A Loop Quantum Gravity proven wrong?

[Nickyv2423]

https://arxiv.org/abs/1411.1935
This paper says LQG does not produce the Unruh effect effect, and therefore must be wrong. What do you guys think.
You can click into the PDF to see the entire paper.

 

[mfb]

This paper says LQG does not produce the Unruh effect effect, and therefore must be wrong.

No it does not. It says LQG does not produce the Unruh effect - I cannot comment on the validity of that statement. There is no experimental evidence for the Unruh effect. The authors conclude that experimental tests of it can either verify or rule out LQG in the future.

 

[kodama]

LQG predicts the Unruh Effect. Comment to the paper "Absence of Unruh effect in polymer quantization" by Hossain and Sardar
Carlo Rovelli
(Submitted on 25 Dec 2014)
A recent paper claims that loop quantum gravity predicts the absence of the Unruh effect. I show that this is not the case, and take advantage of this opportunity to shed some light on some related issues.
Comments: 3 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1412.7827 [gr-qc]
(or arXiv:1412.7827v1 [gr-qc] for this version)

 

[MathematicalPhysicist]

Predicting or not predicting an effect which is only theoretical and not yet proven empirically, now I understand the trouble with physics.

 

[Urs Schreiber]

Notice that the "polymer quantization" used in LQG (as in the article cited in #1: "Absence of Unruh effect in polymer quantization" https://arxiv.org/abs/1411.1935) is so remote from anything else in physics that it is a moot point to argue whether it reproduces any specific effect in physics (whether experimentally observed or hypothesized).

LQG suffers from two problems of approach, the first in the kinematics, the second in the dynamics.

The kinematic problem is that right after the decision to encode the spacetime metric in the holonomy of the Levi-Civita connection (that this works is a theorem) next people pass from actual connections to "generalized connections". A "generalized connection" in the sense of the LQG literature is an assignment of holonomies (or rather parallel transports) to paths which is not required to be smooth or even continuous anymore. This is done right at the beginning and often not emphasised much. The only reason is that understanding the space of actual connections is hard, while the space of these "genealized connections" is simply a vast Cartesian product of copies of the spacetime group. But the problem is that by dropping smoothness and even continuity, thereby all geometry is turned into a dust of points, and the resulting "generalized connections" have no relation to actual field configurations of gravity anymore, even before or after quantization. But now in LQG they go ahead and quantize these dustified fields in the naive pointwise sense, and this is what brings in non-separable Hilbert spaces, the apparent discreteness (worse: dustiness) and the lack of any way to connect any of this back to actual spacetime physics in any limit. When this issue began to at least be appreciated as an issue, people started saying that it is a new way of quantization, and started calling it "polymer quantization". That gives the idea a name and serves at least to highlight that this is not following the rules for what it usually means to quantize, but of course giving the problem a name does not yet solve it.

The second problem of LQG is that, even if this exotic "polymer" quantization of gravity is considered, then there is still no way to define or even solve the Hamiltonian constraint.

In conclusion we have a quantization scheme that drastically departs from the rules right from the get go and then fails to complete even according to those simplified exotic rules.

Therefore it is baseless to argue whether LQG sees the Meissner effect or the Unruh effect or any other effect in physics. What would first need to be established is any relation of LQG to physics as such. Once that is established, then it would make sense to ask how any specific effect in physics translates into a statement in "polymer quantized gravity".

 

[julian]

...next people pass from actual connections to "generalized connections". A "generalized connection" in the sense of the LQG literature is an assignment of holonomies (or rather parallel transports) to paths which is not required to be smooth or even continuous anymore. This is done right at the beginning and often not emphasised much. The only reason is that understanding the space of actual connections is hard, while the space of these "genealized connections" is simply a vast Cartesian product of copies of the spacetime group

See page 258 of "String Gravity and Physics at the Planck Scale":

"While we can restrict ourselves to suitably smooth fields in the classical theory, in quantum field theory, we are forced to allow distributional field configurations. Indeed, even in the free field theories in Minkowski space, the Gaussian measure that provides the inner product is concentrated on genuine distributions. This is the reason why in quantum theory fields arise as operator-valued distributions."

These so-called "quantum configuration spaces" that include distributional fields are not something unique to LQG.

 

[julian]

https://arxiv.org/pdf/gr-qc/0403047.pdf

Separable Hilbert space in Loop Quantum Gravity
Winston Fairbairn and Carlo Rovelli

We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is non-separable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the physics of the theory. We investigate the possibility that these moduli could be only the consequence of a poor choice in the fine-tuning of the mathematical setting. We show that by simply choosing a minor extension of the functional class of the classical fields and coordinates, the moduli disappear, the knot classes become countable, and the kinematical Hilbert space of loop quantum gravity becomes separable.

In the introduction they in addition note that "As pointed out in [14], the nonseparability of $H_{diff}$ is not necessarily unacceptable, because $H_{diff}$ is a kinematical space that must still be reduced by the hamiltonian constraint equation."

 

[tom.stoer]

LQG suffers from two problems of approach, the first in the kinematics, the second in the dynamics.

The kinematic problem is that ... people pass from actual connections to "generalized connections". A "generalized connection" ... is an assignment of holonomies ... to paths which is not required to be smooth or even continuous anymore. This is done right at the beginning and often not emphasised much.

Can you please comment on this? Which set of equations do you mean?

I was aware of the issues in the quantization procedure, especially the was the constraints are implemented (no off-shell closure etc.), but it seems that I overlooked something.

... and the resulting "generalized connections" have no relation to actual field configurations of gravity anymore, even before ... quantization.

Again: Which set of equations do you mean?

The second problem of LQG is that, even if this exotic "polymer" quantization of gravity is considered, then there is still no way to define or even solve the Hamiltonian constraint.

After decades the definition (regularization) is still not fully clear; that's a fundamental problem. But not being able to solve it is not a fundamental problem, right?

Thanks