Quantized Space & Lorentz Contraction in Loop Quantum Gravity

[metrictensor]

Does anyone know how in LQG they avoid the contradiction of a smallest unit of quantized space and Lorentz contraction?

 

[marcus]

Does anyone know how in LQG they avoid the contradiction of a smallest unit of quantized space and Lorentz contraction?

there are two ways
there has been a fork in the road of LQG development and quite a few papers written developing each way

Lee Smolin way uses DSR which modifies the lorentz group to be almost like the usual lorentz group but with a second invariant quantity, not only the speed of light looks the same to observers moving relative to each other but also the Planck length looks the same.
Smolin version of LQG requires DSR (deformed special relativity) and leads to a prediction that in gammaray bursts that have traveled several billion lightyears the most energetic gamma will arrive just slightly earlier----a barely noticeable (under normal circumstance) effect of energy on the speed. He flatly and explicitly makes this prediction and posted a paper about it just last month. Smolin's prediction will be tested in 2007 by the satellite observatory GLAST (gammaray large array space telescope)

Rovelli has another way of addressing the same apparent contradiction.
He has authored some papers about his way of resolving it as well. He does not require any DSR or departure from speed of light at very high energies.
I just had a busy evening and I am sleepy now, but tomorrow, if no one else had done it, I will get some links.

what you have asked is a good question and a lot has been written and I should be able to find several online articles by LQG people showing different ways of accomodating on the one hand special rel (lorentz symmetry) and on the other the Planck scale.

 

[marcus]

Hi metrictensor,
I promised to get back to this when more wideawake

http://arxiv.org/abs/gr-qc/0205108

Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
Carlo Rovelli, Simone Speziale
12 pages, 3 figures
Phys.Rev. D67 (2003) 064019

A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts and give the conditions under which its action is unitary."

this article has been cited by 23 other articles
http://arxiv.org/cits/gr-qc/0205108
(if you want to read more viewpoints and discussion)

including for example this one

http://arxiv.org/abs/gr-qc/0405085
About Lorentz invariance in a discrete quantum setting
Etera R. Livine, Daniele Oriti
25 pages
JHEP 0406 (2004) 050

"A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in the context of quantum gravity, the distance between two points becomes an operator and show through a toy model, inspired by Loop Quantum Gravity, that the notion of a quantum of geometry and of discrete spectra of geometric operators, is not inconsistent with Lorentz invariance. The main feature of the model is that a state of definite length for a given observer turns into a superposition of eigenstates of the length operator when seen by a boosted observer. More generally, we discuss the issue of actually measuring distances taking into account the limitations imposed by quantum gravity considerations and we analyze the notion of distance and the phenomenon of Lorentz contraction in the framework of "deformed (or doubly) special relativity'' (DSR), which tentatively provides an effective description of quantum gravity around a flat background. In order to do this we study the Hilbert space structure of DSR, and study various quantum geometric operators acting on it and analyze their spectral properties. We also discuss the notion of spacetime point in DSR in terms of coherent states. We show how the way Lorentz invariance is preserved in this context is analogous to that in the toy model."

But hey metrictensor! Rovelli's paper is only one side of the discussion!
The other view is that Lorentz symmetry should be mooshed just slightly so that Planck length looks the same to all observers (or words to that effect). that is DSR. this is a major fork in the road for LQG.

 

[Locrian]

Smolin's prediction will be tested in 2007 by the satellite observatory GLAST (gammaray large array space telescope).

Wait a second. Am I to read this as suggesting that a hypothesis containing a quantum theory of gravity is making a prediction that can be tested? This is strange news indeed.

Is there a place I can read more on this? I'm afraid to pull the paper itself, as I may understand very little of it.

 

[metrictensor]

Marcus,

thanks for the posts. I am reading a short Tibetan paper published over 500 years ago that talks about smallest particles and shortest lengths of time.

 

[marcus]

Wait a second. Am I to read this as suggesting that a hypothesis containing a quantum theory of gravity is making a prediction that can be tested? This is strange news indeed.

