# Olaf Dreyer: the Cosmological Constant paradox

1. Sep 5, 2004

### marcus

http://arxiv.org/hep-th/0409048

this is a 4-page paper.
the cosmological constant problem is the worst prediction in the history of physics---conventional Quantum Field Theory predicts a vacuum energy which is 123 orders of magnitude off: wrong by a factor or 10123

why is this? it should be interesting to resolve

Olaf Dreyer finds that the bizarre and humongous discrepancy in QFT vacuum energy arises from the theory not having been formulated in a Background Independent way. He gives a short argument as to why QFT, once it is made B.I., would not have a problem with the cosmological constant.

Background Independent Quantum Field Theory and the Cosmological Constant Problem

2. Sep 6, 2004

### sol2

I printed out this copy last night to review, and found somebody else who has a similar interest that shares your perspective in regards to LQG. If no one responds then the issue is dead to me. So understanding this other persons perspective, and his bend in the LQG direction, I wanted him to explain himself in relation to his views, so I am asking you how you see, in relation to the universe and what it is doing when you bring this link here for review? What are your thought here when you posted this?

Why do you accept the background independance?

Last edited: Sep 6, 2004
3. Sep 6, 2004

### marcus

Philip W Anderson, winner of 1977 Nobel (solid state)

http://almaz.com/nobel/physics/1977a.html

Anderson was born 1923, he was at Princeton and Bell Labs, may still be

we should make an excursion into his thinking now, as also further developed by a young faculty at MIT named Xiao-Gang Wen

--------------------
Footnote: both standard QFT and String stumble over the Cos. Const.
QFT's Standard Model has been impressively successful in predicting
numbers and nothing has improved on it for 20 years. Broadly speaking QFT only makes one mistake (the huge one about CC).
In like manner, String, though largely unsuccessful at predicting numbers (having been worked on for over 20 years), in 2003 was thrown into turmoil by concerns around the Cosmological Constant. Confusion about the CC is at the root of the Landscape-talk and Susskind's Anthropery and the Kachru Trouble about the 10100 string vacuums. The Cos. Const. has been responsible for the "de-scientizing" of String (in the eye's of some). So when someone offers to get rid of the Cos. Const. problem we should listen up. IMHO.
---------------------

Olaf Dreyer is maybe not the main player here---he's a young person at Perimeter who takes risks. The concrete foundation he is using for his short 4-page paper is the thinking of Philip Anderson (extended by Xiao Wen). It is a "condensed matter" field theory model, which Olaf Dreyer exploits to achieve background independence.

http://pupgg.princeton.edu/www/jh/pwa/

http://pupgg.princeton.edu/www/jh/research/Anderson_Philip.htmlx

Last edited: Sep 6, 2004
4. Sep 6, 2004

### marcus

Olaf Dreyer builds his case on these condensed-matter field theory citations (representative of a growing tribe of allied cond-mat research)

P.W.Anderson Science 177,393 (1973)

G.E.Volovik The Universe in a helium droplet Oxford U. Press (2003)

R. B. Laughlin Int. J. Mod. Phys. A18, 831 (2003).

X.-G. Wen Quantum field theory of many-body systems Oxford U. Press (2004)

http://dao.mit.edu/~wen/

I would urge anyone who hasnt already to check it out. he has many sample pages from his book. there is a TOC for the book.
He is at MIT and has quite a few graduate students around him.

here are two recent papers by X-G Wen
http://arxiv.org/abs/cond-mat/0406441
An Introduction to Quantum Order, String-net Condensation, and Emergence of Light and Fermions

http://arxiv.org/abs/cond-mat/0407140
A unification of light and electrons based on spin models

Last edited: Sep 6, 2004
5. Sep 6, 2004

### marcus

I supect that Xiao should have made his world out of
"spin-network condensations" instead of "string-net condensations"
and then the construction would be background independent
(conceptually better) and also would not have
potential problems like the Cos. Const. problem.

it looks to me as if Olaf Dreyer has had this idea, perhaps other too

some of Xiao's pictures look like they might be pictures of spin-networks

6. Sep 7, 2004

### marcus

the usual theory of gravity is background independent, sol, so nobody needs to justify the requirement that a theory have background independence.

challenging the requirement of background independence is off topic here and will distract from the train of thought. Please start a separate thread about it. I am trying to understand how Olaf Dreyer has addressed the problem of the cosmological constant.

