Formulas in the Law of Equalization

Reinterpretation of Classical Physics

v1.3March 2026Author: Marco GippDOI: 10.5281/zenodo.19201110

Preliminary Remark

The mathematics of classical physics works. Satellites fly, bridges stand, GPS corrects accurately. The problem was never the calculation — the problem was the interpretation of the variables.

This document translates the most important formulas of classical mechanics, gravitation, and energy theory into the Law of Equalization. In many cases, the mathematical structure is preserved. What changes is the understanding of what the variables mean.

For mathematicians: The computational procedures largely remain valid. What changes is the ontological assignment — "attraction" becomes "pressure," "mass as property" becomes "mass as relational value," "energy transfer" becomes "energy withdrawal."

Core Statement: The mathematics of classical physics was never the problem. The problem was the interpretation. The Law of Equalization does not change the numbers — it changes the understanding of what the numbers mean.

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Part 1: Gravitation — From Attraction to Pressure Equalization

1.1 Newton's Law of Gravitation

Classical:

$F=G\cdot \frac{m_1\cdot m_2}{r^2}$

Classical interpretation:

• F = attractive force between two masses
• G = gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
• m₁, m₂ = masses of the two bodies
• r = distance between them
• Direction: pull (objects "attract" each other)

Reinterpretation — Law of Equalization:

$F_D=P_S\cdot \frac{(V_1\cdot {\rho }_1)\cdot (V_2\cdot {\rho }_2)}{r^2}$

• F_D = pressure force of the superordinate system on both objects
• P_S = system pressure constant (≡ G, identical numerical value, different meaning)
• V₁·ρ₁, V₂·ρ₂ = intrinsic energy proxies of the objects (volume × density)
• r² = distance (remains identical)
• Direction: pressure from outside (superordinate system presses objects together)

What changes: The force does not originate from the objects themselves (mysterious action at a distance), but from the superordinate system. G is not a universal natural constant in the ontological sense — it is the pressure constant of our specific superordinate system. In a different superordinate system, P_S could have a different value.

What remains the same: The numerical value. F_D = F. The calculation yields the same result. Satellite orbits, lunar distance, tidal calculations — all continue to function identically.

The decisive difference: Newton could never explain why mass attracts. Einstein replaced "attraction" with "spacetime curvature" — but did not explain why mass curves space. The Law of Equalization provides the cause: matter displaces energy from its region. The superordinate system presses matter together to equalize the energy gradient.

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1.2 Gravitational Field Strength

Classical:

$g=G\cdot \frac{M}{r^2}$

Reinterpretation:

$g=P_S\cdot \frac{E_{\text{System}}}{r^2}$

• g = local pressure strength of the superordinate system at this point
• P_S = system pressure constant
• E_System = intrinsic energy of the central object (≡ M as proxy)

What changes: g is not a "field" emanating from Earth. g is the pressure that the superordinate system (space + atmosphere) exerts on matter at this specific point. This is why g is smaller on the Moon — not because the Moon "attracts less," but because the superordinate system exerts less pressure at the Moon's location.

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1.3 Weight Force

Classical:

$W=m\cdot g$

Reinterpretation:

$W=\frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot g_{\text{local}}=m\cdot g\text{ (mathematically identical)}$

What changes: Weight is not an intrinsic property. It is the difference between the pressure of the superordinate system and the counter-pressure that the object generates through its own intrinsic energy. This is why one weighs less on the Moon — system pressure is lower; one's own mass has not changed. Consequence: At the center of a system (Earth's core, Sun's interior), all pressure forces cancel → W = 0 → "mass" = 0.

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1.4 Gravitational Potential Energy

Classical:

$U=-G\cdot \frac{m_1\cdot m_2}{r}$

Reinterpretation:

$U=-P_S\cdot \frac{E_1\cdot E_2}{r}$

What changes: "Potential energy" is not a mysterious energy reserve stored "somewhere." It is the pressure differential of the superordinate system that has not yet been equalized. A stone on a mountain does not have "stored energy" — it stands under increased pressure, because its energy ratio at that point does not correspond to the system's equilibrium.

