Is Loop Quantum Gravity a Machian theory?

[quickAndLucky]

Hi All!
I have heard that loop quantum gravity is a "background independent" theory, in that there is no preferred coordinate system. Is LQG also a Machian theory?

 

[Demystifier]

LQG is based on GR, and GR is not a Machian theory, so LQG is not a Machian theory.

 

[spacejunkie]

As GR (in a particular gauge) is dual to Shape Dynamics (in a particular gauge) and since SD is a Machian theory (if you accept Barbour's definition of Mach's Principle arXiv:1007.3368v1) then in some sense some solutions of GR are Machian.

If you swallow that then a look at the following papers may provide some insight into the OP:-
"Linking shape dynamics and loop quantum gravity"
L Smolin arXiv:1407.2909v1

"LOOP QUANTIZATION OF SHAPE DYNAMICS"
T Koslowski arXiv:1302.7037v1

 

[haushofer]

LQG is based on GR, and GR is not a Machian theory, so LQG is not a Machian theory.

Can you say that if the classical limit of LQG is still unknown? For string theory I'm pretty sure that it's not Machian as it reproduces GR plus stringy corrections and allows for the Minkowski vacuum, but for LQG I'm not sure.

 

[Demystifier]

Can you say that if the classical limit of LQG is still unknown?

It is believed that classical limit of LQG is GR, but there is no rigorous proof. If one day someone proves the opposite, namely that certain precise formulation of LQG does not have GR as its classical limit, then this particular formulation of LQG will be abandoned and a different version of LQG will be called "the" LQG.

Similarly to string theory, LQG is not a single uniquelly defined theory, but a broad and flexible theoretical framework.

 

[tzimie]

It is believed that classical limit of LQG is GR

GR or Cartan-GR?

 

[haushofer]

GR in the vielbein formalism. I guess that's called Einstein-Cartan formalism, but perhaps I'm mistaken.

 

[Demystifier]

GR or Cartan-GR?

I think this question is only relevant at points at which fermions are present:
http://lanl.arxiv.org/abs/gr-qc/0505081