(the black hole entropy paper you cited has no bearing on this and also could use a separate thread)

7. Sep 11, 2004

### marcus

Olaf Dreyer is involved in another controversial issue besides the Cosmo. Const.

It was his original idea back in 2002 that the Immirzi could be 8.088, or rather the reciprocal of that---a number around one eighth.

Now Lee Smolin, with Olaf Dreyer and Fotini Markopoulou to help him, has taken up the banner of this Immirzi.

http://arxiv.org/hep-th/0409056

In Quantum Gravity, area is measured in "quantum pinpricks" and to oversimplify and put it very crudely each pinprick is worth

65.65 x 10-70 m2

It would be nice if it were that simple but there is this parameter called immirzi that scales the pinpricks so that roughly speaking each pinprick is now worth either

$$\frac{1}{8.088}65.65 \times 10^{-70} m^2$$

or

$$\frac{1}{4.21}65.65 \times 10^{-70} m^2$$

Abhay Ashtekar says divide by 4.21 and Lee Smolin says divide by 8.088.

the basic 65.65E-70 square meter area is
$$8\pi\text{planck area}=8\pi\frac{G\hbar}{c^3}$$

Last edited: Sep 17, 2004
8. Sep 11, 2004

### marcus

If you would like a reference for the 1/4.21 see reference [10] in smolin's paper
http://arxiv.org/hep-th/0409056
and also equation (18)
they give the value that the opposition prefer, as well as their own.
or see
http://arxiv.org/gr-qc/0407051
http://arxiv.org/gr-qc/0407052

----------------------------
at this point the exact value of the immirzi seems less interesting than picturing a spin network quantum state of geometry

In Quantum Gravity, a quantum state of the geometry of the universe
is like a humongous ball-and-stick model of a molecule

the nodes (balls) have volume info and contribute a tiny amount of volume to any region enclosing them and the links (sticks) have area info and contribute area to any surface they pass thru. In this way the network supplies the basic geometry information.

A gigantic network seems to be the most efficient way of describing the geometry of the whole universe. it is like a computer data structure which lists everything you need to know about the geometry----bare bones, but from which everything can be derived. Curvature can be gotten from it too.

but the cells of the network need to be very tiny. a given region contains jillions of nodes and links. the network is planck scale.

this area 65.65x10-70 square meter gives an idea
because each passage thru a surface by the network, each puncture, or pinprick, contributes about this much area to the surface

It gives a notion how intense the spin-network quantum state of the universe is, because its jillions of nodes are connected with links so numerous that a square meter has on the order of 1070 links passing thru it.

the geometry of the universe, which is this network, gives area to things by how much it punctures them, and a square meter of area is something it punctures a lot. It has to puncture it about 1070 times because
each puncture only contributes about 10-70 sq. meter of area

I'm picturing this network as being like the fine suds in the sink----- this fine foam of millions of bubbles

Imagine putting a dot or node in the middle of each bubble
and linking two nodes if their two bubbles touch
and in this way replace the foam by a kind of network.

that is how it gets to look like a 'ball-and-stick' model of a complex polymer molecule but with millions of atoms corresponding to the original bubbles

and picture this extending everywhere and describing a quantum state of the geometry of the universe

Last edited: Sep 11, 2004
9. Sep 11, 2004

### marcus

I guess we have to call this quantum needlepoint area something, let's call it a pinprick.

