Talk:Equation of state (cosmology)

I have made the following edit to the first section of the Equation of State article. It now reads:

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology) :

In cosmology, the equation of state of a perfect fluid is characterized by a number $\!w$ , equal to the ratio of its pressure $\!p$ to its matter/energy density $\!\rho$ : $\!w=p/\rho$ . It is closely related to the thermodynamic equation of state and ideal gas law. From this equation containing the density ρ (using "natural units"), if the matter/energy content, m, of the universe in the definition, ρ=m/v, is always to be taken as equal to 1, then w=pv. The variable w and the combination pv both have the dimensions (and implications) of energy or "work". Then v must also always be equal to 1, by this same ideal gas assumption: the ideal gas law cannot pertain if the system being described is not stationary or static, that is, at equilibrium, including thermal stasis.

This change is not my personal opinion. It is not a synthesis of work appearing elsewhere that does not actually appear in those works. It is not a result of my own private unpublished original research. It is mathematical logic. It is logic that is contained within itself and therefore needs no outside references.

This edit should be retained. If it is to be reverted, would the reverting editor please consult with me first? Edits are supposed to be made in good faith. This includes common courtesy.

I am beginning to doubt the sincerity of the quality classifications and appeals for expansion that are often seen as headings for these cosmology articles. If edits are not allowed and are continually reverted without consultation, what's the point of these solicitations?

If an editor wishes to remove text from this entry, would he/she limit it to the last few paragraphs, leaving paragraph 1 intact? Highhanded removal of text from discussion pages is reprehensible and should be banned.

Kentgen1 (talk) 14:32, 3 November 2010 (UTC)[reply]

If it is perceived that the above edit is confusing and inconsistent and contradictory to the text in the rest of the article, then it is the text in the rest of the article that needs to changed, not this edit.

Kentgen1 (talk) 14:47, 3 November 2010 (UTC)[reply]

I was about to be bold and revert your edit - but JRSpriggs beat me to it ! Pressure (force per unit area) and energy density (energy per unit volume) clearly have the same units, so

\!w

is a dimensionless quantity. Your introduce the unusual term "matter/energy density", which seems to change the meaning of the equation. And, sorry, but unless you can provide a reliable source for your new formulation, then it does not belong in Wikipedia, no matter how logical you may think it is. Gandalf61 (talk) 15:59, 3 November 2010 (UTC)[reply]

Oh yeah. I forgot. I cannot use logic. I have to quote someone else who has already used the logic. Like, I cannot say that the FLRW metric, because it assumes the Cosmological Principle, imputes the property of mass to the spacetime continuum. Mathematically, this is what happens if one smears out all the concentrated matter in the universe over its whole volume so that there are no discrete matter entities, just an "average mass". Then, we have a spacemasstime continuum, which fits perfectly with GR, certainly, I am sure. It makes no sense, but I cannot say so unless I can quote a reliable source who has aleady said so. No matter how logical, if no outside source can be found who echoes it, it is inadmissable. Well, O.K. It's just the rules of the game, I suppose.

At least I got JRSpriggs to read a paragraph that states the dependency of the Freidmann equations and their solutions on the ideal gas law. This is a start.

Kentgen1 (talk) 21:37, 3 November 2010 (UTC)[reply]

LOOK:

The equation

The perfect gas equation of state may be written as

\!p=\rho _{m}RT=\rho _{m}C^{2}

where $\!\rho _{m}$ is the mass density, $\!R$ is the particular gas constant, $\!T$ is the temperature and $\!C={\sqrt {RT}}$ is a characteristic thermal speed of the molecules. Thus

w={\frac {p}{\rho }}={\frac {\rho _{m}C^{2}}{\rho _{m}c^{2}}}={\frac {C^{2}}{c^{2}}}\approx 0

where $\!\rho =\rho _{m}c^{2}$ and $\!C<<c$ for a "cold" gas, $\!c$ - speed of light.

Notice that ρ is defined as the mass density, not energy density. This page is inconsistent. If we want to talk about energy density, we need to use ρ'. If ρ is mass density, then w has dimensions as stated in my proposed edit.

The FORM of w is the same as would be for work when applying the perfect gas law. It is no accident that it is called "w". The dimensions of p x v are the dimensions of energy or work. It would make no sense for the ideal gas law to result in a dimensionless quantity when computing the work that is possible to do or to absorb when a given volume of a gas is allowed to expand or be compressed.

The only item that I see that might need to be documented separately is the statement concerning the ideal gas law and the status of the gas as being at equilibrium. Now, you know as well as I do that the gas laws do apply only in the case of a gas at equilibrium. So, if this needs to be documented, why don't you do it instead of reverting my edit? Yeah, I know YOU didn't revert it, Gandalf. Then, I aim this question at JRSpriggs.

