Formulas and Calculations

v1.4 June 2026 Author: Marco Gipp

This document presents the mathematical formulas of the Law of Equalization and demonstrates their application through concrete examples.

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1. The Intrinsic Energy Formula

Basic Formula

$$E=\rho \cdot V\cdot S\cdot k$$

Variable	Meaning	Unit
$E$	Intrinsic energy	MarKOn (MKn)
$\rho$	Density of matter	kg/m³
$V$	Volume of matter	m³
$S$	Stability factor (binding strength of the structure)	dimensionless, 0–1
$k$	Material capacity (energy capacity of the substance per mass)	MKn/kg

The Energy Unit: MarKOn (MKn)

In the Law of Equalization, intrinsic energy is measured in MarKOns (MKn) — the Law of Equalization's own energy unit. Like the joule, the electronvolt or the calorie, this is an energy unit; the Law of Equalization measures energy in its own.

Dimensional check: $[\rho \cdot V]=\text{kg}$, $[S]=1$, $[k]=\text{MKn/kg}$, therefore $[E]=\text{MKn}$. The formula is dimensionally consistent.

Alternative Formulation (via mass)

Since $\rho =m/V$ and $V$ cancels out:

$$E=m\cdot S\cdot k$$

What the Formula Describes

Intrinsic energy is NOT equal to mass. The formula accounts for: density (storage capacity per volume), volume (spatial extension), stability (molecular binding energy), material capacity (specific material properties).

Why this formula describes the cause instead of the symptom: Unlike $E=m{c}^2$, energy here is not derived from mass — in the Law of Equalization it is the other way round. Energy is the primary quantity; mass is not its building block, but its resistance — a relational value that only arises when two systems are compared. Intrinsic energy follows from the properties of matter itself — density, volume, structure ($S$) and material capacity ($k$) — not from mass.

The decisive point lies in the factor $S\cdot k$. In Einstein's $E=m\cdot c^2$, $c^2$ carries the unit J/kg (= m²/s²) — a universal energy-per-mass constant, the same for the entire universe. In the Law of Equalization, $S\cdot k$ carries the same physical dimension (energy per mass), but is material-specific instead of universal. Einstein takes a fixed conversion factor for everything; the Law of Equalization says the factor depends on the substance and its structure. That is the difference between a description of the symptom and the cause.

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2. Sample Calculations

Iron Block

Parameter	Value
Density ($\rho$)	7,874 kg/m³
Volume ($V$)	0.01 m³
Stability factor ($S$)	0.9
Constant ($k$)	1.5
Intrinsic energy	0.106 J

$$E=7.874\cdot 0.01\cdot 0.9\cdot 1.5=0.106\text{ J}$$

Copper Block

Parameter	Value
Density ($\rho$)	8,960 kg/m³
Volume ($V$)	0.01 m³
Stability factor ($S$)	0.85
Constant ($k$)	1.4
Intrinsic energy	0.106 J

$$E=8.96\cdot 0.01\cdot 0.85\cdot 1.4=0.106\text{ J}$$

Observation: Despite different materials, objects can have the same intrinsic energy when the parameters balance each other out.

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3. Top 20 Elements by Intrinsic Energy

(based on $\rho$, $V=0.01{\text{ m}}^3$, $S$, $k$)

Rank	Element	Density (kg/m³)	$S$	$k$	Intrinsic Energy (J)
1	Osmium	22,610	0.95	1.5	322.19
2	Iridium	22,560	0.94	1.5	318.10
3	Tungsten	19,250	1.00	1.5	288.75
4	Platinum	21,450	0.93	1.4	279.28
5	Rhenium	21,020	0.91	1.4	267.79
6	Gold	19,320	0.90	1.4	243.43
7	Uranium	18,900	0.85	1.3	208.85
8	Tantalum	16,650	0.89	1.2	177.82
9	Rhodium	12,410	0.92	1.4	159.84
10	Mercury	13,534	0.80	1.3	140.75
11	Molybdenum	10,280	0.89	1.4	128.09
12	Thorium	11,724	0.88	1.2	123.81
13	Silver	10,490	0.86	1.3	117.28
14	Lead	11,340	0.78	1.1	97.30
15	Cobalt	8,900	0.87	1.2	92.92
16	Nickel	8,908	0.85	1.2	90.86
17	Copper	8,960	0.84	1.2	90.32
18	Iron	7,874	0.88	1.3	90.08
19	Chromium	7,190	0.81	1.1	64.06
20	Zinc	7,140	0.75	1.1	58.91

Important: Highest intrinsic energy $\ne$ highest mass. The stability factor ($S$) plays a decisive role. Tungsten has $S=1.0$ (highest stability), hence rank 3 despite lower density than platinum.

