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.

Reiku... I have not been on this forum for probably about 5 years. Before that you and I go back probably another 5-8 years. Through all that time you have constantly and repeatedly been making threads like this, where you spout mathematics you do not understand, either lifting them from other places (sometimes with a few random and incoherent changes made) or simply inventing them whole cloth. You don't look for actual discussion, in fact I am not sure what you look for because immediately everyone, even the non-mathematicians, see through you. I instantly recognised you, despite my long absense from this forum. The fact you have been doing this now for more than a decade, despite all the negative responses you get, despite the fact you could have actually learn some science in that time, despite the fact you are immediately exposed every time, is clear and irrefutable evidence you have a psychological problem. Perhaps you crave the momentary self-delusion that someone, anyone, will see your post and think "This guy must be really clever!!", even though few, if any, people ever get duped into saying that to you. Perhaps your real life is so horribly miserable, so horribly under achieving, that your only escape, despite always being 'caught', is to role play an intelligent human being on forums (not only this forum but pretty much any forum you can find!). Perhaps someone is holding your family hostage and to keep them alive you are required to do this nonsense day in, day out, for thousands of posts. Whatever it is you should try to resolve that issue you have. In 10 years an actual honest person, really wanting to get into scientific research but for whatever reason left school at 16, could sit their AS/A Levels (2 years), get an undergraduate degree (3 years), a postgrad degree (1-2 years) and then do a PhD (3-4 years). You could have read every textbook associated to an actual physics degree and done every exercise/problem in there. You could have done a part-time degree from the Open University while working a full time job and raising a family. You could have actually achieved something. But you haven't. You are exactly where you were 10 years ago. 10 years. You're what, in your early 30s now? So while actual intellectually honest people your age were learning, growing, developing and bettering themselves to become graduates, scientists, doctors, engineers, you played make believe on forums. I pity you.

Actually Reiku (Gareth Meredith) has not bothered us much recently, as he has found an outlet for his "knitting" here, under the name Dubbelosix: http://www.scienceforums.com/forum/7-physics-and-mathematics/ As you will be able to see, by casual inspection, that place has almost no moderation and is dominated by a handful of psychiatric cases (and commercial spammers). So he's in the right company at last. Occasionally he tries again as a sockpuppet on other fora, but the lifetimes of these excited states are fairly short, due to rapid collisional deactivation Please Register or Log in to view the hidden image! , for instance a recent one here: http://www.thescienceforum.com/pers...urvature-gravitational-waves-temperature.html