Structured Error, Not Random Noise: Deterministic Phase Patterns in Electron Microscopy*

Quantum mechanics is most often interpreted through probabilistic frameworks that treat noise as inherently random. This project explores whether that “randomness” conceals structured error, detectable through advanced electron microscopy. Using a 300 keV scanning transmission electron microscope, I analyze diffraction and interference data under two complementary perspectives: the standard probabilistic interpretation and a deterministic spectral approach. Preliminary analyses of holography datasets at 300 keV suggest that spectral methods can highlight reproducible patterns not captured in standard probabilistic reconstructions, and future work will extend this comparison to more datasets. The outcome of this work may contribute to novel approaches for calibrating electron microscopes and to the broader discussion of alternative interpretation for quantum measurements.

In the orthodox view, probabilities are derived from the absolute value of psi squared, while interference arises through the relative phase of the complex wavefunction. This provides a model of a wave distribution and a probabilistic interpretation of data. Spectral theory seeks to correlate the two directly, treating observed distributions not as irreducibly random but as projections of deterministic phase structure that may be recoverable from apparent noise.