We Will Redefine the Fundamental Concepts of Classical Physics — Mass, Time, Energy, Momentum, Force — with the Formal Function Theory of Fractal Mechanics

1. MASS (m) — In Fractal Mechanics

Classical physics: Mass = amount of matter / measure of inertia

Fractal mechanics: Mass = motif energy × entanglement

Formal equality:

𝑚_𝑓(𝑛) = 𝛾 𝑀(𝑛)² 𝐸_𝑚(𝑛)

Here:

• 𝑀(𝑛)² = 𝑓𝐸𝑛𝑡 (𝑛) → fractal norm / entanglement
• 𝐸_𝑚(𝑛) → internal energy of the motif
• 𝛾 → fractal transformation coefficient

✔ Fractal interpretation:

Mass is determined by the integrity (fEnt) and internal structure (motif energy) of the system.

✔ Physical result:

• If entanglement increases → mass increases
• If entanglement decreases → mass decreases
• If entanglement is zero → mass disappears

This is a definition of mass that does not exist in classical physics.

2. TIME (t) — In Fractal Mechanics

Classical physics: Time = continuous, one-way parameter

Fractal mechanics: Time = fractal iteration steps (n)

Formal equality:

𝑡 ⟷ 𝑛

✔ Fractal interpretation:

Time is the number of steps of the fractal transformation. In other words, time does not “flow”, it evolves.

✔ Result:

• The flow of time is not constant
• The “speed” of time depends on the motif function
• Time is the derivative of the fractal phase function

Φ(𝑛) = 𝜔𝑛 + 𝜙₀

Time = progression of phase.

3. ENERGY (E) — In Fractal Mechanics

Classical physics: Energy = capacity to do work

Fractal mechanics: Energy = fractal phase + motif energy + entanglement

Formal equality:

𝐸_𝑓(𝑛) =∣ 𝑑𝜓_𝑓 / 𝑑𝑛 ∣² + 𝐸_𝑚(𝑛)

Here:

• First term → fractal kinetic energy
• Second term → motif potential energy

✔ Fractal interpretation:

Energy is determined by the behavioral integrity and internal geometry of the system.

✔ Result:

Energy is not constant; It changes with fractal evolution.

4. MOMENTUM (p) — In Fractal Mechanics

Classical physics:

𝑝 = 𝑚𝑣

Quantum physics:

𝑝 = −𝑖ℏ ( 𝑑 / 𝑑𝑥 )

Fractal mechanics:

𝑝_𝑓(𝑛) = −𝑖 ( 𝑑 / 𝑑𝑛 )

✔ Fractal interpretation:

Momentum is the speed of fractal evolution.

✔ Result:

• Momentum is not constant
• Momentum is the derivative of the fractal phase

𝑝_𝑓(𝑛) = ( 𝑑Φ(𝑛) / 𝑑𝑛 ) = 𝜔

5. FORCE (F) — In Fractal Mechanics

Classical physics:

𝐹 = 𝑚𝑎

Fractal mechanics:

𝐹_𝑓(𝑛) = ( 𝑑𝑝_𝑓(𝑛) /𝑑𝑛 )

But:

𝑝_𝑓(𝑛) = 𝜔

Therefore:

𝐹_𝑓(𝑛) = 0

✔ Fractal interpretation:

The fundamental force of fractal mechanics is entanglement flow, not the classical force.

Real force:

𝐹_ent(𝑛) = ( 𝑑𝑓𝐸𝑛𝑡(𝑛) / 𝑑𝑛 )

So:

Force = rate of change of entanglement.

6. WAVE NUMBER (k) — In Fractal Mechanics

Classical physics:

𝑘 = 2𝜋 / 𝜆

Fractal mechanics:

𝑘_𝑓(𝑛) = fTan(𝑛) = tan (Φ(𝑛))

✔ Fractal interpretation:

The wave number is not constant; It depends on the fractal phase.

7. FREQUENCY (ω) — In Fractal Mechanics

Classical physics:

𝜔 = 2𝜋𝑓

Fractal mechanics:

𝜔 = ( 𝑑Φ(𝑛) / 𝑑𝑛 )

✔ Fractal interpretation:

Frequency is the rate of change of the fractal phase.

8. SPACE (x) — In Fractal Mechanics

Classical physics: Space = constant, flat, Euclidean

Fractal mechanics: Space = geometric projection of the motif function

𝑥_𝑓(𝑛) = 𝑀(𝑛)

✔ Fractal interpretation:

Space is not fixed; It expands and contracts according to the motif structure.

9. SUMMARY TABLE

Classical Physics	Fractal Mechanics	Explanation
Mass	𝑚𝑓 = 𝑓𝐸𝑛𝑡 · 𝐸m	Mass = coherence × internal energy
Time	𝑛	Time = iteration
Energy	Ef = ψ′² + Em	Energy = behavior + motif
Momentum	𝑝𝑓 = −i · d/d𝑛	Momentum = fractal evolution
Force	𝐹 = d𝑝/d𝑡	Force = entanglement flow
Wave number	𝑘𝑓 = 𝑓Tan(𝑛)	Fractal frequency orientation
Space	𝑥𝑓 = 𝑀(𝑛)	Space = motif map

10. In the simplest sentence:

Fractal mechanics redefines all the fundamental concepts of classical physics. Each magnitude is derived from the trio of motif + phase + entanglement.

So fractal mechanics:

• Quantum mechanics
• Wave mechanics
• Classic mechanics

It is a wider frame that fits over it.