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# Big Bang 2 and a new beginning of space/time

Author Topic:   Big Bang 2 and a new beginning of space/time
Son Goku
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 (3)
 Message 16 of 33 (667264) 07-05-2012 6:18 AM

The cosmological constant problem and quintessence.
Now, $\color{white} \Lambda^{vac}$ and $\color{white} \Lambda^{ind}$ are very large quantities, corresponding to a huge amount of energy. However they have opposite signs and cancel to incredible precision.
The total $\color{white} \Lambda = \Lambda^{vac} + \Lambda^{ind}$ is tiny compared with either of them. Both $\color{white} \Lambda^{vac}$ and $\color{white} \Lambda^{ind}$ are $\color{white} 10^{55}$ times larger than $\color{white} \Lambda$.
Now to handle an often repeated myth. Many critics of current cosmology say we cannot explain the value of $\color{white} \Lambda$ and that when we tried to do it we get an answer far larger than we should.
This myth is based on early papers that calculated only $\color{white} \Lambda^{vac}$ and found it was far larger than $\color{white} \Lambda$. The reason this was done is because $\color{white} \Lambda^{vac}$ is related to vacuum infinities, you don't need to go into the details of particle physics when there is no matter around, so it's an easier quantity to calculate and you would hope that $\color{white} \Lambda^{ind}$ is unimportant. Unfortunately of course it turns out we need to look at $\color{white} \Lambda^{ind}$ as well. The first papers handling $\color{white} \Lambda^{ind}$ go back to 1975, so anybody still peddling this myth that the cosmological constant is "billions of times larger" than physicists thought is nearly forty years out of date.
So the actual problem we have today is:
Why do the two sources for the cosmological constant cancel so precisely?
At the moment we know the source of most of the cancellation (quite technical, but it can be explained if anybody wishes), however we still need to understand the remainder, which currently looks quite difficult.
This is the most widely accepted idea for Dark Energy, let me sum up the facts:

1. Quantum Mechanical matter automatically introduces a new term to Einstein's equations: $\color{white} \Lambda g_{\mu\nu}$ in order to remove infinities.
2. This term gives rise to an accelerating expanding universe, as explained in my first post on this thread. This matches our universe provided $\color{white} \Lambda$ is small and positive.
3. The Standard Model does seem to predict that $\color{white} \Lambda$ is small and positive, due to precise cancellations between the two terms that contribute to it.
4. The problem is we don't understand this cancellation as much as we would like.
Quintessence
This is another idea for Dark Energy, but observations are making it increasingly unlikely. Basically quintessence is a field filling the universe. It naturally interacts with gravity in such a way as to act like the term: $\color{white} \Lambda g_{\mu\nu}$ It also sets the real $\color{white} \Lambda$ to zero, so no need to worry about cancellations. It also means Dark Energy is an actual substance, the quintessence field. However observations of the universe have caused serious problems for this. The Quintom scenario/problem (found in 2004), means that to match the behaviour of the universe you need at least two of the these fields. Nobody can really think of a convincing way of having two of these fields without us having already noticed them.
Other ideas
All other ideas for Dark Energy are just different things which act like: $\color{white} \Lambda g_{\mu\nu}$ Such as a larger extra-dimensional universe "pressing" on ours or "Cracks/Defects" in spacetime. All these ideas are really cool, but I must emphasis that theoretical calculations and experimental evidence are increasingly favouring Vacuum energy.
Summary
The Cosmological constant(Dark Energy) increasingly seems to be, not a substance, but rather a natural quantity arising from precise cancellations that occur when removing infinities from quantum matter.

