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Physics Without Human Units

A plain-language version of “Dimensionless Physics”

4 min readNo jargon, no mathematicsPhysics

The short version

This paper says nature speaks in pure numbers, not in human units like meters or seconds. It shows how to rewrite every law of physics using only ratios, making familiar constants disappear and revealing deeper patterns.

Why human units hide the truth

People invented units like the meter and the second for daily life. These tools are useful for building bridges or cooking meals. But they are arbitrary. The meter once came from the size of Earth. The second came from the length of a day. These choices have nothing to do with how nature actually works.

When physicists write laws using human units, they need conversion factors. These factors are the famous constants: the speed of light, the gravitational constant, and the quantum constant. The paper says these are not truly fundamental. They only appear because we insist on using human-chosen units. They are like needing to convert between miles and kilometers. The conversion is real but not deep.

A theorem that strips away units

A hundred years ago, a thinker named Buckingham proved something powerful. He showed that any true law of nature can be written using only pure numbers. These numbers are ratios. They compare one thing to another thing of the same kind. No units remain. No conversion factors remain.

The paper uses this theorem as its foundation. It says this is not a trick. It is how nature actually is. The universe does not care about meters or kilograms. It cares only about how big one thing is compared to another.

Finding nature's own scale

If human units are arbitrary, what scale should we use? The paper picks a scale that emerges from nature itself. This scale comes from combining three deep features of the world: the speed of light, gravity, and quantum behavior. These three features give us a natural unit of length, mass, and time. These are called Planck units.

The paper says the Planck scale is not a place or a thing. It is an emergent pattern. It arises from a deeper network of wave correlations. Using this scale, every quantity becomes a ratio. A length becomes "how many Planck lengths." A mass becomes "how many Planck masses." These ratios are pure numbers.

Famous laws become simple

The paper rewrites four famous laws in this pure-number form.

In human units, it needs the gravitational constant. In natural units, it becomes simple: force equals mass times mass divided by distance squared. The constant vanishes. It was hiding in the units all along.

In human units, it needs its own constant. The two forces, so different in strength, share one deep shape. The difference in strength comes only from how much charge or mass things carry, compared to the natural scale.

Third, the Schrödinger equation of quantum mechanics. In human units, it needs the quantum constant. In natural units, this constant vanishes too. What remains shows that mass is really a measure of how much a particle resists spreading out.

In natural units, they too shed their constants. The paper says this reveals the true mathematical bones of reality.

A web of pure numbers

The paper goes further. It says all four fundamental forces can be linked through pure numerical relationships. The strengths of these forces, usually treated as separate facts, connect to each other and to other constants. The paper gives formulas for the gravitational constant and the cosmological constant in terms of these deeper links.

The paper also says the shape of the universe may be a special mathematical shape. This shape is finite and connected to itself in complex ways. It is not simply infinite empty space.

Time as a fractal pattern

The paper adds one more idea. Time is not a simple straight line. It has a fractal structure. This means patterns repeat at different scales, like the branching of a tree or the shape of a coastline. The golden ratio, a number famous from art and nature, governs these time patterns.

This fractal time links quantum events, biological rhythms, and cosmic cycles. The paper says heart beats, brain waves, and the turning of galaxies may all echo the same underlying temporal shape.

What this work does not show

The paper is clear about its limits. It does not derive the exact values of the pure numbers from deeper principles. It does not prove its formulas for the constants through experiment. It does not fully explain why the characteristic masses of particles are so small compared to the natural scale. The fractal time idea remains largely theoretical. The shape of the universe as a special mathematical space is suggested but not confirmed by observation.

The paper calls for future work. It wants someone to derive the pure numbers from first principles. It wants experimental tests of the links between forces. It wants the fractal time idea applied to real problems in medicine and engineering. It wants a complete theory of quantum gravity built in this unit-free language.

Words used here

emergent
appearing as a pattern from simpler underlying rules, like wetness emerging from water molecules
fractal
a shape where the same pattern repeats at every scale, like a tree branch that looks like the whole tree
golden ratio
a special number, about one and a half, that appears in growth patterns throughout nature

Learn more in plain language

This plain-language version was written by an AI model from the text of the paper and checked against plain-language rules: everyday words, no mathematics, no unexplained names. It leaves details out and can still be wrong; the paper is the source of record. To report a problem, open the paper, select the passage and choose Report.

For specialists: the technical digest, quoted from the paper

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

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