Dom't know when I will write the next part out, I have been able to discover something from sonolumiscent equations which could answer the thermal properties. This also ties back to an earlier investigation when I recognized it for the first time.

# Why Acceleration Of A Universe Might Happen

### #52

Posted 14 April 2019 - 11:45 AM

### #53

Posted 14 April 2019 - 03:21 PM

Part 3

We need to cover some Friedmann Langrangian I constructed and then from there, investigate sonoluminscence.

Let’s jump straight into it. From the last post the two equations which interested me was:

[math]m\dot{R}^2 - \frac{8 \pi GmR^2}{3}\rho + \frac{\Lambda mc^2}{3}R^2 = \mathcal{L}[/math]

[math]m\dot{R}^2 = \frac{e^2}{6 \pi c^3} \dddot{R} + \frac{1}{2}eV[/math]

With the last equation I stated:

‘’The last term refers to rotating systems and so will produce Larmor radiation. **Since the viscosity actually refers to the motion of the fluid around the bubble then any charged particles compressed to the region [will] exhibit the behaviour of this equation above!** ‘’

The reason why this was stated because it is believed by a number of scientists that Larmor radiation from accelerated charged particles may be a contributor to the phenomenon. Based only on the fact that magnetic fields have been detected around the ‘’star in a jar’’ - I think this is possible since a rotary feature gives rise to a closed current in which charged particles could be bound in a high momentum, giving off Larmor radiation. Certainly the amount of energy from the source, (if it cannot be described alone by nuclear fusion) could have other additional contributors. Another equation which interested me was the proposed Langragian of the theory:

[math]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{\Delta P(t)m}{\rho_L} = \mathcal{L}[/math]

We’ve established from my point of view that if Larmor radiation is involved here then this equation

[math]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{\Delta P(t)m}{\rho_L} = \mathcal{L}[/math]

Will also then require to add new terms to account for rotational radiation from accelerated motion of charges. According to wiki:

‘’This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse. Both simulation and experimental measurement show that during the critical final stages of collapse, the bubble wall velocity exceeds the speed of sound of the gas inside the bubble.’’

Then already we have an immediate connection between the viscocity of the surrounding fluid and possible increasing temperatures from the accelerated charges contained inside the bubble, under tremendous pressure and possibly strong density (compared to elements on the periodic table). Regardless, it should be obvious this is important because the Reyleigh-Plesset equation is only approximate towards its final stages, in which the bubble undergoes it’s imploding feature -

**But what does any of this have to do with the big bang...?**

The Reyleigh-Plesset Equation and the Friedmann equation share some common features yet I also explained, this was due to the fact they both describe similar physics founding the fluid expansion and collapse modes of the Friedmann equation for a spherical homogeneous distribution of matter.

Let’s draw in on those relationships first, then we will be able to proceed further with my ideas.

The Rayleigh-Plesset equation is

[math]R \ddot{R} + \frac{3}{2}\dot{R}^2 + \frac{4 \nu_L}{R} \dot{R} + \frac{2\gamma}{\rho_L R} + \frac{\Delta P(t)}{\rho_L} = 0[/math]

In which the following variables are defined as:

ρ - is the density of the surrounding liquid, assumed to be constant

R(t) - is the radius of the bubble which when taken as a ratio with itself is by definition related to the scale factor which also features implicit time dependence.

ν - is the kinematic viscosity of the surrounding liquid, assumed to be constant

γ - is the surface tension of the bubble-liquid interface

Now, from the two links to previous blog posts, given in the previous post, we know the relationships of these derivatives from my investigation. Immediately, I see consequence for the local dynamical gravitational theory of Newton since the analogue of this is called the Raychauduri equation and this specific equation contained similar terms found on the LHS of the Rayleigh-Plesset equation:

[math]R \ddot{R} + \frac{3}{2}\dot{R}^2 \ne 0[/math]

since the Raychauduri equation implements

[math]\dot{H} + H^2 = \frac{\ddot{R}}{R}[/math]

I have noticed, from my own work, that the fluid expansion plays a role of coefficient on all the terms in the non-conserved definition of the equations. Nevertheless, the definition above too also implements a fluid expansion of its own. Of course, expanding universes and expanding ‘’bubbles’’ require the same base mathematics. Let’s take a look at one formulation of the equations I have written in the past. If we take one of the time derivatives (preferrably the second term) as a curvature term then we can modify the dynamics of the Reyleigh-Plesset equation in some unique ways. We can also add density and pressure terms, which, if you take relativity seriously enough like I do, then it should be in there. First let us look at a few equations I derived, and then after let’s assume an object can be created from it. The equations which feature similar terms are:

