Core Principle

This axiom establishes three fundamental properties of space, which is one of the three constituents of physical reality identified in Axiom 1:

  1. Three-dimensional — Space has exactly three dimensions of extension (length, width, height) that correspond to our direct sensory experience
  2. Infinite in extent — Space extends without limit in all directions; there is no boundary or edge to space
  3. Infinitely divisible — Space is continuous and can be subdivided without limit; there is no smallest unit of space

These properties arise from basic reasoning about physical extension and our direct experience of reality. Space is the infinite, continuous container within which all matter exists and moves.

What This Axiom Rejects

Axiom 2 stands in direct opposition to three major pillars of modern theoretical physics, each of which contradicts either our direct experience, basic reasoning, or both.

1. Higher Dimensions (String Theory and Beyond)

Conventional View:

Modern theoretical physics, particularly string theory and M-theory, proposes that space has more than three dimensions:

  • String theory requires 10 or 11 dimensions
  • These "extra dimensions" are supposedly "compactified" or "curled up" at sub-microscopic scales
  • These dimensions are purely mathematical constructs with no observational evidence

AAM Position:

The AAM categorically rejects all dimensions beyond the three we directly experience:

  1. Direct Experience: We observe exactly three dimensions of spatial extension—no more, no fewer
  2. Mathematical Abstraction vs. Physical Reality: Higher dimensions are mathematical conveniences that arose from manipulating equations, not from observing nature
  3. Occam's Razor: Adding invisible, unobservable dimensions to make mathematical models work is unnecessary complexity
  4. Sensory Evidence: All measuring instruments, all observations, all experiments occur in three-dimensional space

The AAM View: Space has exactly three dimensions because extension itself is inherently three-dimensional. Any "dimension" beyond these three is either a mathematical parameter in an equation, a confused conflation of time with spatial dimensions, or an abstract concept with no correspondence to physical reality.

2. Finite Space and Big Bang Cosmology

Conventional View:

Modern cosmology, dominated by Big Bang theory, proposes:

  • The universe began from a singularity approximately 13.8 billion years ago
  • Space itself is expanding, carrying galaxies apart
  • Space may be finite but unbounded (like the surface of a sphere)
  • Before the Big Bang, space did not exist

AAM Position:

The AAM rejects the concept of finite space entirely. Space is infinite in extent—it goes on forever in all directions.

Why Infinite Space Makes Sense:

  1. No Logical Boundary: What would be at the "edge" of space? More space. Any proposed boundary leads to logical contradiction.
  2. Conservation Principles: If space were finite and expanding, into what would it expand? The concept of "expanding space" requires pre-existing space to expand into.
  3. Observational Evidence Misinterpreted: Redshift could be explained by light losing energy over vast distances (tired light); cosmic microwave background could be residual radiation from ongoing processes.
  4. Philosophical Problems with Creation: The Big Bang requires something from nothing—a logical impossibility that violates causality.
  5. Infinity is Necessary: As Axiom 5 establishes, there is an infinite amount of matter in the universe. Infinite matter requires infinite space to contain it.

3. Discrete/Quantized Space

Conventional View:

Several modern theories propose that space is fundamentally discrete rather than continuous:

  • Planck Length as Fundamental Limit: Many physicists treat ~10-35 meters as a fundamental "pixel" of space
  • Stephen Wolfram's Computational Universe: Proposes space consists of discrete "nodes" in a computational network
  • Loop Quantum Gravity: Proposes space has a discrete "atomic" structure woven from loops

AAM Position:

The AAM categorically rejects all forms of discrete space. Space is continuous and infinitely divisible—there is no smallest unit of space.

Why Continuous Space Makes Sense:

  1. Direct Experience: We observe smooth, continuous motion, not jerky jumps between discrete positions
  2. Mathematical Convenience Mistaken for Reality: The Planck length is where certain equations break down, not where space itself becomes granular
  3. Infinite Divisibility: If space had a smallest unit, we could ask: "What's between two adjacent units?" The answer must be: more space
  4. Motion Requires Continuity: Smooth motion through space requires that space be continuous. Discrete space would require matter to "teleport" between positions
  5. Computational Metaphor: The universe doesn't "compute"—it simply is. Matter moves through space according to mechanical principles, not computational rules

Supporting Reasoning

Three Dimensions: Why Not More, Why Not Fewer?

Two Dimensions Would Be Insufficient:

  • No way to have crossing paths that don't intersect
  • No way to have complex mechanical structures (no knots possible)
  • Rotation would require leaving the 2D plane

Four or More Dimensions Are Unnecessary:

  • Every physical phenomenon can be described and occurs in three dimensions
  • No observation has ever required a fourth spatial dimension
  • Adding dimensions doesn't solve real physical problems—it only complicates mathematical equations

Three Dimensions Are Natural:

  • Three perpendicular directions exhaust the possibilities for independent spatial extension
  • All mechanical motion and structure naturally exist in three dimensions
  • Our sensory apparatus, measuring instruments, and all observations confirm three dimensions

Infinity: Why Space Cannot Have Limits

The Boundary Problem: If space had a boundary, what would be on the other side?

