View Full Version : Why all these prejudices against a constant? ("dark energy" is a fake probem)
==sample quote==
It is especially wrong to talk about a mysterious “substance” to denote dark energy. The expression “substance” is inappropriate and misleading. It is like saying that the centrifugal force that pushes out from a merry-go-round is the “effect of a mysterious substance”.
==endquote==
http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
9 pages, 4 figures
(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."
The lambda constant is just a constant that naturally occurs when you write down the most general form of the action. With Einstein it was there already at the start! Not something he put in as an afterthought to make cosmology come out right.
==quote==
In fact, it is not even true that Einstein introduced the
λ term because of cosmology. He knew about this term
in the gravitational equations much earlier than his cos-
mological work. This can be deduced from a footnote
of his 1916 main work on general relativity [9] (the foot-
note is on page 180 of the English version). Einstein
derives the gravitational field equations from a list of
physical requirements. In the footnote, he notices that
the field equations he writes are not the most general pos-
sible ones, because there is another possible term, which
is in fact the cosmological term (the notation “λ” already
appears in this footnote).
The most general low-energy second order action for
the gravitational field, invariant under the relevant sym-
metry (diffeomorphisms) is...
...
which leads to (1). It depends on two constants, the
Newton constant G and the cosmological constant λ, and
there is no physical reason for discarding the second term...
==endquote==
tom.stoer
Mar20-10, 05:28 PM
The cosmological constant becomes a mistery as soon as you do not write it on the left hand = "the gravity" side of the equations
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}
but it you write it on the right hand = "the matter" side.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu} - \Lambda g_{\mu\nu}
In vacuum (with T=0) you still have some kind of "matter" which affects spacetime:
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
If you leave this term on the left hand side, the question where it comes from and why it is there, is still open, but it is not a qustion about matter, dark energy or something like that; it is a question about gravity.
lambda is the coupling to the volume of space-time. It belongs on the left-hand side you can see this from the fact that G does not couple to it. G couples to the energy-momentum.
The question is not why it is there but rather what sets its value. In particular why is it so small? One answer coming from the ERG approach is that there is an infra-red fixed point for which lambda=0. Hence on large scales lambda is small.
lambda is the coupling to the volume of space-time. It belongs on the left-hand side you can see this from the fact that G does not couple to it. G couples to the energy-momentum.
The question is not why it is there but rather what sets its value. In particular why is it so small? One answer coming from the ERG approach is that there is an infra-red fixed point for which lambda=0. Hence on large scales lambda is small.
http://arxiv.org/abs/0910.5167 fig 3, 5 seem to suggest only a UV fixed point?
I think Xu and Horava http://arxiv.org/abs/1003.0009 got a IR fixed point, but not at z=1, which I think is what one would like?
BTW, has the evidence shifted away from AS now that CDT seems to have gone over to Horava? And does that mean that CDT is also problematic, since Horava seemed to have all sorts of problems.
http://arxiv.org/abs/0910.5167 fig 3, 5 seem to suggest only a UV fixed point?
I think Xu and Horava http://arxiv.org/abs/1003.0009 got a IR fixed point, but not at z=1, which I think is what one would like?
BTW, has the evidence shifted away from AS now that CDT seems to have gone over to Horava? And does that mean that CDT is also problematic, since Horava seemed to have all sorts of problems.
The IR fixed point is at the origin in fig 3. As you can see there is a trajectory that goes from the UV fixed point to the IR fixed point. But it would seem odd that we sit exactly on that trajectory.
I don't know what your on about with CDT, AS and Horava. CDT does not violate lorentz (at least not in the way Horava does). CDT uses the Regge action which which is a discrete version of einstein-hilbert. So i don't see why you think there is a connection between CDT and horava? If there is its not obvious.
It belongs on the left-hand side you can see this from the fact that G does not couple to it...
The question is not why it is there but rather what sets its value.
Yes. Just like other constants, why is alpha = 1/137?
Why is the ratio of electron mass to planck mass so small?
I think part of the aim of the paper is to deflate some of the hype surrounding this particular constant.
Not to say it's not interesting though! It would be great to get some handle on why it's that particular size.
The IR fixed point is at the origin in fig 3. As you can see there is a trajectory that goes from the UV fixed point to the IR fixed point. But it would seem odd that we sit exactly on that trajectory.
Is that really a fixed point? Also, if it is, is it's stability such that it would explain the cosmological constant (apparently not, since you say it's odd we'd be exactly on that trajectory)?
I don't know what your on about with CDT, AS and Horava. CDT does not violate lorentz (at least not in the way Horava does). CDT uses the Regge action which which is a discrete version of einstein-hilbert. So i don't see why you think there is a connection between CDT and horava? If there is its not obvious.
I'm thinking of - ?
http://arxiv.org/abs/0911.0401
http://arxiv.org/abs/1002.3298
Is that really a fixed point? Also, if it is, is it's stability such that it would explain the cosmological constant (apparently not, since you say it's odd we'd be exactly on that trajectory)?
I'm thinking of - ?
http://arxiv.org/abs/0911.0401
http://arxiv.org/abs/1002.3298
Hmm well both papers mention AS and horava. I think the CDT guys are hoping that it can be both AS and horava depending how they tune their parameters.
The gaussian fixed point is always going to be there as it just corresponds to the vanishing of the dimensionless couplings. But I don't think you need to be on a trajectory that flows to the IR fixed point. Better to read this paper
http://arXiv.org/abs/hep-th/0410119
"Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant."
The cosmological constant becomes a mistery as soon as you do not write it on the left hand = "the gravity" side of the equations
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}
but it you write it on the right hand = "the matter" side.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu} - \Lambda g_{\mu\nu}
In vacuum (with T=0) you still have some kind of "matter" which affects spacetime:
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
If you leave this term on the left hand side, the question where it comes from and why it is there, is still open, but it is not a qustion about matter, dark energy or something like that; it is a question about gravity.
I'd like to get into the habit of thinking of it on the left hand side.
However I'm used to seeing the constant given in the form OmegaLambda. A common estimate is OmegaLambda = .73
That means the (fictional?) dark energy is 73% of critical density. If I express critical density in terms of today's Hubble rate H, then what I seem to get is that
Lambda = 3 *H^2* OmegaLambda
= 3*0.73* (71 km/s per megaparsec)^2 ~ 10-35 second-2
Can you confirm that this is right way to get the lefthandside Lambda from the information we are usually given?
Finbar posted:
lambda is the coupling to the volume of space-time. It belongs on the left-hand side you can see this from the fact that G does not couple to it. G couples to the energy-momentum.
I REALLY like that thought! What's the origin of these two relationships?? I don't mean I doubt it, but what led to these particular couplings?? Is it of purely mathematical origin or instead physical insights...or a combination??
"The man who had the courage to tell everybody that their ideas on space and time had to
be changed, then did not dare predicting an expanding universe, even if his jewel theory was saying so..." and " Even a total genius can be silly,
at times." .....suggests Einstein did not appreciate the nature of lambda early on.
tom.stoer
Mar27-10, 01:41 PM
I'd like to get into the habit of thinking of it on the left hand side.
...
Can you confirm that this is right way to get the lefthandside Lambda from the information we are usually given?
Yes, I can confirm that this is the way you get OmegaLambda. But your interpretation
That means the (fictional?) dark energy is 73% of critical density.
means that (implicitly) you think about it as something that appears on the right hand side: density, dark energy, ...
Yes, I can confirm that this is the way you get OmegaLambda...
That's not what I was asking about. We are constantly being told that OmegaLambda = 0.73, or thereabouts. We can take that as the current estimate.
What I never (or almost never) see an estimate for is LAMBDA ITSELF. The genuine lefthand side article.
That is what I want to calculate. I think it comes to 1.1 x 10-35 second-2
or thereabouts.
Would it be more correct to express it in units of reciprocal area, like in meter-2?
That's what I think of as a common unit for curvature?
What I want confirmation for, or at least your opinion on, is if we are thinking just of the lefthandside form of the cosmo constant, which we are calling Lambda, and if we are given the commonly published figures of 71 for Hubble, and 0.73 for (fictional?) "dark energy fraction,"
then do we use the stated formula to get Lambda? Namely:
Lambda = 3 *H^2* OmegaLambda
George Jones
Mar27-10, 08:53 PM
Lambda = 3 *H^2* OmegaLambda
Yes.
Lambda = 3 *H^2* OmegaLambda
Yes.
Good. Thank you George. So since I'm always seeing the published figures
71 km/s per megaparsec, and 0.73 (for the Hubble rate and the "darkenergy fraction") I can plug the blue thing into google and get Lambda.
3*0.73*(71 km/s per megaparsec)^2
Anybody can do it themselves. If you paste that blue expression into the google window, what you get is:
1.15946854e-35 s^-2
So that is what Lambda "really is", if you round off appropriately:
Lambda = 1.16 x 10-35 seconds-2
plus or minus whatever uncertainty is contributed by the 0.73 and the 71.
And you can change the numbers 71 and 0.73 to agree with whatever the latest observations indicate, and the google calculator will give you the corresponding estimate for Lambda, accordingly.
If Rovelli is right, and the others that share his views on the subject, then this is a basic constant of nature and we better start getting to know it, and getting used to it, and treating with some of the same respect we normally show basic constants.
Bianchi and Rovelli are not saying anything new, are they? Take eg. this 2007 review
http://arxiv.org/abs/0705.2533
"The observational and theoretical features described above suggests that one should consider cosmological constant as the most natural candidate for dark energy. Though it leads to well known problems, it is also the most economical [just one number] and simplest explanation for all the observations. Once we invoke the cosmological constant, classical gravity will be described by the three constants G, c and Lambda"
tom.stoer
Mar28-10, 02:08 AM
I agree, they are not saying anything new. The stress the following
1) it is natural to consider Lambda as a constant of nature
2) one should distinguish between "QFT is the source of Lambda" and "QFT could cause corrections to the value of Lambda"
3) the reason for the puzzle is not Lambda, but Lambda on the right hand side of the equation ...
4) ... plus an idea how to calculate it - which fails by 120 orders of magnitude
Let's assume I have some biological theory; unfortunately it says not so much about about mammals, birds etc. but I claim that this theory provides an explanation of the zoogenesis of the duckbill from first principles. But applying this theory, it predicts the duckbill to look like an orca ...
Now I ask you: does this make the duckbill even more enigmatic, or does it mean that my theory is plainly wrong?
I guess ultimately, one would seek a deeper understanding of why all constants of nature are what they are, and why the laws are like they are. Maybe alot of the mystery around lambda is due to the fact that it appears to be so closely (although there are certainly the known problems with this) related to the expected zero point energy density that it's hard to resist the temptation that there is something more to this - that may or may not explain the value of this constant that in a deeper way that we probably all seek anyway?
As far as I am concerned, I still seek a deeper understanding of all the E-H action where all terms and constants beg for explanation. My working picture at the moment, makes me think, also in line wit some of the statistical approach to this, is to rather think of Einsteins equations as a equation of state, defining an equilibrium, suggesting that the "constants" might not be proper constants, maybe they just appear constant to us at this moment. So maybe it's not that important what the values are, the most interesting thing is the logic that sets it's value. The actual logic today, is our cosmological models, from hubble expansions we infer the value, but this is a human level mechanism, and it's value would in principle evolve with the evolution of human science cosmology. But we still don't have the depper intrinsic physical mechanism for it's evolution.
But I also think that seeking the answer in the form of hidden or dark matter or energy "out there" that are like ordinary matter, except not visible might be a sidetrack. I think the "appearance" of hidden energy or accelerating universe could be better understood from the information point of view, where one considers expanding and accelerating evnet horizons, rather than expanding universes etc. But that's still very underdeveloped.
/Fredrik
Marcus: again, thanks for bringing another great paper to our attention....
Bianchi and Rovelli are not saying anything new, are they?
That seems right, but I did see some different perspectives (new to me) things in the paper, such as:
An effect commonly put forward to support the reality" of such a vacuum energy is the Casimir e ect. But the Casimir e ect does not reveal the existence of a vac-
uum energy: it reveals the e ect of a \change" in vacuum energy, and it says nothing about where the zero point value of this energy is.
and this regarding the coincidence argument:
In order for us to comfortably exist and observe it, we must be .... in a period of the history of the universe where a civilization like ours could exist. Namely when heavy elements abound, but the universe is not dead yet. ....in a universe with the value of lambda like in our universe, it is quite reasonable that humans exist during those 10 or so billions years when omegab and omega lambdaare within a few orders of magnitude from each other.Not much earlier, when there is nothing like the Earth, not much later when stars like ours will be dying.
FRA
I think the "appearance" of hidden energy or accelerating universe could be better understood from the information point of view, where one considers expanding and accelerating evnet horizons, rather than expanding universes etc
yes!!!!!!!!!!
I also think we are current missing much of what appears as an information based universe.
I guess ultimately, one would seek a deeper understanding of why all constants of nature are what they are, and why the laws are like they are
no guessing..absolutely "yes" :
In gravitational physics there is nothing mysterious in the cosmological constant. At least nothing more mysterious than the Maxwell equations, the Yang-Mills
equations, the Dirac equation, or the Standard Model equations. These equations contain constants whose values we are not able to compute from first principles. The
cosmological constant is in no sense more of a "mystery" than any other among the numerous constants in our fundamental theories
I wish the authors would have instead acknowledged they are ALL equally 'mysterious'..
