What is the quanta in LQG and Spinfoam and BI?

[ensabah6]

When gravity is expressed in tools of QFT, the quanta is the spin-2 graviton.

What is the quanta according to LQG, SF, CDT, and other BI theories?

Is it the spin network?

What role does the graviton of QFT quanta play and BI ?

 

[marcus]

I suspect you know the answer to the question already. But it might make an instructive thread for other readers, who might not. You get particles---the socalled "quanta" of a field theory---when you set up a fixed rigid geometry and define matter fields on that geometry and then quantize those fields. In QG you don't do that.

Fields on a fixed rigid geometry leads to a fairly narrow outlook and it's probably better to think of a quantum theory as consisting of a Hilbertspace of STATES of some system which then has OPERATORS defined on it. A Hilbertspace is basically just a vector space with an inner product defined on it (so you have a way to measure lengths and angles between). Measurement operators correspond to a nice kind of matrix, in the finite dim case, with a diagonizability feature.

"Quanta" is not always the best mental picture. Quantum theories do not necessarily involve "quanta" in the usual sense of particle.*

So for example in quantum geometry/gravity you have a Hilbertspace of quantum states of geometry, and you have operators corresponding to making measurements on the the state, like measuring an area.

In Loll's triangulation QG, there is a measurement operator, or "quantum observable" which corresponds to measuring the dimensionality of the space at some given location, at a given scale. The dimensionality of space is not fixed, does not have to be a whole number, and can vary from place to place---it is subject to quantum uncertainty in Loll universes.

But there is no "quantum of dimensionality". Dimensionality does not come in little "bits" or vary in little "steps". It doesn't have "levels" in Loll's model. It's just an uncertain local feature of the universe. And Loll's research team runs simulations of universes in the computer and measures the dimensionality to see how it varies. You can say well maybe dimensionality should have levels or steps. Maybe in the real world it does. But so far in Loll's QG theory it does not.

If anyone would like a link, as a reference for this, there is a Loll QG SciAm article in my sig, and it has further references to technical articles that you can get from arxiv.org.

*In a technical sense you might say that you have gotten "quanta" whenever you diagonalize a matrix and obtain a discrete set of numbers (eigenvalues) down the diagonal. Or when you do the analogous thing with operators on an infinite dimensional state space. So you could talk about area being quantized in Loop Gravity simply because area measurement operators have discrete steps or levels of area. But there is no area "particle". It's not organized the way people normally think when they talk about "quanta".

 

[tom.stoer]

We had a rather long discussion what gravitons are and if they are real.

I don't like these kind of questions as they start from a very foggy idea (the graviton) and somehow give you the impression that everything is well understood. Afterwards everything is compared to this graviton picture.

I could ask: "what are photons?" Answer could be: "the spin-one quanta of the el.-mag. field"

The problem is that photons are idealized mathematical objects (quantized plane waves) w/o direct physical reality. Nobody has ever seen a photon, individual plane waves do certainly not exist in nature, ...

Therefore I would recommend to think abot photons, gravitons etc. as mathematical entities used to decsribe certain aspects of nature. Then the nature of the graviton is no longer the central question, but it is replaced by the question which theory succeeds in descring quantum gravity and eventually predicting experimental results.

This quest will (hopefully) select one theory and will finally give us a hint what the "quanta of spacetime" are. If they are gravitons or spin-network states or something else - who knows?

 

[marcus]

I agree. That is more succinct and technically accurate than the reply I gave.

 

[ensabah6]

We had a rather long discussion what gravitons are and if they are real.

I don't like these kind of questions as they start from a very foggy idea (the graviton) and somehow give you the impression that everything is well understood. Afterwards everything is compared to this graviton picture.

I could ask: "what are photons?" Answer could be: "the spin-one quanta of the el.-mag. field"

The problem is that photons are idealized mathematical objects (quantized plane waves) w/o direct physical reality. Nobody has ever seen a photon, individual plane waves do certainly not exist in nature, ...

