Role of in-house concept analysis done by the QG scientists themselves

[Fra]

I'll start my attempt at looking into Rovelli's thinking and I hope that I didn't misinterpret Marucs ambition with this thread. If I did let me know and I will drop this.

Since the conceptual things do come with and ORDER as per constructions that IMHO should be respected, I'll start in the right end and make progress in step and hopefully Marucs and everyone would agree or disagree with the characterisation. Maybe we should try to the extent possible to comment on and reflect upon Rovelli's thinking, without adding to much of our own thinking even if it may be hard.

Let's first note how Rovelli defines what he means by QG (this may be relevant as there are some different opinons out there as to what needs to be included in the quest):

"Therefore we expect the classical GR description of spacetime as a pseudo-riemannian space to hold at scales larger than lP, but to break down approaching this scale, where the full structure of quantum spacetime becomes relevant. Quantum gravity is therefore the study of the structure of spacetime at the Planck scale."
-- Rovelli, http://arxiv.org/abs/gr-qc/0604045

As I read this, the question I must pose is: Does "planck scale" refers to the scale of the interactions, or the scale of the observer. I hope we can agree that this makes a difference, right?

I think Rovelli does mean that the interaction scale is Planck scale. The observational scale (ie where the observer it) is still the large scale low energy laboratory frame? Right or wrong?

Interesting things could be said about the other possibility, but do stick to Rovelli's view here it suffices to just flag this point for a different discussion.

Note that, with the observer scale beeing the labframe, I mean that it IMPLIES that the inference of the Planck scale interactions does take place relative to an embedding effective spacetime.

Before going on, does anything disagree with this characterisation of Rovellis view? Or maybe suggest that also the observer scale is Planck scale; should we discuss further?

I think this is a basic point, that will confuse the rest of the discussion unless we're on the same page here. Comments?

/Fredrik

 

[suprised]

Kevin, I think you got the idea: I wanted to make it clear that the intended focus is on the conceptual framework developed by the researchers themselves--not by outsiders, be they professional or amateur. It may make the thread unpopular to have that focus, and make the title sound dumb, but that's what I want it to say.

Lol whoelse could possibly make such an analysis other than insiders? This almost sounds as if laymen could do it...

 

[Fra]

I'm jumping to what friend, Mtd2 and Marucs discussed.

Like how can you have geometry without a manifold? Mathematically I follow Marcus argument: individual manifolds can have the same geometry, or encode the same geoemtric information. This is mathematics.

One can associate one manifold ~ on observer. One can similarly to just make a statement about relations between observers (like what's seemingly Rovelli ambition as defined in his RQM paper), and consider such a thing without observers.

So far clear to me.

But I think there may be a risk at going to fast here and throw the baby out with the bathwater.

Because if we required geometric qualities to be observable, we do need an observer. So it's not trivial if the above makes sense from a physics perspective I think.

For me the question isn't wether we can do away with manifolds in geometric models. We can. Or wether we can do away with observers. We can (at least mathematically). The question is what this is useful for physical understanding?

Contained in the last question I asked about the observer scale vs interaction scale, it's not a far stretch to imagine that the low energy observer A, makes observations and inferences on interacting high energy observers B and B'. In this abstraction it seems to me that Rovelli's view CAN make sense, from the point of view of A. There is no problem with this as long as we keep track of what is beeing doing.

This is also what Smoling means by the "Newtonian scheme" in his evolving law talks. It means that from the perspective of observer A - observing B and B' which are then a small subsystems of A's total control domain, time and space CAN be removed! Just like I think Rovelli suggests.

But picture what happens if A and B switches place. Now what? B is the scientist. A is a cosmological (or LARGE) system relative to B.

Too much mathematical detouring and its' easy to loose track of this. I hope this wasn't detouring from Roveli's ideas.

Smolin's thinking is also interesting: http://pirsa.org/08100049/ (this has been posted many times by Marcus in past threads as well) I do not think this thinking signifies Rovelli, it's rather an interesting constrat to Rovelli. Just beeing aware of the constrasting views I find enlightening, even if one can't take side.

/Fredrik

 

[friend]

Well you can decide you don't like some of the new formulations of geometry without space. I'm not trying to sell you on them. Personally I find them interesting. It is interesting that they work.

