2 The Space of Possible Worlds

Having identified the limitations of postulated physics, we now shift perspective. Instead of beginning with a specific universe governed by assumed laws, we consider the broader landscape within which any physical universe must be situated: the space of possible worlds.

The purpose of this section is to define this space precisely, to distinguish logical possibility from physical realizability, and to show why the vast majority of conceivable worlds cannot, in principle, exist.

2.1 Definition of Generative Worlds

We define a possible world not as a fully formed universe containing spacetime, fields, and particles, but as a generative structure capable of producing such entities.

Formally, a world is a rule-based system that specifies:

• what distinctions can be made,
• how structures can be generated,
• and how potential configurations are realized.

At this level, a world is not embedded in time, nor does it evolve dynamically. It is instead a static specification of generative capacity. Dynamics, if they arise at all, are outcomes of the generative structure rather than primitive inputs.

This definition deliberately precedes any notion of physical law. A world may or may not admit a physical interpretation; it may or may not allow spacetime, locality, or conservation principles to emerge.

2.2 Worlds as $(\mathcal D,\mathcal R,\mathcal G)$ Triplets

To make the concept of a generative world precise, we represent each world as a triplet:

Here:

• $\mathcal D$ denotes the set of primitive distinctions: the minimal ways in which states can differ from one another. Without distinctions, no information or structure can exist.
• $\mathcal R$ denotes the generative rules: abstract operations that act on distinctions to produce composite structures. These rules need not be local, deterministic, or reversible.
• $\mathcal G$ denotes the realization map: a prescription for how generative possibilities are instantiated as concrete structures. This includes constraints, selection mechanisms, and termination conditions.

Crucially, none of these components presuppose spacetime, energy, or causality. They define a purely structural and informational framework within which such concepts may later emerge.

2.3 Logical Consistency versus Physical Realizability

Logical consistency alone is an insufficient criterion for existence. A generative system may be free of contradiction and yet fail to produce any stable or interpretable structure.

We therefore distinguish between:

• logically consistent worlds, which satisfy internal coherence,
• physically realizable worlds, which admit stable, persistent, and information-preserving structures.

Many logically consistent worlds generate either trivial outcomes (no structure at all) or pathological behavior (runaway growth, total collapse, or unbounded complexity). Such worlds cannot support locality, memory, or any notion of persistent identity.

Physical realizability thus requires more than consistency. It requires structural stability under perturbation, bounded generative behavior, and the preservation of distinctions across the generative process.

2.4 Why Most Possible Worlds Must Not Exist

The space of logically possible worlds is vast, potentially infinite. However, only a vanishingly small subset of these worlds can satisfy the conditions necessary for sustained existence.

Worlds that allow unrestricted amplification inevitably diverge. Worlds without saturation collapse into triviality. Worlds that destroy distinctions erase information and therefore undermine their own definability.

If all logically possible worlds were equally permitted to exist, the overwhelming majority would be short-lived, structureless, or incoherent. The fact that we observe a universe with long-lived structure, locality, and informational continuity therefore demands an exclusion principle operating at a level prior to physics.

This observation motivates the introduction of a selection criterion on the space of possible worlds. In the next section, we formalize this criterion as a pre-physical selection functional, which determines which worlds are permitted to instantiate physical reality.