  1. More space—but then the boundary wasn't real
  2. "Nothing"—but "nothing" is incoherent; it cannot "be" anywhere
  3. A "wall"—but a wall is something, made of matter, existing in... space

All three lead to contradictions. The only logically consistent answer is that space has no boundary—it is infinite.

Infinite Divisibility: Why Space Must Be Continuous

The Subdivision Thought Experiment: Suppose space had a smallest unit—call it a "space atom." Consider two adjacent space atoms. We can meaningfully ask:

  • "What separates them?"
  • "What is between them?"
  • "How far apart are they?"

Any answer to these questions requires space. The "gap" between space atoms would itself be space, which we could subdivide. Therefore, there can be no smallest unit.

Motion Requires Continuity:

  • In continuous space, an object passes smoothly through all intermediate points
  • In discrete space, it would have to "jump" from one space atom to the next
  • Such jumps would violate conservation of momentum and energy
  • We observe smooth motion, not discontinuous jumps

Implications for the AAM

1. Same Physics at All Scales

Because space is infinitely divisible and uniform at all scales, the same mechanical principles that operate at our experiential level (SL0) also operate at the atomic level (SL-1) and the galactic level (SL1). There are no special quantum rules at small scales or relativistic rules at cosmic scales—just mechanics operating in three-dimensional infinite continuous space.

2. No Spacetime

Time is not a dimension of space. Time and space are separate aspects of reality:

  • Space is the container (Axiom 2)
  • Time is the occurrence of matter in motion (Axiom 9)

Conflating them into "spacetime" is a mathematical convenience that obscures physical reality.

3. Self-Similarity Across Scales

The infinite divisibility of space allows for the hierarchical structure of the AAM:

  • SL-2 (sub-atomic) exists in space
  • SL-1 (atomic) exists in space
  • SL0 (human scale) exists in space
  • SL1 (galactic) exists in space
  • And so on, infinitely in both directions

Each level exists in the same continuous, infinite, three-dimensional space—just at different scales.

4. No Edge Effects or Boundary Conditions

Physics doesn't change at some extreme distance. There is no "edge of the universe" where physics breaks down or becomes undefined.

5. Light Propagation Through Space

Light is wave motion through the aether medium (Axiom 1). The infinite extent of space means aether fills all of space, and light can propagate indefinitely.

6. No Singularities

The Big Bang requires a singularity—infinite density at zero volume. Such a concept is physically meaningless. In the AAM: space has always existed, matter has always existed. No creation event, no singularity, no beginning.

Common Objections and Responses

Objection 1: "Doesn't Einsteinian relativity prove spacetime is real?"

Response: Einstein's mathematical formalism treats time as if it were a dimension for calculational convenience. But mathematical convenience doesn't establish physical reality. Time is fundamentally different from space—you can move freely in any direction in space, but you cannot move freely in time.

Objection 2: "Doesn't the redshift of distant galaxies prove space is expanding?"

Response: Redshift proves that light from distant objects is shifted toward longer wavelengths. The interpretation as "expanding space" is one hypothesis. Alternative explanations include tired light (light losing energy over vast distances) and local motions in infinite space.

Objection 3: "If space is infinite, doesn't that lead to Olbers' Paradox?"

Response: Olbers' Paradox (why isn't the night sky uniformly bright if there are infinite stars?) is resolved by: light loses energy over vast distances (tired light effect), matter is not uniformly distributed in infinite space, and not every line of sight necessarily intersects a star in infinite space with local clustering.

Objection 4: "How can you have infinite space but still have local structure?"

Response: Infinity doesn't mean uniformity. An infinite space can have local clustering of matter, regions of high and low density, structure at all scales, and dynamic processes creating and dissolving structures.

Open Questions for Future Investigation

Theoretical Development

  1. Tired Light Mechanism: Since aether is the medium for light propagation, energy transfer to the medium is inevitable. As light waves propagate through the aether over vast distances, they continuously transfer small amounts of energy to the medium, causing amplitude to decrease.
  2. Matter Distribution and Organization: As similarity levels increase (SL0 → SL1 → SL2...), organization and order DECREASE because higher levels are still settling into stable configurations.
  3. Cosmic Microwave Background: The mechanical processes maintaining the CMB in an infinite steady-state universe will be addressed in future discussions.

Observational Predictions

  1. Big Bang Theory's Shifting Predictions: As telescopes improve, Big Bang cosmology continually adjusts its parameters to accommodate discoveries that don't fit the original model.
  2. Direct Tired Light Evidence: Further investigation needed to identify observational signatures that distinguish tired light energy loss from "expanding space" interpretations.

Relationship to Other Axioms

Axiom 2 directly builds upon Axiom 1's foundation:

  • Axiom 1 established: All phenomena can be reduced to space, matter, and the motion of matter.
  • Axiom 2 specifies: The nature of space—one of those three fundamental constituents.

Foundation for Future Axioms:

  • Axiom 3: Characterize matter (the second fundamental constituent)
  • Axiom 4: Define the universe as the totality of space and matter
  • Axiom 5: Establish the infinite quantity of matter in infinite space