Gravity as Core Influence and Curvilinear Space
A PEI Framework with the 1919 Eclipse Revisited: PART 2
Abstract
The Paudelian Economics Institute (PEI) advances a unified view of gravity as the active influence of a Core that structures the volume around it. This influence manifests in two inseparable expressions: direct pull on matter (force) and the carving of geometric possibilities in the vacuum (curvilinear space). Together, they ensure that all propagation—massive or massless—must conform to the Core’s presence. Revisited through the canal–water analogy, the 1919 eclipse becomes a decisive demonstration of this principle: when space is curvilinear, globally straight motion does not exist.
1. The PEI Core Proposition
PEI begins with a causal statement:
Gravity is the active influence of a Core that structures the volume around it.
This influence is not passive and not merely descriptive. The Core continuously shapes its surroundings, producing two outcomes at once:
Force — how gravity is felt by matter
Geometry — how gravity is obeyed by all motion
These are not alternatives. They are dual expressions of a single origin.
2. Force and Geometry: One Cause, Two Expressions
Force (Matter’s Experience)
Material bodies accelerate toward the Core. This pull is measurable and directional. PEI does not discard force; it grounds force in the Core’s activity.
Geometry (Motion’s Constraint)
Simultaneously, the Core carves the vacuum, bending directions and removing the possibility of globally straight paths. Geometry is not a backdrop—it is made.
Force explains why matter accelerates.
Geometry explains why everything must follow curved paths.
3. The Canal–Water Analogy (Unifying Principle)
The canal–water analogy makes the unity intuitive:
The Core carves the canal.
Curvilinear space is the canal itself.
Motion (matter, light, signals) is the water.
For water with weight (matter), the canal’s slope manifests as force-like acceleration.
For weightless flow (light), the canal still dictates direction—without any pull.
Thus, force and geometry are not competing explanations; they are two readings of the same carved structure.
4. “In Curvilinear Space, Straight Motion Does Not Exist”
This PEI statement is geometric, not rhetorical.
Locally, motion may proceed “straight ahead.”
Globally, once space is curved, rectilinear paths are unavailable.
Motion does not become curved; it is born into curvature.
Ask why a flow curves in a canal. The answer is final: there is no straight channel available.
5. The 1919 Eclipse as a Geometric Demonstration
During the Solar Eclipse of 1919, expeditions led by Arthur Eddington observed that starlight passing near the Sun appeared displaced from its usual positions.
The canonical conclusion was that gravity bends light.
PEI asks a prior question: what was the geometry of space through which that light traveled?
6. Reframing the Eclipse with the Canal–Water Analogy
The Sun as Canal-Carver
The Sun’s Core pre-structures space around it. This curvature exists whether or not light passes through.
Light as Water
Starlight approaches inertially. When it enters the Sun’s gravitational region, it enters a curved canal.
Why the Light Curved
Not because it was pushed or pulled sideways—but because no straight path existed in that region of space. The light followed the straightest paths available within the curved canal.
The eclipse did not show light reacting to gravity.
It showed geometry revealing itself through motion.
7. What the Telescope Actually Measured
The observed stellar displacement was a geometric signature, analogous to inferring a canal’s shape by watching water flow. The instrument detected not force acting on photons, but curvature constraining propagation.
From the PEI standpoint, the word bending misleads:
Water does not bend in a curved canal.
It flows naturally along the canal’s shape.
So did the light.
8. The Vacuum as Structured Possibility
PEI treats the vacuum not as emptiness, but as a field of geometric possibilities continuously shaped by the Core.
Gravity defines which directions exist.
Space becomes a navigable volume only after being structured.
Without the Core, curvature collapses toward flatness—and guided motion disappears.
Space is the consequence of gravitational structuring.
9. Resolving the Force–Geometry Divide
PEI avoids a false choice:
Gravity is not only force.
Gravity is not only geometry.
Gravity is the Core’s active influence—
force for matter, geometry for motion—
unified by one cause.
Force without geometry is blind.
Geometry without activity is empty.
Conclusion
This flagship PEI framework reframes gravity as an active Core influence that simultaneously pulls matter and sculpts space. The 1919 eclipse, revisited through the canal–water analogy, becomes a clean demonstration of the central claim: in curvilinear space, globally straight motion does not exist. Light did not deviate; it faithfully followed geometry.
Gravity, here, is not an external actor nor a passive metric.
It is the structuring act that makes force and geometry possible.