Exploring the Need for a Background-Free Theory of Quantum Gravity

[thermonuclear]

I don’t understand why a ‚background free’ approach for a theory of quantum gravity is needed (or at least enthusiastically defended by LQG fans). I agree about the relational idea and the general covariance as nice features as in GR. Also I see that space-time makes no sense before solving Einstein Equations. But I can imagine a void space-time without any mass and energy, only with a metric (which seams mathematically possible). So, what's the problem about perturbating this background placing a given mass-energy and go further with such an approach?

BR.

 

[marcus]

Originally posted by thermonuclear
I don’t understand why a ‚background free’ approach for a theory of quantum gravity is needed (or at least enthusiastically defended by LQG fans). I agree about the relational idea and the general covariance as nice features as in GR. Also I see that space-time makes no sense before solving Einstein Equations. But I can imagine a void space-time without any mass and energy, only with a metric (which seams mathematically possible). So, what's the problem about perturbating this background placing a given mass-energy and go further with such an approach?

BR.

this is an extremely interesting question.

In his recent (2003) survey paper Smolin makes a big deal
of making QG independent of the background

http://xxx.lanl.gov/abs/hep-th/0303185

"How far are we from the quantum theory of gravity?"

You should download this paper. It is quite remarkable.

arXiv:hep-th/0303185

any problems getting it, let me know

background independences runs through his whole approach
and informs and guides it, you find references to it thruout the
paper.

Just print off the first 30 pages and look at them----save paper
and then you know what if any of the other pages you want, has a table of contents in the front.

Would like to discuss this paper with anyone who has read parts of it and found it interesting

 

[marcus]

Background independence in QG

On page 10, Smolin gives a list of 11 requirements which a satisfactory QG must meet-------questions it must answer---logical conditions it must satisfy


Condition 7---The theory must "be fully background independent. this means that no classical fields, or solutions to the classical field equations, appear in the theory in any capacity, except as approximations to quantum states and histories."

Thermonuclear, do you know enough differential geometry to know what a "diffeomorphism" is?

This is the equivalence relation among objects called differentiable manifolds----often simply called "manifolds" for short.

A manifold does not come with a metric
Manifolds are simpler than the spaces of GR, which have metrics.

To say background independent means you don't have a metric to start with. All spacetime is, is a manifold.

Take a spacetime you are familiar with, and erase the metric, then you have a manifold. Points in it have tangent spaces but there is no inner product or norm or length defined on them--they are just vector spaces who have never heard of metrics.

Then and only then can QUANTUM theory be in charge of the metric.

Smolin says in GR the fact that spacetime is dynamic and non-rigid means that the metric is dynamic. So if the theory is to be a quantum theory the evolution of the metric itself must be quantum mechanical.

He says you must not start with a prior committment to some fixed rigid metric,
even as a background over which to superimpose a quantum metric. (were you thinking about this when you said "perturbation"---some theories that are not background independent start with some classical metric and then add on some quantum metric fuzz to it---he rejects those)

You say: start with a blank vanilla metric that no mass or energy has created. Would it be static or expanding or contracting or what? If it was totally non-expanding and flat (Minkowski) how would adding stuff every change it enough? You would have to make a good guess in picking the metric you started with.

He does not want to start with a guessed-at vanilla metric. He wants to start with no metric at all.

This is really interesting. I don't like your idea but I would like to hear you argue for it some more.

 

[thermonuclear]

Thank you for your answer, marcus.

I also like the beatiful idea of background independence, rooted in Einsteins perception of the need of a relational theory, I'm just trying to understand whether this is really necessary or not.

Background independence in GR means, as far as I understand, that the Lagrangian on a manifold does not contain any fixed fields, or, let's say, fields which are fixed by definition when aplying the principle of least action.

Background dependence means usualy that a field, the metric, is fixed with a predefined value. Then, perturbations of this field aplying Lagrangian theory should give physical solutions. In theory, perturbation can be done on any background that satisfies Einsteins Equations.

In general, I would agree that the second approach is not desiderable, that the background should be treated as a field like others. But it's still unclear for me whether this an argument to assert that there is no spacetime which can be considered as the primordial spacetime without mass-energy (e.g. the flat Minkowski spacetime). Let's formulate this in a more philosophical way (I'm not sure whether this is a good idea, but anyway): How far is spacetime independent from matter and energy? In principle, GR tells us it makes no sense to speak about spacetime before constraining it to a speficic mass-energy scenario. But, if such a spacetime exists (e.g. the flat Minkowski spacetime), is it only a specific solution for an unphysical scenario, or does it represent a primordial state? (I hope this is more or less clear, despite of my bad english).

Your objection:

"start with a blank vanilla metric that no mass or energy has created. Would it be static or expanding or contracting or what? If it was totally non-expanding and flat (Minkowski) how would adding stuff every change it enough?"

may be illuminating in this sense. I think I should take a look to this in detail. Also I will read Smolins paper.

On the other hand other questions might be also interesting, like what happens if spacetime is not a manifold...

Regards.

