## Loop Quantum Gravity

Study matter and its motion through spacetime...

### Re: Loop Quantum Gravity

Joe09 wrote:No its not your fault, i can follow disorganised trains of thought if i understand them, i just dont have the knowledge yet with what your writing.

Soon, ill be doing Foundation Physics Degree this september (i didnt do well at college) and then after ill be doing Bsc Physics with Astrophysics at Leicester

I understand more about star evolution (than would be expected with my physics knowledge) but thats probably because it fascinates me alot more. For my A2 Physics research paper i did 'What is a neutron star?' got an A in that

Leicester have a long history with astrophysics, so you should be able to get very good GR teaching there. Just make sure you choose maths options which includes calculus of several variables and differential geometry as much as possible.
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### Re: Loop Quantum Gravity

newolder wrote:How is a topic 'stickied', I wonder?

In a recent video-google lecture, Lee Smolin uses LQG to predict the speed of light increases with increasing energy but he gave no mathematical symbols in that talk showing how. Fractional dimensions show such features clearly with bit-maps and paint. The separation between 'Mandelbrot islands' (if real) is likely to remain unengineerable for a while yet... Unless someone has drawings of a vacuum energy pump in action.

Oh, interesting, I haven't got that far yet, so haven't come across that "feature". I wonder if that's related to Doubly Special Relativity that people were talking about a while back ?

I thought this table was kind of interesting:

LQGString.jpg (142.82 KiB) Viewed 2914 times

It's the last slide in Lee Smolin's talk. I'm sure string theorists might rank some of the items differently (for example, for "explains initial conditions" I would think they'd give string theory a bit more than a question mark !) , but at least it's a starting point for a quantum gravity hobbyist to compare the two approaches.
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### Re: Loop Quantum Gravity

The prediction is somewhere after 1/2-way... rewatching now for the time-stamp...

Perhaps you feel up to writing summaries of some other cosmo-models since 1998 in this or other topics too, please?
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### Re: Loop Quantum Gravity

When traveling at the speed of light, 100% of momentum is directed towards moving through space (in terms of spacetime) and 0% is directed at moving through time. The reason that the speed of the light is supposed to be the limit, is because you can't have 101% directed towards moving through space as it would follow that you would have -1% of momentum directed towards moving through time, and you'd go backwards which would violate causality.

I guess what he's saying is, that not all 100% momentums are created equal, and thus something with more relativistic mass could have more energy directed at traveling through space. While this would NOT violate causality, I don't know that it's accurate.
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### Re: Loop Quantum Gravity

Starting at around slide 67 in this link, Smolin talks about an energy dependent violation of the SR relation

E2 = p2+m2
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### Re: Loop Quantum Gravity

twistor59 wrote:Starting at around slide 67 in this link, Smolin talks about an energy dependent violation of the SR relation

E2 = p2+m2

Therfore:

mc2 = (sqrt)|p2+m2?
Stephen Colbert wrote:Now, like all great theologies, Bill [O'Reilly]'s can be boiled down to one sentence - 'There must be a god, because I don't know how things work.'

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### Re: Loop Quantum Gravity

num1cubfn wrote:
twistor59 wrote:Starting at around slide 67 in this link, Smolin talks about an energy dependent violation of the SR relation

E2 = p2+m2

Therfore:

mc2 = (sqrt)|p2+m2?

except the "m" on the RHS is the rest mass, whereas your LHS "m" would be the relativstic mass. The formula I gave was the usual relation for the squared length of the energy momentum 4 vector. He's suggesting that might change ....

ETA also I'm using "natural units" where c=1. (Might not be a great choice if c varies !)
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### Re: Loop Quantum Gravity

From that tewb above...

Predictions around 43:18 : Doubly Special Relativity: The speed limit, c, only applies in low energy phenomena. Planck length physics ahead...

45:10 : The speed of light increases with energy: δc/c goes as lPlanck E.
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### Re: Loop Quantum Gravity

Added the topic to my bookmarks.

Thanks a lot for the free education twistor (and newolder)
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### Re: Loop Quantum Gravity

Googling around, I get the impression that there are two variants of LQG around:

Smolin's, which requires Doubly Special Relativity, (or Deformed Special Relativity) and leads to the energy dependent light speed prediction. The second is

Rovelli's which does not require this.

