What is the acceleration formula for particles in Loop Quantum Gravity?

[naima]

There are thousands of papers in Marcus "intuitive" LQG.
I hope that some of his readers will be able to answer my question.
In Classical Physics or in GR we have a formula that gives the acceleration of a particle in a gravitational field.
What is the corresponding formula in LQG?

 

[marcus]

hi Naima, the thread title goes back to early days before the thread became a bibliography. It has lots of papers that are not "intuitive".

Did you try the Zakopane Lectures paper? I'll get a link. Let's see if this has what you are looking for.
http://arxiv.org/abs/0905.4082
LQG propagator from the new spin foams
Eugenio Bianchi, Elena Magliaro, Claudio Perini
(Submitted on 25 May 2009)
We compute metric correlations in loop quantum gravity with the dynamics defined by the new spin foam models. The analysis is done at the lowest order in a vertex expansion and at the leading order in a large spin expansion. The result is compared to the graviton propagator of perturbative quantum gravity.
Comments: 28 pages Nuclear Physics B (2009) http://inspirehep.net/record/821286?ln=en

http://arxiv.org/abs/1109.6538
Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
Comments: 13 pages, Physical Review D (2012) http://inspirehep.net/record/929987?ln=en

 

[atyy]

Try http://arxiv.org/abs/1401.5262, especially the part around Eq 52. I think it is quite speculative, so he is using a mix of physical intuition and how LQG should work if it does.

"The external observer is an accelerated observer which can measure local aspects of the geometry. The states ... describe a portion of a quantum surface, a small facet with given area Af and normal in direction ... The evolution of the facet state in spacetime as seen by an accelerated observer is generated by the unitary operator representing a Lorentz boost ... with a being the acceleration of the observer." [bolding by me]

 

[julian]

There is the paper by Rovelli "Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity"

http://fr.arxiv.org/pdf/1307.3228

"We do not employ the full machinery of spinfoam cosmology [16, 17]. The key to our derivation relies on a
core aspect of the covariant approach: the proportionality between generators of boosts and rotations [15]. This ties space-space and space-time components of the momentum conjugate to the gravitational connection and transfers the discretization of the area spectrum to a discretization of a suitable Lorentzian quantity, which, we show, is related to acceleration."

 

[naima]

Thank you
I find here that for the Rindler observer the acceleration that he "feels" is related to distance between him and the horizon. this distance is constant for him. He feels the heat of the horizon. If he meets a "free falling" observer (x = constant) this observer will tell him that there is no heat an no horizon. It is the same thing with a black hole.
So definining a surface in space time as an horizon determines, for an observer at a given distance of it, a temperature and an acceleration? Is it general?
It looks like Verlinde's paper.

 

[naima]

I have a question about the "eternally" accelerated observer
Look at Fig 1. It is interesting to know that the acceleration is related to the shaded area but the trlation with the distance to H seems more important.
One is global and one is local.
It is obvious to me that if at a given moment the Rindler observer is in a thermal bath this does not depend on his ability to turn off later the engine of his rocket.
Same for the past.
So why do we read this "eternal" word. Is it because equilibrium situations are simpler?

 

[julian]

I have a question about the "eternally" accelerated observer
Look at Fig 1. It is interesting to know that the acceleration is related to the shaded area but the trlation with the distance to H seems more important.
One is global and one is local.
It is obvious to me that if at a given moment the Rindler observer is in a thermal bath this does not depend on his ability to turn off later the engine of his rocket.
Same for the past.
So why do we read this "eternal" word. Is it because equilibrium situations are simpler?

In the quantum theory areas can be given a clear-cut meaning - distances not so much...I was reading something about this and distances - I'll have to find it again.

 

[julian]

I think this is what I was looking at:

https://workspace.imperial.ac.uk/th...ic%2FMSc%2FDissertations%2F2014&CurrentPage=1