I What Are the Empirical Challenges Facing Quantum Gravity Theories?

[Nullstein]

Was a reference provided specific to Rovelli when this was raised earlier in this thread?

Yes, the references given in post #45 address Rovelli of course.

(If you wonder about the model given in Rovelli and Vidotto: This is a spin foam model that doesn't attempt to implement continuous spacetime symmetries in the first place. They are supposed to emerge only on macroscopic scales. Spin foam models start from a discretized version of classical GR and just quantize it, very similar to lattice QFT. The Hilbert space is modeled on fixed graph only, given by the choice of discretization of classical GR. Superpositions of different graphs are impossible.)

 

[*now*]

Thank you, those references also seem quite old and might not account for some recent developments.

This talk from a few years ago seems to expand on some of the issues in the OP paper in the first hour, although I could have a bad link that doesn’t let me watch all of it- hope it works ok here
Also, from what I have seen, at around 50 minutes or so, a list of some developments is displayed in a slide, introduced as to be taken with a smile.

 

[Nullstein]

Thank you, those references also seem quite old and might not account for some recent developments.

Well, the Hilbert spaces used in LQG/Spin foams are still the same today, so the arguments are still valid today. What developments are you thinking of? Can you give some references?

 

[martinbn]

Well, the Hilbert spaces used in LQG/Spin foams are still the same today, so the arguments are still valid today. What developments are you thinking of? Can you give some references?

In the Zakopane lectures, Rovelli constructs and explicitely says that the Hilbert space is seperable.

 

[andresB]

So they can work on whatever they want to work on, without any need for writing proposals for their research?
I am skeptical...

People get paid for doing research?! nobody told that to my 3rd world university.

Joke aside, the issue is not in the highest ranks, pretty much every professor in theoretical physics I know works in whatever he/she wants. The problem is at the Ph.D. and postdocs levels. People tend to go to where the money is, and, in my experience looking for postdocs, there is a disproportionate amount of money and jobs in superstrings and the like. Hence, people tend to flock to those topics resulting in more money being invested in recruiting even more people. It is a "positive" feedback loop.

 

[Nullstein]

In the Zakopane lectures, Rovelli constructs and explicitely says that the Hilbert space is seperable.

That's the same model as the one given in Rovelli and Vidotto. It's formulated on a lattice and doesn't implement any spacetime symmetry at all. There is only the internal Lorentz symmetry at the vertices.

There is no way out. All Hilbert spaces in LQG/Spin Foam models fall under one of the following two cases:

1. The Hilbert space contains uncountably many graphs and states on two different graphs are orthogonal. Then the Hilbert space is non-separable. Continuous symmetries may be implemented, but no nontrivial states can be invariant under a continuous group of symmetries.
2. The Hilbert space is modeled on a lattice, then it may be separable, but no continuous group of spacetime symmetries can be implemented.

The problem is basically that in LQG/Spin Foams, geometry is excited only on lattice-like structures like foams or graphs, i.e. subsets of the manifold that are nowhere-dense. By the Baire category theorem, no neighborhood of any point can be the countable union of nowhere-dense sets. And since states can at most be defined on a countable set of graphs, most points of the neighborhood are not equipped with any kind of geometry and thus no neighborhood can be locally isometric to a region of Minkowski spacetime. In order to circumvent this simple result, there is no other option than to allow geometry to be excited on neighborhoods and no LQG-type model does that.

 

[MathematicalPhysicist]

People get paid for doing research?! nobody told that to my 3rd world university.

Joke aside, the issue is not in the highest ranks, pretty much every professor in theoretical physics I know works in whatever he/she wants. The problem is at the Ph.D. and postdocs levels. People tend to go to where the money is, and, in my experience looking for postdocs, there is a disproportionate amount of money and jobs in superstrings and the like. Hence, people tend to flock to those topics resulting in more money being invested in recruiting even more people. It is a "positive" feedback loop.

Loop that's the keyword here...
We are living in a loop.
Also regarding the ideas in this community.

 

[MathematicalPhysicist]

By community, I am referring to the wide community of BSM.

 

[bland]

Government. (Which gets money from taxpayers.)

Your research is untainted by funds from former 45.

 

[Demystifier]

Your research is untainted by funds from former 45.

What's former 45?

 

[Fra]

But there is no justification for enlarging the symmetry subgroup.