I wish the authors would have instead acknolwedged they are ALL equally 'mysterious'..
Yes, but one can respond to this in two ways, either
1) stop worrying about the "mysterious lambda"
or
2) START worrying about all mysterious "constants". In the generic sense "constant" could also apply to other things than numbers, for example "constant" symmetries, and thus "physical law" itself. Ie. the fact that it may be "just another constant" doesn't make it less mysterious. Maybe we rather just have more "clues" to this particular constant, than say the gravitational constant or plancks constant?
/Fredrik
START worrying about all mysterious "constants".
makes sense and I think in general scientists do....still strikes me as odd that we don't have the first principles to determine the basics in the standard model...clearly we are missing some "information"....pun intended....
Haelfix
Mar28-10, 12:26 PM
The CC is not a problem for GR (well except that it makes various cosmological solutions a little more ugly), but really a generic quantum problem.
It doesn't matter what side of the field equation you put it on, the problem is the same, namely an unnatural cancelation between two quantities that a priori have nothing to do with one another (read no known physical relation).
In the full quantum theory, we are interested in the expectation value of the stress energy tensor <Tuv>, which in vacuum is proportional to < P > Guv by Lorentz invariance. By inspection of Einsteins field equations, this is equivalent to adding a term to the effective cosmological constant.
lambda effective = lambda + 8piG <P>, where lambda is just the old simple (undetermined classical constant of integration) and <P> is the energy density of the quantum vacuum.
Now (lambda effective/8piG) = Pv ~ 10^-47 Gev^4 by experiment (WMAP say).
The problem is that we know how to calculate <P>, generically it is simply summing up all the normal modes of the zero point energy of some field (or sets of fields), up to some cutoff. If we take the cutoff to be Mpl, <P> will be something like ~10^72 Gev^4
and then you notice that (lambda/8piG + <P>) in order to satisfy experimental bounds, must delicately conspire to cancel to something like 120 decimal places. The problem is that there is no obvious physical reason why lambda/8piG (a quantity arising from a classical equation) should have anything whatsoever to do with <P> (a quantum quantity). Now, if there was an unknown symmetry that related them, you might venture to guess that they could cancel exactly, but no such symmetry is known and worse they dont cancel exactly.
I should point out that you can't get around this miracle trivially. Even if you completely ignore everything from the electroweak scale, all the way down to the Planck scale and instead only consider standard model physics, you would set the cutoff value to something like say the QCD scale, you still have about 40 orders of magnitude worth of decimal places to account for.
Now you are of course free to simply set the constant term equal to the tree level or semiclassical contribution to <P> and set them equal to zero. The problem then is you still have to talk about the shift of the vacuum energy, by higher order terms induced by radiative corrections, and so you have to arrange it so that each constant appearing in front of the counterterms is finetuned order by order, such that the final sum approaches the experimental bound.
It is this, more than anything else, that really is the crux of the problem. The thing we measure in our telescopes is necessarily the full theory (b/c quantum mechanics is part of the real world). And in this quantum theory, nothing protects the vacuum energy from radiative corrections.
An analogous (though much less severe) problem occurs for instance, when you consider the smallness of the Neutrino mass relative to say the Higgs vev. If you naively proceed as above, you see that there is an unnatural cancellation that should take place. Of course there, we are rescued by a mechanism that forces the two terms involved in the cancellation to actually be close (this is called the seesaw mechanism).
Haelfix
Mar28-10, 12:56 PM
Its worth pointing out how Supersymmetry almost solves the problem and how it elucidates the nature of the issue.
Assume that <P> appearing above, was for some reason identically zero, then indeed lambda effective would just be a constant of integration and everyone would be happy. No rhyme or reason why its small or big, or whatever. Who cares, its just a number that experiment happened to find. You could invoke the anthropic principle trivially if you really wanted too at that point and no one would mind.
And indeed, in exact rigid supersymmetry it was noted long ago that fermion loops exactly cancel boson loops and the net vacuum contribution is zero (at least perturbatively).
The problem is, exact supersymmetry is not the way the world works, and it must be broken. When you break rigid supersymmetry in this framework you induce terms that necessarily set <p> != 0 (and if you include gravity and make the susy local, the superpotential and the kahler potential will not in general exactly cancel!) and you are back to worrying about how weird it is for physical cancellations to take place of that magnitude (although now, the problem is cut in two on a log scale and may also be sensitive to exactly where the supersymmetry breaking scale is set)
tom.stoer
Mar28-10, 02:17 PM
Haelfix,
I think you agree with Rovelli, but I am not sure. He does not deny that the smallness of lambda is no problem, but e says that one must distinguish between 1) a small classical (tree level) lambda which stays small even if you calculate quantum corrections and 2) zero classical lambda where the non-zero part is purely quantum mechanical.
So acording to Rovelli the problem is why lambda stays small even if it is subject to quantum corrections, not how quantum corrections create lambda which zero classically.
Compare it to the Higgs mass. It is unclear how the Higgs mass is protected against quantum corrections pushing it to the Planck scale. But these effects (or their absence) seems to have nothing to do whith the creation of teh Higgs mass at all. The same applies to all other parameters in the SM. It is a puzzle where they are coming from, but it is fairly well understood how they behave under quantum corrections (the Higgs mass is an exception).
What you are saying about SUSY is the core of the problem. Zero lambda would be fine, but tiny lambda including quantum corrections from broken SUSY is a riddle. But if you look at all other classical field theories they perfectly make sense w/o quantum corrections in a certain regime. If you restrict yourself to tis regime there is no problem with the constants at all.
Haelfix
Mar28-10, 02:58 PM
I don't quite follow.
The way I read the paper was that it wasn't anything new to the standard story I told above, it just restated it differently.
To simplify the terminology, and with total abuse of notation and disregard for constants, i'll just state the above equation again: Lambda total = lambda classical + lambda quantum. Lambda total is fixed by experiment.
You are free to set lt = lc but then you have to explain why lq is zero (this is what I think he wants us to do). You can set lc = 0 but then you have to explain why lq is however many orders of magnitude different than a qft calculation tells us it should be. Or you can insist that there is some sort of mechanism that relates lc and lq such that they are extremely close and the finetuning becomes natural.
The problem is the same in all three cases, its just basically a relabeling of words what you want to call things.
makes sense and I think in general scientists do....still strikes me as odd that we don't have the first principles to determine the basics in the standard model...clearly we are missing some "information"....pun intended....
I think the intrinsic information view that I seek (rather than the extrinsic blockbased info-picture), is generally not something "most physicists" are at least officially interested in as far as I can judge. Maybe secretly, but alot of the reasoning in some research papers still maintains a somewhat realist view of physical law. I think this is still a realist heritage we are still stuck with.
QM and Relativity did away with some realism, but not all of it. Both are somehow attempts at acknowledging the incompleteness and relativit of nature, without abandoning the incompletness and relativity of physical law. There is an ambigousness there IMO, becase _information about physical law_ are not treated on the same footing as _information about the initial state_ of a system, when it IMO should.
/Fredrik
tom.stoer
Mar29-10, 01:44 AM
The problem is the same in all three cases, its just basically a relabeling of words what you want to call things.
I am not quite sure.
Let's try a different approach: for many constants in nature one expects that they are scale-dependent. If they aren't one has to find a mechanism why they are protected. What we measure are not the bare nor the tree-level values but always the "dressed" values where all quantum corrections are already taken into account.
Now we split the constants in a tree level and a quantum correction part (I do not know if this is really a good idea :-)
I think one can state the problem as follows:
1) if we believe in this classical part + quantum correction part story, then we have to solve the two problems what causes the classical part? and why should it be protected against scaling?
2) if we do not believe in this split, we have to solve the problem what causes the cc at all?.
I think what Rovelli is saying is that it's not clear to him why the mechanism which causes the existence of the cc at all should be the same as the mechanism that causes it's scaling.
(example: we understand the mechanism which scales a mass-term in QFT, but we do not understand where this mass term comes from; if we use the Higgs, again we understand the scaling of the Yukawa-coupling, but we do not understand why it is there at all)
Just one question here: why all this quible here if Marcus himself support assymptotic safety? The small value of the cosmological constant is just a consequence of the non trivial fixed point of G x /\ space due to renormalizable non perturbative nature of the Einstein Hilbert action.
tom.stoer
Mar30-10, 12:32 AM
This means that lambda is a term on the left hand side and is somehow protected against UV corrections. Is would solve the problem for its smallness, not for its existence.
What is the current status of asymptotic safety?
Well, asymptotic safety doesn`t work withou lambda...
Here's an alternative take on the CC problem:
http://arxiv.org/abs/1103.4841
The cosmological constant: a lesson from Bose-Einstein condensates
Stefano Finazzi, Stefano Liberati, Lorenzo Sindoni
(Submitted on 24 Mar 2011)
The cosmological constant is one of the most pressing problems in modern physics. In this Letter, we address the issue of its nature and computation using an analogue gravity standpoint as a toy model for an emergent gravity scenario. Even if it is well known that phonons in some condense matter systems propagate like a quantum field on a curved spacetime, only recently it has been shown that the dynamics of the analogue metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. Here we directly compute this term and confront it with the other energy scales of the system. On the gravity side of the analogy, this model suggests that in emergent gravity scenarios it is natural for the cosmological constant to be much smaller than its naif value computed as the zero-point energy of the emergent effective field theory. The striking outcome of our investigation is that the value of this constant cannot be easily predicted by just looking at the ground state energy of the microscopic system from which spacetime and its dynamics should emerge. A proper computation would require the knowledge of both the full microscopic quantum theory and a detailed understanding about how Einstein equations emerge from such a fundamental theory. In this light, the cosmological constant appears even more a decisive test bench for any quantum/emergent gravity scenario.
5 pages, 1 figures
Nima gives it in http://www.cornell.edu/video/?videoID=909 at 13:57, explains that there is no problem in principle at 15:35, and further explains why the solution is considered fine tuned.
The Finazzi-Liberati-Sindoni (FLS) paper could be something of a game-changer, so I want to back up and reconsider what I was saying. Here is an excerpt from their conclusions:
==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. Second, the energy scale of Λ can be several orders of magnitude smaller than all the other energy scales for the presence of a very small number, nonperturbative in origin, which cannot be computed within the framework of an effective field theory dealing only with the emergent degrees of freedom (i.e. semiclassical gravity).
The model discussed in this Letter shows all this explicitly. Furthermore, it strongly supports a picture where gravity is a collective phenomenon in a pregeometric theory. In fact, the cosmological constant puzzle is elegantly solved in those scenarios. From an emergent gravity approach, the low energy effective action (and its renormalization group flow) is obviously computed within a framework that has nothing to do with quantum field theories in curved spacetime. Indeed, if we interpreted the cosmological constant as a coupling constant controlling some self-interaction of the gravitational field, rather than as a vacuum energy, it would straightforwardly follow that the explanation of its value (and of its properties under renormalization) would naturally sit outside the domain of semiclassical gravity.
For instance, in a group field theory scenario (a generalization to higher dimensions of matrix models for two dimensional quantum gravity [19]), it is transparent that the origin of the gravitational coupling constants has nothing to do with ideas like “vacuum energy” or statements like “energy gravitates”, because energy itself is an emergent concept. Rather, the value of Λ is determined by the microphysics, and, most importantly, by the procedure to approach the continuum semiclassical limit. 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. To date, little is known about the macroscopic regime of models like group field theories, even though some preliminary steps have been recently done [20]. Nonetheless, analogue models elucidate in simple ways what is expected to happen and can suggest how to further develop investigations in quantum gravity models. In this respect, 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==
This is a brief paper (besides references, only 4 pages!) with potentially far-reaching implications, it seems to me. I don't recall our discussing it---any comments?
More reasons to mistrust the "dark energy" interpretation of the cosmological constant (and the touted bafflement about its size) can be found in a review article for the special SIGMA issue on Loop gravity and cosmology, written by Larry Sindoni of AEI Potsdam.
http://arxiv.org/abs/1110.0686
Emergent models for gravity: an overview
L. Sindoni
(Submitted on 4 Oct 2011)
We give a critical overview of various attempts to describe gravity as an emergent phenomenon, starting from examples of condensed matter physics, to arrive to more sophisticated pregeometric models. The common line of thought is to view the graviton as a composite particle/collective mode. However, we will describe many different ways in which this idea is realized in practice.
54 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology".
I tend now to expect this Sindoni review of Emergent Gravity will become a basic well-cited paper, and that the SIGMA special LQG/C issue will constitute the next big Loop gravity book. Many of its chapters have now been posted as arxiv preprints. It's clearly going to be a valuable collection.
Lorenzo Sindoni gave a seminar in December 2008 on Emer. and Analog Grav. that is on video http://pirsa.org/08120049/.
Stefano Liberati at SISSA was his advisor, PhD in 2009 if I remember right.
bill alsept
Nov6-11, 07:48 PM
Marcus, I believe I'm interested in the subject of your last three postings but it’s a little beyond me. Do you have the patience to explain it one more time in a simpler way? Thanks
Bill,
I can try to help but I don't know very much about the things Sindoni talks about in his Review paper on Emergent Gravity. Also I don't know much about what is covered in the Finazzi Liberati Sindoni paper. I'm impressed, but it's new stuff to me.