Ashtekar GR (1986?) was formulated without a metric. It was clear you can have geometry without a metric, that was already long ago. A "connection" took its place. A parallel transport function.

And then Noncommutative Geometry (NG) came (when? 1990s?). It needs no space manifold, it only has geometry. You have the option to include a manifold, as a special kind of NG. But you don't need it.

You can think of it as just the fashion of the day. At some point (2008? 2009?) Loop QG stopped needing a manifold. It treats geometry but it has no "space" (in the new manifoldless formulations.)

geometry without space... forgive me if that continues to give me trouble. But all the books I've read, or at least remember reading, always have geometry defined on a space. For as soon as you even mention the word volume and area this implies dimensions of length between points.

One way of having geometry without a metric is to have a network where each node represents a bit of volume and each link between two nodes represents a bit of "contact" area where volumes meet. Given enough of that data you could probably reconstruct an approximate metric. Area+volume data. There are other kinds of data. Some sorts of data are more natural to treat using Feynman-like path integrals. The "path" is the evolving geometry. It is an approach to quantum system, even if it does not use the canonical conjugate pairs and the commutators that you were thinking about.

But now we have nodes (let's not call them points) that represent volume, and links between nodes (let's not call them lines) that represent area... that all sounds like a pretty distorted view of "geometry". It sounds like they are trying to define geometry more abstractly just to get around having to start with the metric which they are trying to derive. Maybe you could give me a link to some paper that makes that clear.

A "quantization procedure" is not the only way that one can arrive at a quantum theory. One does not always have to begin with a classical system and perform some time-honored ritual. One can just use the classicals as heuristics, and try to get insight into other quantum theories, and work by analogy---and then, when you have something, check to see what the classical limit is. Work backwards. Some people are very worried by this, others are not. It may be partly a matter of personal temperament.

We don't even know why nature prefers path integrals or commutation rules in regular QM. But now we're free to invent our own quantization rules, and this without experimental evidence. I am highly skeptical.

I remember watching a video on the Perimeter Institute archive in which the instructor wrote a path integral on the board where the D[g] was over the space of geometries. He had to admit that we don't yet know what that means. But at least the path integral has some justification.

My personal opinion is that all we need to do is justify the Hilbert-Einstein action in the path integral in order to get quantum gravity. Is this being seriously looked at in any of the programs you are aware of? What's wrong with doing that? It seems like the most straightforward way to get QG. Thanks.

 

[marcus]

geometry without space... forgive me if that continues to give me trouble. But all the books I've read, or at least remember reading, always have geometry defined on a space. For as soon as you even mention the word volume and area this implies dimensions of length between points.
...

Friend, I appreciate your sticking to a question like this which is central to understanding. I think I have said this before, but haven't emphasized it enough. The sense in which one has geometry without space is in the mathematics. In the theory, there is no mathematical object (no set, no manifold) that stands for space.

Instead, there are, in the theory, mathematical elements and operations that correspond to making measurements.

If you think about it, this is a perfect imitation of real life. There is, in our experience, no physical substance of space. All we do is make measurements, we move around, we experience geometry, we experience angles, distances, volumes. These are inter-related in various ways and the geometry constrains what we do.

But there is nothing called "space" that you can put your finger on.

So it is in real life, in our everyday, and so it is in the Lqg mathematical theory. There are the measurements, the operators, but there is no manifold.
==================

Of course there are a lot of Lie groups in the construction, they are basic tools describing symmetry. We think with Lie groups. And they are manifolds. When I say there is no manifold I mean no manifold representing space or spacetime. Because a theory of geometry does not need one. No mathematical object of any kind, that stands for space, is needed when one describes geometry.

This might be a good time to take a look at these three papers, if you have not done so already.

April 1780: http://arxiv.org/abs/1004.1780
October 1939: http://arxiv.org/abs/1010.1939
December 4707: http://arxiv.org/abs/1012.4707

As you know if you've taken a look, all say the same thing but in different ways---I find it can help me to see something presented several different ways. And sometimes it helps me to see concretely what is giving trouble rather than just thinking about it abstractly with my pre-existing concepts.

 

[marcus]

...But now we have nodes (let's not call them points) that represent volume, and links between nodes (let's not call them lines) that represent area... that all sounds like a pretty distorted view of "geometry". It sounds like they are trying to define geometry more abstractly just to get around having to start with the metric which they are trying to derive. Maybe you could give me a link to some paper that makes that clear.
...

