1). It's been suggested the Reyleigh-Plesset equation does not describe appropriate heat 2). That heat I suggest may come from cyclotron radiation from the spin of the cavity which has been shown to exceed the speed of light inside of the cavity. 3). I attempt to put corrective factors in including any forces from Van der Waals. \(\frac{1}{R^2} (\frac{\Delta P + (\frac{\mathbf{R}T}{(V_m - b )} - \frac{a}{V^2})}{\rho})[1 - (\frac{T_0}{T})^3]\) \(= \frac{1}{R^2} (\frac{\Delta P + P_{waals})}{\rho})[1 - (\frac{T_0}{T})^3]\) \(= \frac{\ddot{R}}{R} + \frac{3}{2}(\frac{\dot{R}}{R})^2 + \frac{4 \nu \dot{R}}{V} + \frac{2S}{\rho V} + \frac{e^2}{6 \pi mV} \frac{\dddot{R}}{R} + \frac{1}{V}(\frac{e}{m})\frac{\partial \dot{U}}{\partial R}\) Distribution of the density and simplifying some terms I get \(\frac{\Delta P + \mathbf{P}}{R^2}[1 - (\frac{T_0}{T})^3]\) \(= \frac{\ddot{R}}{R}\rho + \frac{3\rho}{2}(\frac{\dot{R}}{R})^2 + \frac{4 m\nu }{V^2}\dot{R} + \frac{2S}{V} + \frac{e^2}{6 \pi V^2} \frac{\dddot{R}}{R} + \frac{\rho}{V}(\frac{e}{m})\frac{\partial \dot{U}}{\partial R}\) \(\Delta P = P - (P_0 - P(t))\) Integrating the volume element we obtain the simplified version of our equations \(\int\ \frac{\Delta P + \mathbf{P}}{R^2}[1 - (\frac{T_0}{T})^3]\ dV\) \(= m\frac{\ddot{R}}{R} + \frac{3}{2}m(\frac{\dot{R}}{R})^2 + d\log_V(4 \rho \nu \dot{R} + 2S + \frac{e^2}{6 \pi V}\frac{\dddot{R}}{R} + \rho_q \frac{\partial \dot{U}}{\partial R})\) or \(\frac{F}{\Delta R} = \frac{E}{\Delta A} \equiv \int\ \frac{\Delta P + (\frac{\mathbf{R}T}{(V_m - b )} - \frac{a}{V^2})}{R^2}[1 - (\frac{T_0}{T})^3]\ dV\) \(= \int\ [\Delta P + (\frac{\mathbf{R}T}{(V_m - b )} - \frac{a}{V^2})]\gamma\ dR\) \(\gamma = [1 - (\frac{T_0}{T})^3]\) [*] SEE NOTES With \(\rho_q\) being a charge density and \(c=1\).The dimensions of this equation is force over length or energy over area. It has an ‘’acoustic energy’’ part given by \(m\frac{\ddot{R}}{R}\) and a wall velocity term \(\frac{3}{2}m(\frac{\dot{R}}{R})^2\). This part \(\frac{\Delta P + \mathbf{P}}{R^2}\) can be seen in terms of an ''acoustic intensity'' term. It’s also been known for the surface tension \(S\) to have a coefficient of \((1 - \frac{T}{T_C})\) where \(T_C\) is the critical temperature (known as the Guggenheim–Katayama formula). As temperature increases the surface tension decreases. [1] - an alternate simplification from a previous Langrangian of the theory we formalised, requires only the additional binding or repulsive energies from Van der Waals forces \(\mathcal{L} = mR \ddot{R} + \frac{3}{2}m\dot{R}^2 + \frac{4 \nu_L m}{R} \dot{R} + \frac{2\gamma m}{\rho_L R} + \frac{e^2}{6 \pi c^3} \dddot{R} + \frac{1}{2}eV + \frac{\Delta P(t)m + \Delta\mathbf{P}}{\rho_L}\) \(= mR \ddot{R} + \frac{3}{2}m\dot{R}^2 + \frac{4 \nu_L m}{R} \dot{R} + \frac{2\gamma m}{\rho_L R} + \frac{e^2}{6 \pi c^3} \dddot{R} + \frac{1}{2}eV + \frac{\Delta P(t)m + (\frac{\mathbf{R}T}{(V_m - b )} - \frac{a}{V^2})}{\rho_L}\) (which is the Langrangian) The repulsive nature of Van der Waals could temporally explain the expanding of the bubble but it seems more likely related to pressures and temperature. [2] - Further, there is a part of this equation \(\int\ \frac{\Delta P + \mathbf{P}}{R^2}[1 - (\frac{T_0}{T})^3]\ dV = m\frac{\ddot{R}}{R} + \frac{3}{2}m(\frac{\dot{R}}{R})^2 + 4 \rho \nu \dot{R} + 2S + \frac{e^2}{6 \pi V}\frac{\dddot{R}}{R} + \rho_q \frac{\partial \dot{U}}{\partial R}\) Namely this expression \(\frac{e^2}{6 \pi V}\) can be fashioned in a different way: \(\frac{e^2}{2 \epsilon_0} \frac{e^2}{4\epsilon \hbar_0 c}\frac{1}{ \pi R^3}\) This is not too far from the difference of such a potential which actually gives rise to the Lamb shift, a direct consequence itself of the vacuum energy, ie. Casimir effect, par the powers of the fine structure \(<\Delta V>\ = \frac{e^2}{4 \pi \epsilon_0} \frac{e^2}{4 \pi \epsilon_0 \hbar c}(\frac{\hbar}{mc})^2\frac{1}{\pi R^3} \ln \frac{4 \epsilon_0 \hbar}{e^2}\) Notice, we have encountered this kind of notation before in investigating Anandan's difference of geometries which was part of the topic of my paper to the gravitational research foundation.

''exceed the speed of sound'' that should be. Obviously nothing can exceed the speed of light lol silly mix up here but cannot edit.