Two Types of Space:Rectilinear and Curvilinear
Abstract
PEI proposes that space exists in two fundamentally different geometric conditions depending on the presence or absence of gravity. In the absence of gravity, space is rectilinear—motion is straight and geometry is flat. In the presence of gravity, space becomes curvilinear—motion bends and geometry appears curved. This article presents the PEI framework in clear, non-technical terms and explains why geometry is treated as a consequence of gravity rather than its cause.
1. Introduction
Most modern discussions of gravity assume that space itself is inherently curved. PEI takes a different starting point.
PEI proposes that space has no fixed geometry of its own. Instead, its geometry depends entirely on whether gravity is present.
From this perspective, there are two types of space:
Rectilinear space — space without gravity
Curvilinear space — space under gravitational influence
These are not different universes or substances, but two geometric conditions of the same space.
2. Rectilinear Space: Space Without Gravity
Rectilinear space is the default condition of space when no gravitational influence exists.
In rectilinear space:
Motion proceeds in straight lines
Directions are uniform and globally consistent
Parallel paths never converge
Geometry is flat (Euclidean)
No natural curvature exists
Rectilinear space is not imposed by assumption. It is observed whenever nothing bends motion.
In PEI’s framework:
Flat space is what remains when gravity is absent.
3. Curvilinear Space: Space With Gravity
Curvilinear space emerges wherever gravity acts.
Gravity, in PEI, is a real, active force emanating from a core—planetary, stellar, or galactic. This force continuously bends motion toward the core.
As a result:
Straight-line motion is deflected
Paths become curved
Directions lose symmetry
Geometry appears non-Euclidean
When all motion within a region bends in a systematic way, observers naturally describe that region as curved space.
PEI emphasizes:
Space does not bend motion.
Gravity bends motion, and space appears curved as a result.
4. Geometry as an Effect, Not a Cause
A central principle of PEI is causal discipline:
Forces act
Motion responds
Geometry records the outcome
Geometry is therefore descriptive, not generative.
Curvilinear geometry does not create gravity.
It is the visible imprint of gravity’s action.
This distinction allows PEI to accept geometric descriptions without assigning them physical agency.
5. Transition Between the Two Types of Space
Rectilinear and curvilinear space are not separate realms. Space transitions smoothly between them as gravitational influence changes.
Near a massive core → strongly curvilinear
Far from the core → weakly curvilinear
Beyond influence → rectilinear
This leads to a key PEI definition:
Curved Space is a volume of gravitational influence.
Where influence fades, curvature fades.
6. Application to Earth and the Cosmos
Under the PEI framework:
Earth’s surrounding space is curvilinear because Earth’s core exerts gravity
If that gravitational influence were removed, space would immediately revert to rectilinear
No geometric “fabric” needs to adjust—motion simply straightens
At cosmic scales:
Galaxies create curvilinear regions around their cores
Intergalactic regions approach rectilinear space
The universe contains both types simultaneously, depending on influence
7. Relationship to Existing Theories
PEI does not reject classical or modern physics. It reorders causality.
Newton described gravity as a force in flat space
Einstein described gravity through curved geometry
PEI proposes: gravity determines geometry
This preserves observation while restoring intuitive cause-and-effect reasoning.
8. Conclusion
PEI’s proposal of two types of space offers a simple, unified framework:
Rectilinear space exists where gravity is absent
Curvilinear space exists where gravity acts
Geometry follows force, not the other way around
By treating space as responsive rather than autonomous, PEI provides a coherent explanation from cosmic scales to local motion—without adding unnecessary assumptions.
PEI Summary Statement
Without gravity, space is rectilinear.
With gravity, space becomes curvilinear.
Geometry reflects gravity’s action—it does not create it.