Talk:Dark energy

Much of this article has been adapted from a press release at http://hubblesite.org/newscenter/newsdesk/archive/releases/2004/12/text/

This appears to be OK from a copyright point of view, as the press release appears to be in the public domain, but we should a) give credit to the source, b) rewrite in a style suited to an encyclopedia article. -- The Anome 18:27, 22 Feb 2004 (UTC)

Yes. I agree. Perl 18:30, 22 Feb 2004 (UTC)

new content

Someone added the following content which reads very poorly, and seems POV, but may be possible to work in more coherently. --zandperl 01:41, 18 Mar 2004 (UTC)

In cosmology, dark energy The concept of dark energy is more-so concerning quantum physics than astronomy. However, it is part of the study of the nature of the universe and thus does form a branch of astronomy. Dark energy is even more of a mysterious subject than dark matter. Dark energy was first proposed by Albert Einstein to explain the phenomenon of galactic acceleration. He claimed that the force behind the unexplained acceleration was dark energy. Dark energy is termed to be thee force directly opposite gravity. For in reality thee galactic expansion should be slowed by gravity rather than sped up. The form of dark energy is disputed. Einstein called the form he theorized the “cosmological constant”. The cosmological constant is represented by the Greek letter lambda (Λ). Its formula is , where G=gravity, c=the speed of light, π=3.14…, and ρ=the energy density of the vacuum of space. Others who believe it has another function than what Einstein thought call the energy “quintessence” (Literally Meaning the “Fifth Element”).

Einstein’s version of the cosmological constant (which I will refer to as Λ) is extremely flawed, however. The Λ dark energy is said by him to form a balance with gravity creating a static or flat universe (model of the universe where there is a set limit to the size of the universe). However, if the universe even slightly expanded somehow, energy is released causing more expansion throwing off the balance. The same is true for contraction. Because of these circumstances Einstein said that his formulation of the Λ was “the biggest blunder” of his life. However, many physicists say it could be the greatest legacy of his life despite these problems. Quintessence is simply another theory on the mechanics of dark matter. There is much less information about this simply because it is a variable to the Λ where the dark energy will push the universe further and further out into the void for infinity. Thus, there may never be a new universe caused by a Big Crunch and then Big Bang in succession. is a hypothetical form of energy which permeates all of space and has negative pressure resulting in an effective "repulsive gravitational force". Dark energy may account for the accelerating universe as well as a significant portion of the mass in the universe. Two proposed forms of dark energy are the cosmological constant and quintessence, where the former is static and the latter is dynamic. Distinguishing between the two requires high precision measurements of the expansion of the universe to see how the speed of the expansion changes over time. Making such measurements is a topic of current research.

Why is it "energy"?

Spacetime metric

I suggest that we delete the old stuff, since the main arguments are essentially contained in the two new subthreads.Bjoern 10:19, 28 Sep 2004 (UTC)

OK, I deleted it. Furthermore I suggest to delete the spacetime metric sub-thread as well since we already established that I utterly screwed up the calculations designed to check the homogenity, mostly by ignoring the signs in the exponents. It is a small wonder since those calculations were done on a proverbial back of an envelope (unlike the calculations of the redshift which I'd be glad to discuss if you don't mind). If you are still intersted how I got exp() out of sinh(), it was the same madness since sinh(r)=[exp(r)-exp(-r)]/2 and this is also where minus sign comes form. As for the curveture scalar I'll surely calculate it at some point in the future and then I'll tell you how it went. I'm sure I'll have a lot of opportunities to do that in due time before I get my PhD in strophysics. Just be patient. Let's concentrate now on conservation of energy in the next sub-thread since it seems a much more interesting subject. 83.24.20.68

How did you check this?

I translated coordinates and got the same form but I might have screw up something then if you are sure it is not homogeneous.

