Is the Friedmann equation derived ONLY from the Einstein Field Equations?

[jonmtkisco]

Hi Pervect,

Since you deleted my last post, and gave me a 3rd warning, the Forum readers no may longer have a context for what this post is about. So I need to make it clear, in the interest of intellectual integrity, that I am confessing my errors and apologizing for misstating the acceptable views about the Friedmann equation.

I have re-adjusted my interpretation of the following excerpt from Simon Singh's 2005 book, "Big Bang, The Origin of the Universe." Singh has a PhD in particle physics from Emmanuel College, Cambridge University and also studied at CERN, Geneva. He has been awarded the Kelvin Medal from the Institute of Physics in 2008, for his achievements in promoting Physics to the general public. Here is the excerpt:

"Friedmann explained how his model of the universe could react to gravity in three possible ways, depending on how quickly the universe started expanding and how much matter it contained. The first possibility assumed that the average density of the universe was high, with lots of stars in a given volume. Lots of stars would mean a strong gravitational attraction, which would eventually pull all the stars back, halting the expansion and gradually causing a contraction of the universe until it collapsed completely. The second variation of Friedmann’s model assumed that the average density of stars was low, in which case the pull of gravity would never overcome the expansion of the universe, which would therefore continue to expand forever. The third variation considered a density between the two extremes, leading to a universe in which gravity would slow but never quit halt the expansion. Thus the universe would neither collapse to a point nor expand to infinity."

Finally, I appreciate that Singh DID NOT actually mean that Friedman explained how his model of the universe could react to gravity in three possible ways, depending on how quickly the universe started expanding and how much matter it contained.

What Singh must have really meant was that the 2nd Friedmann equation was derived ONLY from the Einstein Field Equations. His derivation could not in any way have been influenced by the concept of "escape velocity", i.e., the concept that the expansion rate depended on how quickly the universe started expanding and how much matter it contained.

I note in passing the following statement in the Wikipedia article on the FLRW metric:

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

Having re-adjusted my thinking, I now understand that Wikipedia should be interpreted as saying that the Friedmann equations were derived ONLY from the Einstein Field Equations, and not from the first law of thermodynamics. (The first law of thermodynamics of course says, in the context of an object launched from a gravitational mass, that what goes up, must come down, unless it has enough momentum to escape.) To attribute such a thought to Friedmann or Lemaitre would not only be wrong, but I would also be compelled to take 100% credit for Wikipedia's statement as my own personal theory. The honor would be great, but not worth the penalty. So I must renounce any such theory.

Finally, I ruefully must renounce the unsubstantiated theory if one starts with the 2nd Friedmann equation and substitutes 3M/4PiR^3 for the mass density element, the two equations are functionally equal. Even if it were true (which I am not permitted to suggest here), one MUST ACCEPT that such equivalence is a COMPLETE COINCIDENCE. Surely it is preposterous to suggest that, in deriving his equation from the Einstein Field Equations, Friedmann would have taken any notice of the first law of thermodynamics or its related concept of escape velocity.

I have one final statement to make. The Friedmann equation is unequivocally derived ONLY from the Einstein Field Equations. Any resemblence to the first law of thermodynamics or the escape velocity equation is a coincidence. I repeat it 3 times before bed each night.


Jon

 

[Wallace]

I can't comprehend the series of events that lead to such a bizarre post, however I would comment that the fact that different approaches to a problem yield the same answer (e.g. the Einstein Equations and thermodynamics giving you the same equation for the evolution of energy density) is hardly surprising. It would be much more surprising if they didn't give you the same answer!

There may be a point to your post, but I don't see it?

 

[jonmtkisco]

Hi Wallace,

I apologize if my post was merely stating the obvious. I now understand that if an equation looks like a slight translation of a famously elementary earlier equation, it is almost always a coincidence. Generally in such cases, the later equation really is completely independently derived from another complex theory, and the author is unaware that the theory is virtually identical to a longstanding basic law of physics. Great minds just tend to converge on similar solutions.

My real mistake was to cite a highly respected source who on the surface appeared to agree with my perspective. A source who, unlike any of us, actually purported to read the original Friedmann and Lemaitre papers. Clearly my error there was to rely on a book which was neither a textbook nor a formally peer-reviewed paper. And beyond that, I relied on Wikipedia as a source. It goes without saying that Wikipedia is an unacceptable source for this Forum.

Banning me from participating in the Physics Forum is much too light a punishment. Thank you for helping keep me straight. I look forward to my future beatings, should I be so fortunate.

Jon

 

[Chronos]

I agree the Friedmann equations were derived from Einstein field equations. So what? Are you saying the field equations are wrong, the derivations are wrong, or both? If so, why not simply point out the errors?

