $h = T^4/L^4 \sim T/M$ (since $M = L^4/T^3$), making h the “time per inverse mass” — a natural inverse to geometric density.

This derivation from first principles — measurement as ratio, universality as geometry — confirms $h = T/M$ as the logical dimension. Alternatives fail: Without geometry, no invariants beyond triviality. Planck units, epistemologically, demand this reinterpretation, resolving their artificiality as projections of rational volumes.

4. How the Planck Units Arise as Artefacts

The Planck units are constructed as

$\ell_P = \sqrt{\frac{\hbar G}{c^3}}, \quad t_P = \sqrt{\frac{\hbar G}{c^5}}, \quad m_P = \sqrt{\frac{\hbar c}{G}}$, etc.

These combinations only exist because h has the wrong dimension $L^6/T^4$. They are the mathematical device that makes $E = hf$ and $E = mc^2$ dimensionally compatible under the external-time assumption.

When we replace h with its correct PVT dimension $T^4/L^4$ and use the standard linear velocity $c_{\rm std} = L/T$ and $G = T/L$, every Planck unit reduces to a pure geometric quantity.

5. Table of Planck Units in Standard Physics and PVT

In standard physics we set $G = 1$, $c = 1$, $\hbar = 1$. In PVT we set $G = 1$ (T/L), $c = 1$ (L/T), $h = 1$ (T⁴/L⁴) with $\pi = T/L$.

6. The Geometric Bridge: Temperature

Temperature is the natural bridge between $E \propto m$ and $E \propto 1/m$. With $k_B = T^3/L^3$, temperature has dimension $L^3/T^2$ and unifies the two energy forms geometrically.

7. Conclusion

The Planck units are artefacts of the false dimension of h ($L^6/T^4$ instead of $T^4/L^4$). They exist only to make $E = hf$ and $E = mc^2$ dimensionally compatible under the assumption of external time. When h is given its correct dimension, the entire Planck scale reduces to pure powers of the single geometric quantity $\pi = T/L$. This reduction is the direct mathematical pathway to the 12D volume comparison of PVT.

This shows that the apparent fundamental status of the Planck scale is an illusion created by an inconsistent unit system based on external time.

With the correction of the Planck’s Constant in PVT, the “natural” unit that can be found for all times and all humans as well as all extraterrestrial and non-human cultures is only “dimensioned” “π”, which represents $T/L$ (curvature/length). The Planck scale was the last bastion of the external-time assumption. Removing it reveals the true rational 12D geometry of PVT, where all scales dissolve into pure volume comparisons.

References

[1] Max Planck: Ueber irreversible Strahlungsvorgänge, Annalen der Physik 1 (1900) 69–122, S. 121; doi:10.1002/andp.19003060105

[2] M. U. E. Pohl. Experimental Confirmation of PVT in 5 Minutes: Schwarzschild(radius) to go 2026. https://doi.org/10.5281/zenodo.18834011

[3] M. U. E. Pohl. PVT Spacetime Definition: A Rigorous Mathematical Derivation of 12-Dimensional Spacetime 2026. https://doi.org/10.5281/zenodo.18833891

[4] M. U. E. Pohl. Mass, Charge and Electric Current as Purely Geometric Projections in the Panvitalistic Theory (PVT) 2026. https://doi.org/10.5281/zenodo.18841669

[5] M. U. E. Pohl. Quantization and Singularities in the Macrocosm: Insights from the Panvitalistic Theory (PVT) 2026. https://doi.org/10.5281/zenodo.18841750

[6] M. U. E. Pohl. Deriving the Canonical Wheeler-DeWitt Equation from the Axioms of the Panvitalistic Theory (PVT): A Discussion of the ADM Formalism in PVT 2026. https://doi.org/10.5281/zenodo.18841981

[7] M. U. E. Pohl. Timeless Maxwell Equations as Geometric Volume Balances in the Panvitalistic Theory (PVT) 2026. https://doi.org/10.5281/zenodo.18847562

[8] M. U. E. Pohl. Constraint-Based Dynamics in the Panvitalistic Theory: Replacing the Lagrangian with Volume Invariance 2026. https://doi.org/10.5281/zenodo.18847756

[9] M. U. E. Pohl. Table: Physical Quantities in 12D Panvitalistic Spacetime 2026. https://doi.org/10.5281/zenodo.18882163