 Replies to this message: Message 17 by zaius137, posted 07-06-2012 5:00 PM Son Goku has replied Message 19 by zaius137, posted 07-06-2012 5:16 PM Son Goku has replied

zaius137
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 (1)
 Message 17 of 33 (667391) 07-06-2012 5:00 PM Reply to: Message 16 by Son Goku07-05-2012 6:18 AM

Re: The cosmological constant problem and quintessence.
Son,
Good to converse with you again.
About Einstein’s equations, I believe you left out the gravitational constant.
Yours: $\color{white} G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi T_{\mu\nu}$
Einsteins: $\color{white} G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi GT_{\mu\nu}$
My first problem with your treatment of $\color{white} \Lambda$ and what side of the equation you are placing it.
Lawrence M. Krauss and Michael S. Turner would have us place it on the other side with the Stress energy tensor as follows:
$\color{white} G_{\mu\nu} = 8\pi G(T_{\mu\nu} + P_{vac} g_ {\mu\nu})$
This would be consistent with a Quantum energy flux added to the total momentum energy flux.
I see you can accept the balancing of the universe on the head of a pin. Your equation faces the same shortcomings as when Einstein first proposed the cosmological constant. In other words, to maintain an observable flat universe over time (as time goes by, continuous adjustments must be made to your alpha and beta), simply because an expanding universe alters the state of flatness.
Even if I start off with no $\color{white} \Lambda$, it's automatically generated when I try to get rid of the infinities. That is Quantum matter requires the cosmological constant. So we at least know why it isn't zero.The new terms: $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$ are geometric terms describing how curvature changes as you move through spacetime. ($\color{white} \alpha, \beta$ are just numbers) At first people found them a bit odd.
I find it a bit odd and a bit unlikely also, unless the hand of God is adjusting it continually.
They make the equations much harder to solve and they are not "natural" quantities by which I mean, aside from removing infinities, they don't seem to have a physical explanation. However they were later discovered to have a very important effect, they make spacetimes containing time-machines impossible.
Without this imperative then the terms still make sense. You can make up all kinds of terms to reduce the calculated quantum flux to match the observed dark energy effect but that is again just fantasy.
I do not wish to match your lengthy bloviation with my own, so I will continue with mine in an abbreviated way.
Edited by zaius137, : No reason given.

 This message is a reply to: Message 16 by Son Goku, posted 07-05-2012 6:18 AM Son Goku has replied

 Replies to this message: Message 18 by Dr Adequate, posted 07-06-2012 5:13 PM zaius137 has replied Message 23 by Son Goku, posted 07-09-2012 10:30 AM zaius137 has replied

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 Message 18 of 33 (667393) 07-06-2012 5:13 PM Reply to: Message 17 by zaius13707-06-2012 5:00 PM

Ah, zaius, still lecturing us on physics?
I thought you might keep quiet for a bit.
Hawking's rival says Higgs wager win is icing on cake
Hawking, Britain's most famous living scientist, said the discovery should earn Higgs the Nobel Prize, but admitted in an interview that it would make him \$100 poorer.
"I had a bet with Gordon Kane (of the University of Michigan) that the Higgs particle wouldn't be found," Hawking told BBC News on Wednesday. "It seems I have just lost \$100."

 This message is a reply to: Message 17 by zaius137, posted 07-06-2012 5:00 PM zaius137 has replied

 Replies to this message: Message 21 by zaius137, posted 07-06-2012 5:29 PM Dr Adequate has replied

zaius137
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 (1)
 Message 19 of 33 (667395) 07-06-2012 5:16 PM Reply to: Message 16 by Son Goku07-05-2012 6:18 AM

Re: The cosmological constant problem and quintessence.
Son
1. Quantum Mechanical matter automatically introduces a new term to Einstein's equations: $\color{white} \Lambda g_{\mu\nu}$ in order to remove infinities.
As stated earlier the new dark energy is not a proposed modification to Einstein’s curvature tensor but it is by all definition an addition of energy (albeit dark) added to the stress energy tensor. Personally, I believe dark energy is just fantasy.
2. This term gives rise to an accelerating expanding universe, as explained in my first post on this thread. This matches our universe provided $\color{white} \Lambda$ is small and positive.
The key term here is small and positive and I would add unlikely.
3. The Standard Model does seem to predict that $\color{white} \Lambda$ is small and positive, due to precise cancellations between the two terms that contribute to it.
Too precise, as Einstein lamented over this fact.
4. The problem is we don't understand this cancellation as much as we would like.
I will second that motion

 This message is a reply to: Message 16 by Son Goku, posted 07-05-2012 6:18 AM Son Goku has replied

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 Message 20 of 33 (667396) 07-06-2012 5:18 PM Reply to: Message 19 by zaius13707-06-2012 5:16 PM

Re: The cosmological constant problem and quintessence.
As stated earlier the new dark energy is not a proposed modification to Einstein’s curvature tensor but it is by all definition an addition of energy (albeit dark) added to the stress energy tensor. Personally, I believe dark energy is just fantasy.
And the relevance of your beliefs to reality is ... ?