You put your finger on the key thing in this approach---the finite graph.

In a certain sense you could say that what we have instead of "space" is the set of all finite graphs.

A graph represents a kind of truncation of the information we are going to look at and deal with. We declare we are only going to make a finite number of geometrical measurements, at only a finite number of locations, with a limited number of ways information can to get from one to the other.

This is not clear, I realize. In a sense, chosing a graph to work with finitizes the probem of geometry. It restricts the number of degrees of freedom that space is allowed. So it makes it possible to calculate, prepare the geometric experiment so to speak (as one prepares an experiment in other types of of QM).

The graph is also a "cut-off", analogous to cutoffs in power-series calculations. One is truncating on the basis of geometric complexity, rather than energy or scale. But it is still comparable.

One can take limits over all graphs, and sum over all graphs, just as one can take limits and sum using the natural numbers as an index. It is like a power-series in calculus except using graphs instead of n= 1,2,3...

So that's the "trick" which you will have already discovered, if you took a look at those three papers I mentioned:
April 1780
October 1939
December 4707
or some of the other papers that have come out recently working along the same lines.

Instead of "space" being a manifold, and having one Hilbert H of states of all the geometries of that manifold, one has many possible truncations or simplifications represented by graphs gamma Γ. And for each one we have a Hilbert H_Γ of states of geometry of Γ.

You are entirely and cordially welcome to say that you don't LIKE such a picture It is fine to detest it, as far as I can see. But there are signs that it works. The past year or so has seen unexpectedly rapid progress, so it bears watching.

αβγδεζηθικλμνξοπρσςτυφχψωΓΔΘΛΞΠΣΦΨΩ∏∑∫∂√±←↓→↑↔~≈≠≡ ≤≥½∞(⇐⇑⇒⇓⇔∴∃ℝℤℕℂ⋅)

 

[MTd2]

The most fundamental thing is not space but the event. Event is the most basic entity as it is implied, to me, in sec. 1.2, p.5 of gravitation, and it is labeled by coordinates. Don't think in terms of geometry or mathematical space.

The beginning of this section has a very important quote from Einstein:

"Now it came to me: ... the independence of the
gravitational acceleration from the nature of the falling
substance, may be expressed as follows: In a
gravitational field (of small spatial extension) things
behave as they do in a space free of gravitation . ... This
happened in 1908. Why were another seven years required
for the construction of the general theory of relativity?
The main reason lies in the fact that it is not so easy to
free oneself from the idea that coordinates must have an
immediate metrical meaning."

ALBERT EINSTEIN [in Schilpp (1949), pp. 65-67.

A coordinate is just a label, but we must free ourselves from the notion of metric as being geometry. Notice that until Einstein's death, it was predominant the intuitive, and wrong, idea that to a given topology there is only one correspondent equivalence class of metric. This is wrong, specially in 4 dimensions, in which there can be infinitely many. So, things are even more confusing.

So, in our perspective, we have also to stop thinking even about the topology and think that gravity is something about a collection of events, labeled by coordinates, not really geometry. So, we have to go deeper than GR to understand the philosophy behind GR and so to understand LQG.

 

[marcus]

@MTd2, that's a beautiful contribution to this thread. Thanks.

 

[marcus]

I remember watching a video on the Perimeter Institute archive in which the instructor wrote a path integral on the board where the D[g] was over the space of geometries. He had to admit that we don't yet know what that means. But at least the path integral has some justification...

Exactly. D[g] is what all this is about. However do not think of g as standing for a METRIC. A metric is only one possible way to describe a geometry, and after 30-plus years it has not turned out to be such a good way. AFAIK no one succeeded in putting a measure on the space of metrics. But they did put measure (for integration) on the space of geometries---with the geometries described in other ways.

Renate Loll and friends found "random triangulations" a good way to put a measure on the space of geometries. They do the path integral, by a Monte Carlo method. I have a popular article in my signature---the Loll SciAm article. Have you seen it, or read any other CDT stuff?

Everybody wants to do the path integral. So they find various different ways to put a measure (for integration) on the space of all geometries. In the cases I know of, the measure will turn out to live on a subset of all geometries. The hope is that it is somehow representative---this is Loll's tactic. The subset consists of triangulated geometries using essentially identical building blocks (actually two kinds).

