Part XIV: Relationship to Established Frameworks

A Critical Distinction: Equivalence vs. Deviation

Before examining PSK’s relationship to established frameworks, a fundamental clarification is required to prevent misunderstanding.

PSK Does Not Claim GR or SR Make Wrong Predictions

In every regime where general relativity and special relativity have been experimentally tested, PSK predicts identical observational outcomes. This bears emphasis because it represents a different kind of theoretical proposal than most alternatives to established physics.

PSK is not claiming:

• "Einstein got the numbers wrong"

• "GR makes incorrect predictions that PSK corrects"

• "There are subtle deviations from SR that experiments will reveal"

• "The mathematics of relativity needs modification"

PSK is claiming:

• "The mathematics of GR and SR describe reality accurately"

• "However, what those mathematics represent may be reinterpretable"

• "Spacetime curvature and density gradients may be two descriptions of the same geometric reality"

• "Understanding WHY the mathematics work may require different ontology"

The Equivalence Claim

In the following regimes, PSK predicts outcomes identical to GR/SR:

Special Relativity:

✓ The speed of light is constant for all inertial observers

✓ Time dilation factor γ = 1/√(1-v²/c²) for objects that have accelerated

✓ Length contraction by factor 1/γ

✓ Relativistic momentum p = γmv

✓ Energy-momentum relation E² = (pc)² + (mc²)²

✓ Particle accelerator observations (particles asymptotically approach c)

✓ Cosmic ray muon lifetimes

✓ GPS satellite time corrections

General Relativity:

✓ Light deflection by the sun: 1.75 arcseconds

✓ Mercury’s perihelion precession: 43 arcseconds/century

✓ Gravitational time dilation in Earth’s field

✓ Shapiro time delay

✓ Gravitational redshift

✓ Gravitational wave propagation at speed c

✓ LIGO/Virgo waveform observations from binary mergers

✓ Frame dragging (Gravity Probe B measurements)

These are not approximate agreements. PSK claims exact equivalence in these regimes because PSK’s geometric machinery—density gradients, state-mapping, wake dynamics—produces mathematically identical predictions to GR’s geometric machinery of curved spacetime.

Why This Equivalence Matters

If two frameworks make identical predictions, the choice between them cannot be settled by observation alone in those regimes. The choice becomes:

1. Philosophical: Which ontology is more parsimonious, conceptually clear, or metaphysically satisfying?

2. Empirical in different regimes: Do the frameworks make different predictions in domains not yet tested?

3. Explanatory: Does one framework answer "why" questions the other leaves unaddressed?

PSK’s case rests on all three:

Philosophical: One process (densification) vs. multiple separate phenomena (curved spacetime, quantum fields, thermodynamic arrow, force carriers)

Empirical: PSK makes specific different predictions (neutrino flux, radiometric age ceiling, Hubble recession time dilation)

Explanatory: PSK attempts to explain WHY matter creates gravitational effects, WHY c is constant, WHY entropy increases—not merely THAT these occur.

Where Predictions Actually Differ

PSK is not purely interpretive. It makes falsifiable claims that differ from standard frameworks:

1. Neutrino Emission from Stable Matter

Standard model: Neutrinos only from nuclear reactions (beta decay, fusion, etc.)

PSK: All matter emits neutrinos continuously from volume equilibrium maintenance

Test: Neutrino flux should correlate with mass, not nuclear activity

2. Maximum Radiometric Age

Standard model: Oldest materials can date to ~13.8 Gyr (age of universe)

PSK: No material anywhere can exceed ~4.6 Gyr (critical density threshold)

Test: Sample return from distant stellar systems; extrasolar meteorites

3. Time Dilation from Hubble Recession

Standard model: Distant galaxies are time-dilated by factor (1+z)

PSK: Hubble recession produces no time dilation; only acceleration does

Test: See discussion in Part VI—this remains under debate within PSK

4. Superluminal Self-Propelled Travel

Standard model: Continuous proper acceleration asymptotically approaches c

PSK: Continuous proper acceleration can exceed c relative to origin

Test: May be observationally inaccessible (horizon crossing prevents measurement)

5. Local Hubble Effect

Standard model: Metric expansion negligible below supercluster scales

PSK: Divergence operates at all scales, balanced by coalescence

Test: Precision measurements of bound system dynamics for unexpected recession component

These are the empirical battlegrounds. In tested regimes, PSK reproduces established results. In these specific untested or differently-interpreted regimes, PSK stakes falsifiable claims.