Here is a paper on it with a very interesting looking abstract !

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.

Bit frustrating that there are two variants, but still, better than a landscape !!
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### Re: Loop Quantum Gravity

Didn't Rovelli speak at Strings2010, CERN? I'll have a rootle... brb.

Still rootling...
Regarding [url]Rovelli[/url]^.

Yes, but... Twist the Planck area from unitarity and I can't see how this idea is any different from a landscape beyond the horizon. A googolplex to the power of a Graham, hardly seems to be the beginning of the possibilities implied.

Nope. I've fuxed pu summerz. Rovelli not registered @ http://indico.cern.ch/conferenceTimeTab ... 7#20100125
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### Re: Loop Quantum Gravity

newolder wrote:Didn't Rovelli speak at Strings2010, CERN? I'll have a rootle... brb.

Well, I'm pretty sure he spoke at Cern in 2008. Not sure if it was the strings conference though. Oh yes ....

newolder wrote:

Yes, but... Twist the Planck area from unitarity and I can't see how this idea is any different from a landscape beyond the horizon. A googolplex to the power of a Graham, hardly seems to be the beginning of the possibilities implied.

Sometimes I just don't understand what you young people are saying to each other

Where do you see a googolplex to the Graham ? The string landscape is populated by parameters in the theory - compactifications etc, but in LQG there aren't too many free parameters that I've come across yet. Just the Immirizi parameter so far....
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### Re: Loop Quantum Gravity

twistor59 wrote:...
Sometimes I just don't understand what you young people are saying to each other

Where do you see a googolplex to the Graham ? The string landscape is populated by parameters in the theory - compactifications etc, but in LQG there aren't too many free parameters that I've come across yet. Just the Immirizi parameter so far....

Rovelli, your ref. wrote:In this paper we consider the quantum theory corresponding to this dynamical system. In particular, we consider the quantum operators corresponding to the physically observable quantities A and A′, we show that (1) is true, and that the operator A′ can be obtained (under certain assumptions) from a unitary transformation that implements a local Lorentz transformation in the Hilbert space of the theory.

Edit: Where (1) is from earlier:
Now, our main point is the technical observation that A and A′ do not commute:
[A,A′ ] ≠ 0. (1)

A 'unitary transformation' preserves all constant ratios, doesn't it? What if nature is not unitary?
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### Re: Loop Quantum Gravity

twistor59 wrote:
Joe09 wrote:No its not your fault, i can follow disorganised trains of thought if i understand them, i just dont have the knowledge yet with what your writing.

Soon, ill be doing Foundation Physics Degree this september (i didnt do well at college) and then after ill be doing Bsc Physics with Astrophysics at Leicester

I understand more about star evolution (than would be expected with my physics knowledge) but thats probably because it fascinates me alot more. For my A2 Physics research paper i did 'What is a neutron star?' got an A in that

Leicester have a long history with astrophysics, so you should be able to get very good GR teaching there. Just make sure you choose maths options which includes calculus of several variables and differential geometry as much as possible.

I will thankyou
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### Re: Loop Quantum Gravity

newolder wrote:
Rovelli, your ref. wrote:In this paper we consider the quantum theory corresponding to this dynamical system. In particular, we consider the quantum operators corresponding to the physically observable quantities A and A′, we show that (1) is true, and that the operator A′ can be obtained (under certain assumptions) from a unitary transformation that implements a local Lorentz transformation in the Hilbert space of the theory.

Edit: Where (1) is from earlier:
Now, our main point is the technical observation that A and A′ do not commute:
[A,A′ ] ≠ 0. (1)

A 'unitary transformation' preserves all constant ratios, doesn't it? What if nature is not unitary?

Unitarity in this context is referring to the representation of the Lorentz group on the Hilbert space of quantum states. The transformations need to be represented in terms of unitary operators so that Hilbert space scalar products <| |> are preserved. If they weren't then it would be difficult to proceed, since stuff like normalization wouldn't stay constant in time, and states which are orthogonal to each other wouldn't stay orthogonal.