Now we move on to black holes and try to see why Olaf Dreyer (and others) say that it has to be scaled down still further by the Immirzi.

the reason is that Sachar Hod, in Israel, found the vibration frequencies of black holes and by Bohr's principle of correspondence these should correspond to energy changes or changes in the mass of the hole, and these are accompanied by changes in the area of the event horizon.
when Hod's result is translated into area terms, it predicts that the area should change sort of one pinprick's worth at a time

but not quite, instead the area should change by this number times a pinprick
$$\frac{\ln 3}{2 \pi}$$

-----
Remember each pinprick is worth

65.65 x 10-70 m2

so according to the semiclassical analysis of Hod and others the area of a usual black changes in steps this big

$$\frac{\ln 3}{2 \pi}65.65 \times 10^{-70} m^2$$

now we check out where Olaf Dreyer gets the number 8.088

for reference, a pinprick---the basic 65.65E-70 square meter area---is
$$8\pi\text{ planck area}=8\pi\frac{G\hbar}{c^3}$$
Later on it would be convenient to have a symbol for it. i think I will call it Upsilon (that double-hook capital greek letter)
$$\Upsilon = 8\pi \text{ planck area}=8\pi\frac{G\hbar}{c^3}$$

Last edited: Sep 17, 2004
10. Sep 11, 2004

### marcus

All I am doing right now in this thread is basically just reading
http://arxiv.org/hep-th/0409056
with you.

the paper itself is not all that hard, but sometimes following something in a kind of parallel track can help it sink in. so this is a parallel development which I need to do as part of assimilating the paper

what we are driving for is Olaf Dreyer's equation for the Immirzi gamma number, which if you solve it with your calculator will give 1/8.088. the equation is

$$\sqrt {2} \gamma = \frac{\ln 3}{2 \pi}$$

Olaf (with support from Lee and Fotini) says that when the area of a Schwarz. horizon changes by gaining or losing one puncture by the network then (by god and the all-righteous area formula of LQG) it gains or loses this amount of area

$$\sqrt {2} \gamma \times 65.65 \times 10^{-70} m^2$$

and Hod says by his and others classical analysis of making the Schwarz. solution go boing that it gains or loses this amount of area

$$\frac {\ln 3}{2\pi} \times 65.65 \times 10^{-70} m^2$$

so you can see where the equation comes from, just putting the two gained-or-lost areas equal. they are two different expressions for the "delta A"

the ticklish spot is that Olaf is saying something about the spin-color of a network in a black hole. he is saying that the spins inside a black hole can only be ONE they cannot be one-half. Or at least the spins coloring the legs that cross the eventhorizon.

this is where the infernal squareroot 2 comes from, which otherwise would be squareroot 3/4. Always these damned technicalities!
well at least we havent had to say "entropy" yet, so it is still fairly straightforward

for reference, Upsilon the basic pinprick area--- 65.65E-70 square meter area---is
$$\Upsilon = 8\pi\text{ planck area}=8\pi\frac{G\hbar}{c^3}$$

this is what some people were proposing we use for the planck area anyway, instead of the conventional planck area. john baez has some SPR emails advocating that-----essentially to use 8pi G instead of plain G, throughout

Last edited: Sep 17, 2004
11. Sep 11, 2004

### marcus

Now we get to the Hawking entropy formula. this is all for Schwarz. black holes but I dont always say Schwarzschild.
typically the entropy is considered to be a plain number
and I guess one should be aware that the CONVENTIONAL planck area is Ghbar/c^3 but that various people including john baez have advocated replacing G by 8piG

the thought is that it is 8piG that appears in the Einstein equation of General Relativity and in a bunch of other places, as if Nature really liked G to be multiplied by 8pi. then the formulas are different and quite a few are simpler-looking.

this pinprick area we've been talking about is 8pi times the conventional planck area----it is the "newplanck" area that you would get if you followed john baez suggestion and did what he advocates.
******************

well, Hawking formula relates entropy S to horizon area A, and the question is WHAT AREA DO YOU HAVE TO DIVIDE A BY TO GET S?
S is a number so to get S you have to divide horizon area A by some AREA, nothing else will work.

hawking says divide A by four times the conventional planck area

$$S = \frac{A}{4\text{ planck area}}$$

$$S = \frac{2\pi A}{8\pi \text{ planck area}}$$

$$S = \frac{2\pi A}{\Upsilon}$$

this is just another version of the Hawking entropy formula where we divided by the pinprick area and then compensated by multiplying by 2 pi.