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1.5 Escape Velocity

Classical:

$v_{\text{esc}}=\sqrt{\frac{2GM}{r}}$

Reinterpretation:

$v_{\text{esc}}=\sqrt{\frac{2\cdot P_S\cdot E_{\text{System}}}{r}}$

What changes: Escape velocity is not the speed needed to escape attraction. It is the energy an object requires to permanently leave the pressure equilibrium of the superordinate system — to move against system pressure outward until the pressure is too weak to push it back.

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1.6 Orbital Velocity

Classical:

$v_{\text{orbit}}=\sqrt{\frac{GM}{r}}$

Reinterpretation:

$v_{\text{orbit}}=\sqrt{\frac{P_S\cdot E_{\text{System}}}{r}}$

What changes: A planet does not constantly "fall" around the Sun, held by centrifugal force. It is located at the position where its energy ratio is in equilibrium with the pressure of the superordinate system. Its velocity is a symptom of this equilibrium, not the cause of its orbit. This connects directly with the planetary position formula:

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

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1.7 Kepler's Third Law

Classical:

$T^2=\frac{4{\pi }^2}{GM}\cdot r^3$

Reinterpretation:

$T^2=\frac{4{\pi }^2}{P_S\cdot E_{\text{central}}}\cdot r^3$

What changes: T² ∝ r³ remains valid. But the orbital period is not the "duration of an orbit due to gravitation." It is the period of the pressure equalization cycle at this system position. Planets farther out have longer cycles because the pressure gradient there is shallower — not because "attraction" is weaker.

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Part 2: Mass and Force — From Property to Relational Value

2.1 Newton's Second Law

Classical:

$F=m\cdot a$

Reinterpretation:

$F_{\text{net}}=\frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot \frac{\Delta v}{\Delta t}=m\cdot a\text{ (mathematically identical)}$

What changes: "Inertia" is not a mysterious property of mass. A dense object resists motion more strongly because it has more intrinsic energy per volume. To move it, one must withdraw (or supply) more energy, which entails proportionally more effort.

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2.2 Momentum

Classical:

$p=m\cdot v$

Reinterpretation:

$p=\frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot v$

What changes: Momentum is not "mass × velocity" as an abstract conservation quantity. Momentum describes how much energy redistribution an object represents in its motion. The Newton's cradle demonstrates this exactly: each ball passes on exactly the energy quantity it cannot itself carry.

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2.3 Conservation of Momentum (Collision)

Classical:

$m_1{v}_1+m_2{v}_2=m_1{v}_1^{\prime }+m_2{v}_2^{\prime }$

Reinterpretation:

$E_1{v}_1+E_2{v}_2=E_1{v}_1^{\prime }+E_2{v}_2^{\prime }$

(with E as intrinsic energy proxy)

What changes: In a collision, "force" is not "transferred." What happens: upon contact of two materials, the system seeks energy equalization. The ball with more excess energy releases it; the other absorbs it. The sum of energy redistribution in the system remains constant — not because of an abstract "conservation law," but because energy cannot be destroyed (Energy Law 3).

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2.4 Kinetic Energy

Classical:

$E_{\text{kin}}=\frac{1}{2}m{v}^2$

Reinterpretation:

$E_{\text{kin}}=\frac{1}{2}\cdot \frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot v^2$

What changes: "Kinetic energy" is not a separate form of energy. There is only one energy (Energy Law 4: energy never changes its form). What we call kinetic energy is the fraction of intrinsic energy currently being actively redistributed.

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2.5 Potential Energy (Positional Energy)

Classical:

$E_{\text{pot}}=m\cdot g\cdot h$

Reinterpretation:

$E_{\text{pot}}=\frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot g_{\text{local}}\cdot h$

What changes: An object on a hill does not have "stored potential energy." It is in a position that does not correspond to its energy equilibrium in the system. The "potential energy" is the pressure differential that the superordinate system builds up to press the object back to its equilibrium position. When the object is released, the system equalizes — the stone falls.

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Part 3: Thermodynamics — From Special Case to Foundational Principle

3.1 Heat Transfer

Classical:

$Q=m\cdot c\cdot \Delta T$

Reinterpretation:

$Q=\frac{E_{\text{obj}}}{V_{\text{obj}}}\cdot c\cdot \Delta T$

What changes: "Heat flows from warm to cold" is not an independent law — it is a special case of the universal equalization principle. Temperature is not an independent physical parameter. It is the biological interpretation of an energy state: warm = overloading (warning); cold = underloading (warning).