Until I saw it, I'd never even thought of the question the paper was addressing - "how can the Planck length be a minimum length if you can make it aribitrarily small for different observers by Lorentz contraction ?"

Clever People wrote:It follows that a generic eigenstate of A is not an eigenstate
of A′. If the observer O measures the area and obtains
the minimal value A0, the state of the gravitational
field will be projected on an eigenstate of A. This, in
turn, is not going to be an eigenstate of A′. If then the
observer O′ measures the area, he will therefore find the
state in a superposition of eigenstates of A′. That is to
say, the theory predicts that, for him, the surface does
not have a sharp area. If the experiment is repeated several
times, O′ will observe a probability distribution of
area values. The mean value of the area can be Lorentz
contracted, while the minimal nonzero value of the area
can remain A0.
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### Re: Loop Quantum Gravity

The prediction is somewhere after 1/2-way... rewatching now for the time-stamp...

Perhaps you feel up to writing summaries of some other cosmo-models since 1998 in this or other topics too, please?

I just watched the video (alternative would have been Eastenders !) - interesting talk. I liked the point he made about the greats of the early 20th century working in an isolated way, and having a strong philosophical bent. I remember reading Einstein's little book "The Meaning of Relativity" and wondering WTF he was on about when he kept rabbiting on about ontology and epistemology.

Towards the end, Lee S mentioned GLAST as a potential falsifier of DSR. Do you know if anything has emerged from GLAST on this yet ?
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### Re: Loop Quantum Gravity

twistor59 wrote:...

Clever People wrote:It follows that a generic eigenstate of A is not an eigenstate
of A′. If the observer O measures the area and obtains
the minimal value A0, the state of the gravitational
field will be projected on an eigenstate of A. This, in
turn, is not going to be an eigenstate of A′. If then the
observer O′ measures the area, he will therefore find the
state in a superposition of eigenstates of A′. That is to
say, the theory predicts that, for him, the surface does
not have a sharp area. If the experiment is repeated several
times, O′ will observe a probability distribution of
area values. The mean value of the area can be Lorentz
contracted, while the minimal nonzero value of the area
can remain A0.

Clever stuff.
Ignoring unitarity for a mo', something that calculates a probability of an area value that is statistically smudged and observer dependent looks like the beginning of tiling a landscape to me.

GLAST was renamed to the Fermi Telescope and its 1st year of ops. helped test any energy relation for c with no positive result, as yet: http://www.nasa.gov/mission_pages/GLAST ... _year.html
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### Re: Loop Quantum Gravity

newolder wrote:

Ignoring unitarity for a mo', something that calculates a probability of an area value that is statistically smudged and observer dependent looks like the beginning of tiling a landscape to me.

I suppose if you want to think of the quantum spacetime as a landscape, yes. But my understanding (maybe wrong ?) of the string landscape is that it's a landscape of possible theories, which is something not quite as nice like.

newolder wrote:
GLAST was renamed to the Fermi Telescope and its 1st year of ops. helped test any energy relation for c with no positive result: http://www.nasa.gov/mission_pages/GLAST ... _year.html

Ah thanks. I thought you might know - you seem to have your finger on the astrophysical pulse.
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### Re: Loop Quantum Gravity

Joe09 wrote::shock: i cant get to uni quicker

Mostly its post doctorate stuff I think, and you'll have to be damned good to get involved at any level that will get you in on the ground floor. You'll be at it for a while. But hell I'd give my high teeth to know about this stuff at more than a pop science level. Kudos to twistor for his posts. Bookmark.

I don't like the Big Bang but that clip is superb btw.
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### Re: Loop Quantum Gravity

The Damned wrote:
Joe09 wrote::shock: i cant get to uni quicker

Mostly its post doctorate stuff I think, and you'll have to be damned good to get involved at any level that will get you in on the ground floor. You'll be at it for a while. But hell I'd give my high teeth to know about this stuff at more than a pop science level. Kudos to twistor for his posts. Bookmark.

I don't like the Big Bang but that clip is superb btw.

it's grad school stuff. But as long as you have the math and basic degree of physics knowledge you should be fine

Sorr twistor, I've started reading this stuff yet. maybe over this weekend

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