The general motivation they mention seems to be that the moduli space is too large, and unphysical. After all, what is the original justification for the continuous symmetry? This is why I asked "where the hilbert space is encoded" in the other post.

Separable Hilbert space in Loop Quantum Gravity
Winston Fairbairn, Carlo Rovelli, Oct 25, 2018

"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. "

It seems well put to describe the continuum mathematics as a poor choice of fine tuning of the math.

If one add another constraint - that any observer for example have a finite perspective, or a finite information processing resources; set aside the details, this must necessarily make the set of possibilities smaller; as it must be encodable by the observer. I haven't seen a proper argumentation for this however in any of Rovellis papers before, but the general sense in what they say makes sense, and it's rather the original uncountable set of possible states that is what should be questioned.

But what seems be be going on to a certain extents in most approaches (not just LQG), is IMO starting with something that does not make sense (formal expressions which are pathological from the perspective of "inside agents"), then we are force to "make up" arguments to "tame it". Any arguments are likely flawed or ad hoc. The better way should IMO be to step back before we lost track of what we are doing and ended up with formal expressions that are extrapolated way outside their domain of corroboration. For example the whole continuum business, may well be an approximation of something more fundamental - rather than the other way around, which seems to be the more common attitude.

/Fredrik

 

[Nullstein]

The general motivation they mention seems to be that the moduli space is too large, and unphysical. After all, what is the original justification for the continuous symmetry? This is why I asked "where the hilbert space is encoded" in the other post.

What's unphysical is the singular structure of the theory. The non-separability of the Hilbert space is just a consequence of that. Usual QFTs with non-singular observables don't have this problem. The diffeomorphism symmetry is well motivated, because it's a consequence of classical GR. Any enlargement of this symmetry group is an ad-hoc assumption. If there wasn't the problem with the non-separable Hilbert space, nobody would bother to make it.

"However, the continuous moduli labeling these classes do not appear to affect the physics of the theory"

This claim is pretty unsubstantiated, given that not even a single physical observable (i.e. one that commutes with the constraints) is known in this version of LQG.

[...] it's rather the original uncountable set of possible states that is what should be questioned.

It is being questioned, but the solution is certainly not to just define the problem away. And if you check the literature, you will find that nobody in the LQG community actually uses the Hilbert space proposed in that paper in practice.

 

[*now*]

... Can you give some references?

I think the talk gave some developments and references, including those external to the theory like the BMV tests
Witness gravity’s quantum side in the lab | Nature
Phys. Rev. Lett. 119, 240401 (2017) - Spin Entanglement Witness for Quantum Gravity (aps.org)
Also concerning testing, this is a paper concerning time
Frontiers | On the Possibility of Experimental Detection of the Discreteness of Time | Physics (frontiersin.org)
There may be allowances for incorporation of possible quantum or related aspects, but does the literature considered here include papers for instance like these
[2007.12635] Edge modes of gravity. Part III. Corner simplicity constraints (arxiv.org)
https://arxiv.org/abs/2104.12881 ?

 

[Nullstein]

I think the talk gave some developments and references, including those external to the theory like the BMV tests
Witness gravity’s quantum side in the lab | Nature
Phys. Rev. Lett. 119, 240401 (2017) - Spin Entanglement Witness for Quantum Gravity (aps.org)
Also concerning testing, this is a paper concerning time
Frontiers | On the Possibility of Experimental Detection of the Discreteness of Time | Physics (frontiersin.org)
There may be allowances for incorporation of possible quantum or related aspects, but does the literature considered here include papers for instance like these
[2007.12635] Edge modes of gravity. Part III. Corner simplicity constraints (arxiv.org)
https://arxiv.org/abs/2104.12881 ?

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.

 

[mitchell porter]

allow geometry to be excited on neighborhoods

I find myself wondering what this dictum actually means. That the observables in question are associated with open sets? With submanifolds?

 

[Nullstein]

I find myself wondering what this dictum actually means. That the observables in question are associated with open sets? With submanifolds?

It means, as you have guessed, that the observables are associated (at least) with open sets. In QFT, operators can be smeared with test functions that are defined on extended, 4-dimensional regions and you can probe arbitrarily small regions with that. In loopy theories, operators are smeared along lower-dimensional objects such as edges or faces. These objects are nowhere dense subsets of spacetime, so no countable union of them can form an extended, 4-dimensional region. Since all states in the LQG Hilbert space can be obtained by repeatedly acting on the vacuum with these singularly smeared operators, no geometry can be excited on extended, 4-dimensional regions, because only countably many terms are allowed.