[math]\dot{R}^2 = \frac{8 \pi GR^2}{3}\rho + \frac{\Lambda c^2}{3}R^2[/math]

[math]m\dot{R}^2 - \frac{8 \pi GmR^2}{3}\rho + \frac{\Lambda mc^2}{3}R^2 = \mathcal{L}[/math]

[math]m\dot{R}^2 = \frac{e^2}{6 \pi c^3} \dddot{R} + \frac{1}{2}eV[/math]

The last term refers to rotating systems and so will produce Larmor radiation. **Since the viscosity actually refers to the motion of the fluid around the bubble then any charged particles compressed to the region [will] exhibit the behaviour of this equation above!** Comparing these results with the Reyleigh-Plesset equation

[math]R \ddot{R} + \frac{3}{2}\dot{R}^2 = \frac{1}{\rho}(p_g - P_0 - P(t) - 4 \mu \frac{\dot{R}}{R} - \frac{2 \gamma}{R})[/math]

(since surface tension is \gamma then we may derive from the last equation a direct equivalent with viscosity [math]\mu \dot{R} = \gamma[/math])

(which is another form to write it with terms appearing on the right hand side of the equation) and courtesy of wiki, I extract a quick set of definitions for the terms:

‘’This is an approximate equation that is derived from the Navier–Stokes equations (written in spherical coordinate system) and describes the motion of the radius of the bubble *R* as a function of time *t*. Here, *μ* is the viscosity, *p* the pressure, and *γ* the surface tension. ‘’

It becomes a lot clearer why the dynamics are similar, at least, in respect of like terms. We may use the previous equation later, but I want to concentrate just for now on this form of the equation

[math]R \ddot{R} + \frac{3}{2}\dot{R}^2 + \frac{4 \nu_L}{R} \dot{R} + \frac{2\gamma}{\rho_L R} + \frac{\Delta P(t)}{\rho_L} = 0[/math]

Simply because (it formats) the terms very clearly with relationships to each other and also, it is this form of equation (when setting it to zero) can you formulate a Langrangian. Let’s have a look at that (what I will call this time) the Reyleigh-Plesset Langrangian:

All we do is assume distribution of a mass term

[math]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{\Delta P(t)m}{\rho_L} = \mathcal{L}[/math]

There are some obvious crucial dynamical differences between this equation and the Friedmann equation only within heuristic framework. In fact, drawing on sonoluminiscence, we may think a compression of the material exerted by the forces imploding the material inside the bubble to be nothing more than a cold fusion which releases a large amount of energy. There was detection of excess neutrons from no external source supporting this notion that some kind of fusion is occuring. There is also tantalizing situations and arguments for the case of it being vacuum related, since the amount of energy released can perhaps provide more energy than what can be taken from thermonuclear reactions has been postulated by a number of authors. The kinematic viscosity of the surrounding liquid is often assumed constant but **it is very likely** phase transitions do occur when the bubble expands and inexorably implodes. That kind of ‘’squeezing into a source’’ to produce a nuclear reaction would contain relavant terms to a thermodynamic interpretation of the equation of state which features in previous blog: On Cosmic Seeds and Gravity and that equation takes the form:

[math]T k_B \dot{S} = \frac{\dot{\rho}}{n} + \frac{\rho + P}{n}\frac{\dot{T}}{T}[/math]

This unique equation allowed me to hypothesize for strong reasons a direct relationship between the early ground state fluctuations as gravitational seeds with a variation on the temperaure as

[math]2m\dot{R}\ddot{R} + 2\hbar c R \int k \dot{k} = \frac{8 \pi GmR^2}{3}(\rho + \frac{3P}{c^2})\frac{\dot{T}}{T}[/math]

or

[math]\frac{\dot{R}}{R}\frac{\ddot{R}}{R} + \frac{\hbar c}{mR} \int k \dot{k} = \frac{8 \pi G}{6}(\rho + \frac{3P}{c^2})\frac{\dot{T}}{T}[/math]

The reason why the last equation could do this was because it was specifically formulated to satisfy the Sakharov zero point fluctuation term, which is why, if the phenomenon really does have a relationship with sonoluminscence, just as Schwinger believed, then the same physics must also be implemented. So not only do we need to associate the pressure and density and resulting in a large temperature measured by [math]\frac{\dot{T}}{T}[/math] (which I call the thermal fluid expansion coefficient) but we also need to take into consideration presumably the fluctuations of the form [math]\hbar c \int k \dot{k}[/math] if sonoluminscence has an origin rooted in the vacuum energy. In the next part (part 4), we’ll see if there is anything wrong with any possible reinterpretations of the physics so that maybe a Friedmann-like physics may have any help in progression with the Reyleigh-Plesset equation.

