Dimensionless Physics

In the paper's words

This work presents dimensionless physics as the fundamental language of nature, demonstrating how all physical laws can be expressed as relationships between pure dimensionless ratios rather than anthropocentric units. Building upon the Buckingham Pi Theorem, this document shows that dimensional constants such as G, c, and ħ are not fundamental but emerge from a deeper causal network of wave correlations. When equations are expressed in dimensionless form, these constants vanish, revealing the true mathematical structure of physical reality as pure relationships between dimensionless ratios.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Calculations in quantum field theory predict that the vacuum energy should be on the order of the Planck density, which would correspond to $\Lambda ' \approx 1$, about 122 orders of magnitude larger than the observed value (Weinberg, 1972).

   from 5.3.2 Physical Meaning

2. This is derived from the dimensionless relationships between the density parameters of baryonic matter, dark matter, and dark energy: $\Omega B$ = e ⁻π ≈ $4.32\%, \Omega D = 2$· e ¹⁻π ≈ 23.49%, and $\Omega \Lambda = 2$· e ⁻¹ ≈ 73.57%.

   from 6.6

3. This relationship connects the constant to the golden angle, $\theta g$ ≈ 137.5°, which derives from the golden ratio (Heyrovska, 2005).

   from 7.2 The Pellis Function

4. Quantization and Fractal Time The Temporal Quantization in the Unified Fractal Theory of Time demonstrates that time itself is not linear but fractal, governed by the golden ratio $\phi$ and Fibonacci structures (Pellis, 2025).

   from 8.3 Temporal

5. The Temporal Quantization in the Unified Fractal Theory of Time demonstrates that time itself is not linear but fractal, governed by the golden ratio $\phi$ and Fibonacci structures (Pellis, 2025).

   from 9.0 Conclusion

How it is done

1. Building upon the Buckingham Pi Theorem, this document shows that dimensional constants such as G , c , and ħ are not fundamental but emerge from a deeper causal network of wave correlations.

   from Dimensionless

2. The mathematical framework that formalizes this concept is the Buckingham $\pi$ theorem, which proves that any physically meaningful relationship can be expressed entirely in terms of dimensionless ratios, independent of any specific, arbitrarily chosen system of units (Buckingham, 1914).

   from 1.0 Introduction

3. The Mathematical Foundation: Buckingham Pi Theorem and Dimensional Analysis

   from 2.0

4. Buckingham Pi Theorem: Formalizing Scale Invariance The Buckingham $\pi$ theorem provides the formal mathematical basis for recasting physical laws into a dimensionless form.

   from 2.2 The

What would falsify it

1. The Buckingham $\pi$ theorem predicts n - k = 2 dimensionless parameters.

   from 2.2.2 Significance and

2. Therefore, ( n F - k F) = 0, meaning their existence does not further reduce the number of dimensionless parameters beyond what the standard theorem predicts.

   from 2.2.2 Significance and

3. Calculations in quantum field theory predict that the vacuum energy should be on the order of the Planck density, which would correspond to $\Lambda ' \approx 1$, about 122 orders of magnitude larger than the observed value (Weinberg, 1972).

   from 5.3.2 Physical Meaning

Where the claim stops

1. This principle, known as dimensional homogeneity, asserts that meaningful physical laws cannot equate disparate concepts like mass and time; they must compare like with like.

   from 1.0 Introduction

2. These constants, however, are not fundamental but emerge from a deeper causal network of wave correlations.

   from 1.0 Introduction

3. In an anthropocentric system of units such as the International System of Units, G has an experimentally determined value of approximately $6.674 \times 10^{-11} m^{3} kg^{-1} s^{-2}$.

   from 2.1

Where to read

1. Dimensionless202 words · 1 min
2. 1.0 Introduction387 words · 2 min
3. 2.01,064 words · 5 min
4. 3.0 Defining a1,224 words · 5 min
5. 4.01,041 words · 5 min
6. 5.0 The Universe’s Intrinsic841 words · 4 min
7. 6.0 Dimensionless Theory of593 words · 3 min
8. 7.0524 words · 2 min
9. 8.0519 words · 2 min
10. 9.0 Conclusion307 words · 1 min