Modified Raychauduri Equation With Poincare Symmetry And Non-Conservation

[exchemist]

Not all models, there have been more than several attempts over the past few decades for what are called, emergent gravity theories, or emergent spacetime theories from which spacetime appears to come from more fundamental underlying dynamics - so spacetime would not be fundamental in that sense. Other theories avoid the singularity altogether, some using gravitational repulsion from quantum corrections, others using mechanical approaches like torsion, those theories can avoid not only singularities, but any notion of a beginning to space and time resulting in a never ending cycle of a universe expanding and then contracting. These theories are known as cyclic or bounce theories and are very popular. Penrose himself relatively recently proposed his own version. 

Thanks for this. I have now done a bit of reading. Re emergent gravity, I take it you are referring to the ideas of Verlinde and co, is that right? 

[OceanBreeze]

I’ve been thinking about posting something mathematical that relates to this thread, but I’m not sure what.

 

(pause while I think and talk to myself)

 

[OceanBreeze]

Aha!  I know! I will post the Einstein field equations:

 

[math]{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }}[/math]

 

[math]{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }}[/math]

 

(another pause, posting latex is really tiring you know))

 

[OceanBreeze]

Am I back? Oh Ok And now, I will post the Friedmann solutions:

 

[math]{\displaystyle \left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-{\frac {\Lambda c^{2}}{3}}={\frac {8\pi G}{3}}\rho }[/math]

 

[math]{\displaystyle 2{\frac {\ddot {a}}{a}}+\left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-\Lambda c^{2}=-{\frac {8\pi G}{c^{2}}}p.}[/math]

 

(yawn) break time

[OceanBreeze]

(What? You woke me up?  You want some more?)

 

The two Friedmann equations given above are equivalent to the following pair of equations:

 

[math]{\displaystyle {\dot {\rho }}=-3{\frac {\dot {a}}{a}}\left(\rho +{\frac {p}{c^{2}}}\right)}[/math]

 

[math]{\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}}}[/math]

 

Here, k, the spatial curvature index, serves as a constant of integration for the first equation.

 

(Now I’m on a roll)

 

[OceanBreeze]

The first equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the expansion of the universe is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).

 

The second equation states that both the energy density and the pressure cause the expansion rate of the universe [math]{\displaystyle {\dot {a}}}[/math]  to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of gravitation, with pressure playing a similar role to that of energy (or mass) density, according to the principles of general relativity.

 

(Man, that one flat out tuckered me. Hold on, while I catch my breath)

 

[OceanBreeze]

(Anybody still there/ It doesn’t matter, I enjoy posting to myself)

 

The cosmological constant, on the other hand, causes an acceleration in the expansion of the universe.

The cosmological constant term can be omitted if we make the following replacements:

 

[math]{\displaystyle \rho \rightarrow \rho +{\frac {\Lambda c^{2}}{8\pi G}}}[/math]

 

[math]{\displaystyle p\rightarrow p-{\frac {\Lambda c^{4}}{8\pi G}}.}[/math]

 

Therefore, the cosmological constant can be interpreted as arising from a form of energy which has negative pressure, equal in magnitude to its (positive) energy density:

 

[math]{\displaystyle p=-\rho c^{2}.\,}[/math]

 

(Christ, I'm tired now)

[OceanBreeze]

(Still with me?)

 

These solutions are not considered perfect mathematical representations of the universe, particularly because of the cosmological constant, which is interpreted as arising from a form of energy which has negative pressure, equal in magnitude to its (positive) energy density. This is indeed a problem for the standard model of cosmology as no such form of Dark Energy has ever been detected, only the supposed effects, including the accelerated expansion of the universe.

 

(this has got to be good for my post count)

[OceanBreeze]

(I am getting to the point of all this, be patient)

 

But, is there any justification for replacing the CC term with another that is derived from assuming the universe is rotating?

 

All present observations of the CMB are consistent with zero rotational velocity. Therefore, it makes zero sense to attribute any prominent cosmological role to rotation. In fact, there is no meaningful sense in which the universe could rotate as then the question that must be answered is “rotating relative to what”. Since the universe is all there is, it cannot be rotating relative to anything else. Therefore, any claim that the universe as a whole is rotating becomes a claim for absolute motion; and there is no way to test this empirically since there is nothing else for the universe to be rotating relative to! (see?)

 

The bottom line is, assuming a rotating universe makes no sense, and having pages and pages of spamTex posted on this site in support of such a crackpot claim makes even less sense.

 

 

 

(to be continued and continued and continued until somebody stops me)

 

[exchemist]

(I am getting to the point of all this, be patient)

 

But, is there any justification for replacing the CC term with another that is derived from assuming the universe is rotating?

