Part I: Foundations

The Core Postulate

Proper Space Kinematics rests on a single foundational assertion: space densifies uniformly and isotropically at the constant rate c (the speed of light). This densification occurs everywhere, at all scales, continuously. It is not expansion outward from a point, but densification in place—the geometric substrate itself becoming progressively denser.

The spatial density function ρ(t) increases linearly with time:

ρ(t) = ρ₀(1 + Ht/c)

where ρ₀ is a reference spatial density, H is the Hubble parameter, and c is the speed of light. The Hubble parameter is not independent of c; it emerges from the densification rate.

Volume Preservation and Geometric Equilibrium

Matter maintains constant proper volume against spatial densification. This is not active resistance but passive geometric necessity. As space densifies, two opposing effects emerge from the same process: an inward increase in spatial density, and an outward metric expansion (coordinate divergence). Matter exists at the equilibrium point of these dual manifestations.

The volume preservation condition implies:

V(t)ρ(t) = V₀ρ₀ = constant

This equilibrium—densification balanced against metric expansion—gives rise to gravitational gradients, atomic structure, and the observed stability of matter.

These postulates represent a significant ontological departure from both General Relativity’s curved spacetime and quantum field theory’s particle-field duality. However, PSK aims to reproduce their empirical predictions through different geometric foundations. The departure is in what we claim is happening, not in what we predict will be observed in regimes where these frameworks have been tested.

The Geometry of Space

In PSK, the geometry of space is flat, orthogonal, isotropic, and homogeneous everywhere, to infinite extent. This is axiomatic, not derived. Space is infinite Euclidean volume undergoing uniform densification.

This represents a significant departure from general relativity, where mass-energy curves spacetime and geometry varies with location. In PSK, geometry is invariant. What varies is spatial density. Gravity, time dilation, and other phenomena attributed to curved spacetime emerge instead from density gradients within fundamentally flat space.

The "flatness" observed in cosmology is not a fine-tuned initial condition requiring explanation. It is definitional—a property of the geometric substrate itself.

Space and Time, Not Spacetime

PSK treats space and time as ontologically distinct. This represents a fundamental departure from general relativity, which unifies them into a single four-dimensional manifold called spacetime.

In general relativity: Space and time are aspects of one entity. The metric describes intervals in spacetime, mixing spatial and temporal components. Events are located in a four-dimensional block; the distinction between space and time is observer-dependent. Past, present, and future are equally real in the "block universe" interpretation—all of spacetime exists timelessly.

In PSK: Space is the geometric substrate—flat, Euclidean, three-dimensional, infinite in extent, densifying at rate c. Time is not a fourth dimension. Time is the densification process itself. Space and time have distinct ontological status: space exists and densifies; time is what we call that densification.

There is no unified spacetime manifold to curve. This is why PSK rejects spacetime curvature as an explanation for gravity—you cannot curve a four-dimensional entity that does not exist. Instead, PSK has flat three-dimensional space with density gradients, and time as the process of that space evolving.

This distinction has consequences. In GR’s block universe, the past still exists (elsewhen in the manifold) and the future already exists (we simply haven’t reached it yet). In PSK, the past—sparser density configurations—no longer exists geometrically. The future—denser configurations—has not yet emerged. There is no traveling to the past because there is nothing to travel to. Time is not a dimension along which one could move; it is the process of space becoming denser.

PSK deliberately avoids the term "spacetime" except when referring to what general relativity describes. The framework deals with space (which densifies) and time (which is that densification), not a unified spacetime manifold.

Critical Clarification on Predictions

This ontological difference—treating space and time as distinct rather than unified—does not imply different predictions for gravitational phenomena in tested regimes. PSK’s density gradients in flat 3D space are constructed to produce mathematically identical outcomes to GR’s geodesics in curved 4D spacetime for:

• All solar system tests (perihelion precession, light bending, Shapiro delay)

• Gravitational wave observations (LIGO/Virgo waveforms, propagation speed)

• Cosmological measurements (redshift-distance relation, gravitational lensing)

The frameworks differ in what they claim is fundamentally real (unified spacetime vs. separate space and time-as-process), not in what they predict will be measured in these regimes.

The Speed of Light as the Sole Fundamental Constant

PSK proposes that c is the sole irreducible constant of nature. All other physical constants—the gravitational constant G, Planck’s constant ħ, the fine structure constant α, particle masses—derive from c through the geometry of spatial densification.

The value of c sets the "size" of matter and the amplitude of atomic binding energies. A universe with a different value of c would have correspondingly scaled atoms, scaled time, scaled energies—but the internal ratios and relationships would remain identical. From inside such a universe, the difference would be undetectable.

This raises a philosophical question: is the numerical value of c meaningful in isolation? We measure c in meters per second, but meters and seconds are themselves defined by atomic processes that PSK claims are determined by c. The number 299,792,458 may be an artifact of unit conventions rather than a property of the universe. The value of c may be tautological—the universe’s self-consistency rather than a tunable parameter.

Nevertheless, PSK accepts c as an empirical constant whose particular value has no deeper explanation within the framework. This is where explanation ends and observation begins.