Dubbelosix

You do know that spin 2 gauge theory came from the quantization of the graviton? We haven't actually measured any spin, or as far as I am aware. 

I am not happy with gauge theory, especially within the context of gravity. I have some serious problems accepting it - like for instance, from first principles, gravity isn't even a force. I have been a vocal opponent against quantum gravity in the context of some quantization of a field - I see no evidence and have no reason to think gravitons actually have to exist. 

As for the spin thing, what was found was the following:

[math]\frac{N}{V} = \int^{\infty}_{0} n_{BE}(E) g(E)\ dE[/math]

[math]g(E)[/math] is the density of states per unit volume. For non-interacting particles, which have a kinetic energy you can have

[math]g(E)\ dE = (2S + 1) (\frac{2m}{\hbar^2})^{\frac{3}{2}} \sqrt{E}\ dE[/math]

And of course, this relates to the investigation form the term [math]\frac{V}{N \lambda^3}[/math]. This is the same. So if for instance, 

[math]\frac{V}{N \lambda^3} \leq 1[/math]

then

[math]\frac{V}{N} \leq \lambda^3[/math]

http://web.pa.msu.edu/people/duxbury/courses/supercon/Kishore-Kapale-BEC-talk.pdf

15 hours ago, Dubbelosix said:

Equation 3. appears to have a typo, an extra Gamma term on the LHS, no worry, it is really the following:

 

 

ddt(NV)=N˙V+NV˙=(N˙+3R˙RN)V=NVΓ

 

I want to use this object to create another object which can describe the physics of the condensate in a more appropriate way. To start off, we simply divide by N2

ddt(NVN2λ3)=N˙VN2λ3+NV˙N2λ3=(VNλ3)Γ

In which we can measure the statistics from the interparticle distance where

 

VNλ3≤1

 

Then the interparticle distance is smaller than its thermal wavelength, in which case, the system is then said to follow Bose statistics or Fermi statistics. On the other hand, when it is much larger ie.

 

VNλ3>>1

 

Then it will obey the Maxwell Boltzmann statistics. The latter here is classical but the former, the Bose and Fermi statistics describes a situation where classical physics are smeared out by the quantum. This is one such approach to describing a condensate from the model. Remember, we want a pre big bang universe which was very cold, - Bose condensates are a million times colder than open space. The pre big bang model, may be just as cold or colder.

 

In the same way, the interparticle distance is found from an effective density through some very simple and short manipulations. Without reversible and irreversible notation, the effective density is

[math]= (\frac{dQ}{dt}) + (\rho + P)V \Gamma[/math]

Divide off [math]N\lambda^3[/math]

[math]= \frac{d\mathbf{q}}{dt}(\frac{1}{N}) + (\rho + P)\frac{V}{N \lambda^3} \Gamma[/math]

This is a formulation that can be easily understood as having meaning and context within a Freidmann equation, in which the interparticle distance is (still) satisfied by the physics of Bose or Fermi condensates contained in the term [math]\frac{V}{N \lambda^3}[/math]. The [math]\lambda^3[/math] has also been absorbed by [math]Q[/math] making [math]\mathbf{q}[/math]. At least, this is how I would have imagined it would enter the theory.

I've found a way to describe the spin within the theory like you wanted me to look into as well, so will write that up later.

I feel you are a bit a head of me. You should know, I don't actually consider myself a mathematician. Being a drop out, I have been mostly self-taught over the years.

But I do feel you are a bit ahead of me at this time and you'll need to give me time to read up on these two things.I do appreciate the help though.

I will certainly take a look.

Yes, there seems to be correlation.

The total wave function minimizes the expectation

[math]\int dV |\psi|^2 = N[/math]

It does link the physics. Extract from wiki

'' If the average spacing between the particles in a gas is greater than the scattering length (that is, in the so-called dilute limit), then one can approximate the true interaction potential that features in this equation by a pseudopotential. The non-linearity of the Gross–Pitaevskii equation has its origin in the interaction between the particles. This is made evident by setting the coupling constant of interaction in the Gross–Pitaevskii equation to zero (see the following section): thereby, the single-particle Schrödinger equation describing a particle inside a trapping potential is recovered.''

Will require more reading. 

This looks like a nice paper as well 

https://arxiv.org/pdf/1301.2073.pdf

I will take a look. Thanks. 

A recent article - suggests the same line of investigation I wanted to look at - that is, spscetime can be described fundamentally as threaded together using quantum entanglement. I felt the entangelment of space with space is important in context of an understanding of quantum gravity.

 https://www.scientificamerican.com/article/tangled-up-in-spacetime/

I'd be careful though to assume the ground state implies zero energy as the article suggested - I strongly disagree with this interpretation. The ground state of a field is not zero, it is given by [math]\frac{1}{2}\hbar \omega[/math] - people perhaps, naively assumed that you can count this up in space as an amount of something. This isn't the case, the fluctuations are on a scale that is not observable and the effects of virtual particles seem to be negligible on the macroscopic scale - even photons do not seem to couple to the vacuum ground state of fluctuations. It's not that they do not contain energy, but rather they contain a lot of it when these fluctuations exist for very short time periods. Equally, they have not really travelled much space either to respond to its environment or the medium it is in. 

Whatever ''ground state'' really means, it certainly does not mean zero energy in physics.

