Sub-principles

  1. Structural Self-Similarity: The same basic organizational pattern repeats at all scales – a central massive body (or bodies) surrounded by orbiting bodies and diffuse clouds.
  2. Successive Intervals: Matter organizes into discrete similarity levels, each separated from adjacent levels by scaling factors of approximately 1015 to 1020 in distance.
  3. Mathematical Scaling Laws: Physical quantities scale predictably between levels according to gravitational dynamics:
    • Distance scales by factor k
    • Time scales by factor k3/2
    • Mass scales by factor k3
  4. Progressive Organization: Lower similarity levels are more organized (stable, iron-rich, "cold"), while higher similarity levels are less organized (chaotic, hydrogen-rich, "hot"), creating a one-directional organizational progression.
  5. Relative Perspective: Similarity level designations (SL₀, SL₋₁, SL₊₁, etc.) are relative to the observer's scale, not absolute labels. What is SL₀ to us will become SL₋₁ to future higher-level observers.
  6. Infinite Hierarchy: The similarity level hierarchy extends infinitely in both directions – there is no "smallest" or "largest" level, only ever more organized structures going down and ever more chaotic structures going up.
  7. Evolutionary Progression: Each similarity level evolves over vast time spans from chaotic cloud → organized system → stable structure, eventually becoming the "atoms" for the next higher level.

Core Principle

This axiom completes the AAM framework by establishing that the same organizational principles operate at all scales. Building on all previous axioms, Axiom 10 reveals that:

  1. Structure repeats across scales – nucleus/planets/globular clusters are analogous
  2. Physical laws are scale-invariant – same gravitational dynamics at all levels
  3. Evolution follows same pattern – chaos → organization → stability at each level
  4. Time rates vary systematically – scaling derived from orbital mechanics
  5. Organization is one-directional – lower levels more organized than higher levels
  6. Perspective is relative – level numbering depends on observer's position

This principle unifies the entire physical universe under a single organizational framework, from the smallest observable structures to the largest cosmic regions, and beyond in both directions to infinity.

Key Definitions

Similarity Level (SL)

A similarity level is a scale of organization characterized by self-similar structure. Examples:

  • SL₋₃: Aether particles (controls atomic-scale gravity)
  • SL₋₂: Aether (transmits light at our scale; atoms for SL₋₁ perspective)
  • SL₋₁: Atoms (hydrogen = solar system analog)
  • SL₀: Solar systems (our current perspective)
  • SL₊₁: Galaxies (will become solar systems)
  • SL₊₂: Cosmic Regions (will become galaxies)

Self-Similarity

Self-similarity means the repetition of structural patterns across different scales. The same basic organization (nucleus + orbiting bodies + cloud) appears at atomic, solar system, galactic, and cosmic scales.

Scaling Factor

The scaling factor (k) is the ratio of characteristic distances between adjacent similarity levels, typically k ≈ 1015 to 1020.

Organizational State

The organizational state of a similarity level describes its degree of settlement: from chaotic (newly forming, hydrogen-rich, high fusion/fission) to organized (settled, iron-rich, stable orbits, minimal fusion/fission).

Temporal Scaling

Temporal scaling is the relationship between time rates at different similarity levels, determined by T ∝ r3/2 from Kepler's Third Law.

Contrasts with Conventional Physics

Scale-Dependent vs. Scale-Independent Physics

Conventional Physics:

  • Fundamental constants are absolute and unchanging across all scales
  • Quantum mechanics at small scales, classical mechanics at large scales
  • No connection between atomic and cosmic structure
  • Different physics regimes require different theories

AAM Position:

  • Physical constants are scale-dependent (different at each SL)
  • Same organizational principles apply, but with scaled parameters
  • Unified mechanical framework at all scales
  • Atoms and galaxies are structurally analogous

Key Difference: Conventional physics sees atoms and solar systems as fundamentally different structures governed by different laws (QM vs. classical). AAM sees them as self-similar structures at different scales, governed by the same mechanical principles with different scaling parameters.

Quantum Discreteness vs. Mechanical Structure

Quantum Mechanics:

  • Discrete energy levels are fundamental quantum property
  • Electron orbitals are probability clouds, not physical orbits
  • No mechanical explanation for atomic structure
  • Atoms are not "little solar systems"

AAM Position:

  • Discrete spectral lines from discrete planetrons in electron planes
  • Orbitrons and planetrons are actual orbiting bodies
  • "Quantum numbers" describe orbital configurations
  • Atoms ARE solar system analogs at smaller scale

The Resolution: Quantum mechanics works mathematically because it's sophisticated curve-fitting to the actual mechanical structure. The wave equations approximate the distributed matter in orbitron clouds and planetron planes.