If you look at the three LQG papers I offered, you will see yet another way to make D[g], yet another way to define the path integral. You integrate over all geometries (but this time the geometries are limited to those living on a certain graph, which can be as complicated as you want). In a sense it is very much like Loll's CDT method, a representative subset of geometries, a measure on them, an integral using that measure.

Ultimately the LQG path integral method can give a transition amplitude between two spatial geometries---initial and final geometries.

Where classical GR might give a classical trajectory (a spacetime) from the initial to the final, the quantum theory gives a transition amplitude.

The transition amplitude in effect explores a variety of paths or ways of getting from the initial to final configuration. It is based on a version of the GR action called the Holst action.
Classically this would not be distinguishable from the Einstein-Hilbert, same equations come out. No reason to prefer one over the other. But for the LQG path integral approach the Holst form of the action works better.

John Baez TWF #280 has some stuff about the Holst action for GR. Anyone who hasn't already might want to look at it, for breadth, to be familiar with other actions besides Einstein-Hilbert.

Sketchy answer. Best i can do for now.

 

[friend]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

 

[marcus]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

I don't know the various things that go wrong, friend. Somebody else will have to answer. My reaction when I read your post was simply "first off, how do you define an integration measure on the space of metrics?"

Everything i was talking about in my last post concerned the difficulty of defining a measure on the space of geometries----which (in the special case where you label each geometry with a metric) comes down to defining a measure on the space of metrics.

I don't offhand see any way to get a finite integral, or even a well-defined measure. Would you call that "non-renormalizable"? or is it something that logically precedes non-renorm'ble and is fundamentally worse than it?

 

[friend]

"first off, how do you define an integration measure on the space of metrics?"... the difficulty of defining a measure on the space of geometries

I remember reading stuff on how the Feynman Path Integral was not well defined; problems arose on defining a measure on the space of paths. I think they were able to get a well defined path integral using the Wiener measure that include the exponential as part of the measure. But then once a complex action was introduced, I'm not sure that did not introduce further complications. So when you start talking about measures on even more complicated spaces as space of metrics, etc. I really have to wonder if that has been well defined.

Also, you were kind enough to link me to some of the introductory papers on some of these research programs. But I seem to be having the same problem you are. I can't wrap my brain around where they come up with there starting points, spin networks, and the like. It all seems quite contrived. I suspect that they are starting off with abstractions from simpler geometric formulations. But I don't know where they come up with these ideas. Is it possible, for example, that spin networks come from the curvature scalar in the Hilbert-Einstein action (curvature=spin, get it?)? I don't know.

 

[atyy]

So really, if you know, tell me... what is wrong with simply plugging the Hilbert-Einstein action in the path integral to quantize gravity? It seems like the most straightforward way to go. We already know the Euler-Lagrange equation gives Einsteins GR in the classical limit. And what's more natural than to plug and action integral into the path integral? Is this the method that proves non-renormalizable? Thanks.

Yes. This method is known not to be perturbatively renormalizable. Even though GR may not be renormalizable, it is a perfectly good effective quantum field theory at low energy.

Asymptotic safety is the search for other fixed points of the renormalization flow that would render pure gravity renormalizable, so that gravity could remain a good quantum field theory to arbitrary high energies, and possibly be a fundamental force. A great resource is http://www.percacci.it/roberto/physics/as/index.html.

Within approaches like string theory, gravity is not fundamental and is seen to be just one aspect of something more fundamental. The major theorem constraining what this more fundamental theory is is the Weinberg-Witten theorem, which says the theory cannot be a 4D Lorentz invariant quantum field theory (though it does not rule out Sakharov's induced gravity approach, for reasons I don't understand). Some examples of this philosophy are http://arxiv.org/abs/1009.5127 , http://arxiv.org/abs/1011.5754.

 

[Fra]

The last posts has focused on the PI over the space of gravitational fields. From a technical perspective this integral seems to be a natural focal point between QM and GR as it seems simple, yet confusing. As everyonye usually points out when talking about this is that the PI is not really something well defined. It's just a symbols that looks like mathematics but which merely rather is a statement of intent. It expresses an IDEA of what logic to apply, but the exact details are missing.