The paper on condensates is proving very interesting. It seems related to the thermodynamic interoretation of a wavelength (thermal wavelength). Those wavelengths measure whether a system follows Fermion or Bose statistics. 

The section on thermodynamic properties vanishing at the ground state, is also very interesting - it would tie in with the idea that effects of fluctuations are negligable on the cosmological scale. May answer for a cold, radiationless pre-state of a universe as well. Finding an exact model has been difficult, but it seems like you have offered one.

I will read them, thank you.

yes

Also Einstein has remarked his general theory is unthinkable without an aether. Dirac noted, that quantum field theory was a particular type of aether theory.

If rotation really should enter the picture, this would produce a torsion field which enters the equation with a negative sign. Rotation would not be unusual if we considered gravity as part of the full Poincare group of spatial symmetries which involves the spin and torsion (Venzo de Sabbata) also see Sivaram. For instance, Torsion enters the Poisson equation

[math]\nabla^2 \phi = 4 \pi G(\rho - \mathbf{k}\sigma^2)[/math]

Where [math]\mathbf{k}[/math] is [math]\frac{G}{c^4}[/math] and [math]\sigma[/math] is the spin density which can be calculated the following way:

[math]\sigma = \frac{J}{V} = \frac{m \omega R^2}{L^3} = \frac{m vR}{L^3}[/math]

so

[math]\mathbf{k}\sigma^2 = \frac{Gm^2v^2R^2}{c^4L^6} = \frac{Gm^2}{c^2L^4}[/math]

With torsion there are contributions to the curvature, a curvature term just looks like

[math]kc^2 = - \frac{2U}{mx^2}[/math]

The torsion term alters the effective density in the following way, using an equation of motion I derived which takes into account the absolute acceleration of a spinning universe

[math](\frac{\ddot{R}}{R})^2 = \frac{8 \pi G}{3}(\rho - k\sigma^2) + a_{eul} + a_{cor} + a_{cent}[/math]

Below is a reference to that derivation.

Yes, I am familiar with the Raychauduri equation, inverstigated it a while back. 

I'm not happy with it either. 

And yes, without inflation it would posit problems. This is my opinion anyway - that is not to say, we cannot find alternative models, but they need to be good. 

I am not happy with it, for much the same reasons as Steinhardt. I have never been a fan of the multiverse. 

There seems to be a ''consensus'' that in honest-speaking terms, we only know the size of a universe up to its observable horizon. I have heard a few astrophysicists claim the universe may be many times more bigger than what we can observe.... but took the statement with a pinch of salt, until I heard Susskind say pretty much the same thing, that cosmologists are thinking the universe is many many times the size it is, outside the observable horizon.

Which is interesting, because this really places age problems on a universe, (without inflation) which was designed to make a universe... inconceivably large in just a very small time frame. Hows the horizon problem doing? Do scientists think inflation answers this as well?

Just took a read myself, yeah, they use inflation to answer this as well. Though, wiki really goes over the top on the homogeneity thing, that is a separate thing, though related. The horizon problem is that when you add up the time it takes for space to expand, the universe is still too large when you reconcile it's diameter. So inflation again answers it when you consider it became exponentially large in such a small time frame.

It will certainly help. its the only tedious side to all this I think. 

Maybe they do. I just read on what you where talking about, and it seems reasonable. 

I agree, that more global modelling is required.

I have worked out the primordial spin - to match the spin today, we need an exponential decay model. I know how to construct the model, just done no numerical calculations. I have done some interesting calculations on an extra background contributor - if the particles are charged, and if early enough, the particles inside a universe behaves like it has a cyclotron radiation. That was an interesting theory from this as well.

Interestingly there is evidence our universe once rotated strongly. Mapping of the galaxies have shown about a 1 in a million chance that their spins are by accident. One solution is that the spin of galaxies coupled to the universe when it spun much faster than it did today. 

http://physicsworld.com/cws/article/news/2011/jul/25/was-the-universe-born-spinning

I was very skeptical of a recent investigation which stated there was no preferred direction in the universe and that the universe is perfectly homogeneous. 

It couldn't be further from the truth. A good example is that massive holes, spanning billions of light years exist in the model which cannot be account by inflation models. 

Thank you for the compliment. And I will consider help if I need it. Of course, other people can fiddle with my equations and start their own investigations.

Slow enough I think, that detection of the rotation happens to be so small, scientists have disagreed upon its existence. It [seems] to be consensus that dark flow is real so far. Dust inside the universe couples to the rotation weakly - the universe is highly dynamic inside and the slow rotation doesn't seem to be affecting it (any more) and (if it even does).

Sachwolfe effect? I guess that is some radiation background axis thing, properly the same thing. Too slow for light to couple to it.

Yes I have looked into thermal statistics for the model as well. As well as creation and annihilation operators as well. I will take a read of the links before saying anything else. 

Those papers are interesting, and the last one is helpful for a better investigation into those statistics, which I have looked at in some ... relatively basic forms. 

Yes I too have investigated the universe with torsion - today, the torsion is very small to correspond to the small residual rotation left over known as dark flow. 

I will post up on torsion in my next topic. 

By the way, the rotation axis is only a conjecture: In the Godel metric, no such axis is distinguishable. In our approach, we assume dark flow is too slow to create a divergence in the average curvature over large distances. 

There is nothing wrong, in fact, I have already applied the creation and annihilation operators in some attempts). Certainly, in the diabatic model in my other thread, the creation and annihilation operators will play a role.