Is there a place I can read more on this? I'm afraid to pull the paper itself, as I may understand very little of it.

where did you get the impression that no version of LQG is testable? (from a string supporter maybe? they say all sorts of things )
Smolin's branch of LQG makes a falsifiable prediction and will be shot down in 2007 or 2008 if GLAST experiment goes as planned and does not see the right things

Smolin has made this point in several recent papers

How Far Are We from the Quantum Theory of Gravity (2003)
An Invitation to Loop Quantum Gravity (2004)
Falsifiable Predictions from Semiclassical Quantum Gravity
(2005)

No need to be diffident or reluctant to look at the "papers themselves". how else can you know what they are saying. Better not trust other people paraphrase. "Invitation" is written for non-specialist.
In the case of "Falsifiable" you can look in the introduction and the conclusions section for the author's own summary in general terms, so it's not a total blank wall

here's a list of Smolin's papers
http://arxiv.org/find/grp_physics/1/au:+smolin/0/1/0/all/0/1

on this list you will see links to all three I mentioned: "Falsifiable"
"Invitation" and "How Far". they all talk about prospects for testing LQG.

 

[Locrian]

where did you get the impression that no version of LQG is testable? (from a string supporter maybe? they say all sorts of things )

Honestly, it is less something I hear from some particular group, and more a reflection of my disgruntlement with modern theoretical physics.

I appreciate the links, am doing my best to bravely review the "Falsifiable" paper, and hope you will post as more information on this topic becomes available.

 

[marcus]

.. and more a reflection of my disgruntlement with modern theoretical physics.
...

that I can really understand!
and there is plenty to be frustrated about (not only mod. theo. phys. in general but also) in LQG in particular.

this split betw. Smolin interpretation and other is not something i completely understand. But he is increasingly definite about it, that there must be some tiny difference in speed of photons at very high energy that wd show up for very high energy photons that have traveled billions of LY.

there is plenty to be confused about and frustrated about. but at least he say that for HIS way of formulating LQG it requires this effect to be seen.
it is an unambiguous prediction. no waffling on his part.

but then it seems like Rovelli has a different model of LQG that does NOT require this, so I am still waiting for some clarification.

 

[Locrian]

I did my best to wade through the "falsifiable" paper. I found it odd though; he does make a very specific claim that his hypothesis can be differentiated from the two others.

However, he doesn't, to me, seem to clearly indicate how. I apoligize but can you help me? I don't see the actual prediction, just a prediction that the observation will decide one idea over another.

 

[Hurkyl]

The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area.

Oh, that's cool, I can see how that one works!

 

[selfAdjoint]

Oh, that's cool, I can see how that one works!

Yes, isn't it? I want to study and see how the Rovelli and Smolin versions of LQG differ, to make this disagreement possible. Has Smolin just failed to grasp the subtle point about the spectrum of eigenvalues? Or does his system not have the quantized areas and volumes that the other theorists are so proud of? Note however that if I am not mistaken, no version of LQG has a spectrum of quantized lengths.

 

[marcus]

Does anyone know how in LQG they avoid the contradiction of a smallest unit of quantized space and Lorentz contraction?

this is a really good question and several people on the thread raised issues we should keep thinking about

but the thread stopped, not because anything was resolved, but because we didnt know anything more to add.

now we have a thread "Quantum time" that wolram started, and it connects to this one, so I want to look at this one again

 

[etera]

Hello,
First, the usual version of LQG has a quantized spectrum of lengths (see one of Thiemann's 96 papers)...
Then it is not obvious that Smolin's proposal is inconsistent with Rovelli's analysis. Rovelli simply points out that the behavior of a quantum length under boost is similar to the behavior of the spin of a particle under SU(2). If I try to contract a distance of one Planck unit, i will just have an increased probability of actually measuring a zero distance (here, i completely avoid the measurement problem in quantum gravity...). Then Rovelli doesn't give the relationship between the shift of probabilities and the boost parameter i.e. the precise actiobn of the Lorentz boosts, because this would depend of the precise quantum geometry state. On the other hand, the Smolin proposal, which tries to extract a DSR-like theory from Loop Quantum Gravity, doesn't break the Lorentz invariance but instead uses a deformed (non-linear) action of the Lorentz group. Nobody has checked whether this is the precise action which comes out of LQG - actually, i don't know of somebody who would know how :) Also there is a lot of discussion on what is to be called the space-time in a DSR theory which is based on a nono-commutative geometry. So nobody has yet made robust predictions on the deformation of the length contraction in DSR. I tried to make a little sense of this in my work with Oriti, where actually the LQG toy model is very similar to a DSR theory.
Finally, in 2+1d quantum gravity, LQG is a DSR theory (see the work by the series of papers by Freidel and al.). The length has a discrete spectrum (it replaces the area operator of 3+1d LQG). and everything fits together. The hope is that the same "miracle" happens in 3+1d.. hopefully!

 

[Chronos]

Etera, I had to read that three times before the lights came on. It vaguely reminded me of an essay entitled 'Some Remarks on the Semi-Classical Limit of Quantum Gravity'.