Sub-principles

  1. Time is Not a Substance or Dimension: Time is not an independent physical entity, dimension of space, or flowing substance. It is the occurrence of motion — when motion happens, time happens.
  2. Time is Relative to Motion: All time measurement is comparison of one motion to another. There is no absolute time, no universal clock, and no privileged reference frame for time.
  3. Time Requires Motion: Without motion, there is no time. Time does not "exist" independently — it emerges from the occurrence of motion. No motion means no change, and therefore no passage of time.
  4. Time is Scale-Dependent: The rate of time's passage varies dramatically across similarity levels. A complete cycle at one scale may represent only a tiny fraction of a cycle at another scale.
  5. Time is Eternal: Because motion is perpetual (Axiom 8) and the Universe is eternal (Axiom 4), time has no beginning and no end. Time stretches infinitely into both past and future.
  6. All Clocks Are Motions: Every method of measuring time — atomic clocks, pendulums, planetary orbits, radioactive decay — involves comparing one motion to another motion chosen as a standard.
  7. No Universal Simultaneity: Events that appear simultaneous from one perspective may not be simultaneous from another perspective, because simultaneity depends on which motions are being compared.

Key Definitions

Time
The occurrence of matter in motion. It is not an independent dimension but rather the manifestation of motion itself. When we say "time passes," we mean "motion occurs."
Temporal Rate
The relationship between motion at one scale and motion at another scale. For example, the temporal rate between $SL_{-1}$ and $SL_{0}$ describes how many atomic-scale cycles occur during one solar-system-scale cycle.
Simultaneity
The occurrence of two motions at the same phase in their respective cycles. Because all motion is relative (Axiom 6), simultaneity is also relative and depends on which motions are being compared.
Clock
Any periodic motion used as a reference standard for comparing other motions. Planetary orbits, pendulum swings, atomic vibrations, and radioactive decay all serve as clocks.
Present Moment
The current configuration and motion of all matter in a local region. It is the "now" of immediate experience, defined by the current state of motion in that region.

Core Principle

This axiom establishes time as a derivative concept — it emerges from motion rather than existing independently. Building on:

  • Axiom 1 $-$ Only space, matter, and motion exist (time is not listed as fundamental)
  • Axiom 6 $-$ Motion is unique, continuous, and relative
  • Axiom 7 $-$ Energy is motion of matter
  • Axiom 8 $-$ All matter is constantly in motion

Axiom 9 asserts that time is simply what we call the occurrence of motion. This has profound implications:

  1. No independent time dimension $-$ time doesn't "flow" separately from matter
  2. No time without motion $-$ time requires physical processes
  3. No absolute time $-$ all time is relative to chosen reference motions
  4. No beginning or end $-$ time is eternal like motion
  5. Scale-dependent rates $-$ time passes at different rates at different similarity levels
  6. No time travel $-$ you can't separate time from physical motion
  7. Spacetime is mathematical abstraction $-$ not physical reality

Unlike Einstein's spacetime where time is a dimension geometrically unified with space, or Newton's absolute time flowing uniformly everywhere, the AAM recognizes that time is the happening of motion — nothing more, nothing less.

Contrasts with Conventional Physics

1. Einstein's Spacetime vs AAM's Space and Motion

Einstein's Relativity:

  • Time is fourth dimension geometrically unified with three space dimensions
  • Spacetime is fundamental 4D continuum
  • Time can dilate, contract, and curve with space
  • Gravity is curvature of spacetime
  • Time and space are inseparable aspects of a single entity

AAM Position:

  • Time is occurrence of motion, space is container for matter
  • Time and space are fundamentally different: space is static container, time is dynamic occurrence
  • Time appears to "dilate" due to different motion rates, not geometric effects
  • Gravity is geometric shadowing in 3D space (Axiom 1), not spacetime curvature
  • Time and space are completely separable

Why Spacetime Seems to Work:

Mathematical convenience — treating time as a dimension simplifies equations. It approximates real effects since relative motion does affect perceived time rates. It is a useful tool that makes accurate predictions. But it conflates mathematical representation with physical reality, just as Ptolemaic epicycles worked mathematically but didn't reflect the underlying mechanics.