The idea is to use the QM principles for computing an expectations; you simply ADD all possibilities according to their COUNTS, where the ADDITION is made according to quantum logic and superposition principles.

Usually we just use the reciepe and start from classical actions one way or the other and then defined the quantum operators as per som quantisation trick from the classical (q,p). And we plug it in.

After some renormalizations this usually works out.

But I think it's fair to say that this procedure is not well understood even before trying to put in GR. It's gets more ill behaved when putting in GR.

So what's the analysis that Rovellis does of this situation?

As far as I understand him, as which is the impression you easily get also from the paper "unfinished revolution" Martin quote earlier, that Rovelli's thinks that either you accept QM, or you seek to restore realism. We may not agree on that analysis, but nevertheless hence Rovelli has no ambition as I see it to question the QM scheme.

As I see it, his idea is to find in the theory of Gravity, a new set of variables; the RIGHT set of variables, that makes the QM scheme work out (=to be computable and be at least mathematically well defined).

As I see it, that's what this is all about, the NEW variables of GR. If that works, it would indeed be very nice. The question is then also if the same trick works when matter is added.

Correct me if I mischaracterise anything but I think this is also why Marcus spendts quite a lot of great energy into trying to explain geometry without space time etc. It's ultimately about describing "gravity" in NEW variables. And when expressed in these NEW variables, we hope that the Path integral would be easier to define.

/Fredrik

 

[atyy]

I would say ever since Wilson, renormalization is well understood.

 

[Fra]

I would say ever since Wilson, renormalization is well understood.

There are different flavours of understanding IMO. Obviously there is a good deal understanding, but wether it's sufficient for our purposes I'm in great doubt.

Anyway, that's only half the issue. What about quantum logic implicit in the feymann PI prescription. IMO, there is not yet a satisfactory understanding this that makes me happy.

(The ambition of RG, is to adress how "theories" or "force laws" SCALE with observational scale. I don't want to derail anything here but IMO both these things does connect to the quest for the observer dependnet inside views I always bring up when you insist that this can be done by scaling the observer; which is different from scaling the observers microscope. Two different things, becaue the theory still is encoded behind the microscope in the latter scale and doesn't need rescaling. But we shouldn't discuss that here.)

But anway, this is exactly the point of disagreement. IS our understanding of QM enough? our RG theory good enough?

As I read it, Rovelli takes QM formalism without questioning, and thinks the "problem" is that were using the wrong variables as observables. Or would anyone disagree with this simple characterisation of Rovelli's thinking?

Before I started reading Rovelli's book, I thought rovellis attempting something else; by generalizing the spin-networks to general action networks that would apply also to matter, and which could represent the microstructure of the observer. Maybe that's still possible, but my conclusion was thta it was at least not rovellis original idea, just my projection.

/Fredrik

 

[atyy]

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Also, how does AdS/CFT fit in with this? It is naively a working theory of quantum gravity, maybe not of our universe, but one would imagine that all the issues of QM apply to it.

 

[Fra]

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Maybe we are in reasonable agreement on this. I don't think it's a coincidence, but the non-locality is only apparent IMO. In fact the nonlocality is the result of sticking to too much realism. If you drop some structural realism and isntead adhere to darwinian style views, a lot of apparent nonlocality goes away.

I feel confidence that at some point a new understanding will come. But I'm not seeking to restore realism like bohmians.

Rovelli's characterization in the paper of unfinished revolution paints a picture that either QM is exactly right or you try o restore realism which I think is a pretty blunt characterization that ignores other more subtle views.

/Fredrik

 

[inflector]

The last posts has focused on the PI over the space of gravitational fields. From a technical perspective this integral seems to be a natural focal point between QM and GR as it seems simple, yet confusing. As everyonye usually points out when talking about this is that the PI is not really something well defined. It's just a symbols that looks like mathematics but which merely rather is a statement of intent. It expresses an IDEA of what logic to apply, but the exact details are missing.

The idea is to use the QM principles for computing an expectations; you simply ADD all possibilities according to their COUNTS, where the ADDITION is made according to quantum logic and superposition principles.

...


But I think it's fair to say that this procedure is not well understood even before trying to put in GR. It's gets more ill behaved when putting in GR.

So what's the analysis that Rovellis does of this situation?