 

[Fra]

What's unphysical is the singular structure of the theory.

Yes, this is unphysical, but why? I think it's not because physicists computations crash? I think the biggest problem with singularities, is that the are related to infinite information, in a sense that isn't easily renormalized.

But there are some infinites in other theories, that coincidentally are easily renormalized, but this coincidental success induces an unfortunatey illusion of that it makes universal sense. But the problem for me is the conceptual one with how a finite agent can _relate_ to arbitrary amount of information - in finite time even. So technically, even the curable infinites, are conceptually suspicious. This is why I see it as "unphysical", from the perspective of an observer/agent, which itself is made of matter.

The diffeomorphism symmetry is well motivated, because it's a consequence of classical GR. Any enlargement of this symmetry group is an ad-hoc assumption.

At least from my perspective, it is not trivial to heuristically carry over classical symmetries to an inferential framework where the standards are different(and better). This heuristic reasoning works sometimes, and sometimes not. In GR, I am not convinced that it's well motivated in the context of measurment theory with inside observers. That is "ad-hoc" to me.

/Fredrik

 

[martinbn]

Coming back to this, I have some questions.

That's the same model as the one given in Rovelli and Vidotto. It's formulated on a lattice and doesn't implement any spacetime symmetry at all. There is only the internal Lorentz symmetry at the vertices.

There is no way out. All Hilbert spaces in LQG/Spin Foam models fall under one of the following two cases:

1. The Hilbert space contains uncountably many graphs and states on two different graphs are orthogonal. Then the Hilbert space is non-separable. Continuous symmetries may be implemented, but no nontrivial states can be invariant under a continuous group of symmetries.
2. The Hilbert space is modeled on a lattice, then it may be separable, but no continuous group of spacetime symmetries can be implemented.

The problem is basically that in LQG/Spin Foams, geometry is excited only on lattice-like structures like foams or graphs, i.e. subsets of the manifold that are nowhere-dense. By the Baire category theorem, no neighborhood of any point can be the countable union of nowhere-dense sets. And since states can at most be defined on a countable set of graphs, most points of the neighborhood are not equipped with any kind of geometry and thus no neighborhood can be locally isometric to a region of Minkowski spacetime. In order to circumvent this simple result, there is no other option than to allow geometry to be excited on neighborhoods and no LQG-type model does that.

About 1. I assume you have something specific in mind, because it cannot be true in general without anything additional. For example take any group you like and let it act trivially, then all states are invariant. Do you have a group and and action in mind?

About 2. I don't understand this one. Why would be a spacetime group of symmetries be implemented? The graphs are not a lattice in a apriori space-time. Isn't the space-time and the symmetries supposed to emerge somehow?

 

[Nullstein]

Yes, this is unphysical, but why? I think it's not because physicists computations crash? I think the biggest problem with singularities, is that the are related to infinite information, in a sense that isn't easily renormalized.

The use of the word "singular" here doesn't refer to something becoming infinite. It just means that the spacetime geometry is modeled on structures whose dimension is lower than the dimension of the spacetime manifold.

About 1. I assume you have something specific in mind, because it cannot be true in general without anything additional. For example take any group you like and let it act trivially, then all states are invariant. Do you have a group and and action in mind?

Yes, of course I'm thinking of non-trivial group actions. But more specifically, the action of the diffeomorphism group in this formalism is given by $(U_\phi\psi_\gamma)(\vec g) =\psi_{\phi(\gamma)}(\vec g)$, where $\phi$ is a diffeomorphism. And unless $\phi=\mathrm{id}$, this action has the peculiar feature that $U_\phi\psi_\gamma$ is orthogonal to $\psi_\gamma$.

About 2. I don't understand this one. Why would be a spacetime group of symmetries be implemented? The graphs are not a lattice in a apriori space-time. Isn't the space-time and the symmetries supposed to emerge somehow?

