By Nguyễn Khánh Tùng — Independent Researcher
The NKT Law, based on the interaction between position and varying inertia, offers a powerful framework for understanding motion and transformation in systems across vastly different fields. This new natural law, formulated through the study of real-world data and dynamics, reveals that nature often operates through coordinated products like:
- x⋅px \cdot px⋅p: the position-momentum product
- dmdt⋅p\frac{dm}{dt} \cdot pdtdm⋅p: the inertia-change momentum product
While these expressions may appear mathematical, their implications are deeply practical and observable in multiple domains of science and technology. Below are several key areas where the NKT Law has already shown predictive and explanatory power.
1. Harmonic Motion and Mechanical Systems
In oscillatory systems like pendulums and springs, the NKT Law captures the subtle variation in momentum when mass or stiffness changes over time (e.g., in damped or driven systems).
Example:
A pendulum with a changing bob mass (e.g., due to loss/gain of fluid) follows a trajectory where the sign and magnitude of dmdt⋅p\frac{dm}{dt} \cdot pdtdm⋅p directly influence how it accelerates or resists motion. This provides a more refined picture than classical F=maF = maF=ma.
2. Rocketry and Internal Propulsion
Rockets naturally undergo a changing-mass condition due to fuel burn. The NKT Law models the rocket’s position and momentum in terms of internal mass variation, instead of just applying conservation laws externally.
Key insight:
Rather than treating fuel as an external impulse, the term dmdt⋅p\frac{dm}{dt} \cdot pdtdm⋅p accounts for the dynamic interaction between internal mass transfer and momentum shift — more precisely predicting motion in microgravity and space maneuvers.
3. Planetary Orbits and Celestial Mechanics
Traditional orbital mechanics assume mass constancy, but in reality, celestial bodies exchange mass via radiation, accretion, and tidal interactions.
Application:
The Earth’s orbit is not a perfect ellipse with fixed parameters. By including dmdt⋅p\frac{dm}{dt} \cdot pdtdm⋅p, one can model the real elliptical drift between perihelion and aphelion more accurately — even correcting for minor discrepancies long attributed to “gravitational perturbations.”
4. Thermodynamics and Entropy Systems
In systems where energy, mass, and motion interact — like heat engines or biological metabolism — the NKT Law provides a new way to view entropy flow through mass-momentum coupling.
Future exploration:
The term dmdt⋅p\frac{dm}{dt} \cdot pdtdm⋅p may be used to quantify entropy production rates, especially in systems with both material and energetic exchange, extending the second law of thermodynamics into dynamic, open systems.
5. Biophysics and Structural Evolution
Nature often evolves through internal reorganization — from tree growth to cell division. In such systems, mass is redistributed internally to support motion, growth, or response.
Analogy:
Just as a boat moves by interacting with ocean currents, a tree adjusts its center of mass through growth. The NKT Law provides a mechanical analogue for understanding how internal changes influence external motion or stability.
6. Artificial Intelligence and Optimization Systems
Though seemingly unrelated to mechanics, the principles of momentum and position interaction help describe optimization algorithms where systems adjust their internal “weights” or “inertia” in response to feedback.
Hypothesis:
By applying the logic of the NKT Law to machine learning systems, one might model the internal adaptation of networks in terms of mass-like variables (e.g., learning rates, weight shifts), offering new tools for meta-learning and self-adjusting architectures.
7. Quantum Field Analogy and Color Charge
While still speculative, future extensions of the NKT framework may offer insight into quantum-level interactions, especially where mass-energy fluctuations (e.g., virtual particles) affect momentum fields.
Projection:
In high-energy physics, the law may help reframe how “color charge” and confinement operate by linking internal energy-momentum transfers with spatial variables — a direction currently beyond direct measurement but within theoretical modeling reach.
8. Cosmology and Galactic Evolution
On the largest scales, galaxies and black holes evolve by losing and gaining mass, absorbing stars, and ejecting jets. The NKT Law offers a unifying perspective on how mass change contributes to orbital drift, jet motion, and even expansion of the cosmos.
Insight:
The similarity in shape between black hole accretion and biological scars (as seen in agarwood formation) suggests a fractal, structural correspondence — where the NKT framework may bridge biology and cosmology via geometric and mass-momentum analogues.
Closing Thoughts
The NKT Law is not just a new formula — it is a lens through which many of nature’s transformations can be understood. Wherever position, momentum, and changing inertia co-exist, this law can apply.
It is my belief that the scientific community will find many more applications beyond what I have presented here. From human-made systems to cosmic phenomena, this natural law opens a new chapter in our understanding of interaction, balance, and evolution.
For collaboration, simulation models, or to explore datasets, please contact me at:
traiphieu.com@gmail.com
Nguyễn Khánh Tùng (ORCID: 0009-0002-9877-4137)
ORCID iD: 0009-0002-9877-4137