**********
Now I want to check that the Olaf Dreyer version of the Immirzi gets the correct Hawking entropy formula

the assumption is that at each puncture the spin p =1 so that the dimension of the little microstate hilbertspace there is 2p+1 = 3
now the entropy is the logarithm of the dimension of all the hilbertspaces
collectively
so it is the number of punctures N multiplied by ln 3.

Here is Olaf's gamma
$$\gamma = \frac{\ln 3}{2 \pi\sqrt {2}}$$
each puncture contributes this much area
$$\sqrt{2} \gamma \Upsilon = \frac{\ln 3}{2 \pi}\Upsilon$$

We can use that to learn the number of punctures in
a horizon of given area A.

$$N = \frac{A}{\sqrt {2}\gamma \Upsilon}$$
$$N = \frac{A}{\frac{\ln 3}{2 \pi} \Upsilon}$$

$$S= N\ln3 = \frac{2\pi A}{\Upsilon}$$

that's the right entropy formula

In this thread I am still basically just reading
http://arxiv.org/hep-th/0409056
with you.

for reference, Upsilon---the basic 65.65E-70 square meter area---is
$$\Upsilon = 8\pi\text{planck area}=8\pi\frac{G\hbar}{c^3}$$

Last edited: Sep 17, 2004
12. Sep 12, 2004

### marcus

what I have been finding out in this thread is that there is some sense in the suggestion by Baez that instead of
G = hbar = c = k = 1
or the original planck units which had (dimensioned) quantities with numerical value unity.
Instead maybe, one should be setting
8piG = hbar = c = k = 1-------or the dimensioned analog to that.

One should be doing everything just the same except with 8piG instead of G.

Since I think Baez has been the one to stick his neck out about this I will call these "baez-units" to distinguish them from the 1899 "planck units"

Now why would anyone think that 8piG is more fundamental than G?

the answer is the 1915 Einstein equation which is the main equation of Gen Rel and our premier equation about gravity. Here is how you often see it.

Gab = (8piG)Tab

it is confusing because the letter G is used for the curvature tensor on the LHS and also for the newtonian constant in parens on the RHS. Anyway the central constant there, in parens, is not G it is 8piG. In some sense that proves that 8piG is more fundamental. this is in a dark primitive part of the brain with brute ideas like "dis basic'r n'dat. ugh!" have their dwelling. you take the most basic gravity equation which is the granddaddy of all the other gravity equations and you look at ITS proportionality constant and whatever that is, is the fundamental constant. All prejudice of course.

Now the dreadful prospect to contemplate is, what do baez units look like?
what does it look like if you actually do use 8piG instead of G?

Last edited: Sep 17, 2004
13. Sep 12, 2004

### marcus

some "baez" units (planck but with 8piG instead of G)

$$\text{energy unit} = \frac{\hbar c}{\sqrt \Upsilon}$$

$$\text{force unit} = \frac{\hbar c}{\Upsilon}$$

$$\text{energy density unit} = \frac{\hbar c}{\Upsilon^2}$$

$$\text{pressure unit} = \frac{\hbar c}{\Upsilon^2}$$

$$\text{mass unit} = \frac{\hbar }{c\sqrt \Upsilon}$$

convenient thing about this way of laying out "baez" units is that
you just have to remember that the upsilon area is
65.65 x 10-70 square meters

and that is the baez unit of area (its square root is the unit length)

personally I dont find that too hard to remember, for some reason
and then the rest of the units are reasonably simple to calculate
or estimate rough sizes, from that----cause one knows c and hbar.

Last edited: Sep 17, 2004
14. Sep 13, 2004

### sol2

Well Marcus,

I had appreciated your efforts to develpe this thinking, something has come up that one has to refute before accepting this framework of discussion.

I find it amazing sometimes, that if the shell approaches are not considered, how would one deduce, whether or not spin orientations would work? Gravity probe B would have detected variations, and in these places, "spin orientations," would have also been discovered?

Encapsulating these views( the outer most shell), reveals topological consideration with geometrodynamcis that must be considered?

There is only one way in which to understand this if one knew how to gauge the blackholes dynamcis and entrophy issues relevant to issues arising from the early universe. These dynamics would have been self evident, although the geometrical evolution has not been understood in string theory, I am working on it.

