I What Are the Empirical Challenges Facing Quantum Gravity Theories?

[Nullstein]

An intermediate step, like quantizing Fermi's theory of the weak interactions :P

It might as well become a success story, like quantizing classical electrodynamics. Nobody can tell at this point in time. At least, it's a reasonable approach, no less reasonable than quantizing classical electrodynamics. But it has to be done well. Sure it may fail, but it's worth a try.

Can you e laborate on these canonical variables and what's odd about them?

They have no immediate physical meaning. What you do in LQG is to start from the vielbein formulation of GR, where the basic variables are the frame field and the spin connection. This is reasonable, one needs to do it anyway to allow for the inclusion of spinor fields. Then you make a 3+1 split, which is also reasonable if you want to obtain a Hamiltonian formulation. But then you go ahead and form new variables by adding the spin connection to the extrinsic curvature of the spatial slices. How is this a reasonable physical quantity? It's like adding apples and oranges and only accidentally works in 3 dimensions (because the adjoint representation of $SO(3)$ is equivalent to the defining representation). Morover, one introduces a new parameter (the Immirzi parameter), which classically cancels out, but remains important in the quantum theory. With these new variables, many equations simplify or become more elegant. The theory then looks like a Yang-Mills theory with additional constraints, but at the cost of having had to add apples to oranges in an early step of the calculation.

 

[*now*]

In what sense do these articles provide any new insight into the separability of the LQG Hilbert space? The first three articles are concerned with experimental testing only. And the research by Freidel et al. on edge modes is an independent approach to developing a theory of quantum gravity and so far mostly classical analysis. Little is known yet about the potential quantum gravity theory that is supposed to arise from this. The fourth paper of the series, which is presumably supposed to be on Hilbert space aspects, has been announced, but not appeared yet, so even if you want to count this new approach towards the LQG family of theories, no conclusions about the separability of the Hilbert space can be drawn so far.

Yes, I think I’ve previously linked e.g. a Lorentzian description in LQC somewhere in a thread here. There are varied alternatives and some crossovers and a description of Freidel’s recent work in a talk might interest Introduction to local holography - Laurent Freidel - Bing video . The tests linked for a start might add more weight towards distinguishing between differing descriptions, which might be related to papers such as this-Carlo Rovelli (Dated: February 8, 2018) [Written for the volume “Beyond Spacetime: The Philosophical Foundations of Quantum Gravity” edited by Baptiste Le Biha, Keizo Matsubara and Christian Wuthrich.]

Space and Time in Loop Quantum Gravity
Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.

https://arxiv.org/pdf/1802.02382.pdf

 

[physika]

An intermediate step, like quantizing Fermi's theory of the weak interactions :P

mends and mends botches...

 

[Nullstein]

Yes, I think I’ve previously linked e.g. a Lorentzian description in LQC somewhere in a thread here. There are varied alternatives and some crossovers and a description of Freidel’s recent work in a talk might interest Introduction to local holography - Laurent Freidel - Bing video . The tests linked for a start might add more weight towards distinguishing between differing descriptions, which might be related to papers such as this-Carlo Rovelli (Dated: February 8, 2018) [Written for the volume “Beyond Spacetime: The Philosophical Foundations of Quantum Gravity” edited by Baptiste Le Biha, Keizo Matsubara and Christian Wuthrich.]

Space and Time in Loop Quantum Gravity
Quantum gravity is expected to require modifications of the notions of space and time. I discuss and clarify how this happens in Loop Quantum Gravity.

https://arxiv.org/pdf/1802.02382.pdf

I think I've lost track of what we're talking about here. Are we still discussing Lorentz invariance? Then I don't see how these references support your point.

 

[*now*]

I’d been thinking of issues generally that along with possible narrowing of alternatives discussed in the OP source there is breadth of other possible directions and emphases towards open questions, and those raised may be examples of, but replying has been problematic and on second thoughts I think that absent citing the author’s express words attempting to speak of the author’s possible opinions or intuitions or variations seems very problematic.

 

[arivero]

I was looking for discussion on a old paper by Rovelli and Connes and I wonder we do we keep closing topics...

https://www.physicsforums.com/threa...r-on-time-in-gen-cov-quantum-theories.392819/

I guess it is a general "feature" of forums, but well, this field of science is not fast-paced.