(1) If you can find the calculation again, please show it to me. I don't see how translating the coordinates could give the same form again, sorry. (2) Additionally, did you ever calculate the curvature scalar (the trace of the Ricci tensor) for your metric?

(1) My calculations were the following: I added $\Delta r$ to r, put it into metric and got

$ds^{2}=c^{2}e^{-(r+{\Delta r})/R}dt^{2}+(2c)sinh((r+{\Delta r})/R)dtdr-e^{(r+{\Delta r})/R}dr^{2}$

then I took out $e^{\Delta r/R}$ from all the terms on the right side,

Stop right here. How did you take out $e^{\Delta r/R}$ from the sinh term?

obtaining new metric as $e^{\Delta r/R}ds^{2}$,

That simply is not true! How on earth did you arrive at this result?

which corresponds to multiplying the old metric by a constant meaning that the new metric's form is exactly the same as form of the old one,

Apparently you do not know what it means that the *form* of a metric stays the same under a coordinate transformation! It means that if one uses new coordinates r' and t', one should be able to write the metric as $ds^{2}=c^{2}e^{-r'/R}dt'^{2}+(2c)sinh(r'/R)dt'dr'-e^{r'/R}dr'^{2}$! Simply noting that the new metric is a multiple of the old one does in no way show that its form is invariant under coordinate transformations! (and as pointed out above, it is not even true that the new metric is a multiple of the old one).

except fort the redshift as I presented before, which we would expect anyway, since this was the purpose of constructing this metric.

Sorry, I don't understand what you mean here. Do you want to say that if one transforms the metric by going to $r+Deltar$, one *has* to obtain a factor multiplying the metric, and that that factor *has* to represent the redshift? If yes, then you really have *severe* misunderstandings about General Relativity!

Doing all this I lost minus sign at a few places in this was the way I screwed up the calculation.

Huh? Where do minus signs occur in the calculation above?

(2) I didn't calculate the curvature scalar. Jim 07:55, 28 Sep 2004 (UTC)

Well, as I said, showing that the curvature scalar does not depend on the location is the best way to proof that a metric describes a homogeneous space. So you *really* should consider doing that.Bjoern 10:19, 28 Sep 2004 (UTC)

Conservation of energy

Since we don't know any examples of creating energy ...

But we do know an example of loosing energy: the cosmological redshift! And one could also argue that a body falling due to gravity gains energy "from nothing" (I know that you address that on your webpage, but I do not think that your attempted explanation makes sense). [...] you still have not told me how you got from your calculation involving energy conservation to the metric. [...] I already gave you this link once: http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/energy_gr.html

[...] E.g. dark energy is an example for [creation of energy from nothing].

(1) Why do you think that the cosmological redshift has something to do with losing energy rather than with simple Einsteinian time dilation (called in such a case "metric redshift")?

Have you looked at the link above? It discusses cosmological redshift, if you did not notice.

Yes, and I write about it below.

(2) Maybe a layman could argu that falling due to gravity gains energy "from nothing" but we (knowing at least some physics) are supposed to be able to explain easily this miracle, and as you recall I did it on my webpage. Why do you think that making energy "from nothing" makes more sense than my explanation?

Because energy is not conserved in GR. Look at the geodesic equation. It is *not* the same as Newton's first and second law, from which energy conservation was proven in classiscal mechanics. Look at the divergence of the energy-momentum tensor. It is the *convariant* derivative, not the *coordinate* derivative, and therefore does *not* lead to a global conservation law. All explained at the link above. By simply pointing out (below) that in your opinion, the author (Baez) himself is not sure about that topic, you do in no way invalidate the arguments he presents on that page! So, why don't you address them, for a change?

OK, if you insist I'll try but it will take time. Again, be patient.

As for your explanation on your webpage: I don't remember exactly your argument (IIRC it had to do with time dilation in a gravitational field, and it made little sense how you used that time dilation to explain away the non-conservation of energy); could you please give me the link again?

