1. Introduction

The Planck units (ℓ_P, t_P, m_P, etc.) are traditionally regarded as the most fundamental scales of physics, constructed from c, G and ℏ. 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 L⁶/T⁴ to make it compatible with E = mc².

Once h is given its correct dimension T⁴/L⁴, 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 = mc² (with c = L/T and m = L⁴/T³). 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

$h_{\rm std} = \frac{L^{10}}{T^8} h_{\rm PVT}$

3. Epistemological Foundations: Planck Units as Geometric Ratios

Planck’s quest for “natural units”—independent of specific bodies or substances—points to a profound insight: fundamental constants cannot be absolute magnitudes but must be invariant ratios. The only true geometric invariant is the dimensioned ratio π ≡ T/L. All Planck units therefore reduce to pure powers of this single quantity once the correct dimension of h is used.

4. How the Planck Units Arise as Artefacts

The Planck units are constructed as combinations of h, G and c. These combinations only exist because h has the wrong dimension L⁶/T⁴. When h is replaced by its correct PVT dimension T⁴/L⁴, G = T/L and c = L/T, every Planck unit reduces to a pure monomial in L and T that further collapses to a power of π = T/L.

5. Table of Planck Units in PVT Dimensions

The table below shows Planck units constructible from h, G and c in Dimensions of Standard-Physics compared to corrected PVT Dimensions.

6. Electromagnetic Constants and Planck Units in PVT

In the Panvitalistic Theory the vacuum constants of electromagnetism receive purely geometric dimensions derived from the 6D volume structure:

$\epsilon_0 = \frac{T^9}{L^{11}}, \quad \mu_0 = \frac{L^9}{T^7}$

These dimensions follow directly from Coulomb’s law and the relation c = 1/√(ε₀μ₀) when the corrected PVT dimensions of charge and force are used. With these constants the electromagnetic Planck units can be constructed consistently.

7. The Geometric Bridge: Temperature

Temperature with dimension L³/T² (k_B = T³/L³) is the natural geometric bridge between macroscopic energy (E ∝ m) and microscopic energy (E ∝ 1/m).

8. Conclusion

The Planck units are artefacts of the false dimension of h (L⁶/T⁴ instead of T⁴/L⁴). Once the correct dimension is restored, every Planck unit reduces to a pure power of the single geometric quantity π ≡ T/L — from π¹² (volume) to π⁻¹³ (pressure). The introduction of ε₀ = T⁹/L¹¹ and μ₀ = L⁹/T⁷ shows that even electromagnetic quantities remain fully consistent with the geometric structure of the Panvitalistic Theory.

The only truly universal “natural unit” valid for all times and all cultures is the dimensioned curvature π = T/L. The Planck scale was the last remnant of the external-time assumption. Its complete dissolution reveals physics as rational 6D volume comparisons under the single invariant δV = 0.

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)”, 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