Sindoni http://arxiv.org/abs/1110.0686
FLS http://arxiv.org/abs/1103.4841
I come at this from the perspective of the paper mentioned in the initial post of this thread:
Bianchi Rovelli "Why all these prejudices...?" http://arxiv.org/abs/1002.3966
That, by contrast, is an easy paper to read, very down to earth---you could start there.
They basically say that Lambda (a small constant curvature---or reciprocal area constant) belongs naturally in the Einstein GR equation on the lefthand side because it is allowed by the symmetry of the theory--covariance.
There is no need to think of it as an energy. No need to drag it over the the righthand side where the energy and matter terms are.
No need to get it confused with the QFT Vacuum Energy. That is QFT's problem, they calculate something in a fixed flat geometry context (quite alien to GR) and it comes out ridiculously wrong. So they should deal with it.
Lambda on the lefthandside of the GR equation is a tiny constant curvature determined observationally.
"Dark energy" is a phony idea. "Dark energy problem" is hype. Case closed. So that's simple enough.
Tom Stoer has a good discussion at the beginning of the thread.
Now what you express interest in here is different. I was talking about two new papers that I don't understand and wish someone here would explain to me. THEY PRESENT AN IDEA OF HOW GR COULD EMERGE FROM SOMETHING DEEPER (pre-geometry?) and even HOW LAMBDA MIGHT COME TO BE what it is.
So one thing they do is strengthen the case that we should not think of Lambda as some kind of "dark energy" field. And they say this explicitly. It is a feature that emerges along with the rest of GR, in their scheme, from some more fundamental degrees of freedom.
Today I have been spending time offline trying to read the Sindoni paper. I am woefully unprepared to explain it, or help you.
Same with the Finazzi Liberati Sindoni (FLS). I was struggling with that yesterday. I guess I should get back to it now.
bill alsept
Nov6-11, 09:30 PM
Thanks Marcus I appreciate any help. It is the two papers that interest me. I think I’ll try reading through them a few more times.
Me too, maybe we can help each other out.
There are other papers in this cluster, by Sindoni et al, that appeared earlier this year. They may help us understand.
PatrickPowers
Nov7-11, 07:01 AM
I have read that Albert Einstein declared his introduction of the the cosmological constant greatest blunder of his life.
I have read that Albert Einstein declared his introduction of the the cosmological constant greatest blunder of his life.
Patrick,
there's a subtle point here that is significant but often missed. A very readable discussion, that does not short-cut the facts, is on page 2 of the "Why all these prejudices...?" paper http://arxiv.org/abs/1002.3966:
You might be interested in having a look at the halfpage of discussion leading up to this conclusion, which I quote.
Einstein had in his hands a theory that predicted the cosmic expansion (or contraction) without cosmological constant, with a generic value of the cosmological constant, and even, because of the instability, with a fine-tuned value of the cosmological constant. But he nevertheless chose to believe in the fine-tuned value, goofed-out on the instability, and wrote a paper claiming that his equations were compatible with a static universe! These are facts. No surprise that later he referred to all this as his “greatest blunder”: he had a spectacular prediction in his notebook and contrived his own theory to the point of making a mistake about stability, just to avoid making ... a correct prediction! Even a total genius can be silly, at times.
Why is this relevant for the debate about the cosmological constant? Because short-cutting this story into reporting that Einstein added the cosmological term and then declared this his “greatest blunder” is to charge the cosmological term with a negative judgment that Einstein certainly never meant.
In fact, it may not even be true that Einstein introduced the λ term because of cosmology. He probably knew about this term in the gravitational equations much earlier than his cosmological work. This can be deduced from a footnote of his 1916 main work on general relativity [9] (the footnote is on page 180 of the English version). Einstein derives the gravitational field equations from a list of physical requirements. In the footnote, he notices that the field equations he writes are not the most general possible ones, because there are other possible terms. The cosmological term is one of these (the notation “λ” already appears in this footnote)...
"Dark energy" is a phony idea. "Dark energy problem" is hype. Case closed. So that's simple enough.
"No need to get it confused with the QFT Vacuum Energy. That is QFT's problem, they calculate something in a fixed flat geometry context (quite alien to GR) and it comes out ridiculously wrong. So they should deal with it."
I apologize, but this is ridiculous and completely missing the point. It does not suffice to invent a new theory of quantum gravity, and explain why the contributions to the cosmological constant are smaller then expected at that energy scale. There are hundreds of papers out there with ideas like that, the analog gravity paper is no exception, and the reason none of them has convinced anybody, is because they are only answering the first step in what is a much bigger universality problem.
The real problem is that we know experimentally that at least certain quantum contributions at our normal energy scales do in fact gravitate. Every time you step on a scale, approximately 90% of your weight lies in this magic (I am of course talking about virtual gluon contributions to the mass of nucleons). If this did not gravitate, it would instantly show up in violent departures from the equivalence principle.
Now, let us for simplicity restrict to a world which only includes gravity and QED, since we know a lot about the latter up to at least energy scales of 100 GEV where it is very precisely described by an effective field theory that is weakly coupled, and pointlike.
Now I can't draw it here, but there is a diagram that contributes to the famous Lamb shift, but this time weakly coupled to gravity (so it looks like a tadpole). If we take the cutoff scale as 100GEV, the vacuum energy of this diagram's contribution to the ZPE of the electron is still approximately 10^55 larger than experiment. So, the statement of the problem is now the following:
Why does *this* contribution to the zero point energy of the electron in vacuum vanish (or is tuned or is cancelled by some unknown mechanism) but the analogous diagram, in the environment of atoms that represents the shift in the atomic mass arising from ZPE fluctuations does not (and very accurately gravitates by tests of the equivalence principle).
Now, it gets worse... If you think you have an answer to the above problem, you have to explain another puzzle. Why does the vacuum contributions vanish in the real world (with a mix of complicated matter fields all contributing in various ways), but not in the far more symmetric electroweak vacuum state arising from SU(2)*U(1)? It cannot vanish in both, since the mass of the electron vanishes in the unbroken phase and it is precisely this mass which contributes to both subleading contributions to the aforementioned electron ZPE (some ~10^53 too large) as well as to the classical value of the Higgs potential (its really top quark loops that dominate here, but the electron also does contribute).
The point being, you cannot answer the question by simply begging the question like Rovelli does. Everyone agrees that if you could actually SHOW explicitly that the ZPE vanishes, then you have at least partially solved the problem, but then he doesn't, which is why it is a complete nonanswer.
Anyway, you can be sure that the answer to this puzzle sends whoever solves it straight to Stockholm. So I assure you, it is not 'hype'! Instead it is a problem that has to have a solution, and its just the case that no one has figured one out yet b/c it is very difficult.
(Addendum: If someone do not understand what I am writing above, or the exact details it is probably best to start at the beginning with a classical review paper at least stating the problem clearly)
For cosmologists, Sean Carrol has written a fairly elementary treatment here:
http://relativity.livingreviews.org/Articles/lrr-2001-1/
as well as his CERN course video (highly recommended):
http://www.youtube.com/watch?feature=player_embedded&v=cYVj2RhXxeU
Once you have understood and digested the above, the more theoretically rigorous review is given by Weinberg's classic paper
http://www-itp.particle.uni-karlsruhe.de/~sahlmann/gr+c_seminarII/pdfs/T3.pdf
It looks to me as if Haelfix is just saying stuff that is irrelevant but obvious, stuff everybody knows that does not connect with topic. Earlier I quoted the FLS paper in hope someone might comment. No FLS-relevant comment so far. The Finazzi-Liberati-Sindoni (FLS) paper could be something of a game-changer, so I want to back up and reconsider what I was saying. Here is an excerpt from their conclusions...
==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. Second, the energy scale of Λ can be several orders of magnitude smaller than all the other energy scales for the presence of a very small number, nonperturbative in origin, which cannot be computed within the framework of an effective field theory dealing only with the emergent degrees of freedom (i.e. semiclassical gravity).
The model discussed in this Letter shows all this explicitly. Furthermore, it strongly supports a picture where gravity is a collective phenomenon in a pregeometric theory. In fact, the cosmological constant puzzle is elegantly solved in those scenarios. From an emergent gravity approach, the low energy effective action (and its renormalization group flow) is obviously computed within a framework that has nothing to do with quantum field theories in curved spacetime. Indeed, if we interpreted the cosmological constant as a coupling constant controlling some self-interaction of the gravitational field, rather than as a vacuum energy, it would straightforwardly follow that the explanation of its value (and of its properties under renormalization) would naturally sit outside the domain of semiclassical gravity.
For instance, in a group field theory scenario (a generalization to higher dimensions of matrix models for two dimensional quantum gravity [19]), it is transparent that the origin of the gravitational coupling constants has nothing to do with ideas like “vacuum energy” or statements like “energy gravitates”, because energy itself is an emergent concept. Rather, the value of Λ is determined by the microphysics, and, most importantly, by the procedure to approach the continuum semiclassical limit. 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. To date, little is known about the macroscopic regime of models like group field theories, even though some preliminary steps have been recently done [20]. Nonetheless, analogue models elucidate in simple ways what is expected to happen and can suggest how to further develop investigations in quantum gravity models. In this respect, 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==
To throw in an another stick, I pondered about and inferencial interpreration of the cosmological constant in this in this old thread http://www.physicsforums.com/showthread.php?t=239414 with the purpose of stimulating some thinking
Of course my arguement appeals to general forms of any action, that is understood as -log P where P is a transition probability.
I just compared the FORM of the E-H action, with the FORM of an action I get from a particular construction.
The conclusion is that a kind of integrated "cosmological constant term" appears generically in any action of that form, and it's interpreted as having to do with the observers truncation of confidence. If the maximum probability was 100% then the cosmological constant should approach zero. When the maximum probability is large but finite, due to limited inferrability capacity of the finite obsever, the terms is bound to be non-zero - but finite.
This is not very specific, but it illustrates a alterantive logic, that MIGHT be able to work out specifically.
I think to connect this to the specifici cosmo constant in 4D spacetime, one needs to construct spacetime by inference from the microsctructure of information. Where dimensionality is bound to be emergen as well, perhaps a little bit like a truncated principal component analysis for dimensional regulation, where the truncation is forced upon the inference due to the observers incompleteness.
Then to the point is that all QFT thinking, seems to picture the observer at infinite or in some background - which then effectively has infinite mass - thus the cosmo constant "should be zero" if they only could find out how to cancel the summation properly... but tis perspective fails for gravity, when the observer is inside, so it seems reasonable that the cosmo constant that's effectiuvely inferred by earht based cosmo observations are not expected to be zero. Here the "massive background" does not exist. I think this is at least conceptually related to this issue.
But to get from here to explicit solutions seems hard indeed since it involves the entire chain of complexities, such as mass generation, theory scaling and evolution etc.
/Fredrik
Some readers may have overlooked the points in the Finazzi Liberati Sindoni paper that I'm asking for comment on, so I will boil down and highlight
==quote FLS http://arxiv.org/abs/1103.4841 ==
... 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.
... it strongly supports a picture where gravity is a collective phenomenon in a pregeometric theory. In fact, the cosmological constant puzzle is elegantly solved in those scenarios. From an emergent gravity approach, the low energy effective action (and its renormalization group flow) is obviously computed within a framework that has nothing to do with quantum field theories in curved spacetime. Indeed, if we interpreted the cosmological constant as a coupling constant controlling some self-interaction of the gravitational field, rather than as a vacuum energy, it would straightforwardly follow that the explanation of its value (and of its properties under renormalization) would naturally sit outside the domain of semiclassical gravity.
For instance, in a group field theory scenario (a generalization to higher dimensions of matrix models for two dimensional quantum gravity [19]), it is transparent that the origin of the gravitational coupling constants has nothing to do with ideas like “vacuum energy” or statements like “energy gravitates”, because energy itself is an emergent concept. Rather, the value of Λ is determined by the microphysics, and, most importantly, by the procedure to approach the continuum semiclassical limit. 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. .... In this respect, 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==
Since we are considering a matter of critical judgment here, I might mention that Liberati has well over 3000 citations
http://inspirehep.net/search?ln=en&rm=citation&jrec=1&p=a+Liberati
The guy is a world-class cosmologist/phenomenologist. Still fairly young (40-year-old) and turning out top-cited papers.
His PhD adviser was Dennis Sciama, if the name means anything to you.
In case anyone might be confused about this, Liberati is not part of the Loop QG community. He has never attended the biannual Loops conference. He's more the outsider phenomenologist type---long-time interest in cosmological/astrophysical tests.
No Fra, the FLS paper is not "Rovelli-style" :biggrin:
I didn't read the paper to see what they mean but in my thinking the "cosmological term" in the general action I associated it when it comes to specifically 4D spacetime, can only be understood beyond the "just another parameter" level if we also understand how 4D spacetime emerges, because that is what would somehow factor out that term.
Probably the differences lies in what is meant by emergence. Each time before when I've read Rovelli style papers it was clear that there are different meanings of the concept. I don't believe in any fundamental DOFs. The alterantive concept of emergence is just interacting effective theories, since there is no master theory (since in my view theory attaches to observer machinery), there are no fundamental DOFs. The task thus becomes how to even make something constructure without referring to fundamental DOFs.
The difference for emergence would be in like "emergence FROM something else", or "emergence in terms of just evolution relative to the prior state" where there are no fixed background context at all.