As far as I understand him, as which is the impression you easily get also from the paper "unfinished revolution" Martin quote earlier, that Rovelli's thinks that either you accept QM, or you seek to restore realism.

As I read it, Rovelli takes QM formalism without questioning, and thinks the "problem" is that were using the wrong variables as observables. Or would anyone disagree with this simple characterisation of Rovelli's thinking?

I agree with your point about QM (unless one accepts many worlds). I would prefer to reject many worlds (in its original form), and hope that something like quantum darwinism works or if someone can find a way to make QM emergent (Bohmian?). Why do QM and QG both point to nonlocality - coincidence or not?

Rovelli's characterization in the paper of unfinished revolution paints a picture that either QM is exactly right or you try to restore realism which I think is a pretty blunt characterization that ignores other more subtle views.

(emphasis mine in all above quotes)

Nice topic so far, thanks marcus for keeping the focus tight (and leaving us little room to wander down our respective favorite rabbit holes).

As someone who has been trying to come up to speed on quantum gravity (QG) over the last several years with little prior knowledge, I've noticed the assumption that Fra notes above which seems to me to be quite strongly evident in the entire non-string QG community.

This surprised me at first because one of my first introductions to QG as a problem was reading Smollin's The Trouble with Physics wherein he described two different approaches, the String Theory approach which he characterized as starting with QM, and the LQG approach which Smollin characterized as starting with the principles of GR instead (I can't find the exact words as I'm not home where I have the book but visiting relatives for the holidays). To me, GR has two core principles, background independence and continuous geometry. I believe that what Smollin meant by the idea that LQG starts with the principles of GR is really a statement about the first core idea, background independence and decidedly not about continuity.

Rovelli agrees with this perspective. Note Rovelli's comments from the bottom of page 2 in Unfinished Revolution, the introduction to his book on QG that marcus pointed us to above, http://arxiv.org/abs/gr-qc/0604045:

Roughly speaking, we learn from GR that spacetime is a dynamical field and we learn from QM that all dynamical field are quantized. A quantum field has a granular structure, and a probabilistic dynamics, that allows quantum superposition of different states. Therefore at small scales we might expect a “quantum spacetime” formed by “quanta of space” evolving probabilistically, and allowing “quantum superposition of spaces”. The problem of quantum gravity is to give a precise mathematical and physical meaning to this vague notion of “quantum spacetime”.

(emphasis mine)

So it is pretty clear that Rovelli assumes that this idea is a given and indisputable as he defines quantum gravity as the search for the solution to the formulation of "quantum spacetime."

In all this, it seems to me that little attention, by comparison, is being paid to the idea of taking both key insights of GR as fundamental, i.e. both background independence and continuity. The Bohmian-approach that Fra alludes to as typified by Benjamin Koch in Quantizing Geometry or Geometrizing the Quantum?: http://arxiv.org/abs/1004.2879, for example, is this third approach and one that does not take QM as fundamental. From Koch:

Given the problems in applying the laws of quantum mechanics to the geometry of space-time we want to ask the following question: “Could it be that (classical) geometry is more fundamental than the rules of quantization?”

Now, if one is going to take the position that LQG starts with GR's principles, then it seems to me that this is missing the second important aspect of GR, namely the idea of continuous geometry. Is geometry continuous? GR says it is. So Koch's Bohmian approach seems the one that takes GR seriously and looks at the idea that QM is emergent whereas LQG assumes that QM takes precedence and the observed continuity of GR is emergent. Therefore Smollin's characterization of the dichotomy between the LQG approach and the String Theory approach to quantum gravity is incomplete and misleading.

 

[atyy]

@inflector: Not sure about Smolin, but Rovelli says it's quantum field theory versus general relativity - not quantum mechanics versus relativity. (I don't agree much with Rovelli's philosophy, but would this make more sense to you as the conceptual background to Rovellian LQG?)

 

[marcus]

Rovelli says it's quantum field theory versus general relativity ...

versus? The LQG program's repeatedly stated goal is a "general covariant quantum field theory" or a "background independent quantum field theory".

That was how he described the overall goal of the program when talking at Strings 2008. And in every major overview paper where he boils it down to one goal. You shouldn't need references but i bet i could find 3 or 4 recent instances.

In other words, no 'versus' or conflict. The main aim is to take seriously lessons learned from GR and carry those lessons over to QFT.