2. Absolute Time vs Relative Time

Newton's Absolute Time:

Time flows uniformly everywhere independent of matter or motion. A universal cosmic clock ticks the same for all observers. Time exists even without motion or change, and simultaneity is absolute.

AAM Position:

Time is relative to the motion being observed. There is no universal clock — all time measurement compares motions. Time requires motion; no motion means no time. Simultaneity is relative, depending on which motions are being compared.

Newton's absolute time seemed reasonable because at human scales and speeds, time appears nearly universal. For everyday purposes, assuming universal time works fine — errors only become significant at extreme speeds or gravitational conditions. But motion is clearly relative (Axiom 6), so time must be relative too. No physical mechanism for universal time has ever been identified.

3. Time Dilation: Geometric vs Mechanical

Relativity's Time Dilation:

Moving clocks run slower (special relativity). Clocks in gravity wells run slower (general relativity). Time itself dilates or contracts. This has been verified by atomic clocks on satellites, muon decay, and particle accelerator observations.

AAM Explanation:

The AAM fully acknowledges that clocks run at different rates under different conditions. What it rejects is the geometric spacetime explanation, offering instead a mechanical picture:

  • Objects moving rapidly through aether encounter increased resistance, slowing internal motions (atomic vibrations, decay processes)
  • Objects in strong gravitational fields experience asymmetric gravitational shadowing that alters motion rates
  • "Time dilation" is a real effect on motion rates, not time itself changing
  • Muons live longer because the decay process is slowed by motion through aether

GPS Satellite Corrections:

GPS satellites move at ~14,000 km/h relative to the Earth's surface and sit in a weaker gravitational field. The velocity effect slows their atomic clocks slightly, while the gravitational effect speeds them up. The gravitational effect dominates, producing a net gain of ~38 microseconds per day. These corrections prove that motion rates differ under different conditions — the AAM explains this mechanically, while relativity explains it geometrically. Both make the same predictions.

4. Time Travel vs Motion Patterns

Conventional/Science Fiction View:

Time travel to the past or future is theoretically possible through closed timelike curves in spacetime. Time is treated as a dimension one can move through, raising grandfather paradoxes and causality violations.

AAM Position:

Time travel is impossible because time isn't a place you can go. Time is the occurrence of motion — you cannot separate time from physical processes. Past configurations no longer exist (motion has changed everything), and future configurations don't yet exist (motion hasn't occurred yet). Only the present configuration exists.

Light from distant stars shows their past configuration, but we are not "seeing into time" — we are seeing delayed information. The light took time to travel (motion through space), and the star's current state differs from what we observe.

5. Beginning and End of Time

Big Bang Cosmology:

Time began with the Big Bang 13.8 billion years ago. Time may end with heat death or a Big Crunch. "Before" the Big Bang is considered meaningless.

AAM Position:

Time is eternal because motion is eternal (Axiom 8). There is no beginning — motion has always occurred. There is no end — motion will always occur. The infinite past and infinite future follow from the eternal Universe (Axiom 4), perpetual motion (Axiom 8), and the absence of any creation or cessation event.

Time Scaling Across Similarity Levels

One of the most profound and important aspects of Axiom 9 is that time passes at vastly different rates at different similarity levels.

The Fundamental Principle

The rate at which time passes at one similarity level compared to another is determined by the ratio of characteristic motion cycles at those levels. A complete orbital cycle at one similarity level corresponds to only a tiny fraction of an orbital cycle at the next higher similarity level.

Why Time Scales This Way:

  1. Orbital period depends on distance and speed — larger orbits take longer to complete. At $SL_{0}$, Earth orbits the Sun in 1 year. At $SL_{-1}$, a planetron orbits its nucleus in ~$10^{-15}$ seconds. At $SL_{+1}$, our solar system orbits the galactic center in ~200 million years.
  2. Each similarity level is self-similar to others (Axiom 10) — same basic structure (nucleus + orbiting bodies + cloud), but at vastly different scales with scaling factors of ~$10^{15}$ to $10^{20}$.
  3. Time is occurrence of motion (Axiom 9) — more cycles means more time has passed. Fast cycles mean fast time passage; slow cycles mean slow time passage.

