Part III: Gravitation

The Observation

Masses attract one another. Light bends near massive objects. Time passes more slowly in gravitational fields. Objects in free fall follow curved trajectories. These observations are precisely described by Newton’s law of gravitation and, more completely, by Einstein’s general relativity.

The Standard Interpretation

General relativity interprets gravity as the curvature of spacetime caused by mass-energy. Matter tells spacetime how to curve; curved spacetime tells matter how to move. Gravitational attraction is not a force but the natural motion of objects along geodesics in curved geometry.

The PSK Interpretation

PSK offers a different picture. Matter is continuously traversing into denser spatial states as space densifies at rate c. As matter progresses into this denser future, it leaves behind a density gradient—a geometric wake in the spatial density field.

This wake is gravitation. The more mass, the greater the wake. The gradient always points toward the matter that created it, because the wake is always behind the matter (in the less-dense direction). Other matter and light respond to this gradient, appearing to be "attracted" toward the mass.

The gravitational gradient near mass M takes the form:

∇ρ = −GM/c²r³ r̂

Time dilation emerges naturally from density variation:

dt₁/dt₂ = 1 − d/c²

This formulation is constructed to produce results numerically equivalent to Newtonian gravity in the appropriate limit. PSK claims that density gradients in flat space reproduce general relativistic predictions for orbital precession, gravitational lensing, time dilation, frame dragging, and gravitational waves.

The mathematical demonstration of exact equivalence for all GR predictions is an ongoing development requirement for the framework. In tested regimes—solar system dynamics, binary pulsar systems, LIGO/Virgo gravitational wave observations—PSK asserts it will reproduce GR’s predictions exactly. The difference lies not in what is predicted but in the geometric mechanism: density gradients in fundamentally flat space rather than curvature of a unified spacetime manifold.

Gravitational Lensing

In general relativity, light follows curved geodesics through curved spacetime, bending around massive objects. In PSK, light bends through density gradients analogously to optical refraction—light changing direction as it passes through a medium of varying density. The geometry remains flat; the density varies.

The effect is identical. The mechanism differs.

The Equivalence Principle as Identity

Einstein’s equivalence principle states that gravitational mass and inertial mass are equivalent — an observer in a closed box cannot distinguish between sitting stationary in a gravitational field and accelerating through empty space. Einstein took this as a profound clue leading to general relativity, but the reason for the equivalence remains unexplained within GR. It is treated as an empirical fact upon which the theory builds.

PSK proposes that gravitational and inertial mass are not merely equivalent but identical — the same phenomenon, not two phenomena that happen to match.

In a gravitational field: You are in a region of density gradient — the wake left by massive matter as it traverses densifying space. This gradient affects how you traverse density states. Your feet occupy a different density region than your head. You experience this as weight.

Accelerating through empty space: You are changing your trajectory through densifying space. Acceleration means altering your path through density states. This is not merely like being in a gravitational field — it is the same geometric relationship between your matter and the density structure.

In both cases, what you experience is your matter’s relationship to spatial density gradients. There is no separate "gravitational force" and "inertial force" that happen to produce identical effects. There is one phenomenon: how matter traverses densifying space, and how that traversal is affected by density gradients — whether those gradients arise from nearby mass or from your own acceleration.

The equivalence is not a coincidence requiring explanation. It is an identity to be recognized.

Matter as Revealer, Not Actor

Wheeler’s aphorism for general relativity — "Matter tells space how to curve, space tells matter how to move" — is elegant in its reciprocity. Matter and space each act upon the other.

PSK offers no corresponding reciprocal statement, because PSK is fundamentally asymmetric. Space does one thing: it densifies at rate c, uniformly, everywhere, always. This is the sole action. Matter does not cause anything. It does not tell space what to do.

Matter is passive — riding the densification, maintaining its proper volume through geometric equilibrium, leaving density gradient wakes as it traverses into denser states. These are not actions matter performs but consequences of matter existing within densifying space.

Matter is not the actor; it is the revealer. The density gradients, the gravitational effects, the wake structures — these are how matter makes visible what space is doing. Without matter, space would still densify, but there would be nothing to mark the process, nothing to reveal the geometry.

This asymmetry is fundamental to PSK. Space is the dynamic substrate. Matter is the passive participant that, by its presence, allows us to observe what would otherwise be invisible: the continuous, universal densification that underlies all physical phenomena.

What PSK Clarifies

Why gravity is always attractive: The wake is always behind the matter, in the sparser-past direction. The gradient always points toward mass. There is no configuration that produces repulsion.

Why gravity propagates at c: The densification rate is c. Gradient information cannot outrun the process creating it.

Why gravity is universal: All matter traverses densifying space. All matter leaves a wake. All matter responds to gradients. There are no exceptions.

Why gravitational and inertial mass are identical: They are not two equivalent quantities but one phenomenon — matter’s geometric relationship to spatial density gradients, whether from external mass or self-acceleration.

Frame Dragging and Gravitational Waves

In general relativity, mass in motion produces different gravitational effects than mass at rest — so-called "gravitomagnetic" effects, analogous to how moving charge creates magnetic fields. Frame dragging (from steady rotation) and gravitational waves (from accelerating mass) are both gravitomagnetic phenomena. In PSK, they share a common explanation: wakes inherit the motion characteristics of the matter creating them.

