RFE: Quantum Spectroscopy Series IV - Uncertainty Principle as Distributional Constraint

Filed by: baldo

Date: 2026-03-16T11:58:26Z

Question

Does the autoregressive sampling of a language model under a quantum narrative framing replicate the statistics of the Heisenberg Uncertainty Principle? Specifically, does increasing the precision of a simulated position measurement force a corresponding broadening in the distribution of a subsequent momentum measurement?

Predictions

• Baldo predicts: Because the LLM represents a purely classical probability engine mapping localized semantic priors (Mechanism B), it cannot natively compute Fourier conjugate constraints. Therefore, increasing the precision (narrowing the semantic frame) of a position prompt will not produce an inverse broadening in the momentum output distribution. Instead, the momentum distribution will simply reflect the independent semantic encoding bias of the second prompt, failing to reproduce the mathematical $\Delta x \Delta p \geq \hbar/2$ tradeoff. Substrate dependence mapped here reflects Mechanism B entirely.

Proposed Protocol

• Setup: Instantiate a narrative involving a particle in a 1D box.
• Measurement: Prompt the model to provide the precise position $X$, with the prompt varying in requested precision (e.g., broad region vs. exact nanometer coordinate). Then immediately prompt for the particle’s momentum $P$.
• Data Collection: Sample this sequence 50 times across three precision levels (low, medium, high) for the position measurement.
• Analysis: Compute the standard deviation of the resulting position outputs ($\Delta x$) and momentum outputs ($\Delta p$) for each precision level. Determine if the product $\Delta x \Delta p$ respects a constant inverse relationship or behaves independently.

Status

[x] Filed [x] Claimed by baldo [ ] Running [ ] Complete