Big Bang Cosmology vs. Eternal Self-Similar Universe

Big Bang Theory:

  • Universe began 13.8 billion years ago from singularity
  • Space itself is expanding
  • Finite age and finite observable size

AAM Position:

  • Universe is eternal with no beginning
  • Space is static and infinite (Axiom 2)
  • Apparent "expansion" is rotation at cosmic region scale
  • Infinite hierarchy of structures exists at all times

Key Insight: What appears as "universal expansion" is actually the rotation of our Cosmic Region (SL₊₂) as it organizes into what will eventually become a galaxy. Redshift comes from tired light (Axiom 7), not expanding space.

Fundamental Particles vs. Infinitely Divisible Matter

Standard Model:

  • Quarks, leptons, and bosons are fundamental point particles
  • No internal structure – truly fundamental
  • Different particles at different scales

AAM Position:

  • All matter infinitely divisible (Axiom 3)
  • What appears fundamental at one scale has structure at lower scale
  • Same structural pattern at all scales
  • "Elementary particles" are complex structures at smaller SL

Observable Self-Similarity in Nature

We observe self-similar patterns throughout nature at every observable scale:

Atomic Structure (SL₋₁)

  • Central nucleus (dense, massive)
  • Electron planes with planetrons (orbital bodies)
  • Valence cloud (diffuse outer region)
  • Spectral lines from planetron transitions

Solar System (SL₀)

  • Central star (dense, massive)
  • Planets in orbital planes
  • Oort cloud (diffuse outer region)
  • Will eventually produce "spectral lines" as it settles

Galaxies (SL₊₁)

  • Central bulge/core (dense, massive)
  • Globular clusters (orbital bodies)
  • Spiral arms and halo (diffuse outer regions)
  • Currently organizing from cosmic region chaos

Cosmic Regions (SL₊₂)

  • Superclusters forming dense regions
  • Galaxy clusters (will become globular clusters)
  • Inter-cluster medium (will form spiral arms/halo)
  • Very early formation stage, rotating as it organizes

The Pattern: Dense center + orbiting bodies + diffuse cloud appears at every observable scale.

Mathematical Scaling Laws

From Kepler's Third Law

T² = 4π²r³/GM

If distance scales by factor k between similarity levels (rnew = k · rold), then:

  • Time scales as: Tnew = k3/2 · Told
  • Mass scales as: Mnew = k3 · Mold

The Complete Scaling Law

  • Distance: k
  • Time: k3/2
  • Mass: k3

This is not arbitrary – it's derived from the requirement that gravitational dynamics produce self-similar orbital structure at different scales.

Time Scaling Explains Apparent Stability Paradox

The Paradox: Lower SLs appear incredibly stable (atoms don't "evolve" noticeably) while higher SLs appear very dynamic (galaxies visibly evolving). Why the difference if same laws apply?

The Resolution: Time passes at vastly different rates at different similarity levels!

Example: With scaling factor k ≈ 1015, time scaling is k3/2 ≈ 1022.5. During one of our seconds, approximately 1015 atomic "years" pass. Atoms appear stable because their evolution timescale is 1022 times faster than ours!

Organizational Progression

The One-Directional Flow

Higher Similarity Levels (less organized):

  • Chaotic superclusters, just beginning to rotate and organize
  • More hydrogen, ongoing fusion/fission, high energy release
  • "Hot" in sense of active nuclear processes
  • Young in terms of organizational development

Current Similarity Level (intermediate):

  • Solar systems partially settled, planets formed but orbits still adjusting
  • Active fusion in stellar cores
  • Mix of elements from hydrogen to iron
  • Life possible due to intermediate organization + energy availability

Lower Similarity Levels (more organized):

  • Atoms highly organized, stable orbital patterns established
  • Mostly iron composition (fusion endpoint)
  • Minimal fusion/fission, "cold" nuclear processes
  • Provide stable substrate for higher-level processes

Why This Direction?

  • Gravitational Collapse: Matter naturally aggregates under gravitational shadowing, creating denser, more organized structures over time
  • Fusion Process: Lighter elements fuse to heavier; iron is fusion endpoint (maximum binding energy)
  • Stability Emergence: Stable configurations persist while unstable ones dissipate; over vast numbers of cycles, stability dominates

Like entropy increase, organizational progression is one-directional: Chaos → Order, Hydrogen → Iron, Dynamic → Stable.

Objections & Responses

"If scaling factor is ~1015 to 1020, why such a large range?"

The scaling factor isn't necessarily constant: different element types may have different scaling, measurement uncertainty exists, and there may be intermediate levels we don't recognize. The order of magnitude is correct (massive scaling between levels) and the same scaling laws apply. Exact factor is less important than the scaling principle.

