6 The Informational Field $I(x,t)$

Having established the conditions under which a physical phase can emerge, we now introduce the fundamental physical quantity of the framework. This quantity is not energy, momentum, or a quantum field, but a scalar field encoding coherent informational structure.

All subsequent physical phenomena arise as effective descriptions of the behavior of this field.

6.1 Definition and Interpretation

We define the informational field:

Here, $x$ denotes emergent relational position and $t$ denotes emergent temporal ordering. Neither coordinate is fundamental; both arise from the dynamical behavior of $I$ itself.

The field $I(x,t)$ does not represent information in the Shannon sense alone, nor does it encode semantic meaning. Instead, it quantifies the degree to which distinctions are coherently maintained and propagated across the generative structure.

Regions of high $I$ correspond to stable, persistent structure. Regions of low $I$ correspond to diffuse or weakly correlated configurations. Importantly, $I$ is always non-negative and bounded from above by structural stability constraints.

6.2 Why Information (Not Energy) Is Primary

In conventional physics, energy is treated as the fundamental conserved quantity. However, energy presupposes time-translation symmetry, a Hamiltonian structure, and a well-defined notion of dynamics. All of these are emergent features in the present framework.

Information, by contrast, is logically prior. Without distinctions, no state can be identified, no process can be tracked, and no conservation law can be formulated. Energy is therefore a derived quantity, meaningful only once a physical phase with stable structure has already emerged.

Within this framework, matter, radiation, and energy correspond to different patterns and excitations of the informational field $I$. They are not separate substances, but effective descriptions valid in specific regimes.

By taking information as primary, the framework avoids the need to postulate multiple fundamental fields or interaction types. A single scalar field suffices to generate the full spectrum of observed physical phenomena.

6.3 Relation to Entropy and Coherence

Although $I(x,t)$ is an informational quantity, it is not equivalent to entropy. Entropy measures disorder or multiplicity of microstates, whereas $I$ measures coherence and structural persistence.

The two are related but distinct. In particular, entropy can increase while $I$ remains bounded, provided that coherence is maintained at larger scales.

A useful heuristic relation is:

where $S$ denotes an effective entropy functional. This expression emphasizes that entropy growth reflects redistribution of informational coherence rather than its destruction.

Coherence, encoded in $I$, is the resource preserved by the selection functional $\Xi$. Entropy increase is therefore compatible with the framework, while absolute loss of $I$ is not.

With the informational field defined, we can now specify its dynamics. In the next section we introduce the fundamental evolution equation governing $I(x,t)$ and show how spacetime, structure, and stability emerge from it.