This preprint presents a speculative theoretical framework for interpreting quantum statistical behavior as a possible consequence of structural information loss beyond ordinary environmental decoherence. The work builds on a previous dimensional projection model, but reformulates the idea in the language of quantum information. Instead of treating observation as direct access to a complete physical structure, the framework proposes that an observer accesses only a reduced manifestation of a larger structure. This reduction is interpreted as a form of non-invertible projection, where part of the information remains inaccessible to the observer. A central distinction introduced in this version is the separation between ordinary environmental degrees of freedom and a proposed structural sector. Environmental degrees of freedom correspond to the standard setting of decoherence, where information is effectively lost through interaction with an external environment. The proposed structural sector, however, is introduced as a broader category of observer-inaccessible information that may not be reducible to ordinary environmental noise, thermal effects, or detector limitations. The main hypothesis is that quantum statistical behavior may be understood, at least partially, as the result of non-invertible access to a more complete physical structure. In this view, the observed quantum state is not necessarily the full structure itself, but a reduced description available to a particular observer or measurement context. A key contribution of this version is the introduction of a structural projection-loss concept. The paper shows how such a loss can be quantified in a simple two-qubit example using a Bell state, where the inaccessible structural sector carries correlations that are not recoverable from the observer-accessible state alone. This provides a concrete example of how structural information loss can be treated as a calculable quantity rather than only a philosophical idea. The framework also clarifies its relation to Bell’s theorem. The proposed structural sector is not interpreted as a set of local deterministic hidden variables. Instead, it is treated as an observer-inaccessible quantum sector within the full Hilbert-space description. For this reason, the framework does not attempt to evade Bell’s theorem through local hidden variables, but remains compatible with the nonlocal correlation structure already present in quantum mechanics. The paper further connects the original approximation function from the earlier dimensional projection model to an iterative recovery process. In this interpretation, successive approximation steps correspond to progressive recovery of initially inaccessible structural information. This gives the original approximation law a more operational meaning within the revised framework. The work also discusses how structural projection loss could, in principle, motivate phenomenological corrections to uncertainty relations. These corrections are not presented as established predictions, but as possible testable extensions that would require future derivation and experimental constraint. Potential experimental contexts include precision interferometry, quantum optomechanics, and systems used to test generalized uncertainty principles. This preprint does not claim to replace standard quantum mechanics. Instead, it proposes a speculative but mathematically structured interpretation of quantum statistical behavior as arising from observer-dependent access, non-invertible projection, and possible structural information loss beyond ordinary decoherence.
Márcio Bernardes Jr. Barbosa (Fri,) studied this question.