This is even the constructing principle behind the association in my old post. The idea is that the possible future can only be rated in terms of an action measure in terms of a specific reduced time history. This is why P_max < 1, and thus us why the normally unbounded information divergence IS bounded in this case. And this was also the keys that allows the expectation that the term is small, but strictly non-zero as inferred by a finite observer.
So maybe if we focus on the "emergence of spacetime" the cosmo constant problem will be solved automatically, if done the right way. IMO the emergence of spacetime, is an inference, and it's hosted by an observer. Ie. an extension of the essence that Smolin et all mention in the relative locality idea that spacetime is simply a result of an inference from actual data! Now that data needs to be stored and processed by something with finite capacity. This is where alot of things are missing....
/Fredrik
Bianchi and Rovelli are not saying anything new, are they? Take eg. this 2007 review
http://arxiv.org/abs/0705.2533
"The observational and theoretical features described above suggests that one should consider cosmological constant as the most natural candidate for dark energy. Though it leads to well known problems, it is also the most economical [just one number] and simplest explanation for all the observations. Once we invoke the cosmological constant, classical gravity will be described by the three constants G, c and Lambda"
Thanks for pointing that out! I think you are right. It has been a fairly commonplace view among cosmologists all along. That is, Lambda is not some kind of exotic energy field with possibly varying density and equation of state parameters.
For a while after 1998 people naturally wanted to make sure that they were right---no variation was observed, so there is increasing confidence in the standard Lamda-CDM cosmic model (which treats Lambda as a constant curvature built into spacetime.)
So I don't see that Bianchi Rovelli are saying anything new. They are just puncturing a bubble of hype. Pointing out that the "dark energy" Emperor is walking down the street buck naked :biggrin:
What I do see as new is what Liberati et al are saying. They look deeper into the quantum origin of this classical curvature constant. Why, when spacetime emerges from pregeometry d.o.f., does it emerge with this curvature?
They illustrate with a "what-if" group field theory (GFT) example.
BTW Atyy in a sense you chose the perfect example (that 2007 review) to point out that Bianchi Rovelli's message is mainstream. It was an invited review for a special issue of GRG edited by Herman Nicolai, Roy Maartens, and George Ellis---than which there is no whicher :biggrin:
Does anyone here doubt that quantum vacuum energy exists?
Does anyone here doubt that quantum vacuum energy exists?
Of course not! :rofl: How about this: read the Bianchi Rovelli paper. They discuss quantum vacuum energy at length, and the difficulties with calculating it accurately.
But by all means read the paper. Anyone who wants to join in the discussion should. It is a fairly non-technical easy read.
I already gave the link. But I will again:
http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
9 pages, 4 figures
(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."
There is also a short (4-page) paper by Stefano Liberati et al, which is both relevant and fascinating. It considers where that Lambda constant in classical spacetime geometry might be coming from in an emergent spacetime picture. Classically Lambda is a curvature naturally occurring on the lefthand side of the Einstein field equation, whose value is measured to be about
1.16 x 10-35 second-2
You might want to take a look at the final page of the Liberati paper where they state their conclusions:
http://arxiv.org/abs/1103.4841
The cosmological constant: a lesson from Bose-Einstein condensates
Stefano Finazzi, Stefano Liberati, Lorenzo Sindoni
(Submitted on 24 Mar 2011)
...Here we directly compute this term and confront it with the other energy scales of the system. On the gravity side of the analogy, this model suggests that in emergent gravity scenarios it is natural for the cosmological constant to be much smaller than its naif value computed as the zero-point energy of the emergent effective field theory. The striking outcome of our investigation is that the value of this constant cannot be easily predicted by just looking at the ground state energy of the microscopic system from which spacetime and its dynamics should emerge. A proper computation would require the knowledge of both the full microscopic quantum theory and a detailed understanding about how Einstein equations emerge from such a fundamental theory. In this light, the cosmological constant appears even more a decisive test bench for any quantum/emergent gravity scenario.
=============================
The tendency in observational cosmology in recent years has been to confirm and accept that Lambda is in fact simply a constant and not necessarily connected with the naive QFT calculation of vacuum energy (which is after all based on a non-quantum static flat Minkowski geometry.) To some extent this is a matter of one's background and opinions---I'm not talking about diehard QFT-ers, this is the trend I see in observational cosmology. Here are some illustrative links:
Here is one I found by Paolo Serra et al (2009)
http://arxiv.org/abs/0908.3186
No Evidence for Dark Energy Dynamics from a Global Analysis of Cosmological Data
Paolo Serra (UC Irvine), Asantha Cooray (UC Irvine), Daniel E. Holz (Los Alamos National Laboratory), Alessandro Melchiorri (University of Rome), Stefania Pandolfi (University of Rome), Devdeep Sarkar (UC Irvine, University of Michigan)
Physical Review D
From the Serra et al conclusions [their italics :biggrin:]:
"We find no evidence for a temporal evolution of dark energy—the data is completely consistent with a cosmological constant. This agrees with most previous results, but significantly improves the overall constraints [13, 14, 19, 20]."
Here is another by Tamara Davis et al (2007)
http://inspirehep.net/record/742618
Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes
Astrophysical Journal
One by Wood-Vasey et al (2007)
http://inspirehep.net/record/741585?ln=en
Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
Astrophysical Journal
There is also the "WMAP7" report of Komatsu et al. which appeared in 2010.
This was part of a NASA series of papers presenting the full 7-year data from the WMAP mission.
Here is the link. http://arxiv.org/abs/1001.4538
Page 24 has some constraints on the equation of state number w which in case Lambda is simply a constant would be exactly w = -1. Indeed that is about what you get combining latest WMAP+BAO+SN data. (The high-z supernova data SN is the most effective at constraining w. The BAO data is based on galaxy counts and is also good---they combined all the best.)
For example on page 24 in section 5.1 you see:
"The high-z supernova data provide the most stringent limit on w. Using WMAP+BAO+SN, we find w = −0.980±0.053 (68% CL)..."
That is really really close to -1. As time goes on the constraints seem to tighten and I hear less and less about Lambda considered as an actual "energy". We may be getting closer to accepting it simply as a small constant amount of curvature.
The tendency in observational cosmology in recent years has been to confirm and accept that Lambda is in fact simply a constant and not necessarily connected with the naive QFT calculation of vacuum energy (which is after all based on a non-quantum static flat Minkowski geometry.) To some extent this is a matter of one's background and opinions---I'm not talking about diehard QFT-ers, this is the trend I see in observational cosmology. Here are some illustrative links:
That is really really close to -1. As time goes on the constraints seem to tighten and I hear less and less about Lambda considered as an actual "energy". We may be getting closer to accepting it simply as a small constant amount of curvature.
Hi Marcus, you are mixing up two things here. W = -1 is very much what the simple QFT prescription is about. It is interpreted as arising from a cosmological constant, with units of energy density (g/cm^3). You are also free to think of it as a sort of negative pressure in the context of the FRW lambda dust solution.
What you are confusing this with is the case for w < -1, which is what is commonly known as quintessence (which is a scalar field that mimics the observed cosmological constant in our epoch and introduces an explicit time dependence). That latter involves very exotic physics, and is decidedly NOT predicted by the standard QFT calculation..
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!
So consider an empty box and physics that contains a huge positive cosmological constant term. You can think of weighing the box if you put it on a scale, or alternatively you can think of the geometry that this induces (an expansion scalefactor term that looks like A(t) ~ E^(Ht)) but the problem of having a quantum vacuum density 10^120 orders of magnitude too big is still wrong on physical grounds, no matter what side of the original field equations you put it on in order to solve the equation. An empty box solution simply does not weigh that much, and it does not induce curvature of that magnitude in the real world!
What saves the prediction (but also what defines the problem) is that the quantum vacuum is not the only contribution to the total cosmological constant, we are instructed to cancel it with a classical contribution. This latter is typically arbitrary, and we are thus left with the finetuning problem. Why does 2 apparently different physical quantities, cancel to fantastic accuracy?
So this is the problem! It is not that we have a theory that gives a wrong prediction. We can make our theories give the right value. The problem is that this value is wildly different then what you might consider natural!
One possible resolution is to just say that the quantum ZPE sums to identically zero in a more refined theory. And that is FINE and of course would partially solve the problem! For instance with exact supersymmetry you can show that this is indeed what happens!
However, the solution MUST exist at all scales, not just up at the Planck scale. And so the solution must be transparent within the low energy physics based formalism defined up to 100 GEV. So for instance in the context of supersymmetry, one can see explicitly that the thing that cancels the electron tadpole diagrams, is the analogous selectron diagrams!
So the point is you have to actually SHOW this mechanism explicitly.
To give an analogy it would be like arguing for the clay millenium prize regarding QCD. You can't simply say, 'well we don't observe free quarks in nature, therefore QCD is confining -QED'. The whole point is in *showing* this, mathematically!
mitchell porter
Nov10-11, 12:17 AM
It is not that we have a theory that gives a wrong prediction. We can make our theories give the right value.
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.
I can see two ways around this.
First, you say that there is an objective cutoff, due to new physics. This approach has two further subdivisions, a philosophical approach and a concrete approach.
The philosophical approach applies when you don't know what this objective cutoff is, or what the objective vacuum energy is, so you can't say what the actual value of your finetuned cosmological constant is supposed to be; but you just suppose that its value is such as to cancel whatever the objective vacuum energy is.
The concrete approach would apply if you had a theory which intrinsically exhibits a concrete cutoff, e.g. an energy above which ordinary QFT no longer applies. This implies that you have a quantitative framework in which there is a known objective vacuum energy, and in which you can visibly finetune the cosmological constant to a specific value in order to cancel the objective vacuum energy.
The other primary option would be to work with renormalization somehow. In other words, the vacuum energy is treated as "infinity", the cosmological constant as "finite constant - infinity", and all calculations are performed in a framework where you always actually use a cutoff (and get a resulting dark energy equal to "finite constant"), but this is also a framework where you can show mathematically that the cancellation works at any energy scale.
This "renormalization approach" is sort of halfway between what I called, above, the philosophical approach and the concrete approach. And as I understand it, it resembles how the vacuum energy cancellations for exact supersymmetry work, except that there's no nonzero finite constant left over.
I think AdS/CFT must provide examples of a framework in which the "renormalization approach" applies, because in any given instance of the duality, the bulk space (the AdS space) has a known, nonarbitrary, nonzero cosmological constant, and yet everything fits into the framework of QFT (on the CFT side of the duality). So it would be of interest to understand how AdS/CFT deals with vacuum energy in the bulk, on the way to obtaining a negative cosmological constant.
edit: See this paper (http://arxiv.org/abs/1106.3556) (and talk (http://www.physics.ntua.gr/corfu2011/Talks/kyriakos_papadodimas@cern_ch_03.pdf)).
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.
I can see two ways around this.
If the cutoff is physically motivated, rather than just seen as an arbitrary energy scale, maybe no way around it is needed.
All we need to answer to our earthbased inferences. And I think it's quite fair to say that any earth based observation is necessarily cutoff, at least by the order of ~ m_{earth} c^2. We've have to consume the earth to even make sense out of higher energy probing - which brings me to the point - apart from the issue of BH formation, we could have to use all our own memory and information in that measurement, but then there is no place to encode the feedback. So there has to be a balance.
This may seem like a silly point, but who knows if an "electron would agree on the size of lambda"? I am not so sure about that. Maybe the fact that two observing systmems does NOT agree upon lambda, explains some other interactions taking place in theory space (which then also have a cutoff). Ie. ANY theory has a cutoff originating from the complexity of the encoding system.
Isn't that a third option here? The only tihnk I can imagine is that this _might_ fit vaugely into some of the string dualities and landscape evolutions?
/Fredrik
Let's be clear as to the main issues in this thread. Here is how the Bianchi Rovelli paper lays them out in introduction:
==quote 1002.3966 page 1==
...What we say here does not mean that there is no interest in exploring theoretical explanations of the acceleration alternative to the ΛCDM model. Good science demands us to be a priori skeptical of any theory, even when it works well, and always explore alternatives. Even less are our observations criticisms to the observational work aiming at testing the ΛCDM scenario. Exploring alternative theoretical explanations, and pushing the empirical test of all the theories we have, is obviously good science.
But what we say does mean that it is misleading to talk about “a mystery” (not to mention “the greatest mystery of humanity”), for a phenomenon that has a current simple and well-understood explanation within current physical theories. It is especially wrong to talk about a mysterious “substance” to denote dark energy. The expression “substance” is inappropriate and misleading. It is like saying that the centrifugal force that pushes out from a merry-go-round is the “effect of a mysterious substance”.
There are three stories (of very different kind) that are routinely told in presenting the difficulties of the cosmological constant scenario. These are:
i. The alleged historical rejection of the cosmological constant by Einstein, and then by the general-relativity community.
ii. The coincidence problem.
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.
We believe that there is confusion, either historical or conceptual, in each one of these three stories, as commonly presented, and we discuss them below.
There is probably nothing very original in this note. The points we make here can be heard in discussions among physicists. However, for some reason they do not have much space in the dark-energy literature. We though it appropriate to make them available in writing.
==endquote==
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.
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.
FWIW, here is my as always oddball perspective:
I did read the paper and some key questions is where the raise this:
Does this large energy exist for real? That is, does it have observable eects? In particular: does it act as a source for the gravitational eld, as all forms of energy are known to do? Does it have a gravitational mass (and therefore an inertial mass)?
...
In fact, simple physical arguments indicate that the vacuum energy, by itself, cannot be \real" in the sense of gravitating: if it did, any empty box containing a quantum eld 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.
