I'm not trying to conserve energy locally, just globally. That is where the objection arises.
Then you remain in the Einstein frame of SCC - that is GR.Chronos said:I'm not trying to conserve energy locally, just globally. That is where the objection arises.
That is precisely my intention in this threadSpaceTiger said:If you wish to entirely change a paradigm, you must re-interpret all of the observational evidence in the context of the new paradigm before you can safely say that your theory is viable.
Smoothness was one of the set of three: the horizon, density and smoothness problems of the Friedmann model that Inflation provided an solution for. The reason these three parameters of the universe were problems, i.e. why was the sky isotropic if regions of it are not causally connected, why is its density close to unity, why was the universe so homogeneous, was caused by the deceleration of the universe. Deceleration over the entire age of the universe would have driven these parameters away from the Friedmann flat model solution. Inflation, on the other hand, a short violent exponential acceleration, had the ability of driving these parameters onto the flat model solution.SpaceTiger said:3) Homogeneity and Isotropy
Most models of the universe assume that it is uniform to translations in space (homogeneous) and uniform in direction (isotropic). This does not mean that every point in space is the same on all scales (it obviously isn't), but rather that the universe is smooth on the largest scales. By analogy, the surface of a spherical balloon is homogeneous and isotropic, despite having small bumps and wiggles if you look at it closely enough. Although this point is not controversial (even believers in steady-state cosmology like homogeneity and isotropy), it is actually more difficult to prove than, for example, expansion. Difficult, but not impossible.
The first and most convincing line of evidence (if you believe the big bang) is the cosmic microwave background radiation. If it really is a fingerprint of the early universe, then its extreme uniformity implies homogeneity to one part in 104.
Garth's theory actually has a number that represents "the energy of the universe" that is a constant - you would probably call this a global quantity. Don't be confused by the name he has chosen to give his energy conservation principle. His energy conservation principle is different than that of GR's, because he includes the energy that is in his "scalar field" into the total energy.Chronos said:I'm not trying to conserve energy locally, just globally. That is where the objection arises.
Garth's theory, because of the scalar field and the way it's constructed, DOES have a local (in the mathematical sense used in the paper above) defintion of energy. There is another confusing issue here - physicists and mathemeticians have totally different notions of what local energy conservation means.Abstract: This paper presents a historical account of Emily Noether's proof of two thereoms which have had a great impact on modern physics. Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra, it is of some historical interest to examine how she came to make these discoveries. The present paper is an historical account of the circumstances in which she discovered and proved these theorems which physicists refer to collectively as Noether's Theorem. The work was done soon after Hilbert's discovery of the variational principle which gives the field equations of general relativity. The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein. Noether's theorems solved this problem. With her characteristically deep insight and thorough analysis, in solving that problem she discovered very general theorems that have profoundly influenced modern physics. This resource is appropriate for all users, particularly for girls and women, because it acknowledges women's contributions to STEM.
Thank you for that link, you may also be interested in Nina Byers [URL [Broken] Noether’s Discovery of the Deep Connection Betweenpervect said:If you also go "hmmm, how does Garth's theory get around Noether's thoerem? Does it wind up not being diffeomorphism invariant, because the scalar field gives you in essence a preferred frame?", I *think* you'll be on the right track, though I'm not 100% sure of this point.
Garth said:Thank you for that link, you may also be interested in Nina Byers [URL [Broken] Noether’s Discovery of the Deep Connection Between
Symmetries and Conservation Laws[/URL].
There were two questions left after the formulation of GR, treated separately: the local conservation of energy and the full inclusion of Mach's Principle. Emmy Noether dealt with energy-conservation early on and Brans and Dicke tried to deal with Mach's Principle in the 1960's.
SCC deals with both questions simultaneously.
The problem with the local conservation of energy is that the measurement of energy is frame dependent, in order to conserve energy you need to specify a frame of reference in which it is conserved, a preferred frame. I use Mach's Principle to select that frame.
The question of preferred frames in SCC is a deep one.
The field equations (Jordan frame) are manifested covariant, there are no preferred frames, although the matter field energy-momentum tensor is not conserved. (It is when conformally transformed into the Einstein frame). However if you select one particular fame, the 'Machian' Centre-of-Mass (Momentum) frame for the system in question then in that frame of reference energy is locally conserved.
I hope this helps.
Yes, selfAdjoint, thank you for that observation. I was using the word 'question' to mean 'the question of whether it should be included or not', it may even be emphasised by calling it a 'problem' instead.selfAdjoint said:I would call the Machian principle not a question, as if physics demanded it, but a philosophical preference. Einstein was a Machian at first but found his theory did not support it and was able to abandon it. I am not criticising SCC, just pointing out that there does not appear to be a crying need to build Mach into one's theories.
It is important to see the significance of this "failure of the energy theorem" in GR, for example:The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein.
Energy conservation in the general theory has been perplexing many people for decades. In the early days, Hilbert wrote about this problem as ‘the failure of the energy theorem ’. In a correspondence with Klein , he asserted that this ‘failure’ is a characteristic feature of the general theory, and that instead of ‘proper energy theorems’ one had ‘improper energy theorems’ in such a theory. This conjecture was clarified, quantified and proved correct by Emmy Noether.
