The Friedmann Equation Related To Gibbs Equation?

[Dubbelosix]

 

A previous equation in my past work involved a power equation represented in Freidmann's cosmology

 

[math]m \dot{R}\ddot{R} - \frac{8 \pi Gm R^2}{6}\dot{\rho}  = \mathcal{P}[/math]

 

The fluid equation of cosmology is

 

[math]\dot{\rho} = \frac{\dot{R}}{R}(\rho + 3P)[/math]

 

We obtain after substitution

 

[math]m \dot{R}\ddot{R} - \frac{8 \pi Gm R^2}{6}\frac{\dot{R}}{R}(\rho + \frac{3P}{c^2}) = \mathcal{P}[/math]

 

The modified law for irreversible particle production we have

 

[math]dE = dQ - PdV + (\frac{\rho + P}{n}) dN[/math]

 

and

 

[math]\dot{E} = \dot{Q} - P\dot{V} + (\frac{\rho + P}{n}) \dot{N}[/math]

 

The modified power equation is therefore

 

[math]m \dot{R}\ddot{R} - \frac{8 \pi Gm R^2}{6}(\frac{\rho + 3P}{n})\dot{N} = \mathcal{P}[/math]

 

If we just take a look at the differential form of the modified first law of thermodynamics we have

 

[math]dE = dQ - pdV + (\frac{\rho + p}{n})dN[/math]

 

Solving for the key expression (the last expression on the RHS involving the effective densities) I get;

 

[math](\frac{\rho + p}{n})dN = dE - dQ + pdV[/math]

 

We know this is a key feature in one of our terms in our power equation:

 

[math]m \dot{R}\ddot{R} - \frac{8 \pi Gm R^2}{6}(\frac{\rho + 3P}{n})\dot{N} = \mathcal{P}[/math]

 

The mathematical theory does allow for a stranger equation consisting of many more terms:

 

[math]m \dot{R}\ddot{R} - \frac{8 \pi Gm R^2}{6}(\dot{E} - \dot{Q} + p\dot{V}) = \mathcal{P}[/math]

 

Which might be interesting to look at another time - what is interesting though is that if you introduce the heat per unit particle, the thermodynamic expression should dissolve into something related to the Gibbs equation.

 

The heat per unit particle is given as

 

[math]d\bar{q} = \frac{dQ}{N}[/math]

 

So that the first law reduces to

 

[math]d(\frac{\rho}{n}) = d\bar{q} - qd(\frac{1}{n})[/math]

 

Which is the Gibbs equation.

 

(see references). So it seems possible at first glance, that a fusion of the Gibbs physics can happen in the Friedmann cosmology, especially in the context of irreversible processes. 

 

 

 

ref. https://arxiv.org/pdf/1512.03100.pdf

Edited May 30, 2017 by Dubbelosix

[Super Polymath]

It wouldn't be one evaporating black hole igniting the "vapor radiation" (which BTW still exists between space dust, meteors, planets, stars, & galaxy clusters (the vacuum of space) as sub-Planck length matter that interacts with superluminal velocity in hypertime (doubly special relativity explaining the superluminal galactic expansion would be apart of exponentially special relativity which offers a different kind of quantum mechanics) within ultra-low temp subspace). You see it never gets to absolute zero because there's no actual empty space (other gravity would breakdown because there'd be a missing link in the chain)

 

You see in a dimensionless, flat spacetime with infinite circumference - material aggregates into similar structures an infinite number of times. So even the quantum world has a quantum world. So this subspace containing ultra-low temp vapor radiation has matter in it (tired light, "scattering of the photon into smaller, subliminal with superluminal interactions as an alternate interpretation of quantum mechanics to nonlocality), matter that fills the vacuum of space, which produces the force of gravity as an animate fluid with velocity = c in a dominoe effect.

 

So when our universe expands enough, the last objects will be large ancient black holes removed from long dead stars & galaxies, no longer having matter to consume they will eventually give off enough hawking radiation to destabilize in high powerful explosive white holes that ignite the surrounding vapor radiation into something like the cosmic microwave background (the electromagnetic clouds of the early universe) & the process begins again.