 

[marcus]

Originally posted by thermonuclear


On the other hand other questions might be also interesting, like what happens if spacetime is not a manifold...

Regards.

!



I quail at the very thought of it.

In 1971 Penrose attempted to model space is some radically different
way not requiring a manifold and invented "spin networks"
(or perhaps "quantized directions") and had something published in a 1971 book called "Quantum Theory and Beyond"
edited by T Bastin---also I ve seen a reference to
"Angular momentum: an approach to combinatorial space time" in the same book.

I am completely ignorant of this work--only having seen references to it as the origin of the "spin networks" which are now ironically enough used in the context of manifolds (which Penrose invented them to replace!)

All I know----ALL I know about Penrose's work is that lightning from the sky did not destroy him for having proposed to replace manifolds. So in his train a number of lesser people have gone about trying to do this too--for this is the academic way.

But I shall shut my eyes and ears to all hints of discarding smooth manifolds and smooth mappings (diffeomorphisms) for such thoughts are anathema.

 

[thermonuclear]

Well, this is a very subtle question. I see there are also some discussions in the Astronomy forum.

Background independence may be considered as a step to a fully relational theory. This means, a theory without any independent entity and therefore without an independent background. In GR, there is an assumption of a manifold and a connection, altough the background (i.e. space-time) has no meaning without a metric.

So, if we agree that background independence is necessary, shall we identify this feature only with the metric or with all attributes of space-time? Smolins speaks in terms of metric independence only. That means, the Lagrangian formulation shall contain the metric as a field (the gravitational field), which can be varied to extremize the action. This is a consequence of considering GR valid and follows at least from some axioms like the principle of equivalence or a torsion free connection. So, we are asuming the a validity of GR, which is of course OK.

On the other hand one can start speculating about things like what happens e.g. if the concept of geodesic is not longer valid, as claimed by some VSL theories or if the Lorentz symmetry is broken. And then try to see the consequences for the idea of background independence.

So, as far as I understand, the requirement for a QG is independence of a specific attribute of the background, i.e. the gravitational field or the metric. This assumes that there is no primordial metric, which represents a basic state in the nature of space-time(and it seams that in deed there isn't, as you have argued before).

Probably I haven't said anything new, I was just ordering my thoughts.

I have read parts of the paper and I think it is too dificult for me to understand, because there are too many points which are supposed to be known by the reader. One point is surprising for me: although it is not stated as a specific requirement, it seams that Smolins expects QG to solve the problem of time in cosmology? Is this realistic?

Regards.

 

[marcus]

Originally posted by thermonuclear
. One point is surprising for me: although it is not stated as a specific requirement, it seams that Smolins expects QG to solve the problem of time in cosmology? Is this realistic?

Regards.

Hello thermo,
I am glad you had a look at Smolin's survey paper "How far are we from the quantum theory of gravity?"

http://xxx.lanl.gov/abs/hep-th/0303185

I wish I knew of a more introductory survey of the subject. Maybe someone at PF will suggest one.

You are right that it is very difficult. this is because it surveys the whole ground and must leave a lot unexplained.

For example, he does not define what is meant by "the problem of time in cosmology".

This is not what we ordinarily think of as the problem of what time is, and why does it have a direction, and is it quantized or not and all that. Instead, in cosmology, I think by "the problem of time" they means some very specialized technical thing. Perhaps you know this specialized meaning.

Baez has a 1995 survey paper which discusses the specialized meaning of the problem of time in cosmology. The paper was written for a short course or seminar intended to introduce mathematicians from outside the field of quantum gravity to the spin networks approach. The paper is called "Spin Networks and Quantum Gravity". I can tell you what he says they mean by it, if you are curious. But it seems to me that you probably already know or would not be interested. He refers in turn to a paper by Chris Isham specifically about the problem of time in quantum gravity. Maybe you understand this better, but it seems to me highly technical and devoid of intuitive interest.

Did you end up with any overall impressions (besides difficulty) from Smolin's side-by-side comparison of LQG and String?

 

[thermonuclear]

Besides of the sociological problem regarding both comunities of theoretical physics there are some other points... I have the feeling that the main difference is that LQG has a strong philosophical background (based on GR: diffeomorphism invariance, background independence,...) but, contrary to string theory, it is not able to connect with the low energy limits. By lack of experimental results, the low energy limit seams to be one of the most important features. On the other hand all the stuff about unification of forces is only treated by string theory and not by LQG (although this seams not to be an essential feature). Anyway, I have a lot to learn to understand properly this paper.

There is a connection between the problem of time and the direccion of time, don't you think so? May be I have not understand correctly the meaning of the problem of time. I also think the problem can be formulated in an intuitive way. Of course if we start talking about Hamiltonian constraint and so on we will be far away from an intuitive formulation. The idea that time should not play a role in the fundamental equations means that the empirical evidence of the direction of time has to be recovered. There are already some vague ideas how this may work, e.g. from Carlo Rovelli. Anyway, if you want, may be you can tell us some of your thoughts on this issue.

Regards.