Atomic Scale vs Our Scale

At $SL_{-1}$ (Atomic Scale):

  • A "year" is one complete planetron orbit
  • Duration: approximately $10^{-15}$ to $10^{-16}$ seconds in our time
  • Billions of billions of "years" pass at $SL_{-1}$ in one second of our time
  • Evolution, events, and processes all occur at this vastly accelerated rate

From an atomic observer's viewpoint, our "one year" would seem like countless eons. Our motions would appear frozen in time, and our civilization's entire history would be an imperceptible blip. We would appear essentially eternal and unchanging.

Our Scale vs Galactic Scale

At $SL_{+1}$ (Galactic Scale):

  • A "year" is one complete orbit around the galactic center
  • Duration: ~200–250 million of our years
  • Our entire civilization exists in a tiny fraction of one galactic "year"
  • Multiple mass extinctions on Earth within a single galactic "year"

From a galactic observer's viewpoint, our solar system would appear to move rapidly, with planetary orbits and Earth's rotation happening very fast. Human civilization comes and goes in a microscopic instant, and geological time scales are brief moments.

The "Present Moment" Problem

If time passes at different rates at different levels, what is "now"? The answer is that "now" is relative to the similarity level and the observer. Events simultaneous at $SL_{0}$ may not be simultaneous at $SL_{-1}$. What appears as a single moment at $SL_{+1}$ contains countless moments at $SL_{0}$. There is no universal "present moment" across all scales — each level has its own present defined by its own motion cycles.

Implications for Evolution and Life

At lower similarity levels, time passes much faster, producing more generations in a given "absolute" time span. Evolution proceeds more rapidly from our perspective. At higher similarity levels, time passes much slower, with fewer generations and evolution that appears to proceed slowly from our perspective.

The key insight is that evolution doesn't actually happen "faster" or "slower" — it happens at the same relative rate at each level (so many generations per unit of local time). It only appears faster or slower when viewed from a different similarity level.

Supporting Arguments

1. Motion and Time Are Inseparable

Every method of measuring time involves observing motion:

  • Sundials: Earth's rotation
  • Pendulum clocks: pendulum swing
  • Mechanical clocks: gear rotation
  • Quartz clocks: crystal oscillation
  • Atomic clocks: atomic transition frequency
  • Radioactive dating: nuclear decay

Time measurement is always motion comparison. We compare an unknown motion (the process we want to time) to a standard motion (the clock). When motion stops — even in a thought experiment — time becomes undefined. Faster motion rates correspond to faster "time passage" at that scale. Even our temporal language refers to motion: "time flows," "time passes," "events occur." This all suggests that time is motion, not something separate from it.

2. No Independent Time Detection

Unlike space (which we can measure directly with rulers) or matter (which we can detect directly), we cannot detect or measure time except through motion.

Consider a thought experiment: imagine a completely frozen universe where nothing moves. No motion means no change. No change means no way to measure passage. Time becomes undefined — not just unmeasurable, but non-existent. Time has no independent existence apart from motion.

3. Relativity of Time Follows from Relativity of Motion

If time is the occurrence of motion (Axiom 9), and motion is relative (Axiom 6), then time must be relative too. Observer A measures time using clock A (periodic motion A), while Observer B uses clock B (periodic motion B). If A and B are moving relative to each other, their clocks tick at different rates. Each observes the other's clock running slow — and both are correct from their perspectives. This matches observation: time dilation effects confirm that moving clocks run at different rates.

4. Eternal Motion Requires Eternal Time

From Axiom 8: all matter is constantly in motion, and motion is perpetual. If motion is eternal (no beginning, no end) and time is the occurrence of motion, then time must also be eternal (no beginning, no end). This is internally consistent: Axiom 4 establishes the eternal Universe, Axiom 8 establishes perpetual motion, and Axiom 9 establishes eternal time — all three mutually supporting.

