To my mind it is now clear that you aren't even following your own points, most of what you have written doesn't directly connect with the context in which it is being discussed.
Let me deal with your points:
Because you need to hold to some kind of expositional consistency, so the reader can sort out your points… my opinion. |
General Relativity is usually written in units where G(Newton's constant) and c(the speed of light) are set to 1. This is because their presence just clutters up intermediate calculations. They can always be restored at the end of a calculation when you want to compare results to experiment.
is a geometric factor and is usually kept since it cancels out factors coming from areas of circles. One could work in "circle units" where the equations wouldn't have this factor, but there isn't a need to, unlike the case with G and c.
Further more, which units one uses are irrelevant to this discussion as we are not talking about units.
I am trying to find this paper but only get the abstract. I believe I see what the problem is here, the paper was written prior to the discovery of the accelerating universe (about 1998). |
This point is irrelevant. Let me remind you what has been said.
I claimed that quantum mechanical matter requires the addition of three extra terms to Einstein's field equations. You doubted this and said the terms were invented for no reason. In response to this I provided you with references containing proofs that these terms are required. (If you would prefer freely accessible course notes containing the proofs I can supply those as well.)
Whether one observes the universe to be undergoing an accelerating expansion or not is independent of the mathematical fact that quantum mechanics requires this terms. It is this requirement that I have provided references for.
Of course, the interesting thing is that one of the terms introduced predicts an accelerating universe, which we then saw in 1998. Hence these papers from the 1970s contain predictions we saw later. There is nothing wrong with a piece of theory being written before observation of its predictions (in fact it's better isn't it?, a genuine prediction). Some people were expecting the accelerating universe observations before 1998 for this reason.
I believe that the terms you are using are outdated in there relation to the stress energy tensor. |
They most certainly are not. All modern work on cosmology takes them into account.
Type "The Cosmological Constant Problem and Renormalization Group" into google. A talk by Il Shapiro is the first result. Page 7 of the talk contains the statements I'm making and provides more references. Note the sentence:
"Higher derivative terms are necessary in quantum theory."
Other returns from the search will give other papers which include these terms. As Shapiro's talk is from 2011, I hope you can see these terms are not out of date.
The CMB is another conversation altogether… Try goggling “Cosmic Background fails the shadow test”. |
Again you are ignoring the context of the discussion.
You said the new terms had no physical effects. I said they do, they effect the anisotropies of the CMB. Hence the terms predict physical consequences, refuting your claim.
Whether those consequences are observed is a separate issue.
They actually are observed in case you are wondering. Look at any papers dealing with the data from the WMAP studies of the Cosmic Microwave background to see this.
Theory is one thing… proof is another. |
Okay, once more I shall explain the discussion.
You claimed that the values of the parameters need to be adjusted constantly or tuned.
I said they are not, their values are explicitly predicted by quantum field theory. So not only are the not tuned or adjusted, they cannot be tuned. The have a value fixed by the Standard Model. I then said that if you take the values which are predicted by the Standard Model for these parameters and solve the equations, you get an accelerating expanding universe..
So quantum matter has fixed values for these parameters and even with these modifications (the extra terms coming from quantum mechanics) the field equations still give a solution which is an accelerating expanding universe.
As you can see this is a purely mathematical claim. That theory has fixed values for the parameters and gives an accelerating expanding universe as a solution.
The full proof that this is true is given in the 2007 paper by the General Relativity group at Barcelona (Guillem Perez-Nadal, Albert Roura, Enric Verdaguer) in their paper:
"Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity"
de Sitter spacetime = the accelerating expanding universe solution
stability = still a solution
under isotropic perturbations in semiclassical gravity = the effects of quantum matter, specifically the extra terms introduced by quantum matter
Hence my statement has a mathematical proof. Unless you know of some error in the paper above, then my claim is correct.
In your response "Theory is one thing… proof is another.", although it is vague, I assume you are alluding to this result being purely mathematical and not experimentally supported.
However:
- As I explained, your claim that the theory needs to have its parameters fixed and doesn't give an accelerating expanding universe solution without this fixing is a mathematical statement about the properties of the theory. It is also a provably incorrect statement.
- Experiment comes after we have proven that the new quantum-mechanically modified theory predicts an accelerating expanding universe solution. We then check if that solution is what we actually observe in the universe.
One good check is to see does it predict the right multiploe moment contributions to the CMB.
The l-th multipole moments measure how much the CMB looks like it is the temperature distribution of a set of l objects.
So the 2nd multipole moment would be a measure of how much the CMB looks like the temperature profile of two hot objects.
If the 2nd multipole moment was very large the CMB would look mostly like two hot objects.
The power spectrum is how much each multipole moment contributes to the CMB.
So do we see the right power spectrum? Well, one of the authors of the paper I gave above, Albert Roura, gave a nice talk at Los Alamos. Just search for "Semiclassical stability of de Sitter spacetime & RG running cosmological constant".
On page four of the talk you'll see a picture of the Cosmic Microwave Background and a smaller picture on the bottom right of the power spectrum. The line is the spectrum predicted by the solution he and his colleagues have shown is still a solution when quantum mechanical matter is added. The points are the observed multipole moments.
Let me include that diagram here:
The error on the observed values around the 700th multipole is because our telescopes were not yet good enough to resolve them at the time.
ACBAR has since gone up to l = 2,000. For these more accurate measurements please see the paper:
"Small Angular Scale Measurements of the Cosmic Microwave Background Temperature Power Spectrum From QUaD", available for free from arxiv.org
On the fourth page you will a graph of the power spectrum with results from telescopes all over the world agreeing precisely with the CMB power spectrum predicted by the deSitter (accelerating and expanding) solution.
Edited by Son Goku, : Editing