A spacetime is a manifold equipped with a metric. The graphs are embedded into the spacetime manifold. The metric becomes a quantum field instead of a classical field. (LQG gives meaning only to coarse functions of the metric, smeared along lower dimensional submanifolds.) The points that don't lie on the graph are still there in the spacetime manifold and diffeomorphisms still act on the whole manifold. Such points just don't carry any geometry due to the peculiar nature of the theory. Now the hope is to construct states such that e.g. $\left<\hat g_{\mu\nu}(x)\right>$ (or at least the smeared versions of it) resembles classical solutions to the EFE with some quantum corrections. You can then ask for example if there are diffeomorphisms $\phi$ such that something like $\left<(\phi^*\hat g)_{\mu\nu}(x)\right> = \left<\hat g_{\mu\nu}(x)\right>$ holds. (It is not clear what properties really are desirable, but this is one reasonable thing one could ask for). Then you could call $\phi$ a quantum spacetime isometry.

 

[Fra]

It just means that the spacetime geometry is modeled on structures whose dimension is lower than the dimension of the spacetime manifold.

Do you see this as a physical problem? How?

/Fredrik

 

[Nullstein]

Do you see this as a physical problem? How?

I explained it in my earlier posts. It leads to difficulties with the existence of semiclassical states and the implementation of continuous symmetries.

 

[Fra]

The graphs are embedded into the spacetime manifold. The metric becomes a quantum field instead of a classical field. (LQG gives meaning only to coarse functions of the metric, smeared along lower dimensional submanifolds.) The points that don't lie on the graph are still there in the spacetime manifold and diffeomorphisms still act on the whole manifold. Such points just don't carry any geometry due to the peculiar nature of the theory.

But I think the potential point is that this embedding, is not physically justified. It's an artifact of the mathematical formalism (that is well justified for OTHER domains).

This may be semantics, but I think this is not a physical problem, it's a problem of the choice of mathematics to describe the models, and it's an open question. Ie. there is not physical requirement, that we "must have" a continuum in the Planck domain. The embedding is a mathematical one, and problems with that, is not a physical problem.

/Fredrik

 

[Nullstein]

But I think the potential point is that this embedding, is not physically justified. It's an artifact of the mathematical formalism (that is well justified for OTHER domains).

This may be semantics, but I think this is not a physical problem, it's a problem of the choice of mathematics to describe the models, and it's an open question. Ie. there is not physical requirement, that we "must have" a continuum in the Planck domain. The embedding is a mathematical one, and problems with that, is not a physical problem.

Sure, we don't know what the physics at the Planck scale is like and it may well be discontinuous. But Rovelli's point in the article in the OP is that we should abandon Lorentz-violating theories. Also the non-uniqueness of the discretization is a problem and may render the theory non-predictive if there isn't some kind of universality.

 

[mitchell porter]

It seems like one issue here, is whether you can get "Lorentz symmetry from superposition", to coin a phrase.

Consider a two-qubit superposition. The underlying observables are discrete, both in number and in spectrum, yet the space of quantum states is a continuum (a Riemann sphere) and possesses continuous symmetries, because superpositions have complex coefficients and complex numbers are a continuum.

Do any LQG theorists (or other quantum gravity theorists) explicitly say that they can obtain Lorentz or Poincare symmetry in an analogous way? Or perhaps as the n->infinity limit of something like that?

Penrose's spin networks are supposed to give you full rotational symmetry in such a limit, and I think one dream for twistor theory was that it would do the same for relativistic boosts too?

 

[Nullstein]

It seems like one issue here, is whether you can get "Lorentz symmetry from superposition", to coin a phrase.

Consider a two-qubit superposition. The underlying observables are discrete, both in number and in spectrum, yet the space of quantum states is a continuum (a Riemann sphere) and possesses continuous symmetries, because superpositions have complex coefficients and complex numbers are a continuum.

Do any LQG theorists (or other quantum gravity theorists) explicitly say that they can obtain Lorentz or Poincare symmetry in an analogous way? Or perhaps as the n->infinity limit of something like that?

Penrose's spin networks are supposed to give you full rotational symmetry in such a limit, and I think one dream for twistor theory was that it would do the same for relativistic boosts too?

Well, that's exactly what we have been discussion so far. The singlet state $\frac{1}{\sqrt 2}\left(\left|\uparrow\downarrow\right>-\left|\downarrow\uparrow\right>\right)$ is rotationally invariant, because you can expand the rotated state again in the up/down basis and it turns out to be the same. But in LQG, if you have a spin-network state $\psi_\gamma$ modeled on a graph $\gamma$ and you apply a diffeomorphism $\phi$ to it, then the transformed state $\psi_{\phi(\gamma)}$ is orthogonal to the initial state $\psi_\gamma$ (unless $\phi=\mathrm{id}$) and hence has no chance to be equal to the initial state. Under no circumstances can two nonzero orthogonal vectors be equal. The next question is: Can a superposition of spin-network states, such as $\sum_n c_n\psi_{\gamma_n}$ be invariant? This can at most be true for a discrete group of transformations, because the sum can contain at most countably many terms and a continuous group will create new spin-network states that weren't present in the original sum and thus again be orthogonal.