5. Clocks Measure Motion, Not Independent Time

All improvements in clock accuracy involve finding more regular, consistent motions: pendulums are more regular than sundials, quartz oscillation more regular than pendulums, atomic transitions more regular than quartz, and optical atomic clocks even more regular. We are not getting "closer to true time" — we are finding better standard motions to compare other motions against.

When atomic clocks disagree slightly, we don't say "time is different for these clocks" — we say "these clocks are running at slightly different rates." This confirms that clocks measure motion rates, not abstract time.

Objections & Responses

"Time Feels Absolute to Us"

This intuition comes from several sources: we only experience motion at roughly our similarity level, so atomic motions are too fast to perceive and galactic motions too slow. On Earth, we all share similar motion (Earth's rotation, orbit), so our clocks — both biological and technological — are based on similar processes, creating the illusion of universal time. Neural processes happen at consistent rates for humans, producing a subjective sense of uniform time flow. For everyday purposes, assuming absolute time works fine — errors only become significant at extreme speeds or gravitational conditions.

Just as the Earth feels flat in everyday experience but is actually a sphere, the limited scale of our experience creates a misleading intuition about the larger reality.

"GPS Requires Relativistic Time Corrections"

GPS corrections are real, but they correct for motion rate differences, not spacetime geometry. Satellite velocity through aether affects atomic clock rates mechanically (clocks run slightly slower). The gravitational effect — satellites at higher altitude experience less gravitational shadowing — causes clocks to run slightly faster. The gravitational effect dominates, producing a net gain of ~38 microseconds per day. These corrections can be calculated using motion rate differences without invoking curved spacetime. Same predictions, simpler ontology.

"Time Dilation Is Experimentally Verified"

The AAM doesn't deny time dilation effects — it fully acknowledges that clocks run at different rates under different conditions. What the AAM denies is the geometric spacetime explanation. Moving objects encounter increased aether resistance, which slows internal motions (atomic vibrations, decay processes) mechanically. Muons live longer because the decay process is slowed by motion through aether. Gravitational fields create asymmetric forces on particles, altering internal motion rates. The AAM and relativity make the same quantitative predictions — they differ in mechanism (mechanical vs geometric), not in empirical outcomes.

"Can't Have Motion Without Time"

This objection assumes circularity: motion is change of position over time, so defining time through motion is circular. The AAM breaks this circle by establishing a proper logical order:

  1. Space exists (Axiom 2) — the container
  2. Matter exists (Axiom 3) — the content
  3. Matter moves through space (Axiom 6) — changing spatial relationships between matter
  4. That motion occurs — we call this occurrence "time" (Axiom 9)

Motion is defined kinematically as matter's changing spatial relationships — without reference to time. Time is the derived concept: the label we give to the happening of motion. Just as heat exists (molecular motion) and we label the experience of heat as "warmth" without warmth existing independently, time doesn't exist independently of matter's motion.

"What About Entropy and Time's Arrow?"

What we call "time's arrow" is the one-directional organizational pattern of the Universe across similarity levels. The Universe progresses from higher similarity levels (chaotic) to lower similarity levels (organized), and this progression creates the apparent "arrow" of time. It is not time itself that is directional, but the organizational pattern.

The second law of thermodynamics applies to isolated systems, but the Universe is not isolated — it is infinite (Axiom 2, Axiom 5). Local entropy can increase while the global pattern remains organizational. Meanwhile, motion equations are time-symmetric because motion itself has no preferred direction. The apparent arrow comes from initial conditions and probability — features of how motion works, not a separate property of time. Time's arrow reduces to motion's causality.

"Quantum Mechanics Requires Time as Parameter"

The Schrödinger equation has time as an explicit parameter, and quantum mechanics treats time as a fundamental variable. However, this doesn't prove time is physically independent — only that time is a useful mathematical variable. When QM equations "evolve in time," they are really evolving with motion. The wave function evolution represents a changing configuration, and the time parameter serves as a proxy for motion occurrence.

