Space, Time, and Mass

The theory's account of spacetime (v0.5–v0.6). It resolves the time-circularity left open since v0.1, defines space and time as two readings of one structure, identifies mass with ongoing interaction, pins down energy, and proposes a bridge to special relativity — up to and including E = mc².

1. The problem we started from

Time in the theory looked self-contradictory. Two dependence relations seemed to point opposite ways:

• Locational (top-down): a sub-interaction's "when" is a position inside its parent's interior. The parent's time-frame contains the child.
• Constitutive (bottom-up): the parent only is once its children complete. The parent's existence depends on the children.

Parent contains child (in time); child makes parent (in existence). Apparent circularity: time seemed to flow up and down. But the circularity is an illusion produced by smuggling in an external master-clock — the very thing the theory forbids. Remove the master-clock and the two relations are not competing temporal flows at all. The resolution uses a tool the theory already had.

2. Encapsulation resolves the circularity

Every interaction is zero-duration from the outside. Apply this between adjacent levels, not only at the top:

• From the parent's interior, each child is itself a zero-duration point. The child's rich internal duration is invisible — encapsulated. The parent sees only the child's completed mark, as a single event.
• From the child's interior, the parent has no time at all; the child's own interior is all the time it has.

So a child does not share the parent's clock. What it receives from the parent is not a time-frame but a position — a single point in the parent's ordering. And the parent's time is nothing but the ordering of those child-points.

Each level manufactures its own time, fresh, from the ordering of the completed (point-like) events one level below. That time is then point-like — invisible — to the level above. Time is generated layer by layer and is opaque in both directions.

There is no single substance "time" flowing up or down. There is a new, private time at every level.

3. Time is succession; space is coexistence

Time is the order of succession of a parent's children's completions — read upward (child → parent).

Space is the order of coexistence of a parent's children — the room the parent grants them to be many at once — allocated downward (parent → child).

This is Leibniz's distinction (time = order of successive things; space = order of coexisting things), now equipped with a mechanism: both orders are one thing — the parent organizing its interior full of children — read along two axes. Read along succession, the interior is time. Read across coexistence, it is space.

The directionality follows:

• The content of time (the actual ordering) is contributed by the children's completions. Sourced from below. Time flows up.
• The container of space (the arena of distinctness) is contributed by the parent's interior. Sourced from above. Space flows down.

Same relation, opposite source-directions.

4. One phenomenon, two readings

The phenomenon is the populated interior of an interaction. Space and time are not two substances; they are two ways of reading that one interior — by succession or by coexistence. "Spacetime" is the populated interior; the split into space and time is a choice of reading-angle.

[bridge] This predicts that the space/time split should be observer-dependent: different sub-Forms embedded in the same parent, reading its interior at different angles, will disagree about which events are "successive" (time) and which "coexistent" (space). That is exactly the relativity of simultaneity.

5. The asymmetry generates the signature

Time flows up; space flows down. Opposite directions along the nesting relation.

[bridge] In physics, space and time are not symmetric in the spacetime interval: ds² = −c²dt² + dx² + dy² + dz² — time enters with the opposite sign to space (the Lorentzian, not Euclidean, signature). Opposite direction along one relation is exactly the structure that yields opposite sign in any combined measure. The theory does not bolt on the signature; the up/down asymmetry generates it.

6. Why time is one-dimensional

An ordering of completions is intrinsically one-dimensional — succession is a line. A room of coexistence can hold many independent directions of distinctness — coexistence is a volume. So the theory explains, for free, why time is 1D and space is higher-dimensional.

It gets sharper. Each interaction has exactly one awareness-moment (one B-pole, by the two-poles axiom). A parent therefore reads exactly one completion-sequence → exactly one time dimension. The one-dimensionality of time is a direct consequence of the two-poles axiom.

Why space is exactly 3-dimensional is not explained here. The theory explains why time is 1 and space is many; the specific number 3 remains open (see §13).

7. Everything moves through spacetime at c

[bridge] Standard relativity, intuitively: every object moves through spacetime at exactly the speed of light. What varies is the direction of that motion. Picture a spacetime-velocity arrow of fixed length c; a resting object points it almost entirely along time (ages fast, barely moves through space); a photon points it entirely along space (experiences zero time). The arrow's length is always c; only its angle changes.

Translated into the theory:

An agent spends a fixed total interaction-throughput (= c) splitting between completion (advancing through its children's completions → time) and propagation (spreading through the parent's arena → space).

• Photon: 100% propagation, 0% completion → no internal time, moves at c.
• Resting mass: 100% completion, 0% propagation → maximal aging, no motion.
• Everything real lies between, splitting its fixed budget by its angle.

c is the conversion constant — the exchange rate between the succession-axis (time, read upward) and the coexistence-axis (space, granted downward), and the conserved magnitude of the budget.