 

Given infinite matter, this process naturally makes galactic superclusters form into rings of mid-stage universes surrounding a nucleus of electromagnetic clouds of beginning-stage universes, with a larger expanse of distant hypermassive black holes representing end-stage universes (& the end-stage universes would become the new beginning-stage universes & the mid-stage universes would become the next end-stage universes.

 

This structure looks exactly like every atom we've ever identified, with the galactic supercluster rings representing the proton & electrons orbiting the atomic nucleus, represented by the electromagnetic clouds of the early universe.

 

This theory accounts for blackbody radiation, the virtual particle, dark matter, dark energy, expansion, the observer effect, & unlike string theory it requires no inconceivable dimensionality.

 

Finally, it is a testable theory, as I explain here.

 

P.S., maybe we could help each other, I suck at math, if you could refer me to some free online math material that's worth a masters in pure mathematics, or enough to cover some of these theories, I'd appreciate it.

Edited June 7, 2017 by Super Polymath

[Super Polymath]

There is definitely not one black hole in the all-matter phase, it consists of a static gas of Planck particles, using ''Plank particles'' as a generic term for the primordial fluctuations. You are right, there is no empty space and yes, the micro-universe is an ultracool space, but it seems a universe theoretically approaches the same condition, except with a scale dependence increase.

 

Err, you read my response prematurely, I have edited it & I have a question as well.

 

If you wouldn't mind, could you reread that post & reply to any new developments? Thanks.

[Super Polymath]

Not sure about ''your'' theory, but mine certainly accounts for the CMB. Only low frequency radiation left from the evaporation of the seeds which did fully collapse left behind the radiation we see in space as matter today. In my model, the CMB radiation was spread smoothly with a centrifugal force which replaces dark energy in a pseudo-de Sitter space.

Well "our" theory (because I wholly believe its the truth so 2 individuals would meet middle ground in truth in the path to discovery), does explain the observer effect in a much less "metaphysical" way than does nonlocality of conventional QM:

 

The Double Slit Experiment shows that when reflecting photons off the tracks of other photon beams the wave function of the original beam collapses after it goes through the double slit. Meaning that photons split and go way under the Planck length, and therefore way faster than light, and the Law of Exponentially Special Relativity comes into effect and the superluminal sub-Planckian particles that compose the photons you're sending to the tracks with other photons interact with them and the sub-Planck-scale gravity is so close that it effectively works faster than light to drag the original photon beam and prevent it from flying apart into a "wave".

 

 

 

Edited June 7, 2017 by Super Polymath

[Super Polymath]

I am sorry Polymath, ,maybe you have an understanding into something I do not. I try and keep things simple within the boundaries,of not only physics, but myself :) I hope you appreciate that. 

 

When we start talking about 

 

''material aggregates into similar structures an infinite number of times.''

 

 

I have problems from the on-set you see. I don't believe any structure has any formality to any infinity in nature. 

To quote The Joker when speaking to Batman, "You complete me."

 

I struggle to remain coherent, you struggle to cover every angle. Together, your ideas ground my ideas.

[Super Polymath]

As you can see from this link:

 

http://www.worldscientific.com/doi/abs/10.1142/S0217751X99002013

 

The CMB could come from a tachyonic bath. This is possible if the Planck particles moved through space as though there was no resistance.

 

Yes, & evaporating ancient black holes from the end-stage of our universe would be powerful enough to merge that tachyonic bath into the electromagnetic clouds of the early universe.

 

 

 

 

In short, these regions of the unobserved universe are orbiting these regions pulled by a vaster region of emptiness save for ancient hypermassive black holes, evaporating to form new atoms as the electromagnetic clouds of the nucleus expand to become the galaxy clusters of the electron rings. This forms one of infinite colossal hyper-omega atomic structures.

 

I mean, could you imagine how large [url=https://www.youtube.com/watch?v=dNvdrpEmS48]this steel cog is?

[Super Polymath]

You do need help with some physics. Your idea's are a bit wilder than what I consider with normally. You need some discipline with your theory so that it portrays the physics correctly.