 

[maline]

The graphs are embedded into the spacetime manifold. The metric becomes a quantum field instead of a classical field. (LQG gives meaning only to coarse functions of the metric, smeared along lower dimensional submanifolds.) The points that don't lie on the graph are still there in the spacetime manifold and diffeomorphisms still act on the whole manifold. Such points just don't carry any geometry due to the peculiar nature of the theory.

Why do you claim that the manifold "exists", and in what sense? That is not the way I usually hear people talking about LQG. They usually speak as if the amplitudes for the various graphs and their vertex/edge observables are the full content of the state; i.e. "all that is".

I also don't understand why we are discussing diffeomorphism invariance at all. I thought the graph observables were supposed to correspond to spacetime volumes as identified by measurable criteria, such as GPS readings. In that case, the diffeomorphism freedom (really just a redundancy, like all gauge freedom) has already been factored out.

 

[Nullstein]

Why do you claim that the manifold "exists", and in what sense?

Why do you claim the opposite? I claim it, because that's how it is and how it is written in the literature. Plenty of references have been given in this thread, not only by me but also by others. Spin networks / foams are embedded lower dimensional structures in the spacetime manifold. Quantum gravity is the theory of the quantized metric field $g_{\mu\nu}(x)$, just like quantum electrodynamics is the theory of the quantized vector field $A_\mu(x)$ and so on. All these fields live on a manifold, quantization doesn't change that.

I also don't understand why we are discussing diffeomorphism invariance at all. I thought the graph observables were supposed to correspond to spacetime volumes as identified by measurable criteria, such as GPS readings. In that case, the diffeomorphism freedom (really just a redundancy, like all gauge freedom) has already been factored out.

Diffeomorphism invariance is discussed in quantum gravity, just like gauge invariance is discussed in any other quantum gauge theory. By the way, no local observables exist in GR. All Dirac observables are necessarily non-local (see Torre, "Gravitational Observables and Local Symmetries"), so GPS readings can't constitute observables in QG. In fact, not a single Dirac observable is known so far, except in the very restricted setting of asymptotically flat spacetime.

 

[maline]

By the way, no local observables exist in GR. All Dirac observables are necessarily non-local (see Torre, "Gravitational Observables and Local Symmetries"), so GPS readings can't constitute observables in QG.

"Local observables" at some point in the manifold don't exist, precisely because you can do a diffeomorphism and move everything to somewhere else in the manifold. But the observable "curvature at the point identified by GPS readings (a,b,c,d)" is physically well defined. One could hope to have a theory where all of the quantum observables corresponded to invariants of this sort, and I was under the impression that LQG claims to do this. (After all, the whole idea of "loops" is based on the Wilson loop as an invariant operator in gauge theory...)

 

[Nullstein]

"Local observables" at some point in the manifold don't exist, precisely because you can do a diffeomorphism and move everything to somewhere else in the manifold. But the observable "curvature at the point identified by GPS readings (a,b,c,d)" is physically well defined.

No, that is not enough to define an observable in GR. Diffeomorphism invariance doesn't suffice. The observable also needs to commute with the Hamiltonian constraint.

One could hope to have a theory where all of the quantum observables corresponded to invariants of this sort, and I was under the impression that LQG claims to do this. (After all, the whole idea of "loops" is based on the Wilson loop as an invariant operator in gauge theory...)

Wilson loops in LQG are only invariant under the additional internal symmetry group that arises when the theory is formulated in terms of vielbein fields instead of the metric. They are not invariant under the Bergmann-Komar group, i.e. they don't commute with the other constraints of the theory.

 

[Fra]

Also the non-uniqueness of the discretization is a problem and may render the theory non-predictive if there isn't some kind of universality.

I agreee this is a key problem, but I find it conceptually a more tractable and rational quest than the similar uniqueness problem of ambigous ways to cure poorly defined formal expressions which are similarly unpredictive and conceptually lost.

/Fredrik