 

All present observations of the CMB are consistent with zero rotational velocity. Therefore, it makes zero sense to attribute any prominent cosmological role to rotation. In fact, there is no meaningful sense in which the universe could rotate as then the question that must be answered is “rotating relative to what”. Since the universe is all there is, it cannot be rotating relative to anything else. Therefore, any claim that the universe as a whole is rotating becomes a claim for absolute motion; and there is no way to test this empirically since there is nothing else for the universe to be rotating relative to! (see?)

 

The bottom line is, assuming a rotating universe makes no sense, and having pages and pages of spamTex posted on this site in support of such a crackpot claim makes even less sense.

 

 

 

(to be continued and continued and continued until somebody stops me)

Yes, while I find the send-up of 006's style quite funny, I do think this issue of rotation is non-trivial. Rotation, involving, as it does, acceleration, appears to be absolute rather than relative. And then we get "Mach's Principle" and the fun starts.  

[OceanBreeze]

Your sledgehammer wit hasn't gone unnoticed.

 

That's a relief! I was afraid I was wasting my time.

 

I suppose I do use the thread a bit like a blog.

 

 

Ya think? But, if the admins don't mind why should I . . . .

 

The interesting question ''what is it rotating relative to'', is an old one. In relativity there is no outside to the universe, but we know theories have since departed that we can now talk about such hypothetical things.

 

 

As long as you realize it is hypothetical, there is hope for you.

 

 

As for the math, that is childs play. I know those equations like the back of my hand, I've had to, so I could write about them. When you put the amount of study into the equations as I have, yes maybe one day you will learn it is tiring. 

 

 

I like math very much but I am too busy earning a living to spend all of my time on it.

 

But, I do not find your pages and pages of it anything more than self indulgent spam.

[OceanBreeze]

Yes, while I find the send-up of 006's style quite funny, I do think this issue of rotation is non-trivial. Rotation, involving, as it does, acceleration, appears to be absolute rather than relative. And then we get "Mach's Principle" and the fun starts.  

 

Yes. That is exactly the issue.

[exchemist]

 

 

''But, I do not find your pages and pages of it anything more than self indulgent spam.''

 

 

I could argue the performances you have made in other people threads amount to much the same as well. Just a thought, any one can play these silly point the finger and name-calling games.

 

That's not why I am here.

 

But, as you yourself acknowledge, your style is that of a blogger rather than someone interested in discussion, so it is not entirely surprising that some people get a bit fed up with it and start taking the p1ss. :)

[OceanBreeze]

 

 

''But, I do not find your pages and pages of it anything more than self indulgent spam.''

 

 

I could argue the performances you have made in other people threads amount to much the same as well. Just a thought, any one can play these silly point the finger and name-calling games.

 

That's not why I am here.

 

 

Why are you here? Really, what do you think you are accomplishing other than self indulgence in your pet theory? And, I should remind you that rotating universe theories are nothing new.

[OceanBreeze]

They were never anything new, of course.

 

But for the same reasons, you must realize, physicists have went around saying our universe doesn't rotate because if it did there would be evidence.. oh wait a minute.... there is.

 

There is no evidence other than what you want to see to confirm your belief. That is not science. You should be looking for evidence to disprove your theory, not to support it. When you do that, you find lots of evidence against a rotating universe. And, I have pointed that evidence out to you in the CMB, which you said is absolutely wrong, because you don't like it.

Edited June 13, 2017 by OceanBreeze

[exchemist]

So by your accord, just that we all know,

 

1) You ignore dark flow, whose easiest fix is rotation

 

2) You ignore the chirality problem whose easiest fix is a universal rotation

It seems to me that the disagreement between you two boils down to whether or not there is reproducible evidence for either "dark flow" or chirality.

 

From the little I have read, there does not seem to be  consensus that either exists. If either of them does exist, the effect must presumably be sufficiently small that current observations cannot unambiguously say that they do. Is that fair?

 

If so, then Ockham's Razor would tend to set to one side the extra hypotheses required to explain them - though they might be needed later, if future measurements provided unambiguous evidence.  

Edited June 13, 2017 by exchemist

[OceanBreeze]

Well, I have never heard anyone say the chirality problem is not of consensus. Indeed, that would be a strange statement,knowing that its an observational fact,that most spiral galaxies conform to a particular handedness.

 

 

Never heard that? You must be hard of hearing! Try this paper (and there are many more)

 

We re-examine the evidence for a violation of large-scale statistical isotropy in the distribution of projected spin vectors of spiral galaxies. We have a sample of ~ 37,000 spiral galaxies from the Sloan Digital Sky Survey, with their line of sight spin direction confidently classified by members of the public through the online project Galaxy Zoo. After establishing and correcting for a certain level of bias in our handedness results we find the winding sense of the galaxies to be consistent with statistical isotropy. In particular we find no significant dipole signal, and thus no evidence for overall preferred handedness of the Universe. We compare this result to those of other authors and conclude that these may also be affected and explained by a bias effect.