I see a confusion and/or debate about the "nature" of the zero point energy.
Ie. is it a property of the observED system or a property of the observING system?
The confusion is there only if you think that the zero point energy is a proprety of the observED system. But this is IMO the same mistake as when people thinkg that the collapse fundamentally applies to the observED system rather than to the observING systems state.
If one for a second acknowledges that zero point energy is merely an EXPECTATION the observING system has on the observED system, it seems reasonable to attribute that huge about of INFORMATION (read the large zero point energy) to the environtment of hte observED system, not the system itsel, becaues that's where it's ENCODED, and it's this CODE that has inertia (at least in my addmittedly odd view).
Ie. it's the INTERTIA of the environment that should be HUGE - and indeed it IS! In fact in the observable = scattering matrix picture it's infinite. But my point always was this makes no sense, unless you actually HAVE infinitely massive observers; which you don't.
So I think the observable effects of this would - in principle that is (it's not yet worked out) - is not huge inertia of the empty box of quantum fields; it's the inertia of the observING systems that encodfes the expectations; and in principle I'm sure TWO such internacting observING systems should exhibit a gravitational attraction. Or at least that is the conceptually the principle idea behind the interacting observers - the INERTIA is attributed to the inertia of information updates! and these are not attributes of the observed systems, but rather of observers.
So the universality of "gravity" relies in my hypothesis that ANY two communicating information processing systems, are facing an attracing in terms of a drive to decrease their information divergence. (The technical challanges is still certainly to work this out; in particular to work out explicittly the known 4D metrics and their dynamical equations from the deeper more abstraction information measures)
In particular does it make no sense to consider gravitationa between two infinitely massive systems. This is IMO the main conceptual reason why I think that QFT as the theory of inference as it stands will never quite merge with gravity without ending up with other pathologies.Because QFT, as it's constructued relies on an infinitely massive observer. This is of course realted to, but a distinct point, to the asymptotical backgrounds.
All this would mean "foundational rework" of QFT indeed. But it would ALSO mean fundamental rework of gravity. Classical GR actions or classical geometry can't be in the starting points.
In particular does these ideas mean that I think the IDEA that the effective theory bound by some energy, is constructed by AVERAGING or integrating out the high energy modes are flawed logic as I see it.
/Fredrik
Haelfix
Nov12-11, 06:05 AM
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)..
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.
To remind folks of the logical context in which the discussion here takes place.
...
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. :biggrin: You will get the arxiv link on first or second hit.
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:
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.
You apparently don't quite get it. H. remark is irrelevant to the argument. Of course you can move Lambda to the other side :biggrin:
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.php?p=3503823#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
Nov13-11, 11:55 PM
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?
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.php?p=3503823#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==
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 #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.
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.
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. :biggrin: 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.
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?
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.
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. :smile:
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?
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. :biggrin:
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 ..."
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" :wink:
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.
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.
The Casimir effect clearly shows that the quantum contributions, which we can compute and measure do, in fact, gravitate
But we can't verify the coupling of gravity directly to the individual loops involved in these quantum contributions.
But we can't verify the coupling of gravity directly to the individual loops involved in these quantum contributions.
The shift in the electrostatic energy due to vacuum polarization (experimentally measured in the Lamb shift) contributes an amount large enough that, in case if it did not gravitate, would violate the equivalence principle to a precision of one part in a million. However, we can experimentally verify the equivalence principle to a precision of one part in 1012 and therefore these loops must couple to gravity.
The shift in the electrostatic energy due to vacuum polarization (experimentally measured in the Lamb shift) contributes an amount large enough that, in case if it did not gravitate, would violate the equivalence principle to a precision of one part in a million. However, we can experimentally verify the equivalence principle to a precision of one part in 1012 and therefore these loops must couple to gravity.
I'm not sure if you refer to some new experiments I'm unaware of but I think it's still important to note which domains to theory space where certain "principles" are tested. Ingoring that is one of the things I find most disturbing, extrapolations of "evidence" into new domains are often made without much argument. This is exactly what people also do with things that are well tested for PARTICLE physics which usually means the observer is in a classical laboratory and the system is a very small subsystem. Inferences from such situations just don't generalize to cosmological scenarios. This fact is often ignored on grounds that "such extrapolations worked in the past".
I suspect the 10^12 test you refer to is the classical mechanics test of the torsion pendulum, right?
If there really experiments made that verifies the equivalence principle for actual lamb shift, that would be news for me. I think it's in principle testable, but the problem is as far a I know that the gravitational field on earth is too weak to yield much of a significant possibility to test it here?
But I do not follow all new experiemtns, if someone konws of an actual test of the equivalence principle for lamb shifted systems I would be interested to read about how the experiment was conducted. I have seen some old papers where it was "in principle testable" was devicded, but the conclusion was that in practice it wasn't becaues hte gravity on earth is so weak.
I'm not sure if some astronomic observations of lambshifted systems near more massive bodies is possible? I'm not sure how that would be done.
/Fredrik
@Fra, Here is a reference that is the most referred in the literature but you'd have to go to your library to actually read it: http://slac.stanford.edu/spires/find/hep/www?irn=6818293
Please, read very carefully what I said in my previous comment b/c your response indicated that you had misunderstood it.
The shift in the electrostatic energy due to vacuum polarization (experimentally measured in the Lamb shift) contributes an amount large enough that, in case if it did not gravitate, would violate the equivalence principle to a precision of one part in a million. However, we can experimentally verify the equivalence principle to a precision of one part in 1012 and therefore these loops must couple to gravity.
I looked at Polchinski's paper and understand now why you're right. Thanks.
@Harv, no problem! Joe's article is good and pretty much sums up the current situation. I saw his talk on this topic at KITP back in 2006, you can find it here if you're curious: http://online.itp.ucsb.edu/online/strings_c06/polchinski/
Haelfix
Nov16-11, 07:01 AM
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.
Yea tis true, thats why I qualified my statement. For the nonexperts, what this means in practise is that you need to know all the fields and matter all the way up to the Planck scale, as they will all contribute (naively increasing in magnitude, not necessarily in sign) contributions to the total constant. You can't ignore them. This is also why no first principles solution to the problem exists and probably never will exist (absent the discovery of some highly constraining mechanism or symmetry).
However I think I am correct in pointing out that the apparent magnitude of the problem occurs b/c of the scales mismatch, which is essentially set by the infrared physics.
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.
Yep thats interesting, but I don't quite understand these constructions. What is MSusy specifically here (is it arbitrary)? Also, why wouldn't the mechanism that generates these nonperturbative corrections at the low energy scale (in the language of the effective field theory) not also generate unwanted and observable KK states?
As far as numerology goes. I like the following two observations as well. If you take the cutoff to be the mass of the lightest neutrino, the scales match. Another weird coincidence... The supersymmetry breaking scale seems to be exactly halfway (on a logarithmic scale) between the vacuum energy scale and the Planck scale. Why?
Yep thats interesting, but I don't quite understand these constructions. What is MSusy specifically here (is it arbitrary)? Also, why wouldn't the mechanism that generates these nonperturbative corrections at the low energy scale (in the language of the effective field theory) not also generate unwanted and observable KK states?
By MSUSY I just denoted a generic scale of level spacing. Its value should be related to the string scale, I think, since SUSY is broken at the string scale in this construction.
That's why I did not really want to identify MSUSY with the scale obtained in some 4D EFT from the soft breaking but the numerology looks cute :biggrin:
You probably mean perturbative instead on non-perturbative, right? This computation is in 10D, so there are no KK states involved. That said, at such extremely short distances even in a compactified 4D vacuum all the KK modes become light and the theory does effectively become 10 or maybe 11 dimensional. I think that what one really needs here for a realistic computation is to translate soft SUSY breaking in some 4D EFT into the splittings in the entire string spectrum and then compute the one-loop partition function. My hunch is that the scale of the boson-fermion splitting in the string levels would be related to the gravitino mass scale instead of the string scale and the result of the computation may actually give the correct order of magnitude. What was really neat for me to learn was that the finiteness of the CC in a non-tachyonic non-SUSY string theory is guaranteed by the modular invariance, despite the presence of an infinite tower of contributions in the UV. Here is a nice reference where you can read about these ideas: http://arxiv.org/PS_cache/hep-th/pdf/9503/9503055v2.pdf
@Fra, Here is a reference that is the most referred in the literature but you'd have to go to your library to actually read it: http://slac.stanford.edu/spires/find/hep/www?irn=6818293
Please, read very carefully what I said in my previous comment b/c your response indicated that you had misunderstood it.
Smoit thanks for the link. I haven't read it but that indeed looks like the classical paper I also thought you meant. It could well be that I didn't get your point at all, in that case I'm sorry.
Anyway my point was this: That paper tests WEP to one part in 10^12, but it's all classical mechanics (torsion balance) and relatively speaking macroscopic classical systems (which is dominated by baryonic mass) with classical measurements.
Thus I question the validity of that test when applied to situations where the classical mechanics framework just don't hold. Also just as a ballpark number it seems the contribution of lamb shift to the classical level mass is the order of 1 in 10^15 or so? Which seems to be beyond hte level os current experimental tests?
So I didn't quite get how that classical mechanics test of WEP for 1 part in 10^12 gives any information about the the nature loop corrections in general (which then of course goes outside classical mechanics)?
Perhasp I'm missing something, could you explain?
/Fredrik
Trying to make sure I understand the logic, let me know if I get it wrong:
such individual quantum contributions do gravitate and once they are all added up the total zero-point energy should still gravitate
Are you suggesting that (when considering the origin of mass) since the idea is that the actual classical masses (such as those in the 1971 torsion balance experiment) are largely made up of confined energy such as confined virtual gluons etc, therefore the conclusion is that all such "virtual energies" as infered by all observers(?) must contribute equally to both inertial and gravitatonal mass?
/Fredrik
Also just as a ballpark number it seems the contribution of lamb shift to the classical level mass is the order of 1 in 10^15 or so? Which seems to be beyond hte level os current experimental tests?
I'm not sure where you obtained this ballpark number. I suggest you read page 3 in arxiv.org/PS_cache/hep-th/pdf/0603/0603249v2.pdf.
So I didn't quite get how that classical mechanics test of WEP for 1 part in 10^12 gives any information about the the nature loop corrections in general (which then of course goes outside classical mechanics)?
Perhasp I'm missing something, could you explain?
/Fredrik
If you are questioning how one can measure quantum effects by classical means than you should read a book or take a class in quantum mechanics. The whole reason for inventing quantum mechanics in the first place was the experimental results which could not be explained by classical physics, e.g. the discrete atomic spectra, etc. It seems as though you are questioning the ability to measure quantum effects by classical instruments and I suggest that you simply create a separate thread with the appropriate title to carry on the discussion there.
Trying to make sure I understand the logic, let me know if I get it wrong:
Are you suggesting that (when considering the origin of mass) since the idea is that the actual classical masses (such as those in the 1971 torsion balance experiment) are largely made up of confined energy such as confined virtual gluons etc, therefore the conclusion is that all such "virtual energies" as infered by all observers(?) must contribute equally to both inertial and gravitatonal mass?
/Fredrik
I said nothing about virtual gluons and their contributions to the rest mass of baryons b/c I didn't want to get into discussing lattice QCD results for hardon masses but yes, virtual gluon loops do contribute a significant portion of a baryon's inertial mass and such effects are much more significant than the virtual photon loops Polchinski talks about.
I read the Bianchi & Rovelli paper as well as Chap VIII.2 “The Cosmological Constant Problem and the Cosmic Coincidence Problem” in Zee, Quantum Field Theory in a Nutshell, Princeton Univ Press, 2003 (p 434). I do not find any disagreement regarding the facts, only their reactions thereto. For example:
B&R write, “But to claim that dark energy represents a profound mystery, is, in our opinion, nonsense.” In contrast, Zee introduces this subject by saying, “I now come to the most egregious paradox of present day physics.”
Regarding the coincidence problem, B&R write, “it is quite reasonable that humans exist during those 10 or so billions years (sic) when \Omega_b and \Omega_\Lambda are within a few orders of magnitude from each other.” In contrast, Zee writes, “the epoch when \rho_M \sim \Lambda happens to be when galaxy formation has been largely completed. Very bizarre!”
Both agree that (per B&R) “There is no known 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.” B&R’s reaction to this fact is, “But this does not means (sic) that there is something mysterious in the cosmological constant itself: it means that there is something we do not understand yet in particle physics.” While Zee writes, “But Nature has a big surprise for us. While theorists racked their brains trying to come up with a convincing argument that \Lambda = 0 observational cosmologists steadily refined their measurements and recently changed their upper bound to an approximate equality \Lambda \sim (10^{-3} \mbox{ev})^4!!! The cosmological constant paradox deepens.”
In short, the B&R paper merely argues for a particular emotional reaction to the situation regarding the cosmological constant in physics and cosmology. I would be surprised to see this paper published in a physics journal, since it does not expand upon our knowledge of physics. However, the paper’s use of a timely topic to highlight one aspect of our failure to unify the Standard Model with gravity is not without value. I could see this included in the proceedings for a philosophy of science symposium, for example. It would also be appropriate for a pedagogical journal in physics. It certainly motivated me to look more deeply into the issue. Thanks for posting this, marcus.