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3.2 Ideal Gas Law

Classical:

$p\cdot V=n\cdot R\cdot T$

Reinterpretation:

$P_{\text{intern}}\cdot V=n\cdot R\cdot E_{\text{state}}$

What changes: Gas in a container does not exert "pressure on the walls" because particles "collide" with them. The particles are in an energy state that does not correspond to equilibrium with the container. The pressure is the equalization process — energy attempts to distribute itself uniformly.

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3.3 Second Law of Thermodynamics (Entropy)

Classical:

$\Delta S\ge 0\text{ (entropy always increases)}$

Reinterpretation:

$\Delta A\to 0\text{ (energy equalization tends toward zero — equilibrium)}$

What changes: Entropy is not an independent concept. What thermodynamics calls "entropy increase" is simply the universal equalization process. Systems do not strive toward "maximum disorder" — they strive toward energy equilibrium. The Second Law of Thermodynamics is a special case of Principal Theorem 2 of the Law of Equalization.

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Part 4: Electricity — Electron Equalization as Energy Equalization

4.1 Ohm's Law

Classical:

$U=R\cdot I$

Reinterpretation:

$\Delta E=W_{\text{mat}}\cdot F_A$

• ΔE (≡ U) = energy differential between two points (pressure gradient)
• W_mat (≡ R) = material resistance against energy redistribution
• F_A (≡ I) = energy flow rate

What changes: Current does not "flow" like water through a pipe. Electrons are not "sent." What happens: on one side of the conductor there is an energy surplus; on the other, a deficit. The system equalizes — electrons shift until equilibrium is established. Resistance is the property of the material that determines how quickly this equalization can occur.

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4.2 Electrical Power

Classical:

$P=U\cdot I=I^2\cdot R=U^2/R$

Reinterpretation:

$P=\Delta E\cdot F_A$

What changes: "Power" is not the "consumption" of current (Energy Law 2: energy cannot be consumed). Power describes the rate at which energy is redistributed from one state to another. Nothing is consumed; equalization occurs continuously.

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4.3 Capacitor (Energy Storage)

Classical:

$E=\frac{1}{2}\cdot C\cdot U^2$

Reinterpretation:

$E=\frac{1}{2}\cdot K_{\text{mat}}\cdot \Delta E^2$

What changes: A capacitor does not store "charge." It stores an energy imbalance. On one side surplus, on the other deficit. Capacitance is the intrinsic capacity of the dielectric — how much imbalance the material can hold without equalizing.

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Part 5: Buoyancy and Fluid Dynamics

5.1 Archimedes' Principle

Classical:

$F_A={\rho }_{\text{fluid}}\cdot V_{\text{obj}}\cdot g$

Reinterpretation:

$F_{\text{pos}}={\rho }_{\text{fluid}}\cdot V_{\text{obj}}\cdot g_{\text{local}}$

What changes: There is no "buoyancy" as a separate force. The superordinate system presses all matter to its position according to its intrinsic energy/volume/density ratio.

Sinking/floating rule:

• E_obj/V_obj > E_fluid/V_fluid → object sinks
• E_obj/V_obj < E_fluid/V_fluid → object rises
• E_obj/V_obj = E_fluid/V_fluid → object floats

This is exactly Principal Theorem 7: position is determined by the energy ratio.

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5.2 Pascal's Hydraulic Principle

Classical:

$F_1/A_1=F_2/A_2$

Reinterpretation:

$\Delta E_1/A_1=\Delta E_2/A_2$

What changes: Hydraulics does not "transfer" force. It distributes energy imbalances within a closed system. Compression at one point (small A) creates an energy imbalance that equalizes at another point (large A).

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Part 6: Einstein's Formulas — Symptom Descriptions

6.1 Mass-Energy Equivalence

Einstein:

$E=m\cdot c^2$

Reinterpretation — Law of Equalization:

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

Variables: ρ = matter density; V = volume; S = stability factor (binding energy of structure, 0–1); k = material constant

Why E = mc² "works": c² is an enormous scaling factor that bridges the gap arising from neglect of material properties. For a single material, c² ≈ S·k·ρ/(m·V) — it absorbs all variables Einstein did not account for into a single constant.