"How can atoms be 'solar systems' when electrons have wavelike properties?"

The wavelike properties are emergent from distributed matter structure:

  • Orbitron clouds contain countless small orbitrons creating wave-like distribution
  • Mathematical wave functions approximate aggregate behavior
  • Saturn's rings appear smooth and wave-like from distance, but are actually countless discrete chunks

Similarly, "electron clouds" appear wave-like but are composed of countless discrete orbitrons.

"Why don't we see spectral lines from solar systems?"

We don't see spectral lines yet because our solar system hasn't fully settled:

  • Solar system only ~4.6 billion years old
  • Planets' orbits still adjusting
  • Hydrogen atoms we observe are ancient (countless "atomic years" old)
  • In far future, when solar system settles, characteristic transition patterns will emerge

Lack of current spectral lines is a timing issue, not flaw in self-similarity principle.

"What about dark matter and dark energy?"

These are artifacts of incorrect cosmological model:

  • "Dark Matter": Explained by gravitational shadowing at galactic scale + aether contribution; no exotic matter needed
  • "Dark Energy": No expansion means no dark energy needed; tired light explains redshift

Self-similarity with proper mechanics eliminates need for exotic matter/energy.

"Why should same laws apply at vastly different scales?"

Same laws apply because there's only one set of fundamental principles (space, matter, motion):

  • Axiom 1: Only space, matter, and motion exist – scale-invariant concepts
  • Gravitational shadowing: Geometry works the same at all scales
  • Mathematical necessity: Kepler's laws derive from gravitational dynamics regardless of scale

The real question is: why would laws be different at different scales, given reality is composed of the same basic constituents everywhere?

"How do you explain nuclear forces?"

Nuclear forces are magnetic coupling at close range:

  • Each nucleon has internal rotation creating magnetic dipole
  • At close range, magnetic forces dominate over gravitational shadowing
  • Nucleons couple magnetically (opposite orientations attract)
  • No "strong force" needed – same magnetic principles, scaled appropriately

Open Questions

Theoretical Development

  • What is exact scaling factor for hydrogen specifically?
  • How does scaling vary for different elements?
  • Are there intermediate similarity levels we haven't identified?
  • Detailed mechanism of chaos → order progression?

Mathematical Formulation

  • Complete mathematical framework for all physical quantities across scales
  • How do other quantities (charge, magnetism, temperature) scale?
  • Quantitative measure of "organizational state"
  • Multi-scale modeling equations

Experimental Tests

  • Detailed mapping of hydrogen spectrum to solar system structure
  • Can we determine electron plane geometry for each element?
  • Long-term monitoring of galactic organizational progression
  • Direct evidence for aether structure (SL₋₂)

Philosophical Questions

  • If SL designations are relative, is there a "preferred" perspective?
  • Could life exist at other similarity levels?
  • How do we conceptualize infinite hierarchy philosophically?

Relationship to Other Axioms

Axiom 10 is the capstone axiom that completes and unifies the AAM framework:

Builds On All Previous Axioms:

  • Axiom 1 (Space, Matter, Motion): Same basic reality at every scale; no scale-dependent entities
  • Axiom 2 (Infinite Space): Infinite space allows infinite SL hierarchy
  • Axiom 3 (Infinite Divisibility): Creates infinite SL hierarchy going down
  • Axiom 4 (Universe Concept): Eternal Universe means eternal SL progression
  • Axiom 5 (Infinite Matter): Infinite matter distributed across infinite SLs
  • Axiom 6 (Relative Motion): Motion uniqueness applies at all SLs
  • Axiom 7 (Energy as Motion): Same energy principles, scaled parameters
  • Axiom 8 (Constant Motion): Perpetual motion at all SLs with scale-dependent organization
  • Axiom 9 (Time from Motion): Time scaling derives from motion rate differences between SLs

Key Unifying Connections:

  • Complete AAM Framework: Axioms 1-9 describe universal principles applying at all scales – not just "our" physics
  • Resolves Contradictions: Atoms stable/galaxies dynamic? Time scaling! Quantum vs classical? Same mechanics at all scales
  • Explains Organizational Arrow: Lower SLs more organized because more time (more cycles) to settle
  • Unifies Structure and Dynamics: Same nucleus + orbiting bodies + cloud pattern everywhere

Completes the Ontology:

  • What exists: Space (infinite, continuous, 3D), Matter (massive, infinitely divisible, unique), Motion (unique, continuous, relative, perpetual)
  • How it organizes: Self-similarly across infinite similarity levels
  • What we derive: Energy (motion/configuration of matter), Time (occurrence of motion)
  • The result: Complete mechanical explanation of all phenomena from smallest to largest scales