The link is http://www.geocities.com/wlodekj/sci/gravity.htm

which is rather long and possibly boring article "Einsteinian gravity for poets and science teachers" but you can jump directrly to section Conservation of energy in Einsteinian Gravity and try to find out what is wrong with it. I count on as severe critique from you as possible. If you have some spare time I'd appreciate the critique of the rest of the article as well. Especially the introduction about science, religion, and magic. I'm sure you won't like this article and such a reader is the most valuable as a critic since one learns from him the most.

(3) I guessed the metric. There is no derivation of this metric, beyound constructing it so that it produces approximately right Hubble redshift and zero light interval.

Well, so far you have not demonstrated that you are able to derive a redshift correctly from a given metric.

What is the redshift dreived correctly from this metric?

(4) Unfortunately the link is useless.

Because it contradicts you, right?

No, because it contradicts a few hundred years of experience of physicists that ended in a ban on patents for perpetual motion machines.

I discussed this matter with Dr. Baez (the author) already. He is not sure himself what energy is and leaves the decision to the reader.

He clearly explains the different approaches in the page above. And he says that one only can say that energy is conserved in GR if one uses an "energy pseudo-tensor" for gravitational energy. Since you yourself said, IIRC, that gravitational energy does *not* exist in GR, obviously the only thing left to you is admitting that energy is *not* conserved. If you think it it, please *prove* that it is conserved from the basic equations.

You my be surprised learning that validity of the principle of conservation of energy can't be proven. However falsifying this principle is possible by simply constructing a perpetual motion machine. The principle of conservation is only an experimental fact. And either you believe the principle or you don't. I do, you apparently don't so we have a subject for discussion. When you build a functioning perpetual motion machine I shut up and I change my opinion about the conservation of energy. Unfortunately those things can't be decided either way theoretically. I can only show that some ideas are false, as I believe I did in the case of freele falling bodies that according to gravity physicists create energy out of nothing. If you think I didn't tell me why you think so. I can tell you where you make errors in some of your assumptions that in some instances energy has been created from nothing.

It is possibly because he is an applied mathematician so he isn't accustomed to treating energy as physicists do. For him it might be as well created from nothing but I never seen it treated like that by a physicist. So I'd rather see a link to an article written by a physicist, who migh know what energy means in physics.

Baez knows quite well what energy means in physics. OTOH, you seem to be utterly unaware that and how one can *prove* the conservation of energy in classical mechanics, and why that proof fails in GR.

As I said, one can't prove conservation of energy (apparently your formal training in physics is about the same quality as mine :-) but I hope to improve mine rather soon). What one can "prove" is only that certain theory is consistent or not with conservation of energy. Of course through a suitable definition you may have GR without conservation of energy. I prefer GR with conservation of energy. To distinguish it from GR that does not conserve energy, I call it "Einsteinian gravity". It does conserve energy (however it does not allow the expansion of space, so something for something).

(5) "Dark energy" is still a hypothetical entity even in the mainstram cosmology so it is useless as an example, unless as an example how "gravity physicists" create physical entities (from nothing :-). Jim 07:55, 28 Sep 2004 (UTC)

You miss the point. Dark energy is a hypothesis, right. But it is a hypothesis fully consistent with the equations of GR (or do you dispute that?). But the existence of dark energy in an expanding universe implies the creation of energy from nothing. So, obviously, the creation of energy from nothing is consistent with the equations of GR. Conclusion: the equations of GR do not demand the conservation of energy. q.e.d.Bjoern 10:34, 28 Sep 2004 (UTC)

That's right but, as I said above, it depends how one defines the equations, in particular if one assumes expanding metric or stationary one. Equations are not physics. We have to know physics (whether the universe is expanding or not) to tell which equations to keep and which to dump. We differ in opinions on this subject and that's why it makes the discussion iteresting. 83.24.20.68 12:40, 28 Sep 2004 (UTC)