# Smolin 3SR and third scale Quantum Gravity

1. Jul 24, 2004

### marcus

Third scale QG that Smolin and others are working on attempts to incorporate 3 invariant scales (the speed c, the Planck mass kappa, and the length L = Lambda-1/2) and to have 3SR---triply special relativity---as its flat limit.

this research direction has been attracting more people lately

I just found online what I think is a particularly good source that explains the essential ideas

it is 18 pages of pdf-format slides of a talk Smolin gave in February 2004 at the Polish Winterschool of 2004 ("WS-2004").
http://ws2004.ift.uni.wroc.pl/html.html [Broken]

this was a 10 day teaching symposium on QG Phenomenology organized by Jerzy K-G, and a dozen or so people gave talks and all their talks are online at Jerzy's site. Smolin gave 3 talks at the symposium and what I am talking about is the third talk.

just click on "lectures" and scroll down to smolin and get the third of his talks---the one about evidence.

I printed it out yesterday. Actually I found all three talks really helpful in getting an overall picture of what's happening in the third-scale department.

18 pages is not much, because there are only a few words and/or equations on each page---it is slides---so what you get is the bare-bones outline of an introductory talk on the evidence for the third invariant scale.

(notational problem: not sure if conventional Lambda of Einstein equation is meant or Lambda/3----some people seem to use a cosmological constant 1/3 as big)

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2. Jul 24, 2004

### marcus

more third scale QG papers

Deformed Special Relativity as an effective flat limit of quantum gravity
Girelli, Livine, Oriti
http://arxiv.org/gr-qc/0406100 [Broken]

Triply Special Relativity
Kowalski-Glikman, Smolin
http://arxiv.org/hep-th/0406276 [Broken]

Linear Form of 3-scale Special Relativity Algebra and the Relevance of Stability
Chryssomalakos, Okon
http://arxiv.org/hep-th/0407080 [Broken]
this last is mostly about simple 3SR (special relativity where you require that not just the speed of light, but also a mass and length, be the same for all observers)

------------
my comment: 2SR (with two invariant scales) has been around for a long time and people have been assuming that QG would have some form of it as a flat limit.
so there would be two invariant scales, the speed c, and the planck mass $$\inline \kappa$$
remember that ordinary 1905 SR arose by a distortion or tweaking of Euclidean (Galilean, whatever) relativity so as to make c invariant, this new version did some more distortion or tweaking to get something else invariant.
Giovanni Amelino-Camelia has been a major spokesman both for 2SR and for QG phenomenology
they go together because the most accessible tests of QG are really testing effects of 2SR or 3SR or whatever is the flat limit of QG.

now, the way Smolin and the others are going, it looks like QG will assimilate 3SR and that leads to an interesting situation: if QG has 3SR as its flat limit (as title of Girelli et al paper suggests) then QG connects with the data on galaxy rotation curves supporting MOND and also may find confirmation in the Pioneer anomalous acceleration.

the key is to assimilate this new length L as a fundamental constant.

L is the inverse square root of Lambda the cosmological constant.

we have a fairly good estimate of the cosmological constant, and that is an inverse area, so just flip it and take the square root---that gives the length L.

It is a long length, like a billion-some lightyears.
(it's another way of talking about dark energy and accelerated expansion)
is this length a basic parameter of the universe?

galaxy rotation curves suggest it might be. in any case it seems to be an interesting question

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3. Jul 24, 2004

### marcus

Sorry if this seems overly quantitative. It turns out that this Smolin length is 5 Gpc and here's how to get it from common knowledge.

It's common knowledge the speed of light is 300,000 km/s and the agreed-on best estimate of the Hubble paramter is 71
that is 71 km/s per Megaparsec.

The Hubble length is c/H and you just divide 300,000 by 71
and that gives it in Mpc-----it comes to around 4.2 Gpc.

the other bit of common knowledge needed is that the dark energy fraction is 73 percent-----this gets a lot of play in the media: the cosmological constant that accelerates expansion corresponds to 0.73 of the total energy density of the U.

to get the Smolin length L, you just have to divide 4.2 Gpc by the square root of 0.73

this comes to around 4.94 Gpc if you bother to carry it out with that much accuracy, or roughly 5 Gigaparsecs.