The Nature of Scientific Progress

History shows that major advances often come not from finding small corrections to existing theories, but from recognizing that accurate mathematics can have multiple physical interpretations:

Ptolemaic epicycles accurately predicted planetary positions. Copernican heliocentrism predicted the same positions differently. Both were mathematically equivalent for observations. The choice required examining which framework better explained WHY.

Newtonian gravity accurately predicted orbital mechanics. General relativity predicted the same mechanics (plus small corrections). Both frameworks worked; GR explained WHY (geometry, not force).

Copenhagen quantum mechanics accurately predicts measurement outcomes. Bohmian mechanics predicts identical outcomes. Many-worlds interpretation predicts identical outcomes. All are empirically equivalent; choice is interpretive.

PSK proposes a similar situation: GR’s mathematics work, but PSK offers an alternative account of what those mathematics represent. The equivalence in tested regimes is intentional—PSK aims to explain the same reality from different foundations.

Implications for This Treatise

When PSK says "gravity as density gradients," this should not be read as: "GR’s spacetime curvature predictions are wrong, and here are corrections."

It should be read as: "GR’s predictions are correct, and here’s an alternative geometric mechanism that produces those same predictions."

When PSK says "light as state-mapping," this should not be read as: "Maxwell’s equations fail, and here’s the fix."

It should be read as: "Maxwell’s equations work, and here’s what they might be describing at a deeper level."

The burden PSK bears is not disproving GR or SR—they work. The burden is proving that densification geometry can reproduce their successes while offering additional explanatory power or making successful novel predictions.

Summary

PSK and GR/SR are:

• Empirically equivalent in all tested regimes (same predictions)

• Ontologically distinct (different accounts of what’s happening)

• Potentially empirically distinguishable in specific untested regimes

This is interpretive realism—the claim that accurate mathematics may describe a physical reality different from what we initially supposed.

Whether PSK’s alternative ontology is correct remains an open question. But it is not a question about whether GR and SR make good predictions. They do. It is a question about what those good predictions represent.

PSK and General Relativity

General relativity describes gravity as spacetime curvature caused by mass-energy. PSK describes gravity as density gradients in flat space caused by matter’s traversal through densification. The predictions are intended to be identical; the geometric substrate differs.

PSK does not claim GR is wrong. GR’s mathematics work. PSK proposes a different picture of what the mathematics might represent—an alternative ontology compatible with the same observations.

A fundamental distinction: GR describes a unified four-dimensional spacetime manifold. PSK describes three-dimensional space (which densifies) and time (which is that densification). These are not different coordinate systems on the same entity; they are different ontologies. GR’s "spacetime curvature" has no analog in PSK because PSK has no spacetime to curve. The phenomena GR attributes to curvature, PSK attributes to density gradients in flat space.

PSK and Quantum Mechanics

Quantum mechanics describes phenomena probabilistically with unparalleled accuracy. PSK does not propose different predictions but different interpretations: measurement as state sharing, entanglement as shared past contiguity, superposition as absence of state-sharing rather than simultaneous multiple states.

PSK aligns more closely with relational interpretations of quantum mechanics than with Copenhagen or many-worlds interpretations.

PSK and the Standard Model

The Standard Model successfully describes particle physics with multiple forces, mediating particles, and coupling constants. PSK proposes that these are not fundamental but emergent from a single geometric process at different scales. The mathematical machinery of the Standard Model may be reinterpretable as descriptions of density-field geometry rather than literal particle exchange.

PSK and Thermodynamics

Statistical mechanics grounds thermodynamics in probability over microstates. PSK grounds it in geometry—entropy increases because space increases. The statistical approach describes; PSK proposes to explain why the statistics work out as they do.

Falsifiability

PSK makes several claims that could, in principle, distinguish it from standard frameworks:

(1) Neutrino flux should be proportional to mass, not just nuclear activity. A cold, stable mass should emit neutrinos. (2) The Hubble effect operates at all scales; local recession effects should be detectable in precision measurements. (3) Galaxy rotation curves should emerge from densification geometry without dark matter. (4) Cosmic "acceleration" should be revealed as constant proportional expansion when properly analyzed. (5) The inverse square law for all force-like phenomena arises from the same geometric origin.

If these predictions fail, PSK loses credibility. If they succeed, PSK gains support—though it would not prove PSK "true," only observationally consistent.