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Why all these prejudices against a constant? ( dark energy is a fake probem)

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Haelfix
#55
Nov12-11, 06:05 AM
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Quote Quote by mitchell porter View Post
i.e. You can cancel the QFT vacuum energy, and account for the observed dark energy, by supposing that the cosmological constant = "dark energy - QFT vacuum energy".

But doesn't the QFT vacuum energy depend on the high-energy cutoff? (except when it's always exactly zero at all scales). In which case, the value of the cosmological constant required by the strategy above, will depend on the cutoff.
Sure. In fact it will go like O(M^4) + O (M^2 Me ^2) + .... Where M is the cutoff and Me is the mass of some fermion. Simply taking M -- > infinity, yields a divergent answer.

Of course in the language of effective field theory, we assume that there is new physics and thus a physical cutoff, where the new physics enters to soften the divergence. This is probably up at the GUT scale or Planck scale, but for illustrative purposes, we simply take it to be the absolute minimum that is consistent with experiment. To wit, the electroweak scale. (Incidentally, the classical contribution to the cosmological constant recieves heavy contributions here due to SSB, quark condensates and the like)

Again, this is a regime where the standard model + GR works to fantastic accuracy. And since the problem is already acute it serves to make the point.

In short, properly understood, the cosmological constant problem is essentially an *infrared* problem, not an ultraviolet one. It is another example of a hierarchy problem in physics, except this time the relevant scales are the difference in size between the Hubble scale and particle physics (as opposed to particle physics and the Planck scale).

Asking the question in AdS/CFT is interesting, and trying to tame the problem by trying to soften the scaling into the renormalization group is definitely one of the popular methods that people have tried, however I think the current feeling is that the solution probably won't be found in quantum gravity, but rather is cosmological in origin. Also the renormalization group ideas are a little adhoc and typically reintroduce finetuning elsewhere (Weinberg mentions several such ideas in his review)..
smoit
#56
Nov12-11, 11:41 PM
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Quote Quote by Haelfix View Post
In short, properly understood, the cosmological constant problem is essentially an *infrared* problem, not an ultraviolet one. It is another example of a hierarchy problem in physics, except this time the relevant scales are the difference in size between the Hubble scale and particle physics (as opposed to particle physics and the Planck scale)...
I'd say that the CC problem is definitely a UV problem because we are dealing with a highly relevant operator so you cannot ignore all the extra degrees of freedom arising in the UV. Curiously, in the SO(16)XSO(16) heterotic string with broken SUSY (non-tachyonic) and an infinite tower of stringy states contributing, one gets a finite answer for the CC but unlike the N=1 D=4 SUGRA, where the first non-vanishing term is quadratic in the cutoff, the first non-vanishing contribution to the 10D vacuum energy comes at order Str(M8SUSY)M2string, where MSUSY is the scale of SUSY breaking.
My personal hunch is that to compute the CC, at least the quantum piece, one needs to figure out the string spectrum, which at low energies would reproduce some effective N=1 D=4 SUGRA with spontaneously broken SUSY (e.g. by some F-term), and then just compute the one-loop partition function using that string spectrum. I bet that the naive supergravity result would no longer hold and that the supertrace would also vanish at some higher order like in the example I highlighted here.
marcus
#57
Nov13-11, 11:36 AM
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To remind folks of the logical context in which the discussion here takes place.
Quote Quote by marcus View Post
...
iii. The enormous difference between the small value of the cosmological constant revealed by the cosmic acceleration and the large value that can be derived from quantum field theory.
I think we are mainly concerned with point iii here. A person steeped in QFT viewpoint may view Lambda as a classical fudge or lifeline, to correct for the stupendous ZPE calculated from non-QGR-based QFT.
That is he may think of the embarrassing 120-order-of-magnitude QFT vacuum energy discrepancy as in some sense "correct" but just needing to be "canceled" by some Lambda lifepreserver that the other people are responsible for.

As this points out, there is another possible perspective on the embarrassing QFT discrepancy. That is: it is a QFT problem---probably showing that QFT needs some foundational work. One might for example speculate that the embarrassing vacuum energy might go away if QFT would simply stop using Minkowski geometry, and ground itself in quantum relativistic geometry.