8. Mass is ongoing interaction

The angle's completion-component — how much of the budget is spent completing interactions in place — is what we have called, equivalently, the completion-rate or the amount of interaction. The second name is better: it ties to the theory's existing primitive (Mass = interaction) and names what is counted.

Mass is ongoing/bound interaction. A Form has mass to the extent that it is continuously completing interactions in place. Masslessness is pure propagation — interaction in transit, never completing.

[bridge] This holds across physics, not as metaphor:

• Composite mass (a proton) is ~99% the binding energy of its gluon field — trapped interaction.
• Elementary mass (an electron) is its continuous Higgs-field coupling — ongoing interaction.

Either way, mass = ongoing interaction. A photon has no rest mass because it is interaction-in-transit, never interaction-at-rest.

The photon, exactly: a photon is the mark mid-flight — the stretch of an interaction between A leaving the mark and B becoming aware. The interaction is not yet complete, so by the theory's own rule (time = completions) no time elapses for it, and it moves at c. Absorption (B becomes aware) is the completion — one tick.

9. The angle, and relativity from nesting

The angle — what sets how the budget splits between completion and propagation — is the agent's amount of interaction (completion-rate) relative to its substrate. Changing it rotates space into time.

[bridge] This is the rapidity (the boost parameter); the rotation between time-axis and space-axes is the Lorentz boost. A consequence: a fast-moving Form spends more budget on propagation, so fewer of its interactions complete per external unit — its internal clock slows. That is time dilation.

Crucially, the budget splits relative to the parent interior the agent is embedded in — never absolutely.

This is special relativity's founding move — no absolute frame, only relative motion — produced by the nesting structure rather than postulated. A reference frame, in the theory, is a parent interaction's interior.

10. Energy and momentum

[bridge] Physics builds motion from conjugate Lorentzian pairs. Just as (time, space) form a four-vector, so do (energy, momentum):

So energy is to momentum as time is to space: energy is the time-component of an agent's motion (its rate of completing), momentum the space-component (its propagation through the arena). And mass is the invariant of that pair — the rest-frame residue, sitting where proper time sits for spacetime.

This gives a route, not yet walked, toward the energy–mass relation: if energy is completion-rate and mass is the rest-frame amount of bound interaction, E = mc² should be the statement that a Form's entire rest interaction-content, converted at the budget's exchange rate c, is its energy. (A lead, not a result.)

11. Worked example: the quantum jump

A claim to test: an electron's jump between shells is a momentary "masslessness." Verdict: in line, with one correction that strengthens the theory.

Read the whole event as one interaction with two poles:

• Pole A (mark leaves): the electron drops from the upper shell.
• Mark in transit: the emitted photon — massless, zero proper time.
• Pole B (awareness): the photon is absorbed elsewhere; there the interaction completes — one tick.

The jump's timelessness is the photon's zero proper time. So the masslessness is real — but it lives in the mediating photon, not in the electron shedding its rest mass. The electron's rest mass is its Higgs interaction, which never stops; what is briefly suspended is the specific shell-binding interaction being reconfigured, while the electron sits in a superposition of the two shells.

A quantum jump is the transition of an electron between two bound Forms (shells). During it, the shell-binding interaction is momentarily in-transit rather than completing — a timeless gap — and that timeless, massless component is carried by the mediating photon. The electron retains its rest mass; what is briefly "massless" is the transition itself.

Two reasons this is a good test:

1. A shell is a solidified Form — an attractor of the interaction dynamics. A jump is a transition between attractor basins: precisely the sharp, threshold-crossing behaviour observed in Experiment 1 (the phase transition, the species hand-offs). The discontinuity of a quantum jump is the theory's Crystallization/dissolution dynamics at the smallest scale.
2. The in-transit part is timeless for the electron-state, yet we assign the transition a finite duration (linewidth, lifetime). That is exactly the photon situation — zero proper time for it, nonzero flight-time for us watching from the parent frame. The theory reproduces the split rather than contradicting it.

12. Energy, and E = mc²

In physics, E = mc² is a discovery — the surprise that inert mass and active energy are interchangeable. In this theory it is nearly a tautology, and that is the result.

v0.5 defined mass = ongoing interaction. But "ongoing" is already a rate. A static mass would be a contradiction in terms — mass is the continuing activity of bound interaction. So mass is inherently energetic.

E = mc² is then the statement that mass and energy are the same stuff — bound interaction — measured two ways: mass is the static measure (how much), energy the dynamic measure (the rate of completion). They cannot come apart, because the thing they measure was defined as ongoing.

The definition

Energy is the rate at which a Form completes the interactions that constitute and maintain it. Mass is the amount of bound interaction; energy is the rate of its completion.