15. Sep 15, 2004

### marcus

I think what Lubos said to Sergei Alexandrov in another discussion in another forum is not relevant here, sol. Lubos concludes that anyone is free to take the OLF ideas seriously---although he repeats what Sergei identified as an unfair misconstruction of their term "noiseless". I do take their (Olaf-Lee-Fotini's) ideas seriously
But we are not talking about about Lubos and Sergei.

When you see the main gravity equation written in this really clean form:
Gab = Tab

then you know that someone has adjusted the units so as to set not only c but also 8pi G = 1

So let's take that move out of the realm of pure theory and see what it would look like in real life!

LET'S IMAGINE that we live on a planet just ten percent denser than the earth ( a bit more iron in the core, say) but the same size and otherwise the same.
And let's imagine that we have everyday units of measurement where we have 222 "counts" in a minute instead of 60 "seconds", and that the unit of length is a "palm"----the width of my four fingers (just over 8 centimeters). Let's suppose our mass unit is a "pound" which would be a mass of 434 grams if we measured it in a laboratory on earth.

then, for us, the baez units would be very easy to express in terms of our local everyday units.

baez unit speed = c = speed of light = one billion palms per count.

baez mass = 10-8 pound

baez length = 10-33 palm

all these baez units, which are just the same as planck units except some are modified by a factors of 8pi or the square root of 8pi, would be simply expressed like this-----for instance, the baez energy, the baez force, the baez temperature.

(wonder what Baez himself would think of being bandied about like this, but he was the one who most publicly proposed adjusting planck units by this 8 pi factor so he should not get to complain too loudly)

Last edited: Sep 15, 2004
16. Sep 15, 2004

### sol2

Well, hopefully, the rest of my post was acceptable I can't have a computer nerd validating what might have appeared to be the case of how this post fits where?

As you know, I can go to great lengths to question the validity of perceptions people can have, and the foundations they use. Look at your ole partner in crime, Nereid

I think she undertands now and so does that other fellow. I'd just have to do the same for you I guess :rofl:

Were you in that class picture, Neried(do you think if I continue to spell her forum name wrong this might piss her off?) offered?

best regards always(hope you know that)

Last edited: Sep 15, 2004
17. Sep 15, 2004

### marcus

My aim in this thread is to understand Olaf Dreyer's recent work, especially this short paper mentioned in the first post:

"Background Independent QFT and the CC Problem"

the thrust of this paper is closely allied to that of the one by Carlo Rovelli and Daniele Colosi that appeared a couple of days ago.

Global Particles, Local Particles
http://arxiv.org/gr-qc/0409054

The Quantum Gravity people seem to attacking this problem (and maybe one or two other major ones)-----what happens when QFT is made Background Independent by basing it on the (spin network) quantum geometry of LQG?

Olaf Dreyer says it may solve the Vacuum Energy Problem by making the hugely too big vacuum energy of QFT go away.
Carlo Rovelli says it will mean that particles do not have absolute exisence. You will no longer describe the world as consisting (even in principle) of a collection of particles and their interactions.

What particles appear to exist is merely an artifact of what the experimenter has chosen to measure.

Both the Dreyer and the Rovelli papers are about the future of QFT
and they are both concerned with foundations.

Rovelli paper does not mention the Cosmological Constant but after reading their paper I suspect that the analysis in it can be extended to show why the hugely too big (by 123 orders of magnitude) vacuum energy does not arise.

have to go, must continue this later

18. Sep 15, 2004

### marcus

"The world we live in is just another material whose excitations are described by the Standard Model." ---Olaf Dreyer

Background Independent Quantum Field Theory and the Cosmological Constant Problem
http://arxiv.org/hep-th/0409048

Carlo Rovelli and Daniele Colosi
Global Particles, Local Particles
http://arxiv.org/gr-qc/0409054

Neither paper is concerned with the efforts of String theorists, but I find that together they provoke some doubt in my mind concerning that approach.

Primarily it is because the String approach seems to attribute individual existence to particles.

The String approach seems to say "study the particle---for the world is composed of many many particles and their interactions." It is a traditional ontology going back to Newton. It could be misguided----a wiser ontology might say that space exists analogous to a crystal in condensed matter physics (perhaps as a spin-network or some other complex net of relations) and what are occasionally perceived as batches of particles are ripples or exitations, flaws in the matrix of space.