 

Yes but there's a way to test if that's true though, the idea is that the electron rings around the nucleus become the space between the nucleus & the electron, there's really no other form this matter can take. Like I said, the evolution of the quantum universe happens in hypertime. Using M=E/C^2 you can literally find the rate at which atoms oscillate. Since the gravity waves of an evaporating black hole are intense enough, an artificial black hole (small enough to evaporate quickly) could serve as a the ultimate Planck-scale magnifying glass by revealing tachyons & the theoretical oscillation of atoms according to M=E/C^2. Edited June 7, 2017 by Super Polymath

[Super Polymath]

By the way, Planck physics is not implied in my model specifically, it could be part of it.

 

 

For the gravitational dominated universe to dwarf electromagnetism to create the necessary gravito-nucleo-binding energy happens at the femtometer range, much larger than the Planck vacuum.

You could win the Nobel Prize for this. If you do, you owe me.:p

[Super Polymath]

Yes but there's a way to test if that's true though, the idea is that the electron rings around the nucleus become the space between the nucleus & the electron, there's really no other form this matter can take. Like I said, the evolution of the quantum universe happens in hypertime. Using M=E/C^2 you can literally find the rate at which atoms oscillate. Since the gravity waves of an evaporating black hole are intense enough, an artificial black hole (small enough to evaporate quickly) could serve as a the ultimate Planck-scale magnifying glass by revealing tachyons & the theoretical oscillation of atoms according to M=E/C^2.

Negative energy waves from evaporating artificial black holes, that is how we explain inflation here, that is the way we see atomic oscillation, the tachyon bath that represents the vacuum energy which, when heated above "absolute zero"; becomes a particle. A negative energy wave from an evaporating black hole would reveal virtual particles.

 

"At some point the universe will have expanded until the CMB is below the Hawking temperature and the black hole can then evaporate away, if free from further mass consumption.

 

The Hawking radiation will contribute a negative energy to the black hole and decreases the black hole mass, though at no point does the black hole take on a negative mass. The black hole evaporates and then it is thought that the black hole ends its life in a burst of gamma radiation. The details of its final throes are unknown until a quantum gravity theory is developed."

 

Set up a laser interferometer to detect the increase in our spatial distance from the sun by the width of a hydrogen atom following the observation of an evaporating black hole. Issue is, the universe is still too hot for natural black holes to evaporate, because natural black holes are too large & live too long. The ones that evaporated, creating the Planck epoch, did so too long ago for observation, that light has left our causal horizons. However, artificial black holes on the other hand wouldn't take too long to evaporate; such as the Kugelblitz Engines:

 

Edited June 9, 2017 by Super Polymath

[Super Polymath]

You do need help with some physics. Your idea's are a bit wilder than what I consider with normally. You need some discipline with your theory so that it portrays the physics correctly. 

 

Your formula uses the Cherenkov radiation though.

You have to cover that & consider its composition when mathematically defining slightly different cosmoses than ours. We need to do that, as this theory will yield micro-cosmoses with slightly altered constants every-time you change the type of atom in question. We need to find out what type of atom we reside in if we ever want to break the speed of light in our operations - because that type of atom will literally be the ideal anthropic universe for the evolution of intelligent life. Like I said, technology in the sense that we understand it can't go beneath femtotech without utilizing micro-cosmomorphs, that spread throughout the atomic world (obtaining a limited control of the gravity that controls our atomic world [via the construction Kugelblitz Engines & the nature of self-replicating femtotech]) in the blink of an eye because their fastest space crafts are .20C, but relative to us they're moving at 20% of the speed of light to the power of the speed of light - they become technological tools, far more miniaturized than anything we can build because our miniaturization technologies are limited by the superluminal time dilation occurring beneath the Planck length the smallest components we can play with, are particles.

 

Apply your refined constant to a new branch of math known as fractal cosmology, & we have all of the necessary tools to proceed.

Edited June 9, 2017 by Super Polymath

[Super Polymath]

These bad little mofos leave Warp 9 in the dust

 

When you turn the dial of time up enough 

Edited June 9, 2017 by Super Polymath