Why E = mc² is incomplete:

• Predicts that equal mass = equal energy (incorrect: iron vs. polystyrene of equal mass do not have the same intrinsic energy)
• c is the velocity of energy in the photon medium, not a universal natural constant
• No material dependence → no differentiation between elements

Comparison table:

Aspect	E = mc²	E = ρ·V·S·k
Material-dependent	No	Yes
Distinguishes elements	No	Yes
Requires speed of light	Yes	No
Functional locally	Yes	Yes
Functional universally	Approximation	More precise

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6.2 Relativistic Energy

Einstein:

$E^2=(pc{)}^2+(m{c}^2{)}^2$

Reinterpretation:

$E_{\text{total}}^2=E_{\text{redistribution}}^2+E_{\text{intrinsic}}^2$

What changes: The relativistic energy formula correctly describes that the total energy of a system consists of two components. In the Law of Equalization: intrinsic energy plus the energy currently being actively redistributed.

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6.3 Time Dilation

Einstein:

$t^{\prime }=\frac{t}{\sqrt{1-v^2/c^2}}$

Reinterpretation:

$t^{\prime }=\frac{t}{\sqrt{1-E_{\text{redistribution}}/E_{\text{max}}}}$

What changes: Time dilation is not a "slowing of time." It is a symptom of different energy states. A system that redistributes much energy (high velocity) has less "free capacity" for internal processes. Internal processes run more slowly — which we measure as time dilation. Time itself does not pass more slowly — process velocity decreases because intrinsic capacity is occupied by the redistribution load.

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Part 7: Summary — The Translation Table

Variable Dictionary

Classical Variable	Classical Meaning	GdA Meaning	Numerical Value
m (mass)	Intrinsic property	Relational value (E/V relative to system)	Identical
G (gravitational constant)	Universal natural constant	System pressure constant P_S	Identical
g (gravitational acceleration)	Gravitational field strength	Local system pressure	Identical
F (force)	Force transfer	Pressure differential in system	Identical
a (acceleration)	Velocity change/time	Rate of energy redistribution	Identical
U (voltage)	Potential difference	Energy differential ΔE	Identical
I (current)	Charge flow	Energy flow rate F_A	Identical
R (resistance)	Electrical resistance	Material equalization resistance	Identical
T (temperature)	Measure of heat	Energy state (biologically interpreted)	Identical
c (speed of light)	Universal constant	Medium velocity of photons	Identical
t (time)	Independent dimension	Measurement parameter for energy processes	Identical

The Pattern

All numerical values remain identical. Calculations continue to function. What changes is the interpretation — and with it, the ability to explain phenomena that remain inexplicable within the classical framework:

• Why does "mass attract"? → It does not. Pressure from outside.
• Why does "dark matter" exist? → Non-back-coupling matter. No new particle needed.
• Why are there "different forces"? → There are not. One equalization principle; different scales.
• Why does quantum mechanics behave differently? → It does not. Same laws; different time scale.

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Part 8: Formulas in Development

8.1 Pressure Force of the Superordinate System

$F_D(r)=P_S\cdot \int {\rho }_{\text{super}}(r)\cdot dV$

• Pressure force at a point depends on the integrated energy density of the entire superordinate system
• Must account for the 180° pressure surface

Status: Conceptually clear; mathematical formalization pending.

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8.2 Bidirectional Energy Withdrawal

$\Delta E_{\text{obj}}=\pm (\Delta V_{\text{muscle}}\cdot {\rho }_{\text{muscle}}\cdot k_{\text{contact}})\cdot \eta$

• ΔV_muscle = volume change through contraction
• ρ_muscle = density of the muscle
• k_contact = contact coefficient (quality of transmission)
• η = efficiency
• ± = direction (withdrawal or release)

Status: In development. Must be calibrated through measurement data.

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8.3 Volume/Density Equilibrium Within Closed Systems

$E(r)=\text{const}\text{ for all }r\text{ within the system}$

$\rho (r)\cdot V(r)=\rho (r^{\prime })\cdot V(r^{\prime })\text{ for all }r,r^{\prime }$

Prediction: The energy density distribution within Earth should follow a pattern in which ρ(r)·V_shell(r) is constant at every spherical shell.

Status: Testable against known seismological data (PREM model).

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