It seems to me that the discovery that there has to be much more energy in the universe than was previously believed is a very important discovery. This information was gleaned by taking accurate measures of the velocity of Super Nova as they speed away from us. While I'm not a physicist I recognize the importance of this discovery. It means that any theory of physics from the ultra small to the ultra large must take this fact into account. This is important information akin to the Michaelson Morley discovery that there is no ether and that the speed of light is constant. That fact led ultimately to Einsteins theory of special relativity. So here's the question: what current theory, be it string theory and M theory or theories involving quantum vacuum energy best accounts for this mysterious energy? The specific equation for the spectral energy distribution for the quantum vacuum energy is given at this site: http://www.calphysics.org/articles/PRA94.pdf Unfortunately I'm not educationally equiped to do the analysis to see if the energy formula for the ZPF can account for the "dark energy". The formula given is only for electromagnetic energy, However there are also similar equations for quantum probabilites for the weak, and strong force. These combined equations might account for it - I don't know. I don't know very much about the various string theories, (I actually don't care much for any of them if aethetics play any part in a theory), but I'm wondering if there is any part of those theories that could mathematically account for the dark energy. I'm depending on those of you with more math ability than I have to provide some answers.
Einstein did, in fact, predict an "aether" (ether) but perhaps not one detectible by the Michaelson-Morley experiment. One of a different nature that must exist for there to be a "unification" of the forces. This application also allows for a variance in c over time. See the info at: http://www.tshankha.com/identifying_the_aether.htm and then go to the "Home" page to start the whole shebang. It is an interesting paper that seems to list requirements for us to be able to even consider "quantum applications" at all. This site might have been posted before here on PF, but I wouldn't remember where or when.
Loop gravity gives a tentative handle on Dark Energy Loop gravity is not strictly speaking one of the "string theories" but it is a growing research area in the field of Quantum Gravity, and is a quantum theory of space and time. Loop gravity (broadly interpreted to include several allied non-string approaches to quantizing General Relativity) gives a tentative handle on the dark energy density---also known as the "cosmological constant"---as you can see in a recent paper by Girelli and Livine "Quantizing Speeds with the Cosmological Constant" http://arxiv.org/gr-qc/0311032 The paper is only 4 pages, in PDF format, and it has references in the back to other online Loop Gravity articles dealing with the cosmological constant. I would suggest that since it is very short you might download and print it, to get a taste of what I'm talking about. Most of it will be incomprehensible but if you have it in front of you then I may be able to explain a paragraph here and there and some parts (without formulas) you may get the drift of. This paper is recent---November 2003---and the exciting point of it is this: some versions of Loop Gravity predict a potentially observable quantization of speeds in the early universe----a splitting up of speeds into discrete "steps", instead of the smooth ramp of speeds we usually think of. This quantization into levels of speed would have affected the energetic particles whizzing about in the very early universe and would (IF the loop theory is right) have left its traces in very early radiation, perhaps on the very ancient neutrinos we may someday be able to detect and study. It is calculated that there is a background of neutrinos, still undetectable because of their low energy, similar to the cosmic microwave background but even older. So there is some hope of getting a window onto the very early time when speed may have been quantized. Moreover the levels of speed depend mathematically on the cosmological constant. So there is some tentative way of CHECKING. The cosmological constant can be measured today---as you said by observing supernovae. It is an energy density that no one has been able yet to explain in a satisfactory way, and we do not know if it is really constant. But people often assume that in fact it is constant or at least changes only slowly. So what it is observed to be today (half a joule, or one eighth of a calorie, per cubic kilometer) gives some grip on what it may have been in the very early universe, and that, by means of Loop Gravity, gives predictions of quantized speed levels, and those, in turn, may be observable as traces in ancient radiation. So the circle is closed----one observation (on supernovas) can be compared (via a theoretical calculation) to another observation (of neutrinos) and it will either agree or disagree. If it is consistent with what the theory predicts it will tend to confirm the theory and if it is not consistent it will tend to discredit the theory and force assumptions to be modified or discarded. It is hard, obviously. Like climbing an ice wall. The attempt is to be empirical---use observational checks. Otherwise (if there are no predictions to verify or falsify) making theories is just daydreaming. Quantum gravity theories are very hard to force to the point of making predictions of effects that available instruments can measure. Because the effects of quantum gravity are either very small or else occur only under extreme conditions. At the back of this 4 page paper there is a list of 12 other papers including several longer Loop Gravity online articles that deal with the cosmological constant
Re: Loop gravity gives a tentative handle on Dark Energy You're absolutely right, that paper is practically incomprehensible to me. I think the problem is it uses so much arcane language specific to Loop Quantum Gravity. (Also of course the mathematics) I'm afraid that though I'm not that knowledgeable about the theory I have one very big problem with ALL theories of gravity as representing a discrete essence - as in electromagnetic,weak, and strong forces. For one, they have never discovered a graviton and I'm not sure they've ever discovered a gravity wave either - if I'm wrong please correct me. I know that isn't proof that there is an "absence" of gravity as a fundamental force but on the other hand it indicates to me a "presumption" whenever a theory of gravity force separates itself from the other three forces. I think it's just too big an assumption given the experimental evidence, especially as opposed to the experimental evidence of the other three. Your reply got me interested in learning more about the Cosmological Factor. I found an interest site here: http://super.colorado.edu/~michaele/Lambda/lambda.html Towards the end of it I got partially what I was looking for. The most recent evidence from the Supernovae they estimate the Cosm at approx .71 +-.09 and they have a 99% confidence that Cosm > 0. Then it calculates the vacuum energy using the Planck energy as an upper limit for the sum. Using that figure the Cosm would have to be, (get this), ~10^120! But I started thinking about it. There have been real effects attributed to the vacuum field in the Lamb shift, Van der Waals forces, the Casimir effect, diamagnetism, spontaneous emission, and quantum noise. So one can't easily just write off that 10^120. If one assumes that that the "normal" application of ZPF energy equates to a Cosmological constant of 10^120 perhaps we should believe it but we should add something to it. If gravity isn't a separate force, but is a side effect of mass interacting with quantum effect of the vacuum field, then what would be required is counterbalancing effect of this gravitational action. In other words there is a Cosmological counterforce, Cosm(G), such that 10^120 + Cosm(G) ~ 0.71 As far as the speed of the expansion of the universe changing over time - well that's over my head completely. Eric
Exeric you say: ------------- Your reply got me interested in learning more about the Cosmological Factor. I found an interest site here: http://super.colorado.edu/~michaele/Lambda/lambda.html ---------------- thanks for the link, it looks promising it says it is inspired by Andy Hamilton he is also at Colorado (where that guy Eli Michael is) and Andy has some of the best most fun online stuff about relativity and black holes and astrophysics. Andy's stuff in very accessible to the non-technical browser. I dont have time to check out this Eli Michael thing on Lambda but it is probably in Andy's style and very good so I would almost recommend it sight unseen. It seems to me Exeric that you are learning fast off the web so more power to you! Here is a problem for you, if you choose to take it on. I seem to recall that the density of dark energy is currently estimated to be 0.6 joules per cubic kilometer. (this is 73 percent of some other energy density which I dont remember now but think I could calculate from 0.6 joules if that one is right) Can you confirm this? Does Eli Michael say what the density of dark energy is believed to be? If this is not right, and I have remembered wrong, then what is the currently agreed-on estimate? BTW Does Eli explain why having a contant energy density in space exerts a negative pressure?