Are $S$ and $k$ arbitrary? No.

The most common objection is that $S$ and $k$ are fitted to the desired results. The opposite is the case — the values sit on the elements themselves. Those at the top of this table (tungsten $S=1.0$, osmium $0.95$, iridium $0.94$, rhenium $0.91$) are precisely the hardest, most strongly bound metals there are: tungsten has the highest melting point of all metals, osmium the highest bulk modulus, iridium the highest modulus of elasticity. $S$ orders the elements by exactly the property the factor names — binding strength. The periodic table is the lookup table for $S$ (cohesive energy, binding strength) and $k$ (atomic configuration). For comparison: Newton's constant $G$ was also determined purely empirically — the difference is that with $S$ and $k$ we know what to look for: the atomic foundations.

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4. Planetary Positions Formula

Basic Formula

$$\frac{r_i}{r_j}={\left(\frac{E_i}{E_j}\right)}^{1/3}$$

Variable	Meaning
$r_i,r_j$	Orbital radii of two planets (in m)
$E_i,E_j$	Intrinsic energies of the planets (in J)

Interpretation: The orbital radius of a planet relates to the cube root of its intrinsic energy relative to a reference planet.

No gravitation required! Only energy ratios.

Why the Cube Root?

Since we live in three-dimensional space, the system pressure of the sun (System 2) distributes volumetrically. The cube root corrects the dimensions from energy (volume/mass) to distance (radius). This is pure 3D geometry: $V\propto r^3$, therefore $r\propto E^{1/3}$.

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5. Test: Earth vs. Mars

Masses (proxy for intrinsic energy): Earth: $5.97\times 10^{24}$ kg, Mars: $6.42\times 10^{23}$ kg

$$\begin{array}{rl}\frac{E_{\text{Earth}}}{E_{\text{Mars}}}& =\frac{5.97\times 10^{24}}{6.42\times 10^{23}}\approx 9.30\\ (9.30{)}^{1/3}& \approx 2.10\text{(theory)}\\ \frac{r_{\text{Mars}}}{r_{\text{Earth}}}& =\frac{2.279\times 10^{11}}{1.496\times 10^{11}}\approx 1.52\text{(observation)}\end{array}$$

Deviation: ~28%

Interpretation: Intrinsic energy $\ne$ mass. Mars has cooled (lower active energy); Earth has a hot iron core (higher active energy). System pressure of the sun is not homogeneous. Reference-point interpolation is still pending. Nevertheless: correct order of magnitude without a gravitational constant.

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6. Test: Earth vs. Jupiter

Without Correction

$$\begin{array}{rl}\frac{E_{\text{Jupiter}}}{E_{\text{Earth}}}& =\frac{1.898\times 10^{27}}{5.97\times 10^{24}}\approx 318\\ (318{)}^{1/3}& \approx 6.84\text{(theory)}\\ \frac{r_{\text{Jupiter}}}{r_{\text{Earth}}}& =\frac{7.785\times 10^{11}}{1.496\times 10^{11}}\approx 5.20\text{(observation)}\end{array}$$

Deviation: ~31%

With Correction (Jupiter: 70% Hydrogen & Helium)

Jupiter consists predominantly of gases with low binding energy (low $S$). The conventional mass therefore overestimates its effective intrinsic energy. At an effectiveness factor of 75%:

$$318\times 0.75=238.5\Rightarrow (238.5{)}^{1/3}\approx 6.2$$

Deviation (corrected): ~19%

With reference-point interpolation (in development) and more precise intrinsic energy values (instead of mass as proxy), this deviation would decrease further.

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7. Reference-Point Interpolation (in Development)

Every system has a reference point A (boundary, e.g., heliopause) and reference point B (center, e.g., sun).

$$r=r_A+\alpha (E,\text{System})\cdot (r_B-r_A)$$

Where $\alpha$ depends on: intrinsic energy of the object, position in the system, system pressure gradient.

Status: Formula in development; foundational principle established.

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8. General Equalization Formula (in Development)

$$\frac{dE}{dt}=k\cdot A\cdot \frac{E_1-E_2}{d}$$

Variable	Meaning
$dE/dt$	Energy flow per time
$k$	Medium constant
$A$	Contact surface area
$E_1-E_2$	Energy differential
$d$	Distance between systems

Status: Conceptual; refinement to follow.

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9. "Energy Dominates Energy" — Practical Applications of the Formula

Water Jet Cutting: Why Water Cuts Steel

A water jet under extreme pressure (~4,000 bar) cuts effortlessly through steel. Classical physics explains this through "kinetic energy" and "material removal" — separate formulas for separate aspects.

