The Continuous Photon Stream: A Rigorous Conceptual Framework for Delayed Live Broadcasting in Astronomical Observations

This manuscript presents a theoretical framework reconceptualizing light propagation in astronomical observations as a continuous photon stream'' (CPS), analogous to a delayed live broadcast, rather than discrete static snapshots. We challenge the conventional view of merely observing the past'' by emphasizing the retention of temporal continuity, phase coherence, and evolutionary fidelity in observations, despite finite propagation delays. Through mathematical derivations, reproducible Python simulations based on empirical variability data from Alpha Centauri, global sensitivity analyses using Sobol indices, Bayesian inference for parameter estimation and uncertainty quantification, Monte Carlo uncertainty propagation, and explicit falsifiability criteria grounded in Popperian epistemology, we validate the framework's scientific rigor and empirical testability. Enhanced by TikZ diagrams illustrating spatiotemporal connectivity, comparative tables highlighting paradigmatic shifts, and citations from peer-reviewed journals and verified arXiv preprints with DOIs and URLs, this work integrates quantum optics, relativistic astrophysics, and information theory. A structured, falsifiable roadmap from theoretical validation to potential instrumentation development is provided, upholding standards of credibility, depth, specificity, and methodological precision.