This is analogous to using an angle as a parameter in equations — it doesn't make angle a physical dimension. Mathematical success does not equal physical reality, just as Ptolemaic epicycles used angles as parameters and made accurate predictions without reflecting the actual mechanics.

Open Questions

Theoretical Development

  • What is the precise mathematical relationship between time rates at different similarity levels? Does the scaling factor depend on mass, distance, or other properties?
  • How exactly does organizational progression create the apparent arrow of time? Is time's arrow fundamental or emergent?
  • Why does consciousness experience time as flowing? What neural processes create the sense of a present moment?
  • How do we define simultaneity across similarity levels? What does "at the same time" mean across scales?

Mathematical Formulation

  • Can we reformulate physics using motion as the parameter instead of time? Would this simplify or complicate equations?
  • How do we model systems spanning multiple similarity levels? How does time scaling affect energy transfer between scales?
  • Can a formal mathematical theory of comparing different clocks be developed? How do clock synchronization protocols work mechanically?

Experimental Tests

  • Can we measure the time scaling factor between similarity levels directly?
  • Can we design experiments that distinguish geometric from mechanical time dilation? Are there situations where the AAM makes different predictions from relativity?
  • Are there observable consequences of scale-dependent time that could be tested through atomic structure?

Conceptual Clarification

  • What exactly is the "present moment"? How thick is it? Is there an objective present, or only a subjective one?
  • Is causation temporal, or is time causal? Does causation flow from motion sequences?
  • How do we conceptualize infinite past and future? What does "always" mean in an infinite Universe?

Relationship to Other Axioms

Builds On:

  • Axiom 1 (Space, Matter, Motion) $-$ Time must reduce to these three constituents. Time is not a fourth fundamental entity — it is the occurrence of motion. Space provides the arena, matter provides the content, motion provides time.
  • Axiom 2 (Infinite Space) $-$ Infinite space allows eternal time. No spatial boundaries means no temporal boundaries.
  • Axiom 3 (Mass and Infinite Divisibility) $-$ Infinite divisibility creates an infinite similarity level hierarchy, with each level having its own time rate.
  • Axiom 4 (Universe Concept) $-$ Eternal Universe implies eternal time. No creation event means no time beginning; no end means no time cessation.
  • Axiom 5 (Infinite Matter) $-$ Infinite matter means infinite motions and infinite time. No heat death means motion continues eternally.
  • Axiom 6 (Relative Motion) $-$ Relative motion implies relative time. No absolute reference implies no absolute time. Time inherits all properties from motion: unique for each particle, continuous, and relative.
  • Axiom 7 (Energy as Motion) $-$ Energy is motion of matter, and time is occurrence of motion. Both are derived from fundamental motion — neither is a fundamental substance.
  • Axiom 8 (Perpetual Motion) $-$ Perpetual motion implies eternal time. No motion cessation means no time cessation.

Prepares For:

  • Axiom 10 (Self-Similarity) $-$ Time scaling is a consequence of self-similar structure. The same organizational principles at different scales produce different time rates, unified within a consistent framework across all similarity levels.

Key Connections:

  • With Axiom 1 $-$ Axiom 1 establishes space, matter, and motion as fundamental. Axiom 9 derives time from motion. Together: only three fundamental entities, time is derivative. Gravitational effects on motion explain "gravitational time dilation" mechanically.
  • With Axiom 6 $-$ Axiom 6 establishes that motion is unique, continuous, and relative. Axiom 9 establishes that time is the occurrence of motion. Together: time inherits all properties of motion — unique for each particle, continuous, and relative.
  • With Axiom 8 $-$ Axiom 8 says motion is eternal and perpetual. Axiom 9 says time is the occurrence of motion. Together: time is eternal and perpetual, with no beginning or end.
  • With Axiom 7 $-$ Axiom 7 defines energy as motion/configuration of matter. Axiom 9 defines time as the occurrence of motion. Together: energy and time both emerge from motion — neither is a fundamental substance.