Edit: I'm trying to figure out how to use TeX in PF. Obviously, I haven't found an "in line" tex command yet.
juanrga
Nov19-11, 12:19 PM
The cosmological constant becomes a mistery as soon as you do not write it on the left hand = "the gravity" side of the equations
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}
but it you write it on the right hand = "the matter" side.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu} - \Lambda g_{\mu\nu}
In vacuum (with T=0) you still have some kind of "matter" which affects spacetime:
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
If you leave this term on the left hand side, the question where it comes from and why it is there, is still open, but it is not a qustion about matter, dark energy or something like that; it is a question about gravity.
Sorry but a mystery does not disappear by moving a term, from the right to the left, on the same equation.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
is just so problematic as
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = 0
Sorry but a mystery does not disappear by moving a term, from the right to the left, on the same equation.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
is just so problematic as
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = 0
Wait Juan :biggrin: I don't think you grasped Tom's point! It is quite a valid one if you are familiar with the custom in General Relativity of writing the equation geometry (e.g. curvature terms) on the left and matter terms on the right.
Lambda is a curvature constant and occurs naturally and unsurprisingly in the geometry LHS
(since as Einstein observed early on, it is allowed by the symmetries of the theory).
You only make a puzzle out of it if you consider this natural curvature term to be "matter", and symbolize this by moving it to the RHS of the equation.
If you make this mistake then you baffle your self with asking "Now what could this matter be???!!"
As Tom pointed out the constant curvature term Lambda is analogous to a constant of integration---that you are taught in beginning Calculus class to put in the answer when you integrate. It must be there because it is allowed by the conditions of the problem.
...
In short, the B&R paper merely argues for a particular emotional reaction to the situation regarding the cosmological constant in physics and cosmology. I would be surprised to see this paper published in a physics journal, since it does not expand upon our knowledge of physics. However, the paper’s use of a timely topic to highlight one aspect of our failure to unify the Standard Model with gravity is not without value. I could see this included in the proceedings for a philosophy of science symposium, for example. It would also be appropriate for a pedagogical journal in physics. It certainly motivated me to look more deeply into the issue. Thanks for posting this, marcus.
I think B&R state clearly at the outset that their purpose is to debunk the hype. The paper is aimed at fellow physicists who describe the "cosmological constant problem" in exaggerated language.
They give some examples of this near-hysterical rhetoric right the start of the paper. That is clearly the target.
I think that too much hype tends to damage the prestige and credibility of physics. Physicists have been shouting "wolf" or "fire" or "recreating the big bang" and "theory of everything!" so much that the educated audience has gotten into the habit of discounting what they say as attention-getting rubbish.
Since the intended audience of the paper is other physicists, particle physicists primarily I would say, I can't imagine why they would want to publish it in a philosophical or pedagogical journal. It is a warning to tone down the exaggerated rhetoric.
As such, the arxiv is a good place to post it. Or else possibly in the opinion section of a magazine like Physics Today. It's not a research or review article, after all. But why bother, since arxiv is already a perfect outlet?
I was amused by Smoit pointing out that the article had not been published in a peer-review journal, as if this were a criticism. Rovelli has over 14,000 cites to his over 200 professional articles. He hardly needs to try to peer-publish everything he writes to bolster his trackrecord. Since this piece is primarily advice to fellow physicists to sober-up and cut the hype for the good of the field, I actually doubt it has been submitted anywhere. Arxiv is the perfect place to reach those who are able to get the message.
Zee's response to the facts presented in his text and B&R's paper is that they constitute "the most egregious paradox of present day physics." Why would B&R expect to change that reaction by simply rehashing what is known? Therefore, I would say this paper can only expect to find a sympathetic audience among those not familiar with the technical aspects of the issue, i.e., it's a pedagogical piece.
simplicial
Nov19-11, 02:56 PM
Some other comments on the dark energy problem.
http://www.nature.com/nature/journal/v466/n7304/full/466321a.html
NATURE | NEWS AND VIEWS
Cosmology forum: Is dark energy really a mystery?
Bianchi, Rovelli, Kolb
Nature 466, 321–322 (15 July 2010)
doi:10.1038/466321a
The Universe is expanding. And the expansion seems to be speeding up. To account for that acceleration, a mysterious factor, 'dark energy', is often invoked. A contrary opinion — that this factor isn't at all mysterious — is here given voice, along with counter-arguments against that view.
juanrga
Nov19-11, 03:01 PM
Sorry but a mystery does not disappear by moving a term, from the right to the left, on the same equation.
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = - \Lambda g_{\mu\nu}
is just so problematic as
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = 0
Wait Juan :biggrin: I don't think you grasped Tom's point! It is quite a valid one if you are familiar with the custom in General Relativity of writing the equation geometry (e.g. curvature terms) on the left and matter terms on the right.
Lambda is a curvature constant and occurs naturally and unsurprisingly in the geometry LHS (since as Einstein observed early on, it is allowed by the symmetries of the theory).
You only make a puzzle out of it if you consider this natural curvature term to be "matter", and symbolize this by moving it to the RHS of the equation.
If you make this mistake then you baffle your self with asking "Now what could this matter be???!!"
As Tom pointed out the constant curvature term Lambda is analogous to a constant of integration---that you are taught in beginning Calculus class to put in the answer when you integrate. It must be there because it is allowed by the conditions of the problem.
Sorry guys, but both equations of above are the same. The reason for the which the expression
-\Lambda g_{\mu\nu}
can be written as
\frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
is related to the nature of the vacuum in quantum field theory. Or said in another way, the correct equation is
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} + \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
and setting T=0 for vacuum, as tom did, gives
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
instead of his equation.
The problem is that the difference between the geometry and the matter is of 120 orders of magnitude. This is the CC problem. and this problem is not solved by moving a term from the left of an equation to the right (evidently the discrepancy only moves, it does not disappear :rolleyes:)
Some other comments on the dark energy problem.
http://www.nature.com/nature/journal/v466/n7304/full/466321a.html
NATURE | NEWS AND VIEWS
Cosmology forum: Is dark energy really a mystery?
Bianchi, Rovelli, Kolb
Nature 466, 321–322 (15 July 2010)
doi:10.1038/466321a
The Universe is expanding. And the expansion seems to be speeding up. To account for that acceleration, a mysterious factor, 'dark energy', is often invoked. A contrary opinion — that this factor isn't at all mysterious — is here given voice, along with counter-arguments against that view.
Great! I didn't know about this view getting into print in Nature. Did they have a debate then? What position did Rocky Kolb take? He is a distinguished guy at the U Chicago Astro department---one of the top astrophysics and cosmology departments in the Usa.
http://astro.uchicago.edu/people/edward-rocky-w-kolb.shtml
Ha! I found a free link to the News and Views feature called "Is dark energy really a mystery?" http://www.astro.uu.nl/~vinkj/LSS/Nature_2010_Bianchi.pdf
Bianchi & Rovelli say No it isn't and give a halfpage summary of their reasons.
Kolb says Yes it is, and gives his own halfpage argument.
Here is an excerpt from the condensed version that Bianchi and Rovelli published in Nature journal "News and Views" section, the 15 July issue. They had already disposed of two other arguments and were moving on to the third.
==quote B&R's piece in Nature==
The third objection concerns ‘vacuum energy’. Quantum field theory (QFT) seems to predict a vacuum energy that adds to the cosmological force due to Λ — just as radiative corrections affect the charge of the electron. But this hypothetical contribution to Λ is much larger than the observed Λ. The discrepancy is an open puzzle in QFT in the presence of gravity 6,7. But it is a conceptual mistake to confuse Λ with QFT’s vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT’s vacuum energy — or that of any other mysterious substance. Λ is a sort of ‘zero-point curvature’; it is a repulsive force caused by the intrinsic dynamics of space-time.
Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion — and that of many relativists — that saying dark energy is a ‘great mystery’, for a force explained by current theory, is misleading. It is especially wrong to talk about a ‘substance’. It is like attributing the force that pushes us out of a turning merry-go-round to a ‘mysterious substance’.
...
==endquote==
For the full Nature article see:
http://www.astro.uu.nl/~vinkj/LSS/Nature_2010_Bianchi.pdf
The Bianchi, Rovelli, Kolb piece has a link to B&R's Arxiv article
"Why all these prejudices against a constant?"
http://arxiv.org/abs/1002.3966
This "constant prejudices" article is the topic of this thread, and just to be clear about the purpose and focus of the article it opens by quoting the first sentence of an article in Physics World co-authored by cosmologist Ofer Lahav (prof Astro. at University College, London). This is the kind of hype they are targeting:
==quote Calder and Lahav in Physics World 23 (June 2010), 32–37 ==
“Arguably the greatest mystery of humanity today is the prospect that 75% of the universe is made up of a substance known as ‘dark energy’ about which we have almost no knowledge at all.”
==endquote==
Full article "Dark Energy: how the paradigm shifted"
www.tiptop.iop.org/full/pwa-pdf/23/01/phwv23i01a33.pdf
juanrga
Nov20-11, 05:24 AM
Sorry guys, but both equations of above are the same. The reason for the which the expression
-\Lambda g_{\mu\nu}
can be written as
\frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
is related to the nature of the vacuum in quantum field theory. Or said in another way, the correct equation is
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} + \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
and setting T=0 for vacuum, as tom did, gives
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
instead of his equation.
The problem is that the difference between the geometry and the matter is of 120 orders of magnitude. This is the CC problem. and this problem is not solved by moving a term from the left of an equation to the right (evidently the discrepancy only moves, it does not disappear :rolleyes:)
The above two last equations are incorrect and would be written as
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}
equivalent to
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu} + \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
For vacuum
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + \Lambda g_{\mu\nu} = 0
or (equivalent)
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4}T_{\mu\nu}^{DE}
Another correction. That -\Lambda g_{\mu\nu} can be written as \frac{8\pi G}{c^4}T_{\mu\nu}^{DE} is independent of the nature of the vacuum in quantum field theory. It is a definition. The problem is when T_{\mu\nu}^{QFT-vacuum} is used to compute T_{\mu\nu}^{DE}
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.
I agree in general that there is a fine tuning problem with the cc coming from quantum effects. But I thought the Casimir effect isn't evidence of this since it can be calculated without using zero-energy, like in http://arxiv.org/abs/hep-th/0503158?
I think AdS/CFT must provide examples of a framework in which the "renormalization approach" applies, because in any given instance of the duality, the bulk space (the AdS space) has a known, nonarbitrary, nonzero cosmological constant, and yet everything fits into the framework of QFT (on the CFT side of the duality). So it would be of interest to understand how AdS/CFT deals with vacuum energy in the bulk, on the way to obtaining a negative cosmological constant.
edit: See this paper (http://arxiv.org/abs/1106.3556) (and talk (http://www.physics.ntua.gr/corfu2011/Talks/kyriakos_papadodimas@cern_ch_03.pdf)).
Physics Monkey brought up (http://www.physicsforums.com/showthread.php?t=548726) a paper (http://arxiv.org/abs/1111.1987) that looks at this in a 1+1 Ising model and its gravity dual.
I like Kolb's response to B&R (thanks for providing that article, marcus). He defines "mystery" per Webster's, i.e., “Something not understood or beyond understanding,” then points out that Lambda is not understood. Only way to beat that is provide another definition of "mystery" or provide an origin for Lambda. Since B&R can't do the latter, I'd be interested in hearing their definition of "mystery."
B&R "constant prejudices" paper which is the topic of this thread opens by quoting the first sentence of an article in Physics World co-authored by cosmologist Ofer Lahav (prof Astro. at University College, London). This is the kind of hype B&R are targeting:
==quote Calder and Lahav in Physics World 23 (June 2010), 32–37 ==
“Arguably the greatest mystery of humanity today is the prospect that 75% of the universe is made up of a substance known as ‘dark energy’ about which we have almost no knowledge at all.”
==endquotewww.tiptop.iop.org/full/pwa-pdf/23/01/phwv23i01a33.pdf==
Earlier I quoted an excerpt from the version that Bianchi and Rovelli published in Nature journal "News and Views" section, the 15 July issue.
Anyone who has read the piece in Nature carefully will realize that the operative word is "substance". They argue that it is misleading to talk about Λ (a small constant curvature) as a "substance".
==quote B&R's piece in Nature==
But it is a conceptual mistake to confuse Λ with QFT’s vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT’s vacuum energy — or that of any other mysterious substance. Λ is a sort of ‘zero-point curvature’; it is a repulsive force caused by the intrinsic dynamics of space-time.
===endquote===
Efforts are under way to understand how this "zero point curvature" arises from the underlying quantum dynamics of space-time.
As quantum relativists the authors are naturally interested in how the zero point curvature relates to QG degrees of freedom: "the intrinsic [quantum] dynamics of space-time". There have been several articles about this. For a recent examples see page 41 of the 2010 paper by Meusburger and Fairbairn--also the paper by Han (a member of the Marseille group who has co-authored with B&R.)
==continuing the B&R excerpt==
Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion — and that of many relativists — that saying dark energy is a ‘great mystery’, for a force explained by current theory, is misleading. It is especially wrong to talk about a ‘substance’. It is like attributing the force that pushes us out of a turning merry-go-round to a ‘mysterious substance’...
==endquote==
For the full Nature article see:
http://www.astro.uu.nl/~vinkj/LSS/Nature_2010_Bianchi.pdf
The Bianchi, Rovelli, Kolb piece has a link to B&R's Arxiv article
"Why all these prejudices against a constant?"
http://arxiv.org/abs/1002.3966
As quantum relativist one wants to understand how the Einstein equation (with its zero-point curvature constant Λ) arises.