Be that as it may, I think it would be a good idea if people who want to discuss in this thread would simply READ the relevant section of the paper.
http://arxiv.org/pdf/1002.3966
It starts on page 5. The relevant section is:
IV. THE VACUUM ENERGY IN QUANTUM FIELD THEORY

Perhaps it would help focus discussion if I were to paste some excerpts in. Then those who have read section IV (relevant to our discussion) could refer to some immediately visible text.
For starters here's a clarifying passage from page 6.
==1002.3966==
But what has all this to do with the question whether in (very) low-energy physics the physical value of the cosmological constant is zero or is small?

The question of whether or not there is a cosmological term λ in the low-energy classical Einstein equations, is independent from the question of what is the mechanism that protects this term (zero or small) from being scaled-up to a high scale by radiative corrections. The first question pertains to low-energy gravitational physics; the second pertains to high-energy particle physics. The two are independent in the sense that the second question exists independently from the answer to the first. The first has been already answered by observation, as it should: the cosmological term in the Einstein equations does not vanish. The second is open, and has not been changed much by the observations that λ ≠0. It is just one of the numerous open problems in high-energy physics.

We think that the origin of the confusion is that there are two distinct ways of viewing the cosmological term in the action. The first is to assume that this term is nothing else than the effect of the quantum fluctuations of the vacuum. Namely that λ = 0 in (21) and the observed acceleration is entirely due to the radiative corrections Λ (in the above notation). The second view is that there is a term λ in the bare gravitational lagrangian, which might (or might not) be renormalized by radiative corrections. The two points of view are physically different. We think that the common emphasis on the first point of view is wrong.

In other words, it is a mistake to identify the cosmological constant λ with the zero point energy Λ of a QFT, for the same reason one should not a priori identify the charge of the electron with its radiative corrections.
===endquote===

Anytime anyone wants to pull up a PDF of the Bianchi Rovelli article, just google "constant prejudices" ---it is what the article is about and what it is critical of. You will get the arxiv link on first or second hit.
fzero
#58
Nov13-11, 12:58 PM
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Quote Quote by Bianchi and Rovelli
We think that the origin of the confusion is that there are two distinct ways of viewing the cosmological term in the action. The first is to assume that this term is nothing else than the effect of the quantum fluctuations of the vacuum. Namely that λ = 0 in (21) and the observed acceleration is entirely due to the radiative corrections Λ (in the above notation). The second view is that there is a term λ in the bare gravitational lagrangian, which might (or might not) be renormalized by radiative corrections. The two points of view are physically different. We think that the common emphasis on the first point of view is wrong.

In other words, it is a mistake to identify the cosmological constant λ with the zero point energy Λ of a QFT, for the same reason one should not a priori identify the charge of the electron with its radiative corrections.
From this quote, this seems to me to be very much a strawman argument. As Haelfix has already said in an informed post:

Quote Quote by Haelfix View Post
Now the separate confusion is that there is absolutely no problem whatsoever in moving the cosmological constant term from the left side to the right side of the Einstein field equations in general. You can always do that!

That does not change the predictions or physics in any way, in particular whether the term is renormalized or not!
Specifically, the argument that a quantum field theorist who takes the Einstein theory seriously would treat the bare cosmological term as vanishing is incorrect. Rather, one would include the bare term and then field theory background and radiative corrections would lead to the renormalized cosmological term that is observed. The only reason that this is not done more often in practice is the perturbative nonrenormalizabilty of the Einstein theory, which makes such an exercise rather futile for most purposes. Doing QFT in a curved background will not make these problems go away. However, as far as the classical physics of the Einstein equation goes (observational cosmology is insensitive to quantum fluctuations around the vacuum), it makes no difference where the contributions to the cosmological term arise.

The real prejudice at work here is whether or not the Einstein equation should be considered as a fundamental part of the UV physics or whether it is an IR result derivable from more fundamental physics. In the former case, one obviously needs to include a bare cosmological term from the outset. In the latter case, it is not clear that such a bare term even has an objective meaning in the fundamental theory, so the cosmological term might be entirely due to radiative effects. In either case, the proper treatment of the cosmological constant is entirely dependent on the framework and any simplifying assumptions that are being made.
marcus
#59
Nov13-11, 11:32 PM
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You apparently don't quite get it. H. remark is irrelevant to the argument. Of course you can move Lambda to the other side

The main thing is yes the GR equation is IR. B&R even say "(very) low energy". And QFT is completely out of there. They ought to solve their own preposterous ZPE problem. QFT cannot be considered fundamental because it is built on Minkowski space. Its ZPE arises in a complete other regime from Lambda. Read what Liberati et al has to say about the emergence of Lambda. I quoted some in post #34 http://physicsforums.com/showthread....23#post3503823 earlier in this thread.

