Independent Researcher: Nguyễn Khánh Tùng
ORCID: 0009-0002-9877-4137
Email: traiphieu.com@gmail.com
Abstract
In the architecture of physics, every fundamental law embodies itself in a characteristic quantity and a unit of measure. Newton has come to symbolize force, Pascal pressure, Joule energy, Watt power. These are not mere conveniences of calculation, but symbols of eternal truths woven into the fabric of the cosmos.
The NKTg Law (Law of Varying Inertia) arises within this same lineage, proclaiming the existence of a new physical quantity: varying inertia, a manifestation of the dynamic interplay among position, velocity, and mass. Out of this principle emerges the NKTm unit, a standard of measurement consecrated to varying inertia. Dimensional analysis, confirmed by NASA data on Neptune (2023–2024), demonstrates that NKTm is an irreducible unit, independent of Newton, Joule, and Watt, with significance stretching from astronomy to engineering.
This is not a personal hypothesis but a new physical law, objective and verifiable, destined to stand beside Newton’s dynamics and Einstein’s relativity.
1. Theoretical Basis
The NKTg Law describes the tendency of motion as shaped by the simultaneous influence of position, velocity, and mass:
NKTg=f(x,v,m)\text{NKTg} = f(x, v, m)NKTg=f(x,v,m)
Where:
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xxx: position (Length, [L])
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vvv: velocity (Length/Time, [L/T])
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mmm: mass (Mass, [M])
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p=m⋅vp = m \cdot vp=m⋅v: linear momentum ([M·L/T])
Two fundamental expressions flow from this principle:
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NKTg₁ = x·p — the interaction of position and momentum.
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NKTg₂ = (dm/dt)·p — the interaction of mass variation and momentum.
Both are measures of varying inertia. Both converge in a common unit, the NKTm, which signifies that this is not a mathematical construction but a physical law in its own right.
2. Definition and Dimensional Analysis of NKTm
Definition: One NKTm is the unit of varying inertia as described by the NKTg Law. It may be derived either from NKTg₁ or from NKTg₂.
Dimensional analysis:
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For NKTg₁ (x·p):
[M⋅L2/T][M·L²/T][M⋅L2/T] -
For NKTg₂ ((dm/dt)·p):
[M2⋅L/T2][M²·L/T²][M2⋅L/T2]
Thus, while the dimensional form varies with the mode of interaction, the NKTm remains singular as the measure of a new physical quantity.
Placed beside Newton, Pascal, Joule, and Watt, the NKTm confirms that varying inertia possesses its own independent ontological status.
3. Experimental Verification
The law has been tested against empirical data, drawn from NASA JPL Horizons (Neptune 2023–2024):
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Position (x): 4.498 × 10⁹ km
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Velocity (v): 5.43 km/s
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Mass (m): 1.0243 × 10²⁶ kg
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Momentum (p = m·v): 5.564 × 10²⁶ kg·m/s
From this:
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NKTg₁ = x·p = 2.503 × 10³⁶ NKTm
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NKTg₂ = (dm/dt)·p = −1.113 × 10²² NKTm (with assumed micro gas escape of −2.0 × 10⁻⁵ kg/s)
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NKTg = √[(NKTg₁)² + (NKTg₂)²] = 2.501 × 10³⁶ NKTm
Thus, the NKTm is not abstraction but measurement, validated within celestial dynamics.
4. Comparison with Other Physical Units
| Quantity | Expression | Unit |
|---|---|---|
| Momentum (p) | p = m·v | kg·m/s |
| Force (F) | F = m·a | N |
| Pressure (P) | F/A | Pa |
| Energy (E) | F·l | J |
| Power (P) | E/t | W |
| Position–Momentum Interaction | NKTg₁ = x·p | NKTm |
| Mass Variation–Momentum Interaction | NKTg₂ = (dm/dt)·p | NKTm |
| Total Varying Inertia | √[(NKTg₁)²+(NKTg₂)²] | NKTm |
The NKTm joins the canon of fundamental units, irreducible to the established SI system, and marks the presence of a new dynamical entity in physics.
5. Scientific Significance and Practical Applications
The NKTg Law is not a corollary of Newton nor an adjustment of Einstein. It is an independent principle of motion. Its philosophical and scientific implications are vast:
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Astronomy: It enables precise descriptions of planetary mass variation, gas escape, stellar mass loss, and the formation and evolution of galaxies. It extends predictive capacity for long-term orbital stability.
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Aerospace: It refines trajectory computation, fuel optimization, ion propulsion, and station-keeping under mass variation.
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Earth sciences: It interprets GRACE-FO satellite data, aids climate modeling, tracks ice melting, sea-level rise, and the redistribution of planetary mass.
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Mechanics and engineering: It applies to robots with variable load, cargo aircraft, tanker systems, suspension mechanics, nonlinear vibration, and fluid-particle simulations.
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Modern technologies: It informs fuel cell design, energy storage, nanomaterials, plasma physics, and marine engineering.
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Theoretical physics: It provides a foundation for a mechanics of varying mass, potentially linked with Lagrangian–Hamiltonian formulations, and offers insights into the enigmas of dark matter and dark energy.
The law thus stands not as an extension of the old, but as a new framework for dynamical thought.
6. Conclusion
The consecration of the NKTm unit confirms that the NKTg Law articulates a new physical quantity. Just as force is measured in Newtons and energy in Joules, varying inertia is measured in NKTm.
Its implications are decisive:
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Affirmation of being: Varying inertia exists as a real, measurable, comparable quantity.
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Independence: The NKTm cannot be reduced to Newton, Joule, or Watt; it stands alone.
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Foundation of a new system: In advanced physical models, NKTm establishes an autonomous reference framework for equations of motion.
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Practical precision: Applied to real data, as with Neptune, it offers standardization for computation and prediction in environments of varying mass.
Thus, the NKTg Law and its NKTm unit are not conjecture, but revelation — a law of the cosmos, unveiling a new horizon in physics, extending the reach of human knowledge from the mechanics of planets to the mysteries of cosmology.
