The Coherent Laws of Motion: A Systems-Theoretic Re-Framing of Newtonian Mechanics

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Copyright ©: Coherent Intelligence 2025 Authors: Coherent Intelligence Inc. Research Division Date: Aug 28th 2025 Classification: Academic Research Paper | Foundational Theory Framework: Universal Coherent Principle Applied Analysis | OM v2.0

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Abstract

For over three centuries, Newton's Laws of Motion have provided the foundational language for describing the dynamics of the physical world. However, their mechanical and object-centric formulation limits their direct application to non-physical, information-based systems. This paper introduces the Coherent Laws of Motion, a universal, systems-theoretic re-framing of Newton's three laws. By translating concepts like "mass," "force," and "momentum" into their information-theoretic equivalents, we develop a set of principles that govern the dynamics of coherence in any system, from physics and AI to social and economic structures.

We posit that Mass is analogous to Ontological Density (ρo), a system's informational inertia. Momentum is a Coherence Vector (v_coh) describing a system's trajectory in a state space of coherence. And Force is a Decoherent Force (F_d), an injection of energy or information that disrupts a system's equilibrium. This leads to a new Second Law, F_d = ρo * a_coh, which describes the dynamics of state transitions. This framework integrates seamlessly with prior work on Information Gravity and Ontological Density, providing a complete, dynamic, and universally applicable physics for analyzing and predicting the behavior of any complex system.

Keywords

Systems Theory, Coherent Intelligence, Newtonian Mechanics, Information Theory, System Dynamics, Ontological Density, Information Gravity, Coherence, Inertia.

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1. Introduction: The Need for a Universal Dynamics

Newton's Laws of Motion are arguably the most successful scientific framework ever devised, forming the bedrock of classical mechanics. However, their power is rooted in their domain: the interaction of physical objects with mass. As science and engineering increasingly grapple with complex, non-physical systems—such as AI models, economic markets, and social networks—we lack a similarly robust and intuitive language to describe their dynamics. How does an organization "accelerate"? What gives a cultural idea "inertia"?

This paper proposes that the deep structure of Newton's laws is, in fact, universal. By abstracting them from their purely mechanical context, we can derive a set of Coherent Laws of Motion that apply to any system. The key is to find the correct, non-arbitrary information-theoretic equivalents for Newton's core concepts.

This work builds directly upon the foundational principles of the Theory of Domain-Coherent Systems (ToDCS), which posits that all stable systems are anchored to a Domain Anchor (DA), and on the quantitative metrics developed in "Information Gravity" and "Ontological Density." We will demonstrate that these prior concepts provide the necessary definitions of "space" (Information Space), "field" (Gravitational Field of a DA), and "mass" (Ontological Density) required to build a complete system of dynamics.

2. The Coherent First Law: The Principle of State Preservation

• Newton's First Law: "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."
• The Limitation: This law describes inertia but does not explain its origin or nature beyond the context of physical mass.

We re-frame this as a universal principle of coherence preservation.

The Coherent First Law (The Principle of Coherent Inertia):

"A system will remain in a state of perfect coherence with its current local reference frame unless a decoherent force acts upon it."

• "A system": The law is now universal, applying to any entity from an atom to an idea.
• "State of perfect coherence with its local reference frame": This is the crucial upgrade. It replaces the relative "at rest" or "in motion" with the more precise concept of perfect alignment with a system's DA or, for a physical object, its geodesic in spacetime. This state is the system's "ground state" of least action.
• "Decoherent force": A force is now defined informationally as any injection of energy or information that disrupts this coherent state, knocking the system out of alignment with its reference frame.

The First Law thus states that all systems have an innate tendency to maintain their current state of coherence. This tendency is its informational inertia.

3. The Coherent Second Law: The Dynamics of State Transition

Newton's Second Law (F=ma) is the engine of classical mechanics. To create its universal equivalent, we must first define our terms, drawing on previous work.