 This message is a reply to: Message 19 by zaius137, posted 07-06-2012 5:16 PM zaius137 has not replied

zaius137
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Posts: 407
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 Message 21 of 33 (667398) 07-06-2012 5:29 PM Reply to: Message 18 by Dr Adequate07-06-2012 5:13 PM

Hawking may have folded on the two-channel gamma/gamma and the 4-lepton excess, but the obtained 5 sigma was still from the combination of two separate experiments. Not the independent discovery from two independent experiments. Science spent the money and must receive a return, maybe real, maybe false. I still do not believe in all pervasive fields.

 This message is a reply to: Message 18 by Dr Adequate, posted 07-06-2012 5:13 PM Dr Adequate has replied

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 Message 22 of 33 (667399) 07-06-2012 5:32 PM Reply to: Message 21 by zaius13707-06-2012 5:29 PM

Fortunately reality doesn't give a flying fuck what you believe or whether you understand statistics.
Edited by Dr Adequate, : No reason given.

 This message is a reply to: Message 21 by zaius137, posted 07-06-2012 5:29 PM zaius137 has not replied

Son Goku
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Posts: 1226
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Joined: 07-16-2005

 Message 23 of 33 (667536) 07-09-2012 10:30 AM Reply to: Message 17 by zaius13707-06-2012 5:00 PM

Re: The cosmological constant problem and quintessence.
About Einstein’s equations, I believe you left out the gravitational constant.
No, I was just using relativistic units where it is equal to 1. In human units (meters, seconds, e.t.c) the equation is: $\color{white} G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}$
My first problem with your treatment of $\color{white} \Lambda$and what side of the equation you are placing it.
Lawrence M. Krauss and Michael S. Turner would have us place it on the other side with the Stress energy tensor as follows:
Well things can be placed on any side of the equation you want, fundamental part of algebra.
This would be consistent with a Quantum energy flux added to the total momentum energy flux.
It isn't, as I said only $\color{white} \Lambda$ is not enough, you need the other terms I listed, namely: $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$ otherwise there are infinities. $\color{white} \Lambda$ on its own is not consistent with quantum mechanical matter. (This is a mathematical theorem, reference for proof available on request)
I see you can accept the balancing of the universe on the head of a pin. Your equation faces the same shortcomings as when Einstein first proposed the cosmological constant. In other words, to maintain an observable flat universe over time (as time goes by, continuous adjustments must be made to your alpha and beta), simply because an expanding universe alters the state of flatness.
$\color{white} \alpha$ and $\color{white} \beta$, the terms in front of: $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$ Do not need to be adjusted at all. Where did you get that idea from? You solve the equations and you get an expanding universe, nothing needs to be tuned. Can you explain your thinking behind this? $\color{white} \alpha$ and $\color{white} \beta$ have very little effect on cosmological scales and aren't really relevant for the Big Bang or inflation.
Without this imperative then the terms still make sense. You can make up all kinds of terms to reduce the calculated quantum flux to match the observed dark energy effect but that is again just fantasy.
The terms are not introduced to match Dark Energy. As I said, they are naturally introduced by quantum mechanics. The values given to the parameters (by quantum mechanics) then match the observed evolution of the universe.