 

[marcus]

Hello Jon,
I haven't read your other posts (35 in all) so, like Wallace, I also cannot fathom what occurred. But it is very easy for a bright lad to get into arguments and suddenly find himself banned for a few days. I hope, if indeed you have been banned, that it will be for a short time and that you will re-appear unscathed.

You seem like an intelligent person with an independent turn of thought, who is interested in cosmology. And you have had the sense to get intensely involved with the Friedmann equations, which are central to mainstream cosmology. So what that means to me is that you could potentially be an asset. You just have to avoid arguing with mods, and they are mostly pretty mellow around here so it is not terribly difficult.

If you really are a crackpot then I apologize for giving you bad advice---in that case the proper thing for you to do is flee to the ends of the Earth and hide yourself under a stone. But from this one post you don't sound like a crackpot. You just sound like an intelligent young fellow who has had an argument with a mod. Please continue learning about the Friedmann equations and the standard cosmology model! The universe will still be here when you get back!

 

[jonmtkisco]

Hi Chronos and Marcus,

I'm visibly failing in my effort to not paint myself into the corner of being a crackpot. That's because I'm trying to not get myself banned, as the precipice keeps moving closer. I really appreciate your encouragement Marcus.

If you read my earlier posts mentioning the subject (which is difficult, since two of them were deleted and the other was locked), you would see that I was trying to cite scholarly support for the interpretation (which seems to be widely accepted other than in this Forum) that the startling similarity of the 2nd Friedmann equation to the standard "escape velocity" equation might not be a coincidence. That the first law of thermodynamics must have been firmly in the minds of Friedmann and Lemaitre when they each independently derived the equation from the Einstein Field Equations.

Why that is such a politically sensitive suggestion, I don't know. But now I am under threat of ban unless I adhere to the "party line" that the near identicality of the two equations is complete historical seredipity and coincidence. So at the risk of sounding incoherent, "I'm just following orders".

Jon

 

[marcus]

... I'm trying to not get myself banned, ... But now I am under threat of ban unless I adhere to the "party line" that the near identicality of the two equations is complete historical seredipity and coincidence...

I don't know you, of course, or the history of your advocacy of whatever ideas are at the focus of contention. But I can make some general observations that do not necessarily apply to the situation.

As far as I know there is not much of a "party line" in terms of physics and cosmology doctrine. Maybe there is and I didn't notice because I'm pretty conventional----I love following current professional research literature and i hate any kind of popularization of science, so arxiv.org is my home base.

But I didn't notice much party line as regards unresolved issues within the professional literature.

what I did notice, I think, is a clear but undefined line of "where you stop pushing mods".
At a certain point, the wise individual stops arguing, and also stops expressing bitterness (i.e. griping etc.).
The reason for this has to do with energy and addiction. Mods have very limited energy and they have to maintain calm, courtesy, and intellectual quality. It's quite demanding in a sense. If a person appears addicted to argument, that represents a huge potential drain on time energy and patience, intellectual faculties may already be spread thin and fatigued.
So there is this undefined LINE past which, if you continue arguing, you appear to have a penchant for argument.

So people usually sense this line intuitively and, after having made their point and getting the attention of several people drawn to it, they quiet down and wait for another opportunity or for a new idea to come into their heads.

You seem to be a creative person, so probably if you stay interested in cosmology there will be many many ideas that come into your head, in the course of time.

I used to live in Westchester county many years ago. I'll bet that your handle means you live in Mount Kisco, in the NY area.

 

[jonmtkisco]

Marcus,

Yes I used to live in Mount Kisco, but I moved recently to South Carolina. I'm too lazy to change my handle. Where did you live in Westchester?

Of course you are right that nothing is gained by annoying the mods. So I'm trying to stay on my best behavior and not mention the Friedmann derivation source again.

The "party line" I was referring to was on this very narrow issue, on this Forum only. In general I don't see any politics in the cosmology literature, other than the debate heating up currently between the pro- and anti- string camps, which has now spilled over into pro- and anti- inflation. It ought to get as much attention as dark energy and dark matter.

Jon

I will admit that I'm skeptical of both string- and quantum-mechanical derived theories (such as inflation), because they have an annoying tendency to be fine-tuned ad hoc explanations of already-known problems, rather than reliable predictors of new problems that are subsequently confirmed through other physics. I guess the quantum folks can at least take credit for generally predicting the CMB anisotropies, although multiple different versions of inflation theory were kept alive until the WMAP data ruled most of them out.

As I've already pointed out in my posts, I also think that cosmology literature is very light on the subject of explaining the mechanisms underlying the momentum-like continuation of the original expansion of space. Certainly the FLRW metrics and Einstein Equations are well understood, and perhaps their elegent simplicity causes cosmologists to treat this as a subject with no mysteries left to analyze. I think much remains to be figured out (or at least explained to the rest of us), beyond just how to apply a simple metric.