Here, it will make it clearer if I quote some more Bianchi Rovelli, still page 6, continuing where I left off a couple of posts back:
In other words, it is a mistake to identify the cosmological constant λ with the zero point energy Λ of a QFT, for the same reason one should not a priori identify the charge of the electron with its radiative corrections.

If we get confused about this, we make a funny logical mistake. We have an observed physical phenomenon (the accelerated expansion). A simple physical theory explains it (general relativity with nonvanishing λ). However, particle physics claims that it can provide an independent understanding of the phenomenon (a cosmological term entirely produced by vacuum fluctuation). So we discard the simple explanation. But the new understanding goes wrong quantitatively (by 120 orders of magnitude). Now, every reasonable person would conclude that there is something missing in the particle-physics argument; especially knowing that the argument is already known to be wrong in flat space. But this is not the conclusion that is usually defended. Rather, it is claimed that what is unacceptable, and needs to be changed is the first simple explanation of the phenomenon!

There is no known natural way to derive the tiny cosmological constant that plays a role in cosmology from particle physics. And there is no understanding of why this constant is not renormalized to a high value. But this does not mean that there is something mysterious in the cosmological constant itself: it means that there is something we do not understand yet in particle physics. What could this be?
mitchell porter
#60
Nov13-11, 11:55 PM
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smoit #56, are you saying that for the 10-dimensional SO(16) x SO(16) heterotic string, you can get the observed cosmological constant by assuming a physically reasonable supersymmetry scale? If so, could you then look for a way to compactify six dimensions without adding to the vacuum energy?
marcus
#61
Nov14-11, 12:32 AM
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Quote Quote by mitchell porter View Post
smoit #56, are you saying that for the 10-dimensional SO(16) x SO(16) heterotic string, you can get the observed cosmological constant by assuming a physically reasonable supersymmetry scale? If so, could you then look for a way to compactify six dimensions without adding to the vacuum energy?
Heh heh, yes Smoit. Will you now explain the value of the observed cosmological constant by assuming a 10D string theory?

So far no one has responded to what I quoted from Liberati et al. He is a highly respected QG phenomenologist, not specifically associated with any one approach Loop or other. I quoted from the FLS paper (Finazzi, Liberati, Sindoni) in post #34
http://physicsforums.com/showthread....23#post3503823
Anybody have any direct response to FLS points?

As a reminder, here are excerpts from their conclusions---please go back to #34 to see the full passage:

==quote FLS http://arxiv.org/abs/1103.4841 ==
...The implications for gravity are twofold. First, there could be no a priori reason why the cosmological constant should be computed as the zero-point energy of the system. More properly, its computation must inevitably pass through the derivation of Einstein equations emerging from the underlying microscopic system. ...

... In this respect, it is conceivable that the very notion of cosmological constant as a form of energy intrinsic to the vacuum is ultimately misleading. ... the reasoning of this Letter sheds a totally different light on the cosmological constant problem, turning it from a failure of effective field theory to a question about the emergence of the spacetime.
==endquote==
Fra
#62
Nov14-11, 12:46 AM
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Quote Quote by marcus View Post
There is no known natural way to derive the tiny cosmological constant that plays a role in cosmology from particle physics
...
it means that there is something we do not understand yet in particle physics. What could this be?[/INDENT]
I share this stance.

I'll just want to add that just because there is something we do not yet understand about particles physics (which btw, I think is that QFT formalism simply isn't a ther cosmoloical measurement theory we need due to referencing infinitely massive observers) doesn't exclude there is ALSO sometihng we do not yet understand about gravity.

This seems very much rooted in the konwn issue of observables. I agree with Marcus that to expect a "QFT explanation" of cosmological expansion with QFT as it stands makes not sense IMO. All of QM/QFT is devised as a measurement theory - against a fixed context. This context is either classical reality, or some boundary at infinity where one collects S-matrix data. Of course in classical reality, the background metric is attached to the observer frame. The problem is that all of that makes sense only in special cases. Not in the most general QG domain since all the qualifiers break down.

I think the challange is to find the new framework that extends measurementtheory to cosmological scenarios; first THEN does it make snse to try to see how gravity fits in the corrected picture. This as I see it certainly must included serious reworking on QM&QFT foundations.