 This message is a reply to: Message 17 by zaius137, posted 07-06-2012 5:00 PM zaius137 has replied

 Replies to this message: Message 26 by zaius137, posted 07-10-2012 2:22 AM Son Goku has replied

Son Goku
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Posts: 1226
From: Ireland
Joined: 07-16-2005

 Message 24 of 33 (667538) 07-09-2012 10:38 AM Reply to: Message 19 by zaius13707-06-2012 5:16 PM

Re: The cosmological constant problem and quintessence.
Personally, I believe dark energy is just fantasy.
Well, it is predicted by quantum mechanics and produces an evolution of the universe that matches all observations of WMAP data and distant supernovae. Very strong evidence, but believe what you wish.
The key term here is small and positive and I would add unlikely.
Is there something wrong with it being small and positive, I mean that's what matches the observed universe.
zaius137 writes:
Son Goku writes:
3. The Standard Model does seem to predict that is small and positive, due to precise cancellations between the two terms that contribute to it.
Too precise, as Einstein lamented over this fact.
The prediction is too precise? The cancellation too accurate? I actually don't understand what the problem is. How can a result be too precise?

 This message is a reply to: Message 19 by zaius137, posted 07-06-2012 5:16 PM zaius137 has not replied

Son Goku
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Posts: 1226
From: Ireland
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 (1)
 Message 25 of 33 (667539) 07-09-2012 10:42 AM Reply to: Message 21 by zaius13707-06-2012 5:29 PM

Hawking may have folded on the two-channel gamma/gamma and the 4-lepton excess, but the obtained 5 sigma was still from the combination of two separate experiments. Not the independent discovery from two independent experiments. Science spent the money and must receive a return, maybe real, maybe false. I still do not believe in all pervasive fields.
ATLAS obtained its five sigma result independently. CMS is currently at 4.9 sigma. Where are you getting this information from?
I still do not believe in all pervasive fields.
Again, same as Dark Energy, the idea of quantum fields matches all the information that has come out of every collider ever built. What is your belief based on?

 This message is a reply to: Message 21 by zaius137, posted 07-06-2012 5:29 PM zaius137 has not replied

zaius137
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Posts: 407
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 Message 26 of 33 (667591) 07-10-2012 2:22 AM Reply to: Message 23 by Son Goku07-09-2012 10:30 AM

Re: The cosmological constant problem and quintessence.
Son You stipulate
No, I was just using relativistic units where it is equal to 1. In human units (meters, seconds, e.t.c) the equation is:
I would wonder since you inexplicitly used geometrized units why you did not include $\color{white} 8\pi$ also.
Well things can be placed on any side of the equation you want, fundamental part of algebra.
Does it look like I preformed an algebraic operation? Just start by showing your conversion from:
($\color{white} P_{vac} g_ {\mu\nu}$) to ($\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$)
Really, my point of the position of vacuum energy with the stress energy tensor is to express the current view that dark energy is a form of energy not a property of space itself. Did you catch that?
It isn't, as I said only $\color{white} \Lambda$ is not enough, you need the other terms I listed, namely: $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$ otherwise there are infinities. $\color{white} \Lambda$ on its own is not consistent with quantum mechanical matter. (This is a mathematical theorem, reference for proof available on request)
Please proceed and include some citation for me the hopeless layman..
$\color{white} \alpha$ and $\color{white} \beta$, the terms in front of: $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$ Do not need to be adjusted at all. Where did you get that idea from? You solve the equations and you get an expanding universe, nothing needs to be tuned. Can you explain your thinking behind this? $\color{white} \alpha$ and $\color{white} \beta$ have very little effect on cosmological scales and aren't really relevant for the Big Bang or inflation.
First off, your terms are complete contrivances, they do not relate to any known observed phenomenon. They are known in physics as hidden values and are nothing more than mathematical convinces that facilitate a current solution. I emphasize current as the expansion rate of the universe has varied over time according to the BB paradigm. You do not get these values, as you put it, then solve the equations and you get the expanding universe.
Further, the cosmological constant makes a poor balancing act whether your model is static or biased to a known expansion
quote:
However, there is a basic flaw in this Einstein static model: it is unstable - like a pencil balanced on its point. For imagine that the Universe grew slightly: say by 1 part per million in size. Then the vacuum energy density stays the same, but the matter energy density goes down by 3 parts per million. This gives a net negative gravitational acceleration, which makes the Universe grow even more! If instead the Universe shrank slightly, one gets a net positive gravitational acceleration, which makes it shrink more! Any small deviation gets magnified, and the model is fundamentally flawed.
http://www.astro.ucla.edu/~wright/cosmo_constant.html
As I discussed earlier, conservation of energy in a global sense for the universe is not possible, if matter energy density grows. So a tentative balance is unavoidable unless you want to concede the global conservation of energy is false.
The terms are not introduced to match Dark Energy. As I said, they are naturally introduced by quantum mechanics. The values given to the parameters (by quantum mechanics) then match the observed evolution of the universe.
Specifically, what are these natural introduced quantum values? I do not know of any parameter values from quantum mechanics that could match the observed evolution of the universe that is the point.

