[Paper Review] Gravitational Mass, Its Mechanics - What It Is; How It Operates

Roger Ellman|ArXiv.org|Mar 23, 1999

Relativity and Gravitational Theory1 references3 citations

TL;DR

This paper proposes a classical mechanics-based explanation for gravitational mass, deriving its origin from the finite speed of light, conservation laws, and the impossibility of infinity in physical systems. It shows how gravitational mass emerges in particles, reproduces Newtonian gravity, and explains the equivalence of inertial and gravitational mass without invoking quantum gravity or gravitons.

ABSTRACT

The earlier paper, Inertial Mass, Its Mechanics - What It Is; How It Operates, developed the mechanics of inertial mass. The present paper is for the purpose of equivalently developing gravitation. The behavior of gravitation is well known, as described by Newton's Law of Gravitation. But just what gravitational mass is, how gravitational behavior comes about, what in material reality produces the effects of gravitational mass, has been little understood. The only extant hypotheses involve the unsuccessful efforts to develop "quantum gravitation" and to tie it into the rest of quantum mechanics, and the equally failed attempts to detect "gravitons" and "gravitational waves" in spite of very substantial efforts. From a starting point of only the limitation on the speed of light, the necessity of conservation, and the impossibility of an infinity in material reality, the present paper presents a new and comprehensive analysis of the phenomenon gravitational mass: - how it appears in particles, - how the Newtonian gravitational behavior arises from that, and - how the values of inertial mass and gravitational mass are identical, or, in other words, the mechanics of gravitational mass and gravitation.

Motivation & Objective

• To clarify what gravitational mass fundamentally is, beyond its empirical description in Newton's law.
• To resolve the long-standing mystery of why inertial and gravitational mass are equivalent, without relying on quantum gravity.
• To develop a mechanism for gravitational behavior based solely on classical principles: finite light speed, conservation, and finiteness of physical quantities.
• To provide a material explanation for gravity that avoids the need for undetected particles like gravitons or gravitational waves.
• To establish a consistent mechanical model where gravitational mass arises naturally from the structure of spacetime and energy propagation.

Proposed method

• Starts from the postulate that the speed of light is finite and that physical quantities cannot be infinite.
• Applies conservation of energy and momentum to propagate effects at light speed, modeling how mass-like behavior emerges in particles.
• Analyzes how retarded potentials (delayed propagation) lead to a self-consistent force law resembling Newtonian gravity.
• Demonstrates that the resulting force law produces the same inverse-square dependence as Newton's law.
• Shows that the proportionality constant in the force law matches both inertial and gravitational mass, enforcing their equivalence.
• Uses symmetry and conservation principles to derive the mechanical origin of gravitational mass without introducing new fields or particles.

Experimental results

Research questions

• RQ1 What is the physical mechanism that gives rise to gravitational mass in material particles?
• RQ2 How can the observed Newtonian gravitational force emerge from fundamental principles like finite signal speed and conservation?
• RQ3 Why are inertial and gravitational mass numerically equal, and is this equality a coincidence or a consequence of deeper mechanics?
• RQ4 Can gravity be explained without invoking quantum gravity or undetected particles like gravitons?
• RQ5 What role does the finite speed of light play in the emergence of gravitational mass and its behavior?

Key findings

• Gravitational mass arises as a consequence of retarded interactions and the finite speed of light, not as a fundamental property.
• The resulting force law matches Newton's inverse-square law of gravitation with high fidelity.
• The equivalence of inertial and gravitational mass is not a coincidence but a mechanical consequence of energy and momentum conservation.
• The model avoids the need for gravitons or gravitational waves, explaining gravity through classical field-like behavior from retarded potentials.
• The theory maintains consistency with energy and momentum conservation, and excludes infinite values from physical reality.
• The derivation shows that gravitational mass is a dynamic, emergent property of how energy and momentum propagate at light speed.