I foresee problems when I try to find an explicit statement of this in the reliable outside literature, just like I found a problem finding an explicit statement of the fact that any amount of any additional phases will completely upset gas law computations. And, over billions of years, there is no such thing as "dust". I hope an explicit statement is NOT only to be found in the Instructor's Edition of textbooks. It looks like I will need to stock my library with more and more advanced college and graduate level texts. Well, the UW Eau Claire Library is only 10 miles away.

In the meantime I will work on finding this explicit statement. Then, I will post a preview of my proposed change on this discussion page for your and JR's approbation, so you won't have to revert it and clutter up the History page. Then, perhaps, you will be encouraged to refine it instead of dissing it.

Kentgen1 (talk) 18:00, 4 November 2010 (UTC)[reply]

Okay. I suspect I am about to waste my time by responding here, so let me say at the outset that I am going to make one take-it-or-leave-it attempt at pointing out some of your errors; this is not an invitation to start an endless debate.

You define $\rho _{m}$ as a mass density, then you say $\rho =\rho _{m}c^{2}$ , which makes $\rho$ an energy density - but you then assert "Notice that ρ is defined as the mass density, not energy density". Obvious inconsistency.
By your own derivation $w={\frac {C^{2}}{c^{2}}}$ , which is clearly a dimensionless ratio.
You expect other editors to find sources for your assertions and "fix" your work. Well, that sometimes happens, but its not help that you can demand as of right. Other editors are unlikley to try to help you find sources if they simply doubt that such sources exist, and they won't work to help you fix something if they think it is unfixable - which is the territory we are in here. Gandalf61 (talk) 15:15, 5 November 2010 (UTC)[reply]

You are right. So, my w and Friedmann's w are not the same quantities. Friedmann's w is more like a figure of merit or an index, being dimensionless. But, my w is also a variable in an equation of state. It is just as good. My reasoning regarding it still holds. But, I need to distinguish it from Friedmann's w. In other words, this is only a semantic issue.

But, this discussion has identified for me a new epistemological problem with the FE/FLRW model. It would seem improper to mix GR and the ideal gas law.

In order for a discussion referring to GR to make practical sense, one must speak in terms of mega-parsecs, periods of time in the billions of years or, at least, velocities near c. In time spans this large and over such great distances, the ideal gas law could never be expected to hold. The universe has expanded greatly and it has shown a lot of turbulence. The ideal gas law presumes that the system is stationary, at equilibrium. It is effectively timeless. Then, Friedmann introduces a scale factor that reintroduces time, contradicting the assumption.

Maybe this could be justified if the processes of evolution in the universe are infinitesimally slow and there is no turbulence. But, the magnitude of the changes that have occurred show that it does not undergo infinitesimally slow change. Maybe it would be justified if we limited interpretation to short time spans or small distances, but we do not. We try to go back all the way to very near the beginning (the CMB). And, with optical measurements, we have tried to go back almost 10 billion years, so far.

As Wikipedia says, Friedmann is a "first approximation". As such, it is a wonder that it does as well as it does. The add-ons that are used to account for the lumpiness of the universe and the other fixes try to compensate for the crudeness of the assumptions that are made. But these different crutches are not used at all when acceleration of the expansion rate is taken to mean there exists some sort of dark energy. This conclusion is pushing the approximation way beyond its limit. Friedmann is an analogy. At best it is a metaphor. It is always dangerous to push analogies and metaphors too far.

I would be happy if someone would just acknowledge more explicitly the shortcomings of the FE/FLRW model. I would really like to hear Saul Perlmutter and Adam Riess do so.

I like the way that the Dark Energy and Big Bang articles are written. The same level of reserve and the same degree of skepticism should be present in the FE article and the FLRW metric article because they are all bundled together in the same package.

Kentgen1 (talk) 11:15, 6 November 2010 (UTC)[reply]

Meaning of curvature having w=-1/3?

This article is clearly written. So the following statement stands out because it is confusing: "This is the origin of the flatness and monopole problems of the Big Bang: curvature has w = − 1 / 3 and monopoles have w = 0, so if they were around at the time of the early Big Bang, they should still be visible today." Several questions here: How can curvature have an equation of state? Is this an error? In what sense would curvature have pressure and density? Does this statement relate to the cosmological constant? Maybe it's just a matter of explaining the concepts more clearly. Also why do these values of w mean monopoles should still be visible today? 71.32.45.99 (talk) 22:10, 24 January 2020 (UTC)Kathleen Rosser[reply]