/Fredrik
smoit
#63
Nov14-11, 11:14 AM
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Quote Quote by mitchell porter View Post
smoit #56, are you saying that for the 10-dimensional SO(16) x SO(16) heterotic string, you can get the observed cosmological constant by assuming a physically reasonable supersymmetry scale? If so, could you then look for a way to compactify six dimensions without adding to the vacuum energy?
I don't know! Indeed, the value one gets is a mere coincidence since it's a value for the vacuum energy in 10D. Indeed, assuming MSUSY~(TeV)~10-15MPlank and Mstring~MPlanck one gets Str(MSUSY8)Mstring2~10-120MPlanck10.

As I said before in #56, if you want to compute the CC in a realistic compactification you first need to compute the string spectrum in such a background, i.e. a background that reduces to some N=1 D=4 SUGRA with spontaneously broken SUSY, and then compute the partition function. Again, you'll have not only the zero modes (SUGRA modes) but also an infinite tower of stringy modes, both momentum and winding, plus an infinite tower of various KK modes all contributing to the CC. It would be interesting if one could do this even for a simple, say orbifold, compactification. All I was saying was that quoting the SUGRA result where the first non-vanishing supertrace contribution is quadratic in the cutoff means nothing as this is just a computation in an effective 4D QFT, which is missing an infinite number of contributions, which may alter the result completely. The point is that at such short distances the theory effectively becomes 10 dimensional and no longer just a QFT and the CC computation is UV-sensitive so I'm raising a speculation that this may ultimately address the perturbative quantum part of the problem. There may also be various non-perturbative contributions as well as tree-level pieces, and that's what makes the whole problem so tricky.
smoit
#64
Nov14-11, 11:39 AM
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Quote Quote by marcus View Post
In other words, it is a mistake to identify the cosmological constant λ with the zero point energy Λ of a QFT, for the same reason one should not a priori identify the charge of the electron with its radiative corrections
No sane particle theorist makes such an identification, Markus! Read the Polchinski reference and you'll see that nowhere does he identify the cosmological constant only with the zero point energy. On the contrary, as people have repeatedly said here, the CC receives all kinds of tree-level, perturbative and non-perturbative contributions and the observed tiny value includes of all of them.
marcus
#65
Nov14-11, 12:26 PM
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Good, so you agree with Bianchi Rovelli on that point! You quoted part of what they said on page 6 although it looks like you attributed it to me.

They say it is a mistake to identify the cosmo constant with the QFT zero point energy, and you obviously agree since you claim that no sensible particle theorist would confuse the two.

So now we can go on to the next step in their argument, which continues on page 7. They start by pointing out that vacuum energy by itself does not gravitate, only shifts/differences do, not the zeropoint itself. We all know this--I'm sure you agree with the next passage, however simply for completeness I recap:
An effect commonly put forward to support the “reality” of such a vacuum energy is the Casimir effect. But the Casimir effect does not reveal the existence of a vacuum energy: it reveals the effect of a “change” in vacuum energy, and it says nothing about where the zero point value of this energy is. In fact, simple physical arguments indicate that the vacuum energy, by itself, cannot be “real” in the sense of gravitating: if it were, any empty box containing a quantum field would have a huge mass, and we could not move it with a force, since gravitational mass is also inertial mass. On physical grounds, vacuum energy does not gravitate. A shift in vacuum energy does gravitate. This is nicely illustrated by an example discussed by Polchinski in [3]:...
There is the Polchinski reference you mentioned! I am glad to see you are reading ahead, Smoit. Now we come to the next step in their argument. Let's consider it together, maybe you will find a flaw and point it out to me. Now we are on page 7.
Why does standard QFT have so much trouble adjusting to this straightforward physical fact? We do not know the answer, but there is a general consideration that may be
relevant: in which theoretical context is formulated the argument for large radiative corrections to λ? If it is in a context in which we disregard gravity, then a large vacuum energy is physically irrelevant, because the λ term in the action (14) couples only to the gravitational field g, and is invisible if we disregard gravity. The next option is...