Perhaps instead of individual particles what one should do is study the bulk dynamic properties of space itself, as Einstein started physics doing in 1915, and in a partial imitation of condensed matter physics.

The "condensed matter approach" that Olaf Dreyer adopts here may prove successful not only in solveing the problem of the ridiculously huge Vacuum Energy but also in mirroring nature more generally. He attributes this approach to the Princeton Nobelist P.W.Anderson and cites work by a contemporary leader Xiao-Gang Wen at MIT.

I will get a longer quote from Dreyer and some links

19. Sep 15, 2004

### marcus

http://arxiv.org/hep-th/0409048
Background Independent Quantum Field Theory and the Cosmological Constant Problem

---quote from Olaf Dreyer---

"There are currently two competing views of the role quantum field theory plays in our theoretical understanding of nature. In one view,quantum field theory describes the dynamics of the elementary constituents of matter. The job of the physicist is to figure out what the elementary particles are and to find the appropriate Lagrangian that describes the interactions. The Standard Model of elementary particle physics is the epitome of this view (see[1] for an authoritative exposition of this view).

The other point of view likens the use of quantum field theory to its use in other areas of physics, most importantly in solid state physics. Here, quantum field theory is not used to describe the dynamics of elementary particles. In solid state physics, this would be fruitless, since the dynamics of a large number of atoms is usually beyond anyone’s ability to compute.

It turns out, however, that these large numbers of constituents often have collective excitations that can be well-described by quantum field theory and that are responsible for the physical properties of the material.

The view is then that the elementary particles of the Standard Model are like the collective excitations of solid state physics. The world we live in is just another material whose excitations are described by the Standard Model. The point of view was introduced by P. W. Anderson[2] and has since found a large following (seee.g. [3, 4, 5] and references therein). "
----end quote---

the reference [5] here is to work by the solid state physicist Xiao-Gang Wen.

Here is how Dreyer characterizes the Vacuum Energy problem a bit later in the paper right after equation number (1):

---quote---
"...If one takes this cutoff to be the Planck energy the vacuum energy is some 123 orders of magnitude away from the observed value of the cosmological constant [6], making this the worst prediction in theoretical physics. (For a detailed discussion of this problem see [7,8])..."
---end quote---

Last edited: Sep 15, 2004
20. Sep 15, 2004

### marcus

Compare what Carlo Rovelli, Daniele Colosi have to say
Global Particles, Local Particles
http://arxiv.org/gr-qc/0409054

---from the abstract---
The notion of particle plays an essential role in quantum field theory (QFT). Some recent theoretical developments, however, have questioned this notion; for instance, QFT on curved spacetimes suggests that preferred particle states might not exist in general....
---end quote---

---sample from the conclusions paragraph---

...the distinction between global and local states can therefore be safely neglected in concrete utilizations of QFT. However, the distinction is conceptually important because it bears on three related issues: (i) whether particles are local or global objects in conventional QFT; (ii) the extent to which the quantum field theoretical notion of particle can be extended to general contexts where gravity cannot be neglected; and furthermore, more in general, (iii) whether particles can be viewed as the fundamental reality (the “ontology”) described by QFT. Let us discuss these three issues separately. ...

...Can we base the ontology of QFT on local particles? Yes, but local particle states are very different from global particle states. Global particle states such as the Fock particle states are defined once and for all in the theory, while each finite size detector defines its own bunch of local particle states. Since in general the energy operators of different detectors do not commute ([HR, HR'] nonzero) there is no unique “local particle basis” in the state space of the theory, as there is a unique Fock basis. Therefore, we cannot interpret QFT by giving a single list of objects represented by a unique list of states. In other words, we are in a genuine quantum mechanical situation in which distinct particle numbers are complementary observables. Different bases that diagonalize different HR operators have equal footing. Whether a particle exists or not depends on what I decide to measure. In such a context, there is no reason to select an observable as “more real” than the others.

The world is far more subtle than a bunch of particles that interact.
---end quote---