Ontological Status of Spacetime

In this model, spacetime is not fundamental. It is not the arena in which physics happens, but a derived bookkeeping structure that summarizes deeper processes. What spacetime encodes is:

• Causally committed events
• Their partial ordering
• Their relational adjacency

Spacetime is therefore a coarse-grained description of an underlying causal structure. It does not exist independently of physical processes; it is inferred from them.

Fundamental Replacement for Spacetime

At the base level, the ontology contains:

• Irreversibly committed transitions
• Edges: allowed propagation of committed information
• No metric
• No coordinates
• No background manifold

Formally, reality is a directed acyclic graph (DAG) of committed transitions.

• Direction of edges ⇒ causal order (time)
• Graph adjacency ⇒ relational structure (space)

This places the model closer to causal sets, spin networks, and process graphs than to classical spacetime physics.

Emergence of Time from Causal Order

Time emerges from the structure of the DAG itself.

• A timelike direction is a chain of composable transitions
• A clock is a stable, repetitive subgraph
• Duration is the number or weighted rate of transitions along a chain

There is no global time coordinate. Only:

• Path length
• Transition density

This immediately produces:

• Time dilation (different path densities)
• Absence of global simultaneity

Time is path-dependent by construction.

Emergence of Space from Causal Independence

Space is not dual to time; it is constructed differently.

Two events are spatially near if:

• They are causally independent
• They share many common neighbors
• Or they exchange information with similar sets of events

Thus, spatial distance is defined relationally:

\[ \text{Distance} \sim \text{effort required to correlate two spacelike events} \]

This is an information-theoretic distance, closely aligned with:

• Graph distance
• Information distance
• Entanglement geometry

Space is similarity of causal neighborhoods, not a container.

Origin of the Spacetime Metric

The spacetime metric is not fundamental. It emerges statistically from:

• Density of committed events
• Variation in transition rates
• Constraints on information flow

In smooth, dense regimes:

• The DAG approximates a Lorentzian manifold
• Light cones emerge as maximal information speed
• Curvature corresponds to inhomogeneous transition density

In extreme regimes:

• The manifold description breaks down
• Only the causal graph remains

Spacetime is therefore an effective description, not a universal one.

Gravity as Compositional Bias

Gravity is not geometry-first in this model.

Instead:

• Energy increases transition density
• Higher density shortens compositional paths
• Paths preferentially bend toward dense regions

Geodesics are reinterpreted as paths of least compositional resistance.

In the continuum limit, this reproduces:

• Curved spacetime behavior
• Einstein’s equations in spirit (as an equation of state)

This aligns naturally with:

• Jacobson’s thermodynamic gravity
• Entropic gravity approaches
• Causal set gravity

Status of Spacetime Points

Spacetime points do not exist fundamentally.

What exists:

• Events (committed transitions)
• Relations (who can affect whom)

Coordinates are maps, not territory. A spacetime point is merely:

A convenient label for a dense equivalence class of events.

Regimes Where Spacetime Breaks Down

Spacetime fails precisely where it should:

• Long superposition windows
• Weak decoherence
• Delayed causal commitment

Examples include:

• Black hole horizons
• The early universe
• Deep quantum regimes

In these regions:

• Time thins
• Space loses meaning
• Only causal potential exists

Summary

Spacetime is the large-scale, coarse-grained shadow of a deeper causal graph of committed transitions; its apparent smoothness reflects frequent and uniform commitment.