2024
Reality begins as abstract information itself, with no privileged representation, alphabet, ordering, geometry, or probability measure. Any concrete encoding (binary, ternary, continuous, or otherwise) is a matter of convenience rather than ontology. Entropy, time, and physical law arise only relative to observer-defined representations and coarse-grainings. There is no distinguished substrate or execution mechanism; existence is purely informational.
Since \(\mathbf{P}\) excludes nothing, it necessarily contains finite informational subsets capable of self-reference. The existence of structured, observer-containing worlds requires no external cause; such structures are unavoidable elements of infinite informational potential. Observers are not observing the reality outside—they are sub-sets of it.
A concrete world may be represented as a finite configuration space \[\mathcal{C} \cong \{0,1\}^n,\] where each configuration \(\mathbf{s} \in \mathcal{C}\) is a static informational state. There is no motion or dynamics at this level—only the coexistence of all configurations. The binary representation is not fundamental; it is chosen purely for convenience.
Zero and One (yes, no) are not fundamental either. We might equally well write: \[\mathcal{C} \cong \{Head,Tail\}^n,\]
All configurations are ontologically equal.
Time is an induced ordering arising from traversals through configuration space. An ordering of states is not given a priori; it is defined only relative to observer paths. Timeless configuration space thus precedes experienced temporality.
An observer history is a finite path through the configuration space. \[\gamma = (s_1, s_2, \dots), \qquad s_i \in \mathcal{C}.\] Only a vanishing subset of all possible paths form the observer-compatible set \[\mathcal{T}_{\mathrm{obs}} \subset \mathcal{S},\] where \(\mathcal{S}\) denotes the space of all paths through \(\mathcal{C}\). Only paths in \(\mathcal{T}_{\mathrm{obs}}\) possess a subjective “inside” and are experienced as reality.
Observer paths are not equally weighted. Their measure is governed by compressibility in a spectral representation. Paths admitting efficient spectral encodings dominate the ensemble of experienced histories. Formally, preferred histories minimize spectral description length: \[H_{\mathrm{SSD}} = \arg\min_H \mathcal{L}(H),\] where \(\mathcal{L}(H)\) denotes the minimal spectral encoding length of path \(H\). This statistical dominance yields an emergent, finite, and predictable physics without invoking fundamental dynamics.
The quantum wavefunction \(\Psi\) is not a physical field but an optimal spectral compression of the observer-path ensemble. Superposition and interference reflect shared substructure within compressed descriptions. The Born Rule emerges as a measure over paths: \[P(\gamma) \propto 2^{-\mathcal{L}(\gamma)} \sim |\Psi(\gamma)|^2.\] Thus probability is not fundamental; it is a consequence of informational weighting.
Physical gravitation emerges as a macroscopic manifestation of the statistical weighting of observer-compatible paths in configuration space.
Let \(\mathcal{C}\) be the static configuration space, and \(\mathcal{T}_{\mathrm{obs}} \subset \mathcal{S}\) the set of observer-compatible paths \(\gamma = (s_1, s_2, \dots)\). Each path is assigned a spectral encoding length \(\mathcal{L}(\gamma)\) and a corresponding quantum amplitude: \[\Psi(\gamma) \propto 2^{-\mathcal{L}(\gamma)/2}, \qquad P(\gamma) = |\Psi(\gamma)|^2 \propto 2^{-\mathcal{L}(\gamma)}.\]
The dominant paths are those minimizing their spectral encoding length: \[\delta \int_\gamma \mathcal{L}(\text{state})\, d\lambda = 0.\] These paths correspond to the classical trajectories experienced by observers.
Let \(\rho(\mathbf{s})\) denote the density of reusable microstructure motifs within configuration space. High-density regions correspond to low spectral cost; an observer path naturally “falls” toward them.
In the continuum limit, the effective metric \(g_{\mu\nu}\) is defined by the gradient of spectral cost: \[\mathcal{L}(\gamma) \approx \int_\gamma \sqrt{g_{\mu\nu} \, \dot{x}^\mu \dot{x}^\nu} \, d\lambda,\] so that minimizing \(\mathcal{L}\) coincides with minimizing proper length in spacetime — i.e., geodesics.
Summation over all \(\gamma \in \mathcal{T}_{\mathrm{obs}}\) weighted by \(2^{-\mathcal{L}(\gamma)}\) reproduces a path-integral-like formalism: \[\langle \mathcal{O} \rangle = \sum_{\gamma \in \mathcal{T}_{\mathrm{obs}}} \mathcal{O}(\gamma) \, 2^{-\mathcal{L}(\gamma)},\] where \(\mathcal{O}\) is any observable depending on path configurations.
- Everettian view: All observer-compatible paths exist simultaneously, no branching; probability arises from spectral measure, not collapse. - Wheeler–DeWitt view: Configuration space is timeless; time emerges as an ordering along \(\gamma\). - Classical limit: Low-\(\mathcal{L}\) paths dominate, producing smooth geodesic motion as in GR.
Gravitation is thus not a fundamental force but a statistical-geometric phenomenon: classical geodesics are the trajectories of minimal spectral encoding length through configuration space, weighted by observer-compatible path measure.