I thank ST for this clear exposition of the mainstream view.SpaceTiger said:4) Age of the Universe
Firstly, there are globular clusters. From what we know about stellar evolution, we can model populations of stars and, under the assumption that they were all born at the same time, determine their age. When we do this with Milky Way globular clusters, we get an age of around 12 +- 3 billion years. Not technically a determination of the universe's age, but certainly a lower limit.
What about radioactive elements? Can we somehow use them to infer the age of the universe? It turns out that we can. Recent detections of Uranium-238 and Thorium-232 in stars have allowed us to use the traditional radioactive dating method to obtain an age of 12.5 +- 3 billion years. Again, a lower limit, but completely independent from and consistent with that from stars.
Finally, there are the measured cosmological parameters. When brought together and analyzed carefully, we can very tightly constrain the age of the universe to be 13.7 +- 0.2 billion years. It is very reassuring that this is consistent with both of the above ages. In fact, the standard model predicts that the Milky Way should have formed very early in the life of the universe, so the fact that the other two ages are of the same order (and not much less) is also consistent. One way to falsify the standard model would be to find something that is significantly older than 13.7 billion years. For a while, the globular cluster measurements were thought to represent such a falsification, but with the improvement of both our globular cluster measurements and our cosmological measurements, we are now finding nice agreement.
Finally, as there is no requirement to make up the density closure because the total Omega = 0.33, why "multiply the entities" with the "invention" of DE?The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).
Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.Garth said:In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R0(t/t0) and the age of the universe is simply 14.2 Gys.
That is interesting. Note that model also adds Mach to GR, and also finds it does not need DE to explain cosmological constraints. Does it have any specific falsifiable tests as SCC does?Kea said:Interestingly, this is similar to the age calculated by the recent Wiltshire Machian cosmology.
Hi GarthGarth said:Does it have any specific falsifiable tests as SCC does?
How do you calculate this? For a linearly expanding universe the age is equal to the inverse of the Hubble parameter and this yields 13.77 Gy.Garth said:In comparison the Freely Coasting model, as produced by the SSC gravitational field equations, has a simple evolution R(t) = R0(t/t0) and the age of the universe is simply 14.2 Gys.
You are correct, thank you for spotting that.hellfire said:How do you calculate this? For a linearly expanding universe the age is equal to the inverse of the Hubble parameter and this yields 13.77 Gy.
I don't think the second significant figure is very robust, but we do have a much better handle on Hubble time than previously - unless there is some systematic error.hellfire said:0.71, I had in mind this was the WMAP best fit value.
Thank you for that Chronos as I said my numbers were based on the plain Einstein-de Sitter universe, a spatially flat dust filled model,Chronos said:Just to be fair to the mainstreamers, the vanilla GR prediction for the age of the universe [and look back time] is not generally accepted. Most would offer values closer to those obtained using Ned Wright's calculator:
Plugging in WMAP values yields these results:
Current age of universe: t = 13.67 Gy
z = 1000 t = 436,000 years
z = 20 t = 182 My
z = 8 t = 652 My
z = 6.28 t = 896 My
Also per WMAP, recombination occured around z = 1089, which occurs at t = 378 My.
You can check my cosmological calculator here. It is not as elaborated as Ned Wright ones, but the code is far simpler (cc_e.js). It is of free use, and if you have any questions about equations I can answer via PM. By the way, the age 13.67 Gly for the standard model follows from the assumption of 0.27 Omega matter, 0.73 Omega Lambda (w = -1) and h = 0.71.Garth said:Is there another New Wright page where he shows the equations used in his 'calculator'?
Thank you hellfire,the standard model does seem to be clustering around those values.hellfire said:You can check my cosmological calculator here. It is not as elaborated as Ned Wright ones, but the code is far simpler (cc_e.js). It is of free use, and if you have any questions about equations I can answer via PM. By the way, the age 13.67 Gly for the standard model follows from the assumption of 0.27 Omega matter, 0.73 Omega Lambda (w = -1) and h = 0.71.
.The middle solid curve is for (Omega M,Omega L) = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with(Omega M, Omega L) = (0.73,1.32).
Thank you for that. Yes the reionisation (even a very Extended reionization epoch) and metallicity are most probably connected - to Pop III stars, but how big and how many of them? If you have a few very large Pop IIIs then the ionisation will be patchy and metallicity likewise.Chronos said:The WMAP result suggesting reionization began around z = 20 is the tightest, and most model resistant constraint in current mainstream theory. The SCC limit is obviously more palatable. The other early events, such as rapid evolution of metallicity are not so troubling - at least to this point. Our weak understanding of stellar and galactic chemical evolution deserves much of the blame. But then again, it is not clear why reionization occured at the pace it did [some would say too fast, some too slow]. The evolution of metallicity and reionization could easily be connected. The observations we need to resolve these, and other stubborn problems unfortunately reside in the cosmic 'dark ages' [z>6]. Some exciting projects are, however, in the works:
Square Kilometer Array