In Curvilinear Space, Rectilinear Motion Does Not Exist

The 1919 Eclipse Revisited Through the Canal–Water Analogy: PART 1

Abstract

The 1919 solar eclipse observations are commonly cited as evidence that gravity bends light. Within the Paudelian Economics Institute (PEI) framework, this phenomenon is interpreted more fundamentally: gravity forms curvilinear space, and in such space globally straight motion does not exist. Light did not “bend” in response to a force; it followed the only geometrically available paths. This section reframes the eclipse using the canal–water analogy, clarifying why curved trajectories are not reactions but necessities.

1. The Observational Event

During the Solar Eclipse of 1919, expeditions led by Arthur Eddington photographed stars whose light passed close to the Sun. The stars appeared displaced from their usual positions, indicating that the light’s path near the Sun differed from its path in regions far away.

The conventional reading states that gravity deflected light.

PEI asks a prior question: What was the geometry of space through which that light traveled?

2. The PEI Principle

PEI begins with a geometric axiom:

Gravity forms curvilinear space.

From this, a strict consequence follows:

In curvilinear space, straight motion does not exist.

“Straight” here refers to a global, rectilinear path. Once space itself is curved, such paths are unavailable. Motion can be locally straight—step by step—but globally it must conform to the curvature of space.

3. Gravity as the Canal

The canal–water analogy makes this unavoidable logic intuitive.

• A canal is a pre-existing geometric structure carved into terrain.

• Its curvature exists regardless of whether anything flows through it.

• The canal does not act on water; it defines the path water can take.

In the PEI framework, the Sun’s gravity is the canal. It shapes space into a curved geometry surrounding it. This geometry exists before light arrives and independent of it.

4. Light as the Water

Starlight approaching Earth during the eclipse is the water.

• Light travels inertially.

• It does not steer, correct, or decide.

• When it enters the Sun’s gravitational region, it enters a curved spatial canal.

The light then follows the canal—not because it is pushed or pulled, but because no straight channel exists within that geometry.

5. Why the Light Had No Straight Option

A natural question arises: Why didn’t the light continue straight?

Within the PEI interpretation, the answer is simple and final:

There was no straight path available in that region of space.

In curvilinear space:

• Parallel paths can converge.

• Directions themselves are bent.

• What appears as “deflection” from afar is obedient motion within geometry.

The light did not change direction; it maintained inertial motion along the straightest paths permitted by the curved canal.

6. What the Eclipse Actually Revealed

The eclipse did not show light being acted upon.

It showed space revealing its shape through motion.

The observed stellar displacement was a geometric signature:

• Not evidence of photons responding to force

• But evidence that space near the Sun is not rectilinear

Just as observing curved water flow reveals the shape of a canal, observing curved light paths revealed the curvature of space.

7. Reframing “Bending”

From the PEI standpoint, the word bending is misleading.

• Water does not bend in a curved canal.

• It flows naturally along the canal’s shape.

Likewise:

• Light did not bend at the Sun.

• It followed the geometry that gravity had already imposed.

Curvature is not an effect of motion.

Curvature is the condition of motion.

8. Conceptual Implications

The 1919 eclipse can therefore be restated as follows:

When gravity forms curvilinear space, straight motion ceases to exist as a global possibility.

Motion—whether of mass or light—becomes a tracer of geometry.

This reframing shifts explanation from interaction to structure, from force to form.

Conclusion

Reinterpreted through the PEI framework, the 1919 eclipse demonstrated not that gravity acts on light, but that space near massive bodies is inherently curvilinear. In such space, motion cannot be globally straight. Light followed its path perfectly—not by reacting to gravity, but by obeying geometry.

Gravity, in this view, is not an external agent.

It is the canal of space itself, and motion—like water—has no option but to follow its curves.