I mentioned 16 billion lightyears earlier. the 16 billion Ly is another way of saying 5 Gpc.

the nice thing is that this length scale appears to have something to do with galaxy rotation curves and the the Pioneer anomaly and with quantum gravity. as well as with the accelerated expansion data (underlying the 71 and 0.73 we calculated it from).

(note: still unsure about a factor of the square root of 3, not sure if conventional Lambda or something 1/3 that size is being used)

Last edited: Jul 26, 2004
4. Jul 24, 2004

### marcus

Ted Jacobson was one of the dozen or so lectureres at the
Polish Winterschool WS-2004 in February
Here is a recent paper of his on the same topic as he covered at the symposium.
http://arxiv.org/abs/gr-qc/0404067
Quantum Gravity Phenomenology and Lorentz Violation
Ted Jacobson, Stefano Liberati, David Mattingly
16 pages
"If quantum gravity violates Lorentz symmetry, the prospects for observational guidance in understanding quantum gravity improve considerably. This article briefly reviews previous work on Lorentz violation (LV) and discusses aspects of the effective field theory framework for parametrizing LV effects. Current observational constraints on LV are then summarized, focusing on effects in QED at order E/M_Planck."

In this paper the authors discuss not only LV proper but also extensions of SR like 2SR where there is no preferred frame of reference.

===============
Another of those lecturing at WS-2004 was Tsvi Piran
here is a regular arxiv.org preprint of the talk he gave (better than slides)

http://arxiv.org/astro-ph/0407462 [Broken]

"Gamma Ray Bursts as Probes of Quantum Gravity"
Tsvi Piran
Lectures given at the 40th winter school of theretical physics: Quantum Gravity and Phenomenology, Feb. 2004 Poland

"Gamma ray bursts (GRBs) are short and intense pulses of $\gamma$-rays arriving from random directions in the sky. Several years ago Amelino-Camelia et al. pointed out that a comparison of time of arrival of photons at different energies from a GRB could be used to measure (or obtain a limit on) possible deviations from a constant speed of light at high photons energies. I review here our current understanding of GRBs and reconsider the possibility of performing these observations."

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5. Jul 25, 2004

### marcus

from page 5 of those Smolin slides I see the length scale L
is calculated to be roughly
1.25E26 meters
(several billion Ly)
I used an independent figure for the cosmological constant
and got roughly 1.5E26 meters
(16 billion Ly)

At least for now I'll assume that this length smolin is using is the reciprocal square root (not of the conventional Lambda but) of Lamda/3. (which is actually easier to work with in the cosmological equations)

the thing to remember is that if you have a figure for the dark energy density rho-sub-lambda, or call it the vacuum energy density if you want,
then it is related to Lambda/3 by

$$\frac{\Lambda}{3} = \frac{8\pi}{3} \rho_{\Lambda}$$

this is in natural units, if you have to put G into it then it is

$$\frac{\Lambda}{3} = \frac{8\pi G}{3} \rho_{\Lambda}$$

and to get Smolin's "third scale" length L
you just take inverse square root of Lambda/3.
Now the WMAP satellite data tells us rho_Lambda is 0.73
of the critical density and the rest is just arithmetic

$$\frac{\Lambda}{3} = 0.73 H^2$$

$$L = \frac{c}{\sqrt{\Lambda/3}}=\frac{c}{\sqrt{ 0.73} H}$$

Last edited: Jul 26, 2004
6. Jul 25, 2004

### marcus

the length L is a handle on the accelerated expansion
and either the cosmological constant (a curvature term) or the dark energy density depending on how you say it

if you want that key energy density or curvature to look the same to all observers, then you want that length L to be an invariant length. and be the same for all observers

so that is one motive for modifying SR to include L as invariant scale

but then the story gets more intricate

if you take the square of a speed and divide by a length you get an acceleration

in natural units where c = 1 in fact, 1/L is an acceleration
or if you put c into it, you have c2/L
a few centimeters per day per day----very slight accel
Now if L is a fundamental physical constant then this acceleration is too, one would imagine.
And indeed this acceleration looks like it shows up in the Pioneer anomaly and the galaxy rotation curves.

Look at pages 8,9,10 and 11 of Smolin's notes. the fit is embarassingly snug

the graphic evidence of plots of rotation curves is impressive
maybe it is just a coincidence but some coincidence!
nothing substitutes for looking at the pictures, in this case, IMO.

