Is Loop Quantum Gravity a Machian theory?

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Discussion Overview

The discussion centers on whether loop quantum gravity (LQG) can be classified as a Machian theory, exploring the relationship between LQG, general relativity (GR), and Mach's principle. The scope includes theoretical implications and the nature of LQG in relation to classical limits and alternative formulations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that since LQG is based on GR and GR is not a Machian theory, LQG cannot be considered Machian.
  • Others propose that certain solutions of GR, when viewed through the lens of Shape Dynamics (SD), could be interpreted as Machian, suggesting a potential connection to LQG.
  • There is uncertainty regarding the classical limit of LQG, with some believing it to be GR, while others note the lack of rigorous proof for this claim.
  • Participants discuss the flexibility of LQG as a theoretical framework, indicating that it is not a singularly defined theory.
  • Questions arise about the relevance of different formulations of GR, such as Einstein-Cartan formalism, particularly in contexts involving fermions.

Areas of Agreement / Disagreement

Participants express differing views on whether LQG can be classified as Machian, with no consensus reached. The discussion remains unresolved regarding the implications of the classical limit of LQG and its relationship to GR.

Contextual Notes

There are limitations in the discussion regarding the definitions of Mach's principle and the conditions under which LQG might be considered Machian. The relationship between different formulations of GR and their implications for LQG is also not fully clarified.

quickAndLucky
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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?
 
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LQG is based on GR, and GR is not a Machian theory, so LQG is not a Machian theory.
 
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
 
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Demystifier said:
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.
 
haushofer said:
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.
 
Demystifier said:
It is believed that classical limit of LQG is GR

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

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