Therefore I would recommend to think abot photons, gravitons etc. as mathematical entities used to decsribe certain aspects of nature. Then the nature of the graviton is no longer the central question, but it is replaced by the question which theory succeeds in descring quantum gravity and eventually predicting experimental results.

This quest will (hopefully) select one theory and will finally give us a hint what the "quanta of spacetime" are. If they are gravitons or spin-network states or something else - who knows?

I personally am willing to accept a name for gravity that is analogous to the role the photon plays in QED, gluons in QCD, W and Z bosons in weak force, etc.

 

[ensabah6]

I suspect you know the answer to the question already. But it might make an instructive thread for other readers, who might not. You get particles---the socalled "quanta" of a field theory---when you set up a fixed rigid geometry and define matter fields on that geometry and then quantize those fields. In QG you don't do that.

Fields on a fixed rigid geometry leads to a fairly narrow outlook and it's probably better to think of a quantum theory as consisting of a Hilbertspace of STATES of some system which then has OPERATORS defined on it. A Hilbertspace is basically just a vector space with an inner product defined on it (so you have a way to measure lengths and angles between). Measurement operators correspond to a nice kind of matrix, in the finite dim case, with a diagonizability feature.

"Quanta" is not always the best mental picture. Quantum theories do not necessarily involve "quanta" in the usual sense of particle.*

So for example in quantum geometry/gravity you have a Hilbertspace of quantum states of geometry, and you have operators corresponding to making measurements on the the state, like measuring an area.

In Loll's triangulation QG, there is a measurement operator, or "quantum observable" which corresponds to measuring the dimensionality of the space at some given location, at a given scale. The dimensionality of space is not fixed, does not have to be a whole number, and can vary from place to place---it is subject to quantum uncertainty in Loll universes.

But there is no "quantum of dimensionality". Dimensionality does not come in little "bits" or vary in little "steps". It doesn't have "levels" in Loll's model. It's just an uncertain local feature of the universe. And Loll's research team runs simulations of universes in the computer and measures the dimensionality to see how it varies. You can say well maybe dimensionality should have levels or steps. Maybe in the real world it does. But so far in Loll's QG theory it does not.

If anyone would like a link, as a reference for this, there is a Loll QG SciAm article in my sig, and it has further references to technical articles that you can get from arxiv.org.

*In a technical sense you might say that you have gotten "quanta" whenever you diagonalize a matrix and obtain a discrete set of numbers (eigenvalues) down the diagonal. Or when you do the analogous thing with operators on an infinite dimensional state space. So you could talk about area being quantized in Loop Gravity simply because area measurement operators have discrete steps or levels of area. But there is no area "particle". It's not organized the way people normally think when they talk about "quanta".

Does the graviton appear in these theories?

 

[atyy]

Does the graviton appear in these theories?

Yes. It must almost certainly appear in any quantum theory of gravity. We know that general relativity does work as a quantum theory in the weak field limit, and in that limit there are gravitons (http://arxiv.org/abs/gr-qc/9512024). A successful theory in both strong and weak fields must reproduce the already successful weak field theory, so the more complete theory should also have gravitons.

http://arxiv.org/abs/0711.0146 : "We have defined a spinfoam model for finite values of the Immirzi parameter γ, for the euclidean as well as for the lorentzian theory. ...... It would be of particular interest to check whether this model gives the correct graviton propagator."

http://arxiv.org/abs/0909.1882 :"Similar asymptotic analysis of the 4-dimensional models was initially performed by Barrett and Williams, and formed the basis of investigations of the graviton propagator structure of these models."

Although a common classification of gravity theories is background and non-background independent, I believe a better classification is whether the gravitational field is fundamental or emergent. Asymptotic Safety and LQG treat the gravitational field as fundamental, while string theory and condensed matter approaches hypothesize that the gravitational field is emergent.