This ties energy to the autopoietic core (v0.3: Action is the way a Form maintains its existence): energy is the rate of Action — how hard a Form is working to remain itself.

Rest energy is the cost of existing

Decay is automatic; existence is active. Even at rest, a Form must continually re-complete its bound interactions to keep from dissolving.

Rest energy (mc²) is the irreducible cost of existing — the maintenance-rate a Form must sustain just to stay itself. More mass → more to maintain → proportionally more rest energy. Stop paying, and the Form dies back into the substrate.

This part is airtight — it follows from "mass = ongoing interaction" plus "existence is active maintenance," with no bridge to physics required. The massless case checks out too: a photon does no self-maintenance, so it has no rest energy, yet carries energy through propagation (E = pc); and it cannot be at rest, having no completion-component to define a rest state.

Where the c² comes from

Einstein's own reading: c² is a unit conversion — the factor translating mass-units into energy-units. The physics of E = mc² is the identity of mass and energy; the c² is the exchange rate. The theory already owns that rate: c is the conversion between the completion-axis (time) and the propagation-axis (space). It appears squared because energy sits on the time-axis, and reaching it from the rest interaction-content crosses the conversion twice. [bridge] Honestly: the identity mass ≡ energy is derived; the c² is motivated ("the exchange rate, twice"), not rigorously pinned.

Momentum, conservation, the full relation

[bridge] Energy is the completion-share (time-component) of an agent's interaction-throughput; momentum is its propagation-share (space-component). They combine by the same Minkowski metric whose signature came from the time-up / space-down asymmetry: E² = (pc)² + (mc²)². At rest: E = mc². Pure propagation: E = pc (the photon). Mass is the invariant of the pair.

Energy is conserved because total interaction-throughput is conserved; via Noether it is the quantity conjugate to time — clean here because time just is the succession of completions. Time-translation symmetry is the uniformity of the completion-process along the succession-axis.

The one-line result

Mass is ongoing interaction counted; energy is ongoing interaction timed. E = mc² says they are the same — which the definition of mass made unavoidable. Rest energy is the cost of existing.

Two honest weak points: the c² factor is motivated, not derived; and the kinetic term is subtle (a moving Form's own completion-rate slows while its parent-frame energy rises — no contradiction, but not cleanly derived here). Rest energy is the airtight part. Full treatment in 05_ENERGY.md.

13. What is committed, what is conjectured

Theory-internal commitments

• Time is the order of succession of a parent's children's completions; space is the order of their coexistence.
• The two are readings of one structure (the populated interior), with opposite source-directions (time up, space down).
• An agent spends a fixed interaction-throughput split between completion (time) and propagation (space).
• Mass is ongoing/bound interaction; masslessness is interaction-in-transit.
• A reference frame is a parent interaction's interior; all motion is relative to it.
• Time is 1-dimensional because each interaction has one awareness-pole.

Conjectured bridges to physics (leads, not results)

• Opposite source-directions → the Lorentzian metric signature.
• Observer-dependence of the reading-angle → relativity of simultaneity.
• The fixed budget → the constant-magnitude four-velocity; c as its magnitude and the succession/coexistence exchange rate.
• The angle → rapidity; budget re-splitting → Lorentz boost and time dilation.
• (energy, momentum) as the conjugate Lorentzian pair; mass as its invariant; a route toward E = mc².

14. Open questions

1. Why space is exactly 3-dimensional. v0.5 explains why time is 1D and space is many-D, not why space is 3.
2. The continuous angle. Completion-ordering looks discrete; spatial room looks continuous; relativity needs them to mix continuously. The likely repair — at enormous child-counts the discrete ordering coarse-grains into effectively continuous time — is a promissory note.
3. What the angle is measured against, made precise. "Relative to the parent interior" is the right shape; turning it into a definite quantity (the analog of relative velocity) is unfinished.
4. Deriving c. Is c literally the maximum completion-processing rate, and can its finiteness be derived rather than posited?
5. The kinetic energy term. §12 nails rest energy (mc²) cleanly. The kinetic term is subtle: a moving Form's own completion-rate slows while its parent-frame energy rises — no contradiction, but not yet cleanly derived.
6. Deriving the c² factor, not just its shape. Why exactly twice, and can the magnitude of c be fixed from the completion/propagation structure?
7. Energy quantization. If time is discrete (a succession of completion-ticks), energy (rate of completion) may be naturally quantized — does ħ enter as "interaction per tick"?
8. Composition across levels. Each level has its own time and space; how do the per-level spacetimes compose into the single spacetime we observe inside the One Interaction? ("Sensed time is composite" now needs a spatial counterpart: "sensed space is composite.")

Space, Time, Mass, and Energy — v0.5–v0.6. Builds on Foundations and the Asymmetric Epistemic Principle. Changelogs in 04_SPACETIME.md and 05_ENERGY.md in the project repo.