**Edited by Dubbelosix, 14 April 2019 - 08:25 PM.**

### #54

Posted 14 April 2019 - 05:46 PM

Part 5 ''let's cut down some more things,'' I suspect this will take about 7 posts, but I hope it is instructive rather than boring.

**Let’s Uncover the Mysteries of the Universe**

*… to persuade in any way, the fellow posters of the science forum, it will assure you that it relies on one hypothesis and from there you can judge whether it holds credible theory.*

** Postulation:** That the Friedmann equation for an expanding bubble is one side of another jigsaw puzzle which sheds light on the thermal applications and many others.

Lets play a game, let’s take phrases from the sonoluminescent equations I wrote in my blog and the part of the game involves translating that into an application for cosmology.

**First phrase:**

‘’This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse.’’

*COURTESY OF WIKI *

*…. now converting this into cosmology*

‘’This equation, though approximate, has been shown to give good estimates on the motion of the universe under the acoustically-driven, quantum-field **except** during the final stages of collapse.’’

You might think this is word salad, but rest assured, acoustic implications in Landau energy levels (giving rise to the Zeeman effect including quantum hall edge effects).

*https://www.nature.c...1567-019-0446-3*

Let’s continue the game….

‘’Additional energies due to the wall viscosity coupling to internal charge dynamics does give a new additional feature to the slightly modified Rayleigh-Plesset equation which took into account thermal variations - which now, we give in the form with additional assumptions made about the wall kinematic viscosity with the motion of charges inside of the bubble.’’

*…. Now convert to cosmology again ~*

‘’Additional energies due to the horizon viscosity coupling to internal charge dynamics does give a new additional feature to the slightly modified Friedmann equation which took into account thermal variations - which now, we give in the form with additional assumptions made about the horizon kinematic viscosity with the motion of charges inside of the universe.’’

*Giving rise to Larmor/Cyclotron radiation is the main reason why we may expect a large contribution in early rotating model of the cosmos would give rise to a large percent of residual radiation. Stars also contribute to the background radiation field. If the universe was small enough, it gave inflation enough time to spread radiation to all the visible horizon…. But the horizon problem exists and there are supercold regions billions of light years across that cannot be explained in conventional means. These are all subjects I have considered and in some ways, came to some decent answers I will cover another time.*

The possibility of ‘’acoustic effects’’ driving a quantum field must be taken seriously in light of how similar the sonoluminescence expansion matches many parameters to a Friedmann equation that so far seems connected deeply with the math each demonstrate… but as I said, we learn very interesting things from the bubble model.

**Let’s See What All The Fuss Is All About!!**

Following work in the link:

Chapter 2 - Cavitation and Bubble Dynamics - Christopher E. Brennen

We find a fuller derivation for the Rayleigh-Plesset equation than what has been previously been shown in the blogs.

The Rayleigh-Plesset equation that allowed a temperature variation of the system with other dynamics we haven’t properly covered yet is:

[math]\frac{p - p_{\infty}}{\rho}(1 - (\frac{T_0}{T})^3) = R \ddot{R} + \frac{3}{2}\dot{R}^2 + \frac{4 \nu \dot{R}}{R} + \frac{2S}{\rho R}[/math]

With this time [math]S[/math] playing the role of the surface tension (a clue that the equation is a surface tension equation). Additional energies due to the wall viscosity coupling to internal charge dynamics does give a new additional feature to the slightly modified Rayleigh-Plesset equation which took into account thermal variations - which now, we give in the form with additional assumptions made about the wall kinematic viscosity with the motion of charges inside of the bubble:

[math]\frac{p - p_{\infty}}{\rho}(1 - (\frac{T_0}{T})^3) = R \ddot{R} + \frac{3}{2}\dot{R}^2 + \frac{4 \nu \dot{R}}{R} + \frac{2S}{\rho R} + \frac{e^2}{6 \pi mc^3R} \frac{\dddot{R}}{R} + \frac{1}{2R^2}(\frac{e}{m})\dot{V} [/math]

[math]= R \ddot{R} + \frac{3}{2}\dot{R}^2 + \frac{4 \nu \dot{R}}{R} + \frac{2S}{\rho R}+ \frac{e^2}{6 \pi mc^3R} \frac{\dddot{R}}{R} + \frac{1}{2R} \frac{\partial \dot{V}( R)}{\partial R}(\frac{e}{m})[/math]

(features famous charge to mass ratio)

We know some things about the functions of this equation, as [math]R[/math] the bubble radius decreases in sonoluminscence the wall viscosity increases with a singularity at [math]R = 0[/math] (so take this as a non-physical situation). There are no pointlike dynamics involved here.