...But then there is a catch: if λ is different from zero, then (φ ,η) is not a solution...
And so they go down the list of ways to address QFT's problem. Trying different theoretical contexts. This I think is the heart of their argument. See what you think.
smoit
#66
Nov14-11, 01:36 PM
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Quote Quote by marcus View Post
They say it is a mistake to identify the cosmo constant with the QFT zero point energy, and you obviously agree since you claim that no sensible particle theorist would confuse the two.
What audience are they addressing in their paper? Undegraduates who just had a quantum mechaniscs class and learned about the zero-point energy? What is it that's new in their paper that particle theorists did not know already?

What I and many people have already said here is that apart from the perturbative piece, the CC contains several other types of contributions - tree-level and non-perturbative. Why is this so hard to grasp?
smoit
#67
Nov14-11, 01:58 PM
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Quote Quote by marcus View Post
An effect commonly put forward to support the “reality” of such a vacuum energy is the Casimir effect. But the Casimir effect does not reveal the existence of a vacuum energy: it reveals the effect of a “change” in vacuum energy, and it says nothing about where the zero point value of this energy is. In fact, simple physical arguments indicate that the vacuum energy, by itself, cannot be “real” in the sense of gravitating: if it were, any empty box containing a quantum field would have a huge mass, and we could not move it with a force, since gravitational mass is also inertial mass. On physical grounds, vacuum energy does not gravitate. A shift in vacuum energy does gravitate. This is nicely illustrated by an example discussed by Polchinski in [3]:...
This "simple argument" is obviously flawed since an empty box containing all quantum fields in our vacuum already contains ALL contributions - tree-level and quantum, which all add up to the tiny value. There is no experiment that I'm aware of where one can separate the total tree-level contribution to the CC from the total quantum contribution to the CC. Only if someone could magically switch off the tree-level piece and the mass of the "empty" box would still be tiny, would one be able to claim that the zero-point energy does not contribute much to the inertial mass.

The Casimir effect clearly shows that the quantum contributions, which we can compute and measure do, in fact, gravitate and I definitely agree with Polchinski. Every quantum field contribution produces an upward (for bosons) or downward (for fermions) shift in the vacuum energy. The Casimir effect clearly indicates that such individual quantum contributions do gravitate and once they are all added up the total zero-point energy should still gravitate, unless one has exact supersymmetry and they all precisely cancel.
marcus
#68
Nov14-11, 02:08 PM
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One might say this to a QFT'er. You have a 120 order of magnitude problem in YOUR theory. It is not GR's problem. If you think you can fix it with some of the dodges Smoit mentioned, go for it and good luck to you! So far we don't see it getting fixed by those means, however.

On the other hand if you really want a quantum gravity fix, then be clear about it. You are going to have to move QFT out of the Minkowski context, and you will ultimately have to rebuild QFT on a quantum geometry basis, e.g. LQG.
smoit
#69
Nov14-11, 02:37 PM
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Quote Quote by marcus View Post
So far we don't see it getting fixed by those means, however.
We? Meaning all the retired mathematicians who post on the physics forum?
marcus
#70
Nov14-11, 02:44 PM
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Quote Quote by smoit View Post
We? Meaning all the retired mathematicians who post on the physics forum?
Yes Mr. Smolin-and-Woit and despite a bt of sarcastic snarling and grumbling we and our like are legion.

But in fact when I said "we" I was interpreting from the passage from Bianchi and Rovelli that I quoted in post #65:

"Why does standard QFT have so much trouble adjusting to this straightforward physical fact? We do not know the answer, but ..."
marcus
#71
Nov14-11, 03:02 PM
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Since we are discussing the argument on page 7 of the Bianchi Rovelli paper, I should give the link again:
http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
(Submitted on 21 Feb 2010)
The expansion of the observed universe appears to be accelerating. A simple explanation of this phenomenon is provided by the non-vanishing of the cosmological constant in the Einstein equations. Arguments are commonly presented to the effect that this simple explanation is not viable or not sufficient, and therefore we are facing the "great mystery" of the "nature of a dark energy". We argue that these arguments are unconvincing, or ill-founded.
9 pages, 4 figures

An easy way to get the paper is simply to google "constant prejudices"
The arxiv link should turn up as the first or second hit.
Anyone coming in new would be well-advised to read the paper. It is easy to understand and puts the discussion here in a clearer light.
smoit
#72
Nov14-11, 03:33 PM
P: 72
Quote Quote by marcus View Post
Since we are discussing the argument on page 7 of the Bianchi Rovelli paper, I should give the link again:
http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
(Submitted on 21 Feb 2010)
FYI, after almost 2 years, the authors have so far failed to publish it in a refereed journal.


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