The theory rests on five foundational postulates.
Postulate 1 — Configuration Space
- Physical reality consists of a timeless configuration space \(\Omega\).
- Each configuration \(\omega \in \Omega\) specifies a complete arrangement of fundamental degrees of freedom.
- Configurations do not evolve in time.
- Configuration space carries complex phase structure.
Postulate 3 — Compatibility Classes
- Each record corresponds to the set of configurations compatible with the correlations included in that record.
- This set defines the compatibility class:
\[
\Omega_r = \{\, \omega \in \Omega \mid \omega \text{ is compatible with the correlations encoded in } r \,\}.
\]
- Compatibility classes represent the configurations indistinguishable with respect to the correlations represented in the record.
Postulate 4 — Closure Geometry
- Correlations among degrees of freedom may imply additional correlations.
- A closure operator represents the implication structure among correlations and thereby defines the refinement relations among records, forming a refinement partial order whose chains represent admissible record refinements:
\[
r_1 \preceq r_2
\]
- Record structures therefore form a refinement lattice.
-
This structure induces an invariant distinguishability measure called closure distance:
\[
d_c(r_1, r_2)
\]
representing the minimal restructuring required for one record to correspond to the correlations represented in another.
-
Closure distance accumulates discretely:
\[
d_c = N\,\delta_c
\]
where \(\delta_c\) is the closure quantum, the minimal distinguishable increment of correlation capacity.
Postulate 5 — Observers, Closure Dynamics and Measurement
- An observer is a structured subsystem within configurations whose internal degrees of freedom include records. Observers are defined purely structurally; no assumption of consciousness or subjective experience is made.
- Closure dynamics is the observer-relative evolution of an observer’s record state as it traverses configuration space along refinement chains defined by closure operators.
- A measurement corresponds to closure dynamics in which the observer’s records change such that the compatibility class defined by those records changes.
- Closure dynamics, rather than any fundamental evolution of configurations, corresponds to observer-relative change. Observer-relative quantum amplitudes and probabilities emerge from the inherited complex phase structure of compatibility classes, while classical time, motion, and spacetime trajectories emerge as coordinate representations of closure distance along record refinement chains.