Appendix A

Appendix A: Comparison with Sean Wade’s Proper Space Kinematics

Background

In April 2013, Sean Wade published a paper titled "Proper Space Kinematics" in Progress in Physics (Volume 2, pp. 29–34). Wade also presented this work in 2014 at a physics conference. This appendix provides a detailed comparison between Wade’s framework and the one developed in this treatise.

References:

Wade, S. (2013). Proper Space Kinematics. Progress in Physics, 2, 29–34. https://www.progress-in-physics.com/2013/PP-33-08.PDF

Wade, S. (2014). Proper Space Kinematics [Video presentation]. https://youtu.be/ftbbLpRPgZs

Key Similarities

The Name and Core Concept

Both frameworks use the name "Proper Space Kinematics" and propose that space is undergoing densification at rate c. Wade writes: "Proper Space is a real, three-dimensional space clocked by proper time that is undergoing a densification at the rate of c." This is strikingly similar to the core postulate of the present treatise.

Rejection of Stationary States

Wade states: "A static ruler of fixed length is a forbidden item; an absolutely stationary observer is a nonsensical frame of reference that does not exist." In his 2014 presentation, he emphasized that "rest is really forbidden" and "any frame of rest is a forbidden frame of reference." The present treatise similarly rejects truly stationary frames.

c as Characteristic Rate

Both frameworks reframe c as the "characteristic velocity" of the universe — the rate of densification — rather than merely a speed limit. Wade uses c as both the densification rate and a label for the universe itself.

Time Dilation from Densification

Both frameworks derive time dilation effects from the densification process. Wade explains that faster-moving objects "travel through less points" and therefore experience less densification, which manifests as time dilation.

Isotropic Nature

Wade emphasizes that densification "is isotropic — there is no center from which expands or contracts." This aligns with the present treatise’s assertion that densification occurs uniformly everywhere.

Arrow of Time

Both frameworks connect the arrow of time and entropy to the densification process. Wade notes that densification "speaks to the arrow of time because this moves in one direction only."

Key Differences

Mathematical Approach

Wade develops explicit coordinate transformations between "proper space" (z, τ), "object space" (x, t), and "stationary space" (y, τ). He provides equations such as dz = dx + cdt, defines a "waxing velocity" w = dz/dτ = α(v + c), and introduces a temporal dilation coefficient α. The present treatise is more conceptually developed but less mathematically formalized — a limitation acknowledged in the Discussion section.

Matter/Energy Distinction

Wade introduces an unusual distinction using imaginary numbers: matter is "material" and energy is "immaterial" (i-material), with a 90-degree phase relationship between them. He asserts that "all particles move at the speed of light" and that mass and energy appear differently to each other due to this phase difference. He claims "E = mc² is overdetermined." The present treatise does not adopt this matter/energy phase framework.

Quantum Mechanics

Wade attempts to replace quantum mechanics entirely, attributing wave-particle duality to the "complex quality of mass" and the phase relationship between matter and energy. The present treatise takes a different approach: reinterpreting quantum phenomena (entanglement as past contiguity, measurement as state-sharing, superposition as incomplete state-specification) without eliminating QM’s predictive framework.

State-Mapping and Geometric Intersection

The picture developed in this treatise — continuous geometric coincidence at historical density states, matter sharing state through intersection, the dissolution of "light as traveling photons" into state-sharing relationships — appears to be entirely original. Wade’s paper and presentation do not develop anything similar. This includes the insight that matter is continuously coincident with distant matter at sparser historical density states, and that electromagnetic phenomena are state-sharing through this intersection geometry.

Gravity

The present treatise treats gravity as density gradients (wakes) created by matter traversing densifying space. Wade’s paper explicitly focuses on kinematics "without forces" and notes that his approach will "divorce gravity from space." He does not develop a gravitational mechanism within his densification framework.

Nuclear Forces

The present treatise interprets the strong nuclear force as steep density gradients at small scales (the same phenomenon as gravity at a different scale) and the weak force as geometric shedding. These interpretations are absent from Wade’s kinematics.

Cosmological Framework

The present treatise develops a detailed cosmological picture: the critical density threshold at approximately 4.6 billion years ago, the distinction between spatial measures (Hubble radius) and temporal measures, the eternal universe without origin, and the reinterpretation of the cosmic microwave background. Wade’s paper raises cosmological questions ("Is densification in the universe constant? What does this mean for cosmology?") but does not develop cosmological applications.

Points versus Extended Objects

In his 2014 presentation, Wade emphasized a distinction between test points and extended objects: "This densification looks almost exactly like contracting space but that’s only to consider a test point... however it’s important that you consider an object that has dimension and that is what’s going to make this different." While this distinction is noted, Wade does not develop the concept of proper volume preservation that is central to the present treatise.

Summary of Comparison

What Wade established (2013): The name "Proper Space Kinematics." The core concept of spatial densification at rate c. Coordinate transformations between proper space, object space, and stationary space. The waxing velocity w and temporal dilation coefficient α. Rejection of stationary frames. The arrow of time from densification. The matter/energy phase relationship (not adopted here).

What the present treatise develops independently: Continuous geometric coincidence at historical density states. State-sharing through geometric intersection as the basis for electromagnetic phenomena. Gravity as density gradients (wakes). Strong and weak nuclear forces as manifestations of densification geometry. The critical density threshold and cosmological timeline. Entanglement as past contiguity. The inverse square law from intersection geometry. Detailed treatment of electromagnetic phenomena (radio, light, reflection, refraction, polarization, lasers). The volume preservation principle.

The two frameworks share a foundational insight but diverge significantly in their development. The present treatise acknowledges Wade’s priority in naming and in articulating the densification postulate, while the extensive applications to electromagnetism, gravity, nuclear forces, quantum phenomena, and cosmology represent original work.