Presumably one of the first aims is to formulate geometry as a (background indep.) quantum field theory. Since matter fields live in geometry it seems reasonable that the first item on the agenda would be QG. Geometry would be the first field to quantize. Then start including matter (like in the recent paper "Spinfoam Fermions".)

The overall (explicitly consistently repeatedly stated) goal is QFT.
=====================

The tension you are thinking of is probably not with QFT per se, but with the outlook of those among today's (or anyway yesterday's) particle physicists who habitually think in terms of a fixed geometric background. A lot of inertia there, deeply engrained habit of viewing the world as fields living on a manifold with fixed geometry.

I think it may no longer be so widely shared among particle physicists. But even so you might call it the (traditional) particle physics perspective. If relativists are in conflict with something it is more apt to be with that fixed-geometry picture of the world. Not in conflict with the goal of a a general relativistic QFT!

 

[MTd2]

Heh, this post of mine was enlightening to myself, heh:

https://www.physicsforums.com/showpost.php?p=3059480&postcount=37

I think that quoting from Einstein Gravitation and section 1.2 should be kept in mind like a mantra.

 

[inflector]

versus? The LQG program's repeatedly stated goal is a "general covariant quantum field theory" or a "background independent quantum field theory".

That was how he described the overall goal of the program when talking at Strings 2008. And in every major overview paper where he boils it down to one goal. You shouldn't need references but i bet i could find 3 or 4 recent instances.

In other words, no 'versus' or conflict. The main aim is to take seriously lessons learned from GR and carry those lessons over to QFT.

I certainly see the development of a "generally covariant quantum field theory" as Rovelli's (and LQG's) goal too. He, and evidently most non-String QG theorists as well, believe that the lesson of GR is that "spacetime is a dynamical field" and that of QM is "that all dynamical field are quantized." A generally covariant QFT melds those lessons together quite well.

@inflector: Not sure about Smolin, but Rovelli says it's quantum field theory versus general relativity - not quantum mechanics versus relativity. (I don't agree much with Rovelli's philosophy, but would this make more sense to you as the conceptual background to Rovellian LQG?)

I think Rovelli's perspective is pretty clear, as marcus showed above, and it seems like a valid conceptual basis given that you believe the two lessons he draws from GR and QM. A generally covariant QFT seems like the only rational goal if you take those lessons as a starting point.

I find Koch's approach interesting because there has been much less work done in that type of approach. Doesn't mean it is better necessarily, just that it is less tilled soil. Koch is questioning the very lessons that Rovelli takes as a given.

 

[marcus]

EDIT: OOPS! Here I am responding to one of yours several posts back. I had something else to do and didn;t notice your most recent. this may be redundant. No more explanation needed
++++++++++++++++++++++++++++++++++++++
Inflector, I can try to respond to what I think is the general drift of your post #49.
You asked in particular about Rovelli. It's important to realize how central to LQG he is and how conservative/gradualist he is.

His idea is that physics does not proceed by trying to solve all problems at once (including the meaning of quantum mechanics ). You have to be pragmatic and go step by step. Take seriously the lessons of past theories, try to carry over all you can of the most important lessons. Only change what you are forced to change. Don't try to wipe the slate clean and make a totally fresh start.

There was even something about this in his most recent paper http://arxiv.org/abs/1012.4707. Listing 3 things that the program was NOT trying to do.
Some things might be worthy goals but just more practical to save for later.

So yes, try to use the basic ideas of Quantum Mechanics as currently practiced.

Once we have a general relativistic QFT, people can move on to undertake other reforms perhaps.

Sometimes I think Fra wants to reform everything at once Your quotes of Fra reminded me of that. Personally I'm pragmatic, let's see how Rovelli's gradualist approach works. (right now if you follow the papers it is going ahead very fast, working well.)

There may be times when a radical total-reform style is appropriate, and other times when a conservative style is.

And you have to look at the people---physics is a human (even social) endeavor.

Until recently there were few people working in LQG, and few ways for young researchers to get in. The 2007 Zakopane school made a big difference. The 2006 establishment of a ESF (euro. sci. found.) QG funding agency made a difference. And there used not to be so many career opportunities. That seems to be changing.

