Causal Structure, Derived Geometry, and the Problem of Time: A Preliminary Framework

Preliminary statement. Formalization is ongoing.

For several years I have been developing a theoretical framework in which causal structure is ontologically fundamental — more fundamental than spacetime, more fundamental than quantum mechanics, and more fundamental than information in the Shannon sense. What follows is a preliminary statement of the core claims. It is not yet a complete theory. The mathematics remains unresolved in ways I will describe.

The core claims

Spacetime is not fundamental. It is emergent (or more precisely, decompressed via a functor F: 𝒢 → ℰ) from underlying causal structure. A toy functor mapping from a compressed causal category 𝒢 to an emergent geometric category ℰ demonstrates the basic mechanism: causal order, with a simple counting entropy, generates geometric structure including dimension, branching, and boundary entropy analogous to entanglement entropy. Time appears as a coordinate in the emergent representation. It is not in the source category.

This is directional because compression is irreversible. The emergent representation cannot be uniquely mapped back to its source — information is lost in the transition. The arrow of time is not a thermodynamic fact layered onto a time-symmetric substrate. It is a consequence of the irreversibility of compression itself. Lost information is the arrow of time.

Quantum mechanics is not fundamental either. It is a compressed encoding of causal relationships — an extremely good one, which is why it works. Its apparent weirdness — superposition, measurement, entanglement — may be artifacts of the encoding, analogous to the way color is an artifact of how electromagnetic wavelength gets compressed into perceptual experience. The Wheeler-DeWitt equation, which contains no time, points in this direction. AdS/CFT, in which a timeless boundary theory encodes a bulk with emergent time, points in this direction. The framework I am describing is the generalization: causal structure is the boundary; everything else is the bulk.

On causal set theory

Causal set theory starts from the right place. The partial order — event A precedes event B — is a genuinely timeless structural fact. There is no time coordinate in the causal set itself. Causality is prior, and geometry, including spatial distance and temporal interval, is meant to emerge from it. This is correct, and it is why the approach has been productive.

The problem is the dynamics. To say anything about how the universe evolves, causal set theorists introduce what they call classical sequential growth dynamics — a framework describing how new elements get added to the causet. The language is immediate: elements are “born,” the causet “grows,” addition happens “sequentially.” Time, which was supposed to be absent from the fundamental description, reappears in the dynamics. It was never eliminated. It was moved.

This is not a minor notational problem. It reflects a deeper issue: causal set theory correctly identifies that the static structure is timeless, but has not yet found a way to describe change — or the appearance of change — without reintroducing time as a primitive. The sequential growth framework is, functionally, putting time back in through the back door.

The framework I am describing differs here in a specific way. The functor F is not a process that happens. It is a timeless mathematical relationship between two structures — one more compressed, the other more geometrically explicit (the decompression map F: 𝒢 → ℰ). The relationship between them exists the way mathematical relationships exist: atemporally. What we experience as dynamics, as evolution, as time passing, is what it is like to be embedded in the emergent representation rather than the fundamental one. It does not need to be added to the fundamental level because it was never missing — it is what the emergent level looks like from the inside.

This is the distinction causal set theory has not yet made cleanly. The structure is timeless. The appearance of dynamics is not something added to the structure. It is what emergence looks like from within.

The selection principle

The framework requires an account of why some causal structures exist as persistent patterns and others do not. The principle I have been developing — which I have called elsewhere the Information-Theoretic Imperative and Compression Efficiency Principle — is not a temporal process of selection. It is a timeless mathematical fact: only causal structures with sufficient compression properties achieve the recursive stability required to exist as persistent patterns in the emergent representation. We experience this as evolution, as learning, as the directionality of physical processes. But the selection is not happening over time. Time is what we call the experience of moving through compression trajectories from within the emergent representation.

What this is not

This is not Wheeler’s “it from bit.” I am not claiming information is the substance. I am agnostic about substance — about what underlies the causal structure at the most fundamental level. What I am claiming is that the observable structure of reality is causal-informational, and that geometry and time are emergent from it rather than prior to it.

This is not causal set theory, though it is adjacent and owes a debt to it. The distinction is specific: causal sets correctly identify the timeless structure but reintroduce time in their dynamics. The framework I am describing locates the appearance of dynamics entirely in the emergent representation, not in the fundamental one.

What remains unresolved

The formalism is incomplete. Compression, emergence, selection, and persistence are all temporal concepts in ordinary language and in most available mathematics. I have not yet found a formulation that eliminates this without smuggling time back in through the same door causal set theory uses. I believe the solution involves treating the functor F strictly as a timeless mathematical relationship rather than a process — the map exists, it does not happen — but making this fully precise requires work I have not completed. This is the hard problem of the theory. Naming it clearly is more useful than obscuring it.

Scope

This framework is not isolated. The same principles — causal structure as prior, compression as the selection mechanism, time and geometry as derived — appear to underlie questions I have been working on across regulatory science, AI governance, and the architecture of learning systems. The convergence is not coincidental. It is what you would expect if the framework is correct.

An invitation

Related work is appearing that converges toward parts of this framework without the unifying structure. Engagement, critique, and collaboration are welcome — particularly from anyone working on the formalism problem of genuinely timeless causal structure, and from anyone who thinks I am wrong about where causal set theory goes astray.