A formal study of observers inside a deterministic classical world finds that they can still face hard limits on what they learn. In the model, those limits depend on the kind of record an observer can obtain, the information available in its initial ready state, and whether it is trying to reconstruct an object's past or predict its future.
A controlled world with embedded observers
The analysis represents classical particles in symplectic vector spaces, mathematical spaces that encode position and momentum. It uses formal subjects, ready systems and allowed transformations to represent learning inside the model.
The analysis covers 27 formal cases. It varies three learning tasks—retrodiction, or learning about the past; repeatable learning; and prediction—alongside three choices for the manifest variable, meaning the record available to the subject, and three choices for the ready state, meaning its initial resource.
Three kinds of knowledge boundary
The model distinguishes three kinds of epistemic horizon, a formal boundary on what can be learned. A total horizon allows no learning; a knowledge-balance horizon permits only a restricted class of variables, called Poisson variables, and at most half of the object's degrees of freedom—the independent coordinates needed to describe it; and there is no horizon when the object's precise underlying state can be learned. If the manifest variable is trivial, the model always produces the total horizon.
The past is not equally accessible in every version of the model. When the manifest variable is Poisson, Poisson or trivial ready states limit retrodiction to Poisson variables, while a complete ready state permits every surjective linear variable—a variable whose possible outputs cover the whole stated output space. With a complete manifest variable, the object's identity variable can be retrodicted regardless of whether the ready state is trivial, Poisson or complete.
Repeatability changes the picture
Requiring a measurement to be repeatable—so the same information can be recovered again—makes the initial ready state decisive. Trivial ready states allow only constant variables to be learned repeatedly. Poisson ready states allow only Poisson variables, while complete ready states allow every surjective linear variable for both Poisson and complete manifest variables.
Prediction carries the tightest restrictions
Future-directed learning is more constrained in the authors' comparison. With a trivial ready state, subjects with either Poisson or complete manifest variables can predict only constant variables, creating a total predictive horizon. With Poisson manifest variables and Poisson ready states, a partial variable—one that captures only part of the object's state—can be predicted if and only if it is Poisson.
The model also makes prediction depend on preparation support: the set of initial states the preparation can cover. For a complete manifest variable paired with a Poisson ready state, full preparation support permits prediction of every surjective linear variable. The paper states a necessary-and-sufficient prediction condition in this case involving preparation support and the subspace that prediction cannot access.
The result captures a formal trade-off. Perfect knowledge of the final state requires full preparation support, while maximizing non-empirical knowledge removes empirical knowledge of the final state.
At the other end of the model grid, complete ready states remove the predictive horizon in the configurations covered by the analysis. Every surjective linear variable can be predicted with Poisson manifest variables, and the same is true when both the manifest variable and ready state are complete.
A result about the model, not everyday observers
The findings are conditional on a finite-dimensional classical toy theory and its specified transformations. They are model-internal results, not evidence that human or real-world observers face the same horizons or that the framework derives full quantum mechanics.
The stated analysis also leaves open how multiple subjects would compare records and how agency—the choice of measurement interaction—would be represented. The manifest variables and ready-state resources remain assumptions whose physical justification is unresolved.
The document is an arXiv version 1 preprint in the quant-ph category dated 26 August 2026.
Paper data and sources
Original title: The View from Within: What Can Embedded Observers (Not) Learn?
Authors: Tomáš Gonda, Johannes Fankhauser, Gemma De les Coves
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text