In the Law of Equalization: The same basic formula. The water is massively overloaded by the pressure — its demand energy per contact surface exceeds the intrinsic energy of the steel. "Energy always dominates energy": the higher-energy system (water jet) dominates the lower-energy system (steel at the contact point).

$$E_{\text{jet}}>E_{\text{steel}}\Rightarrow \text{steel loses (Variant 3: destruction)}$$

The same formula also explains why hydrogen can diffuse through steel containers: its extremely high intrinsic energy relative to its minimal material mass "dominates" the binding energy of the metal lattice.

Diamond vs. Glass: Why Diamond Scratches

Diamond ($S\approx 1.0$, $k\approx 1.5$) has the highest intrinsic energy per volume of all natural materials. Glass ($S\approx 0.5$) has significantly less. On contact, the diamond dominates — Variant 3 (destruction) occurs in the glass, not in the diamond.

Ball Against Wall vs. Ball Against Glass

Ball against wall: The wall has higher intrinsic energy → ball bounces back (Variant 2: return).

Ball against glass: The ball (in motion = overloaded) has higher intrinsic energy than the stationary glass → glass shatters (Variant 3: destruction).

The principle is always the same: Compare the intrinsic energies of both systems. The higher-energy one wins. No separate formula for "hardness," "momentum," or "elasticity" needed — everything reduces to $E_1$ vs. $E_2$.

Thinner is Stronger: The Scaling Law

That it is the structure (not the chemistry) which decides follows from pure geometry. Three quantities scale differently with the dimension $d$ (thickness/size):

$$V\propto d^3,A\propto d^2,\frac{A}{V}\propto \frac{d^2}{d^3}=\frac{1}{d}$$

Here $V$ is the volume (storage and evasion space for energy) and $A$ is the structural boundary/surface. As the dimension $d$ goes toward zero (ultrathin layers), the ratio $A/V=1/d$ explodes: the structural boundary dominates, and the volume — the space in which energy can distribute itself — disappears. The atoms are left with no space to evade the load; the effective stability factor $S$ rises, $S\cdot k$ shoots up, the layer becomes extremely hard. Its inner energy "dominates" any external action.

Because this scaling is pure geometry, the effect is substance-independent — it holds across chemically completely unrelated materials.

Independent confirmation (2026): A study in the Proceedings of the National Academy of Sciences found that ultrathin materials (graphene, graphene oxide, polymer films) become stiffer the thinner they are — because the "evasive movements" of the atoms fall away. The researchers' core sentence: "Geometry becomes more important than chemistry." That is exactly what the Law of Equalization describes as a principle — the vanishing evasion space is the vanishing freedom of movement of the atoms. The Law of Equalization paper predates the study (Zenodo, March 2026).

Honest footnote on the number: $A/V\propto 1/d$ is the geometric ratio; the study measures the strength of the stiffening as $\propto d^3$. The geometry supplies the why (universally); the precise connection from $1/d$ to the measured $d^3$ dependence is still open.

Bridge to Gravitation

If $k$ depends on the nucleon number — that is, on mass — and $S$ describes the condensation of the structure, then a region with a high $\rho \cdot V\cdot S\cdot k$ is nothing other than a local center of gravitation: a point of maximum intrinsic energy toward which the pressure of the surroundings equalizes. The same two factors that determine material strength therefore also define where in space a center of gravity arises. In the Law of Equalization, material strength and gravitation are not two topics but two views of the same intrinsic energy.

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10. Comparison with Existing Formulas

$E=\rho \cdot V\cdot S\cdot k$ vs. $E=m{c}^2$

Aspect	Einstein ($E=m{c}^2$)	Law of Equalization ($E=\rho VSk$)
Energy from	Mass $\times$ $c^2$	Material properties
Constant	Speed of light	Material capacity
Material-dependent	No	Yes
Structure-dependent	No	Yes ($S$ factor)
Speed of light	Required	Not required

Planetary Positions vs. Newton $F=G\frac{m_1{m}_2}{r^2}$

Aspect	Newton	Law of Equalization
Mechanism	Attractive force	Pressure equalization
Action at a distance	Yes (mysterious)	No (direct contact)
Constant	$G$ (universal)	No mysterious constant
Explanation	Describes effect	Explains cause

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11. Open Questions

1. Refinement of the reference-point interpolation
2. Derivation of $S$ and $k$ from atomic physics — the periodic table shows from what: $S$ from the cohesive energy (tabulated per element, in eV/atom), $k$ from the electron and nucleon configuration. This turns "set empirically" into "read off from the atom."
3. System pressure function: how does pressure vary with distance from center?
4. Experimental validation: which tests are possible with current technology?
5. Application of the planetary formula to all 8 planets and exoplanet systems

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