 

[ensabah6]

Yes. It must almost certainly appear in any quantum theory of gravity. We know that general relativity does work as a quantum theory in the weak field limit, and in that limit there are gravitons (http://arxiv.org/abs/gr-qc/9512024). A successful theory in both strong and weak fields must reproduce the already successful weak field theory, so the more complete theory should also have gravitons.

Although a common classification of gravity theories is background and non-background independent, I believe a better classification is whether the gravitational field is fundamental or emergent. Asymptotic Safety and LQG treat the gravitational field as fundamental, while string theory and condensed matter approaches hypothesize that the gravitational field is emergent.

In this weak field limit, though how does time treated in general covariance, when treated quantum mechanically, and how does time slow down w/gravitons? What is the threshold between weak and strong field?

 

[Haelfix]

'Time', however you want to define that, is treated exactly as its treated in General relativity + tiny quantum mechanical departures from GR which are of no observational consequence macroscopically, or at least, none that we know off. So for instance, a gravitational doppler shift would work in the same exact way and so forth.

The weak field approximation breaks down somewhere when E^2/Mpl^2 is of order 1 or larger.

Thats actually pretty good. So while it may miss Planck scale nonperturbative physics, about 3 or 4 orders of magnitude away its a well defined and controlled expansion capable of capturing quite a bit of the quantum mechanics of black holes for instance.

 

[Fra]

When gravity is expressed in tools of QFT, the quanta is the spin-2 graviton.

What is the quanta according to LQG, SF, CDT, and other BI theories?

Is it the spin network?

What role does the graviton of QFT quanta play and BI ?

As I see it the more important distinction is the general question of what you consider to be an observable?

From my point of view one can imagine two extremes

- QFT style with a fixed background context, where the measurement is defined relative to the context. The problem is only that the choice of context appears ambigous and can be chosen at will - or to give you the answer you want.

- As rovelli argued in this papers, his idea of BI indepndent observables is that a the true complete observables can not depend on an ambigous choice of context. So Rovelli's idea seems to be that complete observables - the ones which the laws of physics specify/predict - are observer independent. But in this view the context, which is normally needed to make sense out of a measurement is wiped away. The observer independent abstraction somehow takes on a realist construct that disturbs me at least. This construct is them immune to regular questioning since no single inside observer can make an physically realizable inference of this structure. It's somehow a structure you just have to have faith in.

I see both views as extremes and there is hopefully a third way. (Maybe the admittedly more fuzzy, but more conceptually consistent idea of relationally evolving contexts, where part of the evolution is simply inpredictable and more takes on the form of learning rather than deterministic evolution)

/Fredrik

 

[ensabah6]

'Time', however you want to define that, is treated exactly as its treated in General relativity + tiny quantum mechanical departures from GR which are of no observational consequence macroscopically, or at least, none that we know off. So for instance, a gravitational doppler shift would work in the same exact way and so forth.

The weak field approximation breaks down somewhere when E^2/Mpl^2 is of order 1 or larger.

Thats actually pretty good. So while it may miss Planck scale nonperturbative physics, about 3 or 4 orders of magnitude away its a well defined and controlled expansion capable of capturing quite a bit of the quantum mechanics of black holes for instance.

Do we have direct evidence GR is valid in this regime where graviton-QFT is not? I thought GR treats time as a coordinate whereas QFT splits time from space

 

[Haelfix]

We don't know what replaces the QFT picture at strong coupling. A nonperturbative treatment or a UV completion is required to solve the equations and this is called by definition 'quantum gravity'. On general consistency grounds we are pretty sure that the classical theory is not and cannot be valid there.

Regarding the time problem, I think you are getting yourself confused with several different (not necessarily related) issues that show up in the quantization of general relativity. The problem of 'time' really manifests itself in canonical quantization and not the path integral method. In CQG the hamiltonian vanishes and there is no obvious time evolution (instead the information lies in the constraints, which annihilate the wave functional). See the Wheeler De Witt equations.