Black Hole Mergers and Cosmological Probes in Energy Quantum Theory

This monograph presents a comprehensive analysis of black hole mergers and gravitational-wave detection through the lens of Energy Quantum Theory (EQT)—a process-oriented framework in which physical reality is constituted not by static entities, but by the dynamic evolution of an energy quantum density field $\rho(\mathbf{r}, t)$. We reinterpret the merger process as a self-catalytic gradient collapse governed by the nonlinear equation $\dot{\rho} = k \rho^2$, with cosmic expansion understood as global gradient dilution ($\nabla \rho \propto (1+z)^{-4}$) rather than metric stretching. A central insight of EQT is that **cosmological redshift shifts the observed frequency band relative to the source frame, causing detectors with fixed intrinsic response to sample different temporal segments of the same underlying physical process for events at different redshifts**. Consequently, direct comparison of raw observational quantities (e.g., $\tau_{\text{obs}}$, $f_{\text{obs}}$) across events is physically meaningless. **EQT resolves this by inverting the dynamical equation to reconstruct the source-frame evolution, thereby enabling apples-to-apples comparisons of merger dynamics across cosmic time—a unique advantage over waveform-matching approaches**. From this reconstructed common process, we derive the EQT characteristic time relation $\tau_{\text{emit}} \propto f_{\text{emit}}^{-3/2}$ and introduce the dimensionless $L/R$ ratio (computed in the source frame) as a universal discriminant: binary black holes exhibit $L/R \sim 10^1$, while binary neutron stars show $L/R \sim 10^4$ due to tidal delay from cross-frequency coupling between gravitational and electromagnetic energy quanta. We articulate EQT’s detection philosophy: observation is not passive reception but resonant participation within a detector’s intrinsic frequency window. This yields concrete design implications for LISA, Einstein Telescope, and Athena. The framework leads to testable predictions—including deviations from the $\mathcal{M}_c^{-5/3}$ scaling law, a low-frequency cutoff in gravitational-wave spectra (signaling a graviton mass), and cosmic-scale imprints of cyclic gradient freezing. Finally, we argue that the human observational window ($10^{10}–10^{20}$ Hz) is not accidental but a necessary condition for complexity and intelligence, offering a physics-grounded rationale for SETI. By unifying black hole dynamics, cosmology, and measurement theory under a single process ontology, this work positions EQT as both a predictive physical framework and a coherent metaphysical alternative to spacetime substantivalism.