I would say it's possible we are looking at a modification of newtonian gravity with an acceleration quantity entering into the picture and this quantity is

$$a_0=\frac{c^2}{6L}=1.2\times 10^{-8} cm/sec^2$$

the figure of 1.2E-8 cm per second per second is what Smolin gives on page 5

the gist of this is that the stars in a galaxy are so far from center that they are going in almost straight paths and their acceleration towards the center is only a tiny tiny amount of accleration----and it looks like in a regime like that accelerations may be a bit larger than is predicted by pure inverse square------accel may not tail off as fast, way out in the tail (goodness knows maybe it is a quantum effect such things have been known to happen).

And the scale of this departure from inverse square behavior, if it is actually occurring, is the important thing----how small do accelerations have to be before you notice. And the scale of this departure, suggest Smolin and others, is this length L (which is proposed to be a basic universal constant)

and the tiny acceleration that goes along with that very long length L.

Last edited: Jul 25, 2004
7. Jul 25, 2004

This is very intriguing. I had heard of Doubly Special Relativity, but also that there were problems with it. I admit I don't know enough about it, nor even this Triply Special variety, but my question nonetheless is thus:

Are there any ways that we can experimentally verify whether or not Triply Special relativity actually exists instead of the normal special relativity? And if so, does this imply we'd need a Triply General Relativity?

8. Jul 25, 2004

### marcus

At the start of thread I mentioned Winterschool WS-2004
http://ws2004.ift.uni.wroc.pl/html.html [Broken]
this was a ten-day symposium on Quantum Gravity Phenomenology

phenomenology means looking for ways of testing a theory by
discovering and calculating measureable effects

these days, what QG phenomenology boils down to is divising tests for DSR and TSR (different ways of bending the pure Lorentz symmetry)

At WS-2004 they had several observational people lecturing as well as theorists,
mostly: Ultra-High-Energy-CosmicRay (UHECR)and
GammaRay Burst(GRB) astronomy
an overview at WS-2004 was given by Ted Jacobson

Tsvi Piran of jerusalem U gave the GRB talks
Paolo Lipari gave the UHECR lectures

the point is that (although the instruments out there are not good enough yet) a bunch of better instruments are going up and they will be able to look for distortions in Lorentz symmetry, so it is good to look at these guys slides and the graphs they have made of data so far and see how they will be going about their observational checking when the better instruments are working----you get a sense from their talks that they are already working on it and already (with the tools they have) starting to narrow down the constraints

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9. Jul 25, 2004

### marcus

this Smolin length
the presumption is that it is constant
(because it is just a synonym for the cosmological constant---the
cos const is the inverse square of this length L)

and that if L is 16 billion lightyears now
then it was 16 billion lightyears back at the dawn of time back when
things were hotter
and denser than they are nowadays
and quantum fluctuations ruled the world and

moreover it will still be 16 billion lightyears when the sun is a
cooling cinder and earth-life has died or migrated to other stars.

We have had constant lengths before, but they were small
like Planck length. We never had a large constant length like this.
The other vast distances and times all change.
the hubble parameter changes
the hubble time changes
the age of the universe changes
these are all vast extreme infrared things but they change.

the presumption is that the cosm. const. Lambda does not.
(It might if it happened to be a manifestation of "quintessence"
but quintessence is a speculative idea somewhat on the margin)

suddenly by surprise we have a constant that
is a very long length

Last edited: Jul 26, 2004
10. Nov 11, 2004

### marcus

I have to say I probably made a numerical mistake in this thread

and I realized that I had made a mistake in arithmetic. I will try to correct this

In planck terms, which is the clearest easiest way to keep track of important constants like this,

Lambda = 3.4E-122

the damned ENERGY DENSITY that people substitute for Lambda and call dark energy, given in planck terms, is this Lambda divided by 8pi

so it comes out

rho_Lambda = 1.3E-123

but that is just a distraction, if we are going to say the smolin length is the reciprocal squareroot of Lamda then it comes out

L_smo = 5.4 E60

that is actually a nice easy to remember length because of the 60
and it comes out to be 9.5 billion lightyears, if I remember right.
but always mistrust damned conversions of units.

and these numbers are from the common consensus data of
71 for the hubble
and 0.73 for the "dark energy" fraction Omega_Lambda
that they often give you, from WMAP and all that