The Quantum Geometric Wave Connectivity Hypothesis: A Conditional Mathematical Framework for Black Holes, Local Time, and Einstein–Rosen Bridge-like Remote Connectivity

I propose in this paper a conditional hypothesis, the Quantum Geometric Wave Connectivity Hypothesis (QGWC), which can be formalized, derived, and rendered to yield observational predictions. The principal body of the hypothesis (H1–H6) asserts that under conditions of extreme gravity, black holes, solar-scale high-energy plasmas, and quantum observation, quantum states, the rate of time flow, the observed energy, and spatial connectivity should not be regarded as fixed objects sharing a universal synchronized time. If a black hole is not a purely classical body but a vast, complex, chaotic quantum or stringy state, then perturbations of its underlying wave-form may alter local geometry, time dilation, and quantum observational outcomes. At a deeper quantum-geometric level, two regions externally far apart may become effectively connected through an Einstein–Rosen bridge-like geometric configuration. Using local proper time, observer-dependent energy (including the Unruh and Hawking effects), quantum measurement operators, the semiclassical Einstein equation, black-hole perturbation theory, and wormhole throat conditions, I construct a mathematical framework for the hypothesis, and explicitly demonstrate in the section on Causality and Information Protection that it does not violate the no-signaling theorem. I also introduce extended sub-propositions H7–H11—a "Wave-form Composition Hypothesis" M+W→F and a "Quantum Geometric Wave-form Transport"—as further attempts to formalize matter, wave-form, and identity. This extension is explicitly marked as a science-fiction physics conjecture, kept distinct from the main hypothesis. In the concluding section I provide a graded judgment regarding "hypothesis vs. conjecture": the principal body (H1–H6) is a hypothesis; H7 is an established proposition; H8–H9 are conditional hypotheses; H10–H11 are science-fiction physics conjectures. This record contains both the English version (qgwc_v2_en.pdf) and the Traditional Chinese version (qgwc_v2.pdf) of the paper, together with their XeLaTeX source files. The companion paper "Wave-form Monistic Cosmology" extends this work into an ontological framework. See Related Identifiers.