# In LQG, do objects attract via gravitons or curved spacetime

1. Aug 4, 2015

### kodama

planet earth and the sun. in GR, gravity is not a force but simply a manifestation of spacetime curvature. the sun curves spacetime and the earth is simply traveling through geodesic motion through curved spacetime.

in string theory, the sun and earth exchange virtual gravitons through a massless spin-2 field that couples to stress-energy tensor. this creates effects identical to gravity.

in LQG, which picture explains the attraction the sun and earth have for one another, is earth traveling through curved spacetime or is it via graviton exchange?

is there a quantum mechanical description of how mass-energy curves spacetime? i.e how does quantum mechanical matter interact quantum mechanically with quantum spacetime that produces curved space?

are there any QG that does not have any notion of gravitons, but explains gravity in terms of curved spacetime?

2. Aug 4, 2015

### ohwilleke

LQG theories are generally formulated from first principles in terms of the structure of space-time in a manner that is discrete at a scale generally assumed to be the Planck scale. In other words, to the extent that there are gravitons in LQG, this is a conclusion of the theory, rather than one of its axioms.

I don't know enough to say whether gravitons and/or spacetime curvature arise emergently from that starting point, although I do know that a key property of space-time in most LQG theories (its number of space and time dimensions) does arise emergently, rather than being put in by hand as it is in GR and string theory. Another property of space-time that is assumed in GR and in string theory is that space-time is a smooth, continuous manifold with no non-local connections. In contrast, in most LQG theories, the locality of space-time connections is also an emergent quality observed only statistically, and not perfectly in every case.

3. Aug 7, 2015

### julian

Rovelli et al have made much progress in calculating background independent scattering amplitudes with the use of spin foams. This is a way to extract physical information from the theory. Claims to have reproduced the correct behaviour for graviton scattering amplitudes and to have recovered classical gravity have been made. "We have calculated Newton's law starting from a world with no space and no time." - Carlo Rovelli (here gravitons are emergent degrees of freedom - and this is just one result). Curved spacetime and classical GR as the semi-classical limit is also supposed to emerge hopefully! Not sure what the current status of this key issue is.

Last edited: Aug 7, 2015
4. Aug 7, 2015

### kodama

if you have curved spacetime do you really need gravitons and vice versa?

5. Aug 7, 2015

### julian

Deeper question than I would like to get into - I think there is another thread on gravitons and GR. I'll just say that what Rovelli is doing is a way to recover low–energy physics (though in LQG gravitons are to be thought of as like quasi particles I think). In the absence of establishing an unequivocal proof that LQG has the correct semi-classical limit...it is something.

Here are a couple of interesting papers by Smolin I found:

"Newtonian gravity in loop quantum gravity" http://fr.arxiv.org/pdf/1001.3668

"We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton’s law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime."

"General relativity as the equation of state of spin foam" http://fr.arxiv.org/pdf/1205.5529 :

"Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson’s argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson’s argument to be run. I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria and argue that the third should also be satisfied in loop quantum gravity. I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action."

Last edited: Aug 7, 2015
6. Aug 7, 2015

### julian

Ping:

$\hat{R}_{\mu \nu} - {1 \over 2} \hat{R} \cdot \hat{g}_{\mu \nu} = \kappa \hat{T}_{\mu \nu} [\hat{g}]$

When you do a canonical quatization you are working in the Hamiltonian formulation (which includes the matter hamiltonian). How exactly would you get back to the above equation? Possibly you would consider the initial value Cauchy problem for GR and work backwards?

When you look at the Cauchy problem the field equations split into `evolution' equations (actually gauge transformation equations) and constraint equations (admissibility conditions on the initial data and which are also an imprint of four-fold diffeomorphism invariance of the theory) - the quantum version of these constraint equations are which then become the constraint equations of LQG - which are the main equations of the theory.

Last edited: Aug 7, 2015
7. Aug 7, 2015

### julian

The reason why the quantum constraints are the main equations of LQG is because:

"Lectures on Loop Quantum Gravity" by Thomas Thiemann

http://arxiv.org/pdf/gr-qc/0210094v1.pdf

"Imposition of the Constraints
The two step process in the classical theory of solving the constraints $C_I = 0$ and looking for the gauge orbits is replaced by a one step process in the quantum theory, namely looking for solutions $l$ of the equations $\hat{C}_I l = 0$. This is because it is obviously solves the constraint at the quantum level (in the corresponding representation on the solution space the constraints are replaced by the zero operator) and it simultaneously looks for states that are gauge invariant because $\hat{C}_I$ is the quantum generator of gauge transformations."

Last edited: Aug 7, 2015