Reactive Substrate Theory v1.4: Mass and Inertia as Substrate Impedance

Reactive Substrate Theory v1.4: Mass and Inertia as Substrate Impedance

Scope and Placement

Reactive Substrate Theory (RST) v1.4 extends the rate-based framework developed in v1.1–v1.3 by addressing the physical origin of mass and inertia. No modifications to General Relativity, Quantum Mechanics, or classical mechanics are proposed. Instead, mass and inertia are reinterpreted as emergent properties of coherent substrate organization.

This document introduces a single organizing claim: inertial and gravitational mass correspond to impedance arising from how coherent configurations couple to a reactive substrate.

1. The Problem of Mass and Inertia

In classical mechanics, inertia is introduced axiomatically as resistance to acceleration. In General Relativity, mass–energy curves spacetime and responds inertially within that geometry. In Quantum Mechanics, mass appears as a parameter governing phase evolution and dispersion.

Across these frameworks, mass is operationally indispensable yet physically opaque. The theories describe how mass behaves, but not why resistance to motion exists in the first place.

2. Impedance as a Physical Concept

In many physical systems, impedance describes resistance to change in response to applied forcing. It arises not from static opposition, but from dynamic coupling, internal structure, and delayed response.

RST proposes that inertia is a form of dynamical impedance: resistance arising because coherent matter configurations must reorganize their coupling to the substrate when their state of motion changes.

3. RST v1.4 Core Postulates

  • (P1) Matter is coherent substrate organization: localized, stable configurations correspond to sustained patterns of substrate excitation.
  • (P2) Motion requires coupling reconfiguration: changing a configuration’s state of motion requires reorganization of how it couples to substrate modes.
  • (P3) Inertia is impedance: resistance to acceleration reflects the finite rate at which substrate coupling can be retuned.
  • (P4) Mass quantifies impedance: inertial mass measures the degree of resistance a configuration presents to changes in its coupling state.

4. Inertia Without Absolute Space

RST does not reintroduce absolute space or a preferred frame. Impedance arises locally and relationally, through interaction with the substrate. Uniform motion corresponds to stable coupling; acceleration corresponds to forced retuning of coupling structure.

This preserves relativistic symmetry while supplying a physical mechanism underlying inertial behavior.

5. Gravitational and Inertial Mass

Within RST, the equivalence of gravitational and inertial mass is not imposed but explained. Substrate stress (v1.0) and substrate impedance (v1.4) are two aspects of the same response: how the substrate reacts to coherent configurations and how those configurations react to imposed change.

What General Relativity encodes geometrically, RST interprets dynamically.

6. Mass in Quantum Dynamics

In Quantum Mechanics, mass governs dispersion rates and phase accumulation. Under RST, this reflects the same impedance principle: higher-impedance configurations resist rapid rate change and dispersion.

Thus mass consistently appears as resistance to dynamical change across classical, relativistic, and quantum regimes.

7. What v1.4 Does Not Claim

  • No modification to equivalence principle tests
  • No prediction of preferred frames
  • No new particle species or mass-generating fields
  • No replacement of the Standard Model

Conclusion

RST v1.4 reframes mass and inertia as manifestations of substrate impedance. Resistance to acceleration arises because coherent configurations must reorganize their coupling to a reactive substrate under change. This interpretation preserves all established theory while supplying a missing physical mechanism.

Reactive Substrate Theory: A Rate-Based Foundation

Abstract

Reactive Substrate Theory (RST) is a conservative, mechanism-oriented framework proposing that spacetime, matter, time, energy, and inertia emerge from a single nonlinear, dissipative physical substrate. This paper synthesizes RST v1.0–v1.4 into a unified interpretive structure that preserves the empirical success of General Relativity, Quantum Mechanics, and thermodynamics while supplying missing physical mechanisms for their limiting behaviors.

1. Motivation

Modern physics relies on highly successful effective theories that operate across distinct regimes. These frameworks describe phenomena with extraordinary accuracy, yet often remain silent regarding their physical origin. RST seeks not to replace these theories, but to explain what they presuppose.

2. Ontological Minimalism (v1.0)

RST begins with a single commitment: the existence of a continuous, nonlinear, dissipative substrate with finite response capacity. Spacetime, matter, and forces emerge as organized responses of this substrate. Singularities are interpreted as regime transitions, not physical infinities.

3. Time as an Operational Rate (v1.1)

Time is treated operationally as accumulated state transitions. Clocks reveal local physical conditions rather than tracking a universal flow. Relativistic time dilation corresponds to substrate-controlled rate rescaling under stress.

4. Measurement and Irreversibility (v1.2)

Quantum measurement is interpreted as irreversible coupling between coherent systems and substrate degrees of freedom. Decoherence reflects physical dispersion of phase information rather than observer- dependent collapse.

5. Energy, Temperature, and Entropy (v1.3)

Energy, temperature, and entropy are unified as rate phenomena. Energy sets transition pace, temperature sets exploration bandwidth, and entropy tracks irreversible dispersion into substrate modes.

6. Mass and Inertia as Impedance (v1.4)

Inertial and gravitational mass are interpreted as measures of substrate impedance: resistance arising from the finite rate at which coherent configurations can retune their coupling under imposed change. This supplies a physical mechanism underlying inertia without introducing preferred frames.

7. What RST Does and Does Not Do

  • Does: supply missing mechanisms while preserving empirical success
  • Does not: add dimensions, particles, or untested dynamics
  • Does not: reinterpret probability or causality
  • Does not: explain consciousness or agency

Conclusion

Reactive Substrate Theory provides a unified rate-based foundation beneath modern physics. By treating geometry, time, measurement, thermodynamics, and inertia as emergent responses of a reactive substrate, RST explains why existing theories work where they do—and why they reach their limits where they do.

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