The Wavefunction as Compression:
Spectral Complexity, Emergent Quantum Behaviour,
and the Informational Action Principle

Juha Meskanen

June 2026

Abstract

Papers I–V [meskanen2001, meskanen2002, meskanen2003, meskanen2026iv] established a purely information-theoretic, classical framework in which spacetime geometry, gravitational collapse, cosmic expansion, and the relational scale factor all emerge from a finite bit budget n without hard-coded physical laws. One feature of the observed universe remains unexplained by that framework: the wave-like behaviour of the microcosm. This paper proposes and investigates the hypothesis that the quantum wavefunction is the universe’s data-compression codec. Internal observers, themselves composed of compressed structures, perceive their constituent degrees of freedom as wave-like for the same reason that pixel-observers inside an MPEG-compressed movie would perceive their world as governed by a Discrete Cosine Transform: they are observing compressed information. We formalise and implement this as a Spectral Complexity measure Cs — a continuous, computable complexity — and show that Solomonoff-like suppression under Cs selects smooth, law-like, wave-governed configurations over chaotic ones, resolving the Boltzmann brain problem without additional axioms. Numerical simulations demonstrate the emergence of inertia and interference from spectral compression alone.

Contents
1 Introduction
2 The Compression Hypothesis
2.1 The MPEG Analogy
2.2 The Dithering Analogy and the Born Rule
2.3 Fermions, Bosons and Pauli Exclusion
3 Spectral Complexity
3.1 From Kolmogorov to Spectral Complexity
3.2 Resolution of the Boltzmann Brain Problem
4 Numerical Results
4.1 Emergence of Smooth Spacetime
4.2 Emergence of Inertia and Interference
5 Conclusion
Open Problems
Simulation Code

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