Sonoluminescence as a Macroscopic Settlement Window: A Two-Phase Accounting Interpretation of Single-Bubble Collapse

In single-bubble sonoluminescence (SBSL), an acoustically driven bubble collapses to its minimum radius, achieving approximately 12 orders of magnitude of energy focusing and emitting ultraviolet light pulses of 50–500 ps duration. Mainstream candidate models—adiabatic compression, shock focusing, Bremsstrahlung radiation, plasma recombination, and electrical microdischarge—each cover only part of the observed facts. A deeper difficulty is that the Rayleigh-Plesset equation and all its variants uniformly lose mathematical self-consistency at the collapse endpoint, where the wall velocity approaches the liquid sound speed and the volume compression reaches approximately 10⁶. This paper argues that this collective breakdown is not a technical failure of hydrodynamic description but a signature of the emergence of a settlement boundary: when the bubble collapses to its minimum radius, it constitutes a macroscopic settlement window under the CGP-Ω protocol, structurally isomorphic to the black hole event horizon as a mandatory audit point of two-phase accounting. On the settlement boundary, the description language must switch from continuum fluid mechanics to the discrete evaluation of the settlement cost function C[ρ] = D_KL + βΔE − ηN. This paper establishes a three-parameter exact structural correspondence between the bubble settlement acceleration a_settle ≡ max |R̈| and the black hole surface gravity κ, between the effective settlement temperature T_settle^eff and the Hawking temperature T_H, and between the bubble settlement area A_bubble and the horizon area A_horizon. The computed value T_settle^eff ~ 2×10⁴ K is consistent in order of magnitude with the experimentally observed effective blackbody temperature. Applying the C[ρ] grammar to the collective φ₂→φ₃ transitions of gas atoms inside the bubble directly yields, without additional assumptions, the answer to the core puzzle of why noble gases produce 3–4 orders of magnitude more light than diatomic gases—rooted in the vibrational-rotational degrees of freedom of diatomic molecules acting as non-radiative dissipation channels for settlement energy. This paper further provides three independently testable quantitative predictions: the R_min^-(3γ+1) scaling law for spectral temperature, a universal temperature curve for different noble gases after rescaling by a_settle, and the Planckization trend of the spectrum under extremely high acoustic driving.

sonoluminescence, single-bubble cavitation, settlement boundary, two-phase accounting, CGP-Ω protocol, black hole horizon correspondence, C[ρ] cost function, Unruh effect