And specifically, in connection with the cosmological constant, one presumably wants to understand a LENGTH. The length scale of this small ubiquitous constant curvature.
What underlies this length is not understood, but there are some intriguing ideas.
BTW the length in question is easy to calculate from standard estimates of cosmological parameters and is 9.3 billion ly. Same order of magnitude as several other length scales basic to cosmology.
I mentioned Meusburger and Fairbairn's paper where this length plays a role. Also Han's paper.
BTW B&R themselves have a simple 2-page paper about the physical meaning of this length, and of the quantum group deformation parameter (essentially an exponential form of the length)---I'll get that link too, it might be of interest.
http://arxiv.org/abs/1105.1898
Here is the link for Han's paper:
http://arxiv.org/abs/1105.2212
Cosmological Constant in LQG Vertex Amplitude
Muxin Han
(Submitted on 11 May 2011 (v1), last revised 12 Jun 2011 (this version, v2))
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity) embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.
6 pages, 5 figures
I'm not sure where you obtained this ballpark number. I suggest you read page 3 in arxiv.org/PS_cache/hep-th/pdf/0603/0603249v2.pdf.
Right, my mistake, sorry! Anyway this was just a side note, the major point was below.
If you are questioning how one can measure quantum effects by classical means than you should read a book or take a class in quantum mechanics. The whole reason for inventing quantum mechanics in the first place was the experimental results which could not be explained by classical physics, e.g. the discrete atomic spectra, etc. It seems as though you are questioning the ability to measure quantum effects by classical instruments and I suggest that you simply create a separate thread with the appropriate title to carry on the discussion there.
No, my point was rather the realism implicit in classical mechanics vs the "measurement" with infinitely massive observerrs implicit in QFT, and how this compares to finite observers making measurements on their environment. Sometimes which I think is forced once we move in theory space.
But I read the Polchinski's paper and he raises hte question, why the gravitation apparently difference between what's confined within an atom vs what's outside the atom.
In my view the difference is that if you study an atom, you have a virtually infinitely massive classical observer that via scattering experiments in principle studies a small subsystem.
This is assymetric to the case where a small finite observer looks into it's own environment.
In the latter case there is a natural cutoff, due to the observers mass. In the former case there is no natural cutoff, which is why the cutoff is introduced ad hoc. When comparing QFT framework and classical mechanics without respecting this, I think one is missing something important. After all, "mass in classical mechanics" is just a parameter, whose measurement is also classical.
I think QG takes us into the domain of non-classical observers and quantum systems.
QFT is more like classical observers and quantum systems.
classical mechanics is classical observes and classical systems.
This influences what types of observeables we get. But this is related to questions raise in the paper too. I just put it differently since I am neither into strings nor LQG. My perspective is that of inference, where interactions are explained in terms of observer observer inferences. Here the complexity of the observers is paramount as it constrains the whole picture.
/Fredrik
Anyone who has read the piece in Nature carefully will realize that the operative word is "substance". They argue that it is misleading to talk about Λ (a small constant curvature) as a "substance".
The title of the Nature article is, "Is dark energy really a mystery?" The "abstract" reads,
The Universe is expanding. And the expansion seems to be speeding up. To account for that acceleration, a mysterious factor, ‘dark energy’, is often invoked. A contrary opinion — that this factor isn’t at all mysterious — is here given voice, along with counter-arguments against that view.
Nowhere does Kolb use the word "substance" in his response.
This article presents, as advertised, arguments "that this factor isn't at all mysterious ... along with counter-arguments against that view." Thus, Kolb showed that Lambda is "mysterious" per Webster's definition. B&R need to likewise show that Lambda is not "mysterious" per some non-idiosyncratic definition. They fail to do so. It's that simple.
IMO the core "mystery" is mainly that we don't understand how to merge two successful frameworks. In particular how to describe "empty space". Specifically I see it as boiling down to how it's _measured_. Here GR and QM/QFT just don't compare even if similar word "vacuum" is used for the two things.
I tend to see that the main issue with measurments and expectations is that it requires and observer. Ie. empty space makes no sense unless it has a boundary by wich to interact with it - thus it's all about the boundary and how it confines things. Here the difference is obvious. It's almost like two complementing pictures. The observer is sitting at difference sides of the horizon.
To observe a small subsystem, or to observer a possibly open environment are so different that concepts tested in one domain don't apply. So I don't thikn it's any "mystery", it's more like an obvious "missing part" in our understanding. The two theories are disjoint in theory space. That's more a missing piece of hte puzzle more than a mystery IMO.
/Fredrik
I was amused by Smoit pointing out that the article had not been published in a peer-review journal, as if this were a criticism. Rovelli has over 14,000 cites to his over 200 professional articles. He hardly needs to try to peer-publish everything he writes to bolster his trackrecord.
Bianchi has 21 professional articles, 17 of them published. I'm sure that as a postdoc, he likewise "hardly needs to try to peer-publish everything he writes to bolster his trackrecord". :biggrin:
I was nevertheless amused at how you chose to criticize the article.
To get back to serious matters, what we observe at cosmological scale is acceleration, not a possibly mythical "dark energy" substance causing the acceleration. I think it's a bad idea to use "dark energy" as a code-name for the acceleration one wants to explain. If one is actually talking about the observed acceleration, as something to be explained, one should call it acceleration. So, with that adjustment, Kolb says
==quote Kolb in the Nature piece==
Einstein’s cosmological constant Λ is the simplest explanation for [acceleration]: it adequately fits the data, and there is no reason to exclude it. But the magnitude of Λ necessary to explain the observations places it far “beyond [our] understanding”. If the cosmological constant is the explanation for [acceleration], Λ must be about (10^28 cm)−2. The length 10^28 cm is absurdly large, and cannot at present be related to any other known or expected length scale in nature. Attempts to explain this new length scale fail by many, many orders of magnitude.
==endquote==
This is the core of what Kolb has to say. This length, which I said earlier is 9.3 billion ly, is not understood. Oh, and large too. :smile:
Quantum relativists, including Bianchi and Rovelli, would certainly not dispute that. A lot of thought has been devoted to understanding how that length fits into our picture of nature.
B&R have an interesting 2-page paper about it, which Kolb obviously did not know about, in which they give references to the literature going back to the 1990s.
Their take is basically that it could have to do with an intrinsic limit on angular resolution. A limit on our ability to detect and measure angle, that is analogous (although they don't say this) to the "Planck length" limit on our ability to detect and measure length, area...etc.
There is currently no concept of "Planck angle". So in effect B&R are probing into the possibility of defining one. That is what the "zero point curvature" they mention in the Nature article is actually about, as I see it.
If there actually is a minimum detectable angle (in, say, a deSitter or asymptotically deSitter universe with an intrinsic event horizon) then in Quantum Relativity one would be forced to use the quantum group instead of SU(2). One would have to use the q-deformed SUq(2) instead of SU(2).
This has the side-effect of making certain series in LQG convergent. So it's interesting that it has an intuitive physics meaning, as well as the math significance.
Anyway, Rocky Kolb eloquently pointed out how interesting it would be to understand this event-horizon type length 9.3 billion ly. This is right in line with B&R interests. So he fails to actually engage with their position, and actually strengthens their case.
What they are basically saying, to paraphrase, is "let's not jump the gun and attribute acceleration to some queer mythical substance, when we don't actually know what underlies this length 1/√Λ."
http://arxiv.org/abs/1105.1898
A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
Eugenio Bianchi, Carlo Rovelli
Published in Phys.Rev. D84 (2011) 027502
To get back to serious matters, what we observe at cosmological scale is acceleration, not a possibly mythical "dark energy" substance causing the acceleration. I think it's a bad idea to use "dark energy" as a code-name for the acceleration one wants to explain. If one is actually talking about the observed acceleration, as something to be explained, one should call it acceleration.
I agree we should replace the term "dark energy" with "accelerated expansion." Then attempts to explain the data (distance modulus vs redshift) without accelerated expansion would not trip over the meaning of "dark energy." For example, in arXiv:gr-qc/0605088v2 (appeared in QGC) Garfinkle provides a "dark energy model" without accelerated expansion.
All they are saying is "let's not jump the gun and attribute acceleration to some queer or mythical energy, when we don't actually know that some actual energy is involved."
Then the title of the article should've been something like, "Do we need an energy to explain accelerated expansion?" In which case, Kolb would have to rewrite his contribution.
I agree we should replace the term "dark energy" with "accelerated expansion."...
So glad you agree! Misleading words people use over and over again can have a really crippling effect on how we think collectively. It takes intelligence and mental independence to cut through.
Then the title of the article should've been something like, "Do we need an energy to explain accelerated expansion?" In which case, Kolb would have to rewrite his contribution.
Yes! Absolutely. When you write for a magazine feature like "News and Views" my understanding is the editor has control of things like title and lead summary. In this case the editor obviously framed the discussion as he or she understood it and thought it would appeal to the readership.
Well. That's how the real world operates :biggrin: It's not a big deal. Better to get your message out with a little distortion than not to reach the Nature journal audience.
Well. That's how the real world operates :biggrin: It's not a big deal. Better to get your message out with a little distortion than not to reach the Nature journal audience.
Absolutely!
Physics Monkey
Nov30-11, 08:44 PM
I agree in general that there is a fine tuning problem with the cc coming from quantum effects. But I thought the Casimir effect isn't evidence of this since it can be calculated without using zero-energy, like in http://arxiv.org/abs/hep-th/0503158?
I always found it interesting that Jaffe's paper does not mention what might be called the topological Casimir effect. In this case the fields are confined by the topology of compact space instead of by any "perfectly conducting sheets" and so forth. Naively, it seems that there is no coupling dependence in such a situation.
I always found it interesting that Jaffe's paper does not mention what might be called the topological Casimir effect. In this case the fields are confined by the topology of compact space instead of by any "perfectly conducting sheets" and so forth. Naively, it seems that there is no coupling dependence in such a situation.
Are you saying that although observation of the "normal" Casimir effect isn't proof that the vacuum energy exists, an observation of the topological Casimir effect could demonstrate it?
Returning to main topic of thread and e.g. RUTA's recent comments the gist seems to be that we probably have an interesting cosmological scale to understand, that being (depending on whether one writes it as a time or a length)
9.3 billion years, or 9.3 billion lightyears
You could imagine this as a limit on angular resolution---that nature has a smallest distinguishable angle. Personally I (almost) never heard of such a thing and my head spins slightly when I think of it. If I knew of some body of conventional physics research that incorporates a smallest measurable angle of the right magnitude it would not seem so farfetched.
But as it is, if I want to think of this as a "Planck angle" or extreme minimal angle I have to kind of grit my teeth and swallow hard.
Anyway here is a "Planck angle" or θmin = (Planck length)/(9.3 billion light years) radian.
See post #103 for more about this angle--which comes up in the quantum-group version of the rotation group.
Or you could just think of Λ as the zero-point curvature that is intrinsic to nature's geometry.
And as curvature that would be an inverse area, so that 1/Λ is an area.
And therefore 1/√Λ is a length.
Which length we believe to be 9.3 billion LY based on the large amount of supernova data which has accumulated.
This zero point curvature of nature's geometry is very small, and therefore its reciprocal, the area, is very large---and therefore the corresponding natural distance scale, the squareroot of that area, is large. But still it is kind of in the same ballpark with other cosmology distance scales, so perhaps easier to assimilate as "curvature-related" idea than it is in the guise of an angle.
I calculated this zero point curvature constant back in post #10
http://physicsforums.com/showthread.php?p=2633720#post2633720
so if you want you can see how to get it, and update the estimate as needed. If H is the current value of the Hubble parameter then:
Λ = 3ΩΛH2
So 1/√Λ must be
1/sqrt( 3ΩΛH2) and we can try this in google calculator:
1/(sqrt(3*.73)*(71 km/s per Mpc))
When I put that into the googlebox I get 9.306 billion years...thanks google for this nice constant of nature :biggrin:
Or you could just think of Λ as the zero-point curvature that is intrinsic to nature's geometry.
And as curvature that would be an inverse area, so that 1/Λ is an area.
And therefore 1/√Λ is a length.
Which length we believe to be 9.3 billion LY based on the large amount of supernova data which has accumulated.
...:biggrin:
Today's paper by Tony Padilla and co-author picked up on the vacuum curvature idea and how you could empirically isolate it from contributions from particle physics vacuum energy. (Currently grossly overestimated using flat-geometry QFT particle physics.)
Padilla is at Nottingham, same department as John Barrett and Kirill Krasnov. Nottingham hosted the main QG conference in 2008.
http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
Ian Kimpton, Antonio Padilla
(Submitted on 5 Mar 2012)
We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.
4 pages
Padilla's paper depends on prior work http://arxiv.org/abs/1106.2000 by Copeland et al. Copeland is also at Nottingham. This was published earlier this year in Physical Review Letters.
It would be nice if relativists could cleanse the cosmological curvature constant of contribution from QFT vacuum energy, which particle physicists are having such a hard time determining. Then instead of a "cosmological constant problem" it could be seen for what it is: simply a flatspace QFT zeropoint energy problem. Terms like "dark energy" could be dropped and the volume of hype could be turned down a notch.