 This message is a reply to: Message 23 by Son Goku, posted 07-09-2012 10:30 AM Son Goku has replied

 Replies to this message: Message 27 by Son Goku, posted 07-10-2012 3:06 PM zaius137 has replied

Son Goku
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Posts: 1226
From: Ireland
Joined: 07-16-2005

 (2)
 Message 27 of 33 (667628) 07-10-2012 3:06 PM Reply to: Message 26 by zaius13707-10-2012 2:22 AM

Re: The cosmological constant problem and quintessence.
zaius137 writes:
I would wonder since you inexplicitly used geometrized units why you did not include $\color{white} 8\pi$ also.
Why does it matter?
Does it look like I preformed an algebraic operation? Just start by showing your conversion from:
($\color{white} P_{vac} g_ {\mu\nu}$) to ($\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$)
They can't be converted into each other. $\color{white} \Lambda g_{\mu\nu}$ is a separate term to $\color{white} \alpha H^{1}_{\mu\nu} + \beta H^{2}_{\mu\nu}$.
I was saying it doesn't matter which side $\color{white} \Lambda g_{\mu\nu}$ is put on.
Really, my point of the position of vacuum energy with the stress energy tensor is to express the current view that dark energy is a form of energy not a property of space itself. Did you catch that?
$\color{white} \Lambda$ has units of energy no matter which side of the equation it's on. It really doesn't matter which side of the equation it appears on.
Please proceed and include some citation for me the hopeless layman..
A proof that the terms I listed above are necessary in the presence of quantum mechanical matter is given in:
S. A. Fulling, Aspects of Quantum Field Theory in
Curved Space-Time
(Cambridge University Press, Cambridge,
1989).
The original paper is:
R. M. Wald, Commun. Math. Phys. 54, 1 (1977).
First off, your terms are complete contrivances, they do not relate to any known observed phenomenon.
They do, they contribute to anisotropies in the Cosmic Microwave background.
They are known in physics as hidden values and are nothing more than mathematical convinces that facilitate a current solution. I emphasize current as the expansion rate of the universe has varied over time according to the BB paradigm. You do not get these values, as you put it, then solve the equations and you get the expanding universe.
Yes, you do. Again I can give you a paper proving it. With those terms the solution is an entire four-dimensional history of a universe which has accelerating expansion. Can you show me a paper with detailed mathematical calculations showing this does not occur.
Specifically, what are these natural introduced quantum values? I do not know of any parameter values from quantum mechanics that could match the observed evolution of the universe that is the point.
I've described them in the posts above. Quantum Mechanics naturally induces a small positive value of $\color{white} \Lambda$ through renormalisation. The value it predicts matches the observational value obtained from studies of distant supernovae.

 This message is a reply to: Message 26 by zaius137, posted 07-10-2012 2:22 AM zaius137 has replied

 Replies to this message: Message 28 by zaius137, posted 07-11-2012 12:07 AM Son Goku has replied

zaius137
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 Message 28 of 33 (667662) 07-11-2012 12:07 AM Reply to: Message 27 by Son Goku07-10-2012 3:06 PM