Equally, as bubble radius decreases in sonoluminscence, the temperature of the reaction near the center of the bubble increases.

*Small excerpt: Notice that if ‘’ Equally, as bubble radius decreases in sonoluminscence, the temperature of the reaction near the center of the bubble increases,’’ is so uncanny since the same physics applied to the early big bang phase.*

When the temperatures are reaching tens of thousands of degree's during collapse it said the [standard] Rayleigh-Plesset equation becomes incompatible. This will give rise to the magnetic fields detected around them.

*Second excerpt: If indeed the high energy state makes the Rayleigh-Plesset equation incompatible and in consequence gives off significantly detectable magnetic fields, then it it not unreasonable that the early universe too had a magnetic field. With magnetic phyiscs, comes possibilities of Lorentz violation in CPT symmetry. It would in effect, explain the excess of matter over antimatter… but with one exception, our universe would require a preferred frame of reference – but it’s a challenge I would like to take on against the late and great Einstein. But unfair though, physics has went a long way since his tragic death.*

Further, we suspect some kind of cohesive (''attractive'') force pulling dynamics towards the center of the bubble where a fusion may be happening (since detection of neutrons without any external source has been published). Wiki draws up a nice summary of some of the aspects we know about the phenomenon

- The light flashes from the bubbles last between 35 and a few hundred picoseconds long, with peak intensities of the order of 1–10 mW.
- The bubbles are very small when they emit the light—about 1 micrometre in diameter—depending on the ambient fluid (e.g., water) and the gas content of the bubble (e.g., atmospheric air).
- Single-bubble sonoluminescence pulses can have very stable periods and positions. In fact, the frequency of light flashes can be more stable than the rated frequency stability of the oscillator making the sound waves driving them. However, the stability analyses of the bubble show that the bubble itself undergoes significant geometric instabilities, due to, for example, the Bjerknes forces and Rayleigh–Taylor instabilities.
- The addition of a small amount of noble gas (such as helium, argon, or xenon) to the gas in the bubble increases the intensity of the emitted light.

Only if any cyclotron radiation arises from the energy source can this equation presented to have any formal basis in reality, but drawing on relationships to how a universe-boundary has with it galaxies that couple to its motion is akin to believing the charges inside of the bubble couple to kinematic viscosity located on the boundary. Or the main equation can be seen in terms of a Friedmann equation like form which allows a unique representation of it:

[math]= \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}[/math]

Where we use [math]U[/math] as the potential difference and [math]c=1[/math].

Some facts of our investigation:

- as the bubble radius decreases, we speculate the temperature increases due to an increasing pressure on the kinematic motion inside of the bubble.

- as the radius decreases, the boundary kinematic motion of the surrounding fluid increases. This is conjuction with an increasing temperature also keep in mind and perhaps an increasing density towards the center of the bubble were fusion processes may be happening (due to sources of neutrons without any external source).

- as the bubble radius decreases as a function of time the energy increases as a function proportional to [math]\ddot{R} \propto \dddot{R}[/math] and satisfies a path that is an exponentially decreasing logarithmic spiral (also a function of time).

- we speculate, as the horizon viscosity increases causing a coupling of internal charge dynamics giving rise to that radiation

- we also have a fluid expansion coefficient [math]\frac{\dot{R}}{R}[/math] on the viscosity which we can identify from our Friedmann studies and speculate importance with bubble expansion. We'll look more into those kinds of relationships in a later date.

Before I write out part 6, I'll give you a hint at what may help you find the solution yourself, it relies on the Rayleigh-Plesset equation of the form

[math]\frac{P_0 - P_{\infty}}{\rho}(1 - (\frac{T_0}{T})^3) [/math]

Located on the left hand side. Take notice in particle, the presence of the temperature and the pressure terms, do they look familiar?

**Edited by Dubbelosix, 14 April 2019 - 06:30 PM.**