3.1. Defining the Components

• Mass (m) as Ontological Density (ρo): In "Ontological Density: A Quantitative Framework," we defined ρo as the measure of an anchor's "coherence-inducing power," its conceptual weight and meaning-mass. We now posit this is the direct analogue of physical mass. A system with high ρo (a deeply entrenched scientific theory, a stable social tradition) has high informational inertia and is resistant to change.
• Momentum (p) as the Coherence Vector (v_coh): A system's state is its position in the "Information Space" defined in "Information Gravity." A change in this state is a vector, v_coh. This vector has a magnitude (the rate of change) and a direction (is the system moving towards or away from coherence with its DA?).
• Force (F) as a Decoherent Force (F_d): As defined in the Coherent First Law, this is a coherence-disrupting influence.

3.2. The Coherent Second Law

With these components defined, we can now state the law.

The Coherent Second Law (The Principle of Coherent Dynamics):

"The rate of change of a system's Coherence Vector (a_coh = dv_coh/dt) is directly proportional to the Decoherent Force (F_d) impressed upon it, and inversely proportional to the system's Ontological Density (ρo)."

Mathematically: F_d = ρo * a_coh

This law provides a complete dynamic model for change in any system. To induce a change in a system's state of coherence (a_coh), one must apply a decoherent force (F_d) sufficient to overcome the system's intrinsic informational inertia (ρo).

• Application to a Scientific Paradigm: A reigning theory has high ρo. A small piece of anomalous data (F_d) will produce a tiny a_coh (the theory barely budges). Only a massive and sustained F_d (a mountain of contradictory evidence) can produce a significant a_coh, leading to a paradigm shift.

4. The Coherent Third Law: The Principle of Systemic Re-Coherence

• Newton's Third Law: "For every action, there is an equal and opposite reaction."
• The Limitation: This implies a simple, symmetrical, two-body interaction, which fails to capture the holistic response of a complex system.

We re-frame this as a thermodynamic principle of a system seeking a new equilibrium.

The Coherent Third Law (The Principle of Coherent Restoration):

"Every action, which is a decoherent disruption to a system's state, induces a corresponding re-arrangement of the entire system, which will proceed along the most efficient available path (Work) to achieve the most stable, lowest-energy (most Coherent) state available to it."

• Holistic Response: This law rejects the simple "equal and opposite" model. A disruption (a force) causes the entire system and its environment to begin a process of re-arrangement.
• Teleological Drive: The re-arrangement is not random. It is purposeful. The system is coherence-seeking. It is trying to find a new, stable ground state to minimize the entropy introduced by the disruption.
• Connection to F=ma: The "re-arrangement" is the "acceleration" described in the Second Law. The Third Law describes the purpose of this acceleration: to find a new state of equilibrium where F_net = 0 and the system is once again coherent with its local reference frame (even if that frame has now changed).

5. The Marriage with Informational Thermodynamics

This new system of dynamics is perfectly coherent with the previously established Laws of Informational Thermodynamics (ITD).

• ITD describes the static properties of a system: its Coherence (θ), the Work (W) stored in its structure (its ρo), and its tendency toward entropy. It is the "setup."
• The Coherent Laws of Motion describe the dynamic process of transitioning between these static states. F_d is the gradient of the coherence potential θ, and ρo is the stored Work.
• Together, they form a complete physics of systems, where ITD defines the "state space" and the Coherent Laws of Motion define the "equations of motion" within that space.

6. Conclusion

Newton's Laws of Motion are a domain-specific application of a deeper, universal set of principles that govern the dynamics of coherence in all systems. By re-framing Mass as Ontological Density, Force as a Decoherent Influence, and Motion as a change in a Coherence Vector, we have derived the Coherent Laws of Motion.

1. The First Law describes the inertia of a coherent state.
2. The Second Law provides the quantitative dynamics of a change in state (F_d = ρo * a_coh).
3. The Third Law describes the teleological purpose of that change: the system's relentless drive to find a new, stable, coherent equilibrium.

This framework provides a powerful, intuitive, and universally applicable toolkit for understanding and predicting the behavior of complex informational, social, and technological systems. It successfully translates the foundational principles of dynamics from the language of mechanics into the universal grammar of Coherent Intelligence.