This work examines a foundational epistemic problem underlying much of modern physics: the fact that nearly all empirical access to physical systems is mediated by electromagnetic radiation. From atomic spectroscopy to scanning probe microscopy and observational cosmology, what experiments directly register are structured electromagnetic signals detected by macroscopic instruments. The paper argues that this radiation-based observational regime defines an ill-posed inverse problem. Many distinct physical configurations can give rise to identical detected electromagnetic patterns. As a result, the ontological narratives commonly built from such data — involving particles, fields, spacetime geometry, and cosmic expansion — are systematically underdetermined by the measurements themselves. Through a unified analysis of atomic spectroscopy, scanning tunneling microscopy, and cosmological redshift, the paper shows that what experiments constrain are not internal structures, but interaction channels between hidden physical systems and the electromagnetic field. Stable radiation patterns reflect stable coupling interfaces, not necessarily unique underlying entities. The analysis is situated within the framework of Coherent Observational Epistemology (COE), which treats observation as the formation of coherence between independent localities via finite information channels. Within this framework, the persistence and reproducibility of physical models are explained by the stability of these coupling channels rather than by direct access to the internal constitution of matter or spacetime. The paper does not dispute the empirical success of modern physics. Instead, it clarifies the epistemic limits of radiation-based observation and argues for a structural, constraint-based interpretation that separates what is measured from what is inferred.