Re: The cosmological constant problem and quintessence.
Son thanks for the response.
Why does it matter?
Because you need to hold to some kind of expositional consistency, so the reader can sort out your points my opinion.
A proof that the terms I listed above are necessary in the presence of quantum mechanical matter is given in:
S. A. Fulling, Aspects of Quantum Field Theory in
Curved Space-Time (Cambridge University Press, Cambridge,
1989).
The original paper is:
R. M. Wald, Commun. Math. Phys. 54, 1 (1977).
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). I believe that the terms you are using are outdated in there relation to the stress energy tensor.
If you can find it try an article in Scientific American March 2009, volume 300 Number 3 (article on A Quantum threat to Special Relativity).
They do, they contribute to anisotropies in the Cosmic Microwave background.
The CMB is another conversation altogether Try goggling Cosmic Background fails the shadow test. http://www.sciencedaily.com/...ases/2006/09/060905104549.htm
Yes, you do. Again I can give you a paper proving it.
Theory is one thing proof is another.

 This message is a reply to: Message 27 by Son Goku, posted 07-10-2012 3:06 PM Son Goku has replied

 Replies to this message: Message 29 by Son Goku, posted 07-11-2012 5:32 AM zaius137 has replied

Son Goku
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Posts: 1226
From: Ireland
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 (3)
 Message 29 of 33 (667677) 07-11-2012 5:32 AM Reply to: Message 28 by zaius13707-11-2012 12:07 AM

Re: The cosmological constant problem and quintessence.
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. $\color{white} 8\pi$ 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 $\color{white} S_{HD}$ 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 $\color{white} \alpha, \beta, \Lambda$ 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:

1. 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.
2. 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

 This message is a reply to: Message 28 by zaius137, posted 07-11-2012 12:07 AM zaius137 has replied

 Replies to this message: Message 30 by zaius137, posted 07-16-2012 8:31 PM Son Goku has replied

zaius137
Member (Idle past 2895 days)
Posts: 407
Joined: 05-08-2012

 Message 30 of 33 (668055) 07-16-2012 8:31 PM Reply to: Message 29 by Son Goku07-11-2012 5:32 AM

Re: The cosmological constant problem and quintessence.
Son sorry for the delayed response but that is just life.
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. $\color{white} 8\pi$ 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.
I understand you could not present the field equation in a reasonable way because of all the deep calculations you are performing. I view your equivocations as an avoidance of omission.
Further more, which units one uses are irrelevant to this discussion as we are not talking about units.
That is an assumption on your part.
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.
Yes one of the term predicts an accelerating universe, it also predicts an expanding version a static version and if stretched predicts a contracting version.
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.
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.
The CMB only shows what the value of the cosmological constant must take. It is interesting that NO values can be presented from Quantum field theory to match the prediction. If you us the contributions of say those found in the Casimir Effect the following value for the cosmological constant is infinity.
Theory is one thing proof is another.
You claimed that the values of the parameters $\color{white} \alpha, \beta, \Lambda$ need to be adjusted constantly or tuned.
The values of alpha and beta are renormalization parameters. In your citation there is reference to solutions by the Bunch-Davis vacuum which some claim is not even relevant to the primordial universe. My point being that any solution you wish to examine is dependent on the evolutionary era of the Big Bang. Making matters even worse is that if the universe is non-local what can be said about these parameters, them being fixed as you claim.
I said they are not, their values are explicitly predicted by quantum field theory.
You miss the whole point these values fine tune the cosmological constant, the value of the constant is what is in question.
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"
I believe I have found the document and cannot deem it as support to your claims. If you have the exact URL please provide it.
under isotropic perturbations in semiclassical gravity = the effects of quantum matter, specifically the extra terms introduced by quantum matter.
The rest of your response is a nice little bloviation on CMB. Thanks for that.
It was once thought the cosmological constant was zero (things were nice), if vacuum energy is set to zero (or renormalized to zero) by just saying that the absolute value of energy density cannot be observed you cheat Einstein. Because all kinds of energy create curvature and there is no way you can take the huge quantum values (zero point energy) seriously.

 This message is a reply to: Message 29 by Son Goku, posted 07-11-2012 5:32 AM Son Goku has replied

 Replies to this message: Message 31 by Son Goku, posted 07-17-2012 5:08 AM zaius137 has not replied Message 32 by Son Goku, posted 07-17-2012 5:22 AM zaius137 has not replied

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