This paper is something of a conundrum to me. Tony Padilla is a particle theorist by group membership and training.
How will the paper be received by relativists? Or will it not even be received---because wild and over the top? My impression after re-reading is that Padilla has a lot of nerve.
http://www.nottingham.ac.uk/~ppzphy7/webpages/people/antonio_padilla/
This may be good. Or may not. He has a highly personal style. See video clips here:
http://www.nottingham.ac.uk/~ppzap4/
On further investigation I find I'm halfway to becoming a fan of the guy. A native of Liverpool BTW, and a soccer player. BA and Masters in Math at Cambridge. Here's a YouTube about the paper I referred to earlier [ http://arxiv.org/abs/1106.2000 ]that was published in Physics Review Letters January 2012 (after the reference to the Beatles was removed). It is by Edmund Copeland, Tony Padilla, and a couple of others.
http://www.youtube.com/watch?v=AlmVKJelaAk Copeland (older guy) also appears in the YouTube clip.
Tony begins discussing the cosmological constant at minute 4:50 of the clip.
Here's something about Brady Haran, the guy who made this video and a bunch more:
http://www.bradyharan.com/
As a reminder of the main topic here, this quote from Bianchi and Rovelli's piece in Nature sums up what the thread is about:
==quote B&R's piece in Nature July 15, 2010==
But it is a conceptual mistake to confuse Λ with QFT’s vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT’s vacuum energy — or that of any other mysterious substance. Λ is a sort of ‘zero-point curvature’; it is a repulsive force caused by the intrinsic dynamics of space-time.
...
...
Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion — and that of many relativists — that saying dark energy is a ‘great mystery’, for a force explained by current theory, is misleading. It is especially wrong to talk about a ‘substance’. It is like attributing the force that pushes us out of a turning merry-go-round to a ‘mysterious substance’....
===endquote===
More back a few posts in post #97 http://physicsforums.com/showthread.php?p=3626952#post3626952
Sorry to say I do not have a working link to the B&R piece in Nature. If you have a subscription, it's
Cosmology forum: Is dark energy really a mystery?
Eugenio Bianchi, Carlo Rovelli, and Rocky Kolb
Nature 466, 321–322 (15 July 2010)
However they make the same arguments at greater length and in more detail in this article:
Google "bianchi prejudices constant" and get http://arxiv.org/abs/1002.3966
====================
The new element, which I first learned of yesterday, and which is discussed in the previous two posts #111 and #112, is
this paper by two physicists in the particle theory group at Nottingham (Nottinghamsters? :biggrin:):
http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
Ian Kimpton, Antonio Padilla
(Submitted on 5 Mar 2012)
We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.
4 pages
Padilla's paper depends on prior work http://arxiv.org/abs/1106.2000 by Copeland et al. Copeland is also at Nottingham. This was published earlier this year in Physical Review Letters.
Bianchi and Rovelli are not saying anything new, are they? Take eg. this 2007 review
http://arxiv.org/abs/0705.2533
"The observational and theoretical features described above suggests that one should consider cosmological constant as the most natural candidate for dark energy. Though it leads to well known problems, it is also the most economical [just one number] and simplest explanation for all the observations. Once we invoke the cosmological constant, classical gravity will be described by the three constants G, c and Lambda"
So far I think this is the most relevant on-target response. We shouldn't even be surprised by what B&R are saying. The observational data, of which there are massive amounts, indicate we are dealing with a curvature constant of nature. Like the speed constant c, it does not change over space and time. Or there are no indications that it does. Just a constant term in the Einstein equations governing the universe's geometry. The data that has come in since Atyy's quote was written (2007) only serves to confirm this.
The new feature, at this point, is that some people think they have a way to separate out and measure the bare L, a way to somehow discount any possible contributions of QFT "vacuum energy". That is what Tony Padilla's paper is about.
Interestingly, he has a YouTube clip talking about this and related matters for general audience. It has Padilla and a the senior author Edmund Copeland talking about a paper they published in Physical Review Letters in January 2012, that the March 2012 paper is based on.
http://www.youtube.com/watch?v=AlmVKJelaAk
To just get the part about the cosmological constant, skip to minute 4:50.
Copeland and Padilla are particle theorists in the HEP theory group at Nottingham---their starting point differs from that of Bianchi and Rovelli, who of course are quantum relativists. The conclusions, though, are remarkably compatible.
What they are talking about in the YouTube is their January paper where they developed a mathematical technique to "degravitate" the QFT vacuum energy, to zero-out its effect. So that left the road clear for Padilla's March 2012 paper where he presents this as a way to determine the clean bare curvature constant Lambda (devoid of of QFT contribution).
See the abstract and link for Cleaning Up the Cosmological Constant, in the preceding post.
Dark energy is of course not a "real" problem, it's a question of fine tuning, like the hierarchy problem. There's no inconsistency, so if our theories were ultimate theories, there'd have no problem. But if we believe our theories are just temporary, then fine tuning suggests new physics. Of course since we don't know if our theories are by amazing good luck ultimate theories, solving a fine tuning problem is a matter of taste. Anyway, in line with the Fab Four (http://arxiv.org/abs/1112.4866), how about:
Ellis, Inhomogeneity effects in Cosmology (http://arxiv.org/abs/1103.2335)
DGP 4D Gravity on a Brane in 5D Minkowski Space (http://arxiv.org/abs/hep-th/0005016)
Nicolis, Rattazzi, Trincherini The galileon as a local modification of gravity (http://arxiv.org/abs/0811.2197)
Hi Atyy, I shall argue that Padilla has an unusually interesting modification of gravity here and one that can be tested. It is a variant of ordinary GR that reproduces the solar system tests of GR to satisfactory precision. IOW it is just as good as GR as far as we are able to tell.
So far! (There is more testing work to be done.)
In this variation on GR, the coupling to matter is mediated by a scalar field (not the Higgs field but something distantly analogous.)
I invite you to watch the YouTube of Copeland and Padilla, or perhaps you already have!
It's amusing in spots, and enlightening, I think. It was made BEFORE Padilla came around to the "cleaning up" idea to get a pure constant curvature.
BTW Padilla gave a presentation of this last July at PASCOS 2011 (Cambridge DAMPT)
http://www.damtp.cam.ac.uk/research/gr/workshops/PASCOS/2011/presentations/Padilla-pascos2011.pdf
PASCOS 2011 = The 17th annual symposium on Particles, Strings, and Cosmology.
http://www.damtp.cam.ac.uk/research/gr/workshops/PASCOS/2011/
If you happen to glance at the program, he gave his talk Wednesday 6 July in Session 3: Modified Gravity. So I guess we have to call what he is talking about "modified gravity" though it is different from, and to me more interesting than all the other modified gravities that I am used to seeing. This scalar field that mediates the coupling of matter to geometry is quite elegant, I think. And it makes the curvature impervious to QFT vacuum energy, so no wonder we don't see a gravitating vacuum energy effect!
This opens the door for relativists to offer a geometrical explanation for why the curvature constant Lambda is what it is.
Padilla mentions the Galileon stuff in the introduction of his PRL paper (http://arxiv.org/abs/1106.2000), and says that it is closely related. The Galileon stuff was originally motivated by DGP - which passed First-Year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Constraints on Non-Standard Cosmological Models (http://arxiv.org/abs/0908.4276).
Padilla mentions the Galileon stuff in the introduction of his PRL paper (http://arxiv.org/abs/1106.2000), and says that it is closely related. The Galileon stuff was originally motivated by DGP - which passed First-Year Sloan Digital Sky Survey-II (SDSS-II) Supernova Results: Constraints on Non-Standard Cosmological Models (http://arxiv.org/abs/0908.4276).
Good point! What about his current paper? The March 2012 one. My impression is that by the March paper he is on to a fairly unique approach, one he calls "novel". At that point comparison with other non-standard variants of GR is no longer appropriate. You may find evidence to the contrary--I don't see any.
Good point! What about his current paper? The March 2012 one.
Hmmm, seems unrelated to the Fab Four idea.
Hmmm, seems unrelated to the Fab Four idea.
You know, I think you're right! He cites the Fab Four paper when he really doesn't need to; just in passing to make a minor point.
Here's the link to Padilla's article again:
http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
Ian Kimpton, Antonio Padilla
(Submitted on 5 Mar 2012)
We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.
4 pages
==a key quote==
In summary, then, we have proposed a novel way to clean up the cosmological constant problem. By coupling matter to a composite metric, g ̃ab(φ, ∂φ, . . .), satisfying the property (1),
we have been able to eliminate the troublesome vacuum energy from contributing to the dynamics of the system. Thus one ought to be able to choose the vacuum curvature to take on an empirical value, as dictated by observation, with a clean conscience. This is the take home message of this paper.
==endquote==
===============EDIT TO REPLY TO NEXT POST================
Hi Paulibus, since I can still edit I'll reply here. I simply agree. It makes sense to me too. So much for "dark energy". I doubt we're ever going to be able to use it to run the family car :biggrin: or grind the corn to make the tortillas! But I wanted to say that I relished your reference to that perceptive French expression for non-Baconian speculations (la haute poppicocquerie) and was glad to hear about Helge Kragh's book
"Higher Speculations -- Grand Theories and Failed revolutions in Physics and Cosmology" O.U.P, 2011.
Paulibus
Mar9-12, 01:28 AM
What ( Kimpton and Padilla) are talking about ....is a mathematical
technique to "degravitate" the QFT vacuum energy ....
Because the Equivalence Principle rules GR, would this mean that the same mathematical
technique would also “deinertialise ” the QFT vacuum energy? Seems reasonable to me. I can’t see how either the gravitational or inertial mass of the entire universe’s vacuum energy could be detected and measured; spring balances and accelerating rockets are useful only for relatively local stuff.
Hi Paulibus, beyond what I said in post #121 by way of reply
I want to emphasize the testabiliity angle which is one of the possibilities that makes this proposal exciting:
==quote page 4, http://arxiv.org/pdf/1203.1040v1.pdf ==
As we have seen, any solution to GR, with arbitrary cosmological constant, is a solution to our theory. However, it is clear that the reverse is not true. Our theory is expected to permit solutions that are not present in GR. This opens up the possibility of finding some interesting and potentially testable new features. Work is under way to study the impact of these new features, beginning with cosmological solutions of the specific model presented here.
==endquote==
Also to reiterate the main result for clarity
==quote page 2==
Actually, we can go even further. Any solution of GR, vacuum or otherwise, is also a solution to our theory, whatever the value of the vacuum curvature. As the vacuum energy drops out of the dynamics, we are free to choose the vacuum curvature with a clean conscience. Indeed, one can straightforwardly check that the field equations are satisfied by the choice,
G ̃ab = −Λ ̃g ̃ab + τab, T ̃ab = −σg ̃ab + τab ( 9 )
where τab describes the matter excitations above the vacuum, σ is the vacuum energy, and Λ ̃ is the vacuum curvature.
This follows from the fact that the equations of motion are linear in E ̃ab, with constant contributions dropping out completely. In particular, this means that the standard ΛCDM cosmology, with Λ chosen empirically without any concern, is a perfectly good solution to our theory, and does not suffer from the same fine tuning issues as the corresponding solution in GR.
==endquote==
Assuming this initiative goes thru, the ball is now in the relativist's court. It is they who must explain the value of the constant vacuum curvature, if it needs explaining.
Does it need any more explanation than, for example, the value of Newton G?
Perhaps, perhaps not. We'll see.
Ben North
Apr9-12, 01:03 AM
Take 2 silver plates shaved like cds and place them close together..spin them(not with any type of shaft but with an external encompassing globe) and the casimir effect will create a negative pressure in between the two discs. The centrifugal force created from the discs spinning at high speeds that would normally push exotic matter outward will push the exotic inward on itself. -λ= F/C-M)
any thoughts??
==sample quote==
It is especially wrong to talk about a mysterious “substance” to denote dark energy. The expression “substance” is inappropriate and misleading. It is like saying that the centrifugal force that pushes out from a merry-go-round is the “effect of a mysterious substance”.
==endquote==
http://arxiv.org/abs/1002.3966
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
9 pages, 4 figures
(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."
Posts about "exotic matter and the Casimir engine" and "exotic matter and the Casimir effect" wouldn't really belong in this thread.
What's being discussed in the thread is the widely (but not universally!) shared view that the observed expansion speedup is best explained as simply due to a constant Λ which occurs naturally (along with Newton G) in the Einstein equation.
These two constants G and Λ are those allowed by the symmetry of the theory and so *must* appear in the equation. Either or both could, of course, have turned out to be zero, but in fact neither did: both are positive.
This is the (classical) equation which to the best of our knowledge governs the evolution of geometry.
So it's inappropriate to talk about "dark energy" or "zero point energy" in this context, any more than one would drag in such stuff in connection with Newton G.
There need be no mention of "exotic matter" fields to explain the value of Λ any more than one needs such inventions to explain the value of G.
Seen from this perspective, since today's quantum field theory is based on a rigid flat geometry in which dynamic expanding geometry necessarily cannot be captured, it can have little or no relevance to explaining Λ: whatever oversized value of "vacuum energy" QFT theoreticians might come up with has no bearing on the observed value of the cosmological constant. They just need to go back and get their flatspace vacuum energy right.
For an interesting recent contribution to this discussion see Kimpton Padilla's paper.
http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
Ian Kimpton, Antonio Padilla
(Submitted on 5 Mar 2012)
We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.
4 pages
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