2025
We propose an observer centric informational framework in which physical law emerges from compression. Reality is identified with the totality of possible informational configurations, without privileging any specific encoding. Observers are coherent substructures whose histories are weighted by description length. Because predictable, law-like structure compresses most efficiently, observer-conditioned probability concentrates on maximally compressible histories.
Quantum mechanics and general relativity arise as complementary compression mechanisms. Hilbert-space structure provides an optimal spectral encoding of microscopic correlations, while geometry provides an optimal encoding of macroscopic relational structure. Observers therefore most probably find themselves in histories where both spectral and geometric compression are simultaneously near-optimal.
The apparent fine-tuning of physical constants is reinterpreted as a selection effect associated with a critical weighting of description length, yielding an effectively parameter-free description of physics.
Keywords: Spectral Complexity, Minimal Description Length, Emergent Gravity, Observer-Conditioned Typicality, Quadratic Gravity, \(R^2\) Action.
Reality is a finite static informational totality \(\mathcal{C} = \{0,1\}^n\).
Configuration Space: All \(2^n\) configurations exist simultaneously and timelessly.
Ordered Traversals: A history \(\gamma\) is an ordered path through bit-space. All possible paths exist; however, the sampling measure is non-uniform.
The Observer: An observer is a localized informational substructure that maintains internal coherence and persistent memory across a history \(\gamma\).
Time is not an ontological primitive but a coordinate internal to the compressed representation of a path. Causality emerges because histories with low-complexity transitions are exponentially more probable than chaotic ones.
We propose that physics is the result of the observer mapping raw bit-string histories onto two primary, complementary compression channels.
Microscopic correlations are most efficiently compressed via a spectral representation. We define the complexity \(C_Q\) as a Sobolev-type seminorm: \[C_Q[\gamma] = \sum_{k} k_{\text{eff}}^2 |A_k|^2\] where \(k_{\text{eff}}\) is the minimal frequency distance. This functional penalizes high-frequency "roughness." The wavefunction \(\psi\) is thus the minimal smooth encoding of discrete informational structure. Quantum behavior (interference, superposition) emerges because Fourier-like modes are the optimal basis for microscopic data compression.
Macroscopic relational structure is compressed via geometry. Unlike the Einstein-Hilbert action, the informational cost must be positive-definite to ensure vacuum stability. We employ a quadratic Ricci functional. At the continuum level, the effective geometric cost can be written as: \[C_G[\gamma] = \alpha \int R^2 \sqrt{-g} \, d^4x + \beta \int \|a + \Gamma(v,v)\|^2 ds\]
\(R^2\) Penalty: Ensures all curvature costs information, preventing "negative information" instabilities.
Geodesic Enforcement: Deviations from geodesics increase the description length of a path, forcing observers to perceive "inertial" motion.
The probability \(\mathbb{P}\) of an observer history \(\gamma\) is determined by the joint minimization of spectral, geometric, and interaction complexity:
\[\mathbb{P}(\gamma \mid O) = \frac{1}{Z_O} \exp \Big[ -\lambda_c \big( C_Q(\gamma) + C_G(\gamma) + C_{\text{int}}(\gamma, G) \big) \Big]\]
The parameter \(\lambda\) weights the "stiffness" of the laws of physics. We posit that \(\lambda\) is fixed at a critical value \(\lambda_c\) representing a phase transition between chaos and crystalline order. Only at \(\lambda_c\) can "intelligent" observers exist who are complex enough to record history but simple enough to remain predictable. Thus, \(\lambda\) is an emergent property of the observer’s existence, not a free constant.
Gravity is the necessary coupling between the two compression channels. The interaction term represents the informational cost of mapping a wavefunction \(\psi\) onto a manifold \(G\): \[C_{\text{int}} \sim \int |\psi|^2 R \, \sqrt{-g} \, dV\] Variation of the total functional with respect to the metric yields field equations where curvature responds to spectral density. Gravity is not a force; it is the geometric "warping" required to minimize the total global compression cost of an informational structure.
A potential tension exists between "minimal complexity" and the "complex action" of intelligent agents. We resolve this by observing that "death" (entropic dissolution) represents a transition to a high-entropy, high-frequency state. In the spectral domain, the dissolution of a coherent observer costs an astronomical amount of informational "bits" (\(\sum k^2 |A|^2\) spikes as \(\psi\) fragments).
Intelligence: The strategic expenditure of local complexity to avoid global informational decoherence.
Active Inference: An intelligent observer selects paths that minimize the integrated complexity over future horizons. Swimming against a current to avoid a waterfall is the most probable path because the "cost of swimming" is lower than the "cost of fragmentation."
At first glance, the appearance of the parameter \(\lambda\) in the universal informational measure may seem to contradict the claim that the present framework is parameter-free. This apparent tension arises from a misclassification of the role played by \(\lambda\).
The theory itself introduces no free parameters at the ontological level. The informational substrate, the space of all histories, and the complexity functionals \(C_Q\), \(C_G\), and \(C_{\text{int}}\) are fully specified without reference to any tunable constants. The parameter \(\lambda\) does not characterize the universe; rather, it characterizes the measure induced by conditioning on the existence of a particular observer.
Formally, \(\lambda\) functions as a Lagrange multiplier conjugate to description length, analogous to inverse temperature in statistical mechanics. Different values of \(\lambda\) define different valid measures over the same space of histories. All such measures exist simultaneously. However, for any specified observer, the probability of sustained coherence is sharply peaked around a characteristic value \(\lambda^*(O)\). Observers therefore find themselves in universes with an apparently fixed \(\lambda\), not because this value is fundamental, but because other values render their continued existence exponentially unlikely.
In this sense, \(\lambda\) is not a free parameter to be chosen, but an inferred quantity determined by the observer’s informational structure. The apparent fine-tuning of physical laws is thus a selection effect rather than an ontological assumption. The framework remains genuinely zero-parameter: no constants are specified prior to conditioning on observer existence, and no degrees of freedom remain unconstrained by the theory.
The universe is the path of least informational resistance. By replacing Kolmogorov complexity with computable spectral and geometric metrics, we propose that:
1. Quantum Mechanics is the optimal micro-compression. This is what we
2. General Relativity is the optimal macro-compression.
3. Intelligence is the self-maintenance of these compressed boundaries.
Observer-conditioned histories are distributed according to description length. Observers therefore experience the most compressible (predictable, smooth, structured) histories compatible with their existence.
The PsiEmergentSim PoC implements the principles of the Dual-Compression framework numerically. Although the continuum geometric cost term \(\int \|a + \Gamma(v,v)\|^2 ds\) is not explicitly computed, its effect emerges from the combination of:
Spectral Complexity Penalty (\(C_Q\)): Large accelerations or sharp deviations in the observer trajectory produce high-frequency Fourier components, which are heavily penalized. This reproduces the information-theoretic cost of non-geodesic motion.
Candidate Proposal Bias (Inertia): New candidate positions are sampled around smooth extrapolations of the observer’s previous trajectory. This preferentially selects paths with minimal local curvature in discrete steps.
Curvature Interaction (\(C_{\text{int}}\)): The observer experiences informational penalties when deviating from regions of low curvature as encoded in the discretized GBitwave grid. This approximates the effect of geodesic enforcement.
Together, these components reproduce the continuum geodesic penalty statistically. The PoC thus demonstrates that both quantum-like smoothness and emergent geodesic motion arise naturally from description length, without any hard-coded laws.
Note: Observers in the simulation effectively select paths that minimize total complexity, providing numerical evidence that \(\lambda\) acts as a selection parameter for observer coherence rather than a fundamental constant.