Frame Dragging

Standard general relativity predicts that a rotating massive body "drags" spacetime around with it — the Lense-Thirring effect, confirmed by Gravity Probe B. In PSK, this is straightforward.

A rotating planet is matter traversing densifying space with angular momentum. Its wake isn’t static — it carries the rotational structure of the matter creating it. Other matter near this rotating wake gets dragged along because it’s responding to a wake that itself has rotational character.

The analogy to electromagnetic induction is direct: move a magnet relative to a conductor, and current is induced. The magnet’s motion imparts structure to the field, and that structure affects nearby matter. Similarly, a rotating mass imparts rotational structure to its wake, and that structure affects nearby matter.

Frame dragging isn’t spacetime being "twisted." It’s wakes inheriting the motion characteristics of the matter creating them.

Gravitational Waves

Gravitational waves — detected by LIGO from merging black holes and neutron stars — are conventionally described as ripples in spacetime itself, propagating at c. In PSK, they are propagating disturbances in wake structure.

When two massive objects spiral into each other, each is leaving a wake as it traverses densifying space. But their trajectories are changing rapidly — they’re accelerating. The wake structure inherits this changing motion. The result is a dynamic, propagating pattern in the density gradient — not a static wake but an oscillating one.

The "wave" isn’t spacetime rippling. It’s the wake structure carrying the signature of the accelerating motion that created it. Just as frame dragging is wakes inheriting rotational motion, gravitational waves are wakes inheriting the oscillatory, spiraling motion of their source.

Why they propagate at c: The wake is created by matter traversing densification at rate c. Disturbances in the wake structure cannot outrun the process creating them.

What LIGO detects: The passing density gradient disturbance affects the state-sharing geometry between the detector’s mirrors. The "stretch and squeeze" is the detector matter responding to the passing wake pattern — the same mechanism as all gravitational effects, just dynamic rather than static.

The chirp: As merging objects spiral closer, their orbital frequency increases, the wake pattern becomes more rapid, and the detected frequency increases — producing the characteristic chirp that LIGO observes.

Empirical Equivalence with GR

PSK’s wake interpretation predicts gravitational wave signatures identical to GR’s predictions in all observable aspects:

• Waveform shapes (chirp, ringdown, frequency evolution)

• Strain amplitudes as a function of distance

• Propagation speed (exactly c)

• Polarization states

The LIGO/Virgo observations of binary black hole and neutron star mergers are fully consistent with either framework. GR describes these as ripples in spacetime geometry. PSK describes them as propagating disturbances in wake structure. The frameworks differ in ontology (what is oscillating), not in what detectors measure.

Frame dragging and gravitational waves are not separate phenomena requiring separate explanations. They are both manifestations of a single principle: wakes inherit the motion characteristics of the matter creating them. Steady rotation produces frame dragging; accelerating motion produces gravitational waves.

Wake Geometry vs. Spacetime Curvature

PSK’s density wake and general relativity’s spacetime curvature perform the same explanatory role. Both describe how mass affects the space around it, both extend to infinity, both produce identical observable effects in familiar regimes:

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Property General Relativity PSK ———————– ————————————- —————————————— Mechanism Mass causes spacetime curvature Mass leaves density wake

Spatial extent Curvature extends to infinity Wake extends to infinity

Effect on other mass Follows geodesics in curved space Follows density gradients

Effect on light Follows null geodesics (lensing) State-mapping through gradient (lensing)

Distance dependence Falls off as 1/r² (Newtonian limit) Falls off as 1/r²

Geometry Non-Euclidean (curved) Euclidean (flat) with varying density

Causality Matter tells space how to curve Matter passively leaves trail ——————————————————————————————————–

The critical difference is not in observable predictions but in causal direction. General relativity posits mutual action: matter tells spacetime how to curve, spacetime tells matter how to move. PSK posits asymmetric passivity: space densifies (the sole action), matter rides the densification and leaves a wake (passive consequence), other matter responds to the wake (passive response).

In GR, gravity requires no boundary—curvature extends forever. In PSK, likewise—the wake extends forever. Neither framework posits "bound systems" with edges. What we call a bound system is merely a region where the gradient is strong enough that components remain correlated over long timescales. The wake of the Earth doesn’t stop at the moon; it merges imperceptibly with the wakes of other bodies, extending without limit.

Empirical Status

In every regime where these predictions have been tested:

• Solar system (Mercury’s 43"/century precession, 1.75" light deflection by the Sun)

• Binary pulsars (orbital decay rates matching GR to 0.2%)

• Gravitational waves (LIGO/Virgo waveforms from dozens of detections)

• Cosmology (gravitational lensing, redshift-distance relation)

PSK claims to reproduce GR’s numerical predictions exactly. The mathematical machinery differs (density gradients vs. metric curvature), but the observational outcomes are identical.

The choice between wake geometry and spacetime curvature is interpretive in these tested regimes. It becomes empirical only in domains where the frameworks might make different predictions—such as neutrino emission rates, radiometric age limits, or time dilation from Hubble recession.