About centrality---there are still only a few tens of people who are really active in LQG and nearly all began as PhD students or postdocs working for 4 people---Ashtekar, Rovelli, Lewandowski, Thiemann. Quite a few have worked with all of them! I also should mention Barrett.

Smolin is brilliant and has lots of original ideas but he has not worked much in LQG proper for, I guess, over 5 years. He has not brought up any PhD students who are active in LQG. His postdocs investigate more periferal stuff. What he contributes is valuable in itself, but not central or typical. He explores related areas and ideas---like a scout or outrider if you can put up with a colorful image like that.

So for simplicity if you want to know what is happening in LQG you focus on Rovelli's papers and what his students/postdocs are doing. And likewise to some extent with Ashtekar and Thiemann (I also mentioned John Barrett at Nottingham, who has several irons in the fire including LQG).

To keep it simple, here are Rovelli's 2010 papers. Just to look at the titles, the recurrent themes, and the co-authors (remember physics is a human social activity, not pure ideas.)

 

[marcus]

To partly respond to Inflector's general questions about LQG, here are Rovelli's 15 LQG papers for this year.
http://arxiv.org/find/grp_physics/1/au:+rovelli/0/1/0/2010/0/1

You can see here some of those active in the LQG program (many are co-authors) and what some of the current goals are---what problems are getting addressed.
==quote arxiv.org==
Showing results 1 through 15 (of 15 total) for au:rovelli

1. arXiv:1012.4719 [pdf, ps, other]
Spinfoam fermions
Eugenio Bianchi, Muxin Han, Elena Magliaro, Claudio Perini, Carlo Rovelli, Wolfgang Wieland
Comments: 8 pages, no figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)

2. arXiv:1012.4707 [pdf, ps, other]
Loop quantum gravity: the first twenty five years
Carlo Rovelli
Comments: 24 pages, 3 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

3. arXiv:1012.1739 [pdf, ps, other]
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
Comments: 6 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)

4. arXiv:1011.2149 [pdf, other]
Generalized Spinfoams
You Ding, Muxin Han, Carlo Rovelli
Comments: 16 pages, 3 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)

5. arXiv:1010.5437 [pdf, ps, other]
Spinfoams: summing = refining
Carlo Rovelli, Matteo Smerlak
Comments: 5 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)

6. arXiv:1010.1939 [pdf, other]
Simple model for quantum general relativity from loop quantum gravity
Carlo Rovelli
Comments: 8 pages, 3 figures
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)

7. arXiv:1010.0502 [pdf, ps, other]
Local spinfoam expansion in loop quantum cosmology
Adam Henderson, Carlo Rovelli, Francesca Vidotto, Edward Wilson-Ewing
Comments: 12 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)

8. arXiv:1006.1294 [pdf, ps, other]
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
You Ding, Carlo Rovelli
Comments: 11 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)

9. arXiv:1005.2985 [pdf, ps, other]
Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
Carlo Rovelli, Matteo Smerlak
Comments: 4 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); Classical Physics (physics.class-ph)

10. arXiv:1005.2927 [pdf, other]
On the geometry of loop quantum gravity on a graph
Carlo Rovelli, Simone Speziale
Comments: 6 pages, 1 figure. v2: some typos corrected, references updated
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

11. arXiv:1005.0817 [pdf, ps, other]
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
Emanuele Alesci, Carlo Rovelli
Comments: 24 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc)

12. arXiv:1005.0764 [pdf, ps, other]
Face amplitude of spinfoam quantum gravity
Eugenio Bianchi, Daniele Regoli, Carlo Rovelli
Comments: 5 pages, 2 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc)

13. arXiv:1004.1780 [pdf, other]
A new look at loop quantum gravity
Carlo Rovelli
Comments: 15 pages, 5 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

14. arXiv:1003.3483 [pdf, ps, other]
Towards Spinfoam Cosmology
Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto
Comments: 8 pages
Journal-ref: Phys.Rev.D82:084035,2010
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Extragalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th)

15. arXiv:1002.3966 [pdf, other]
Why all these prejudices against a constant?
Eugenio Bianchi, Carlo Rovelli
Comments: 9 pages, 4 figures
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
==endquote==

 

[friend]

To get a better idea of the conceptual foundation of various research programs, it might be helpful to consider the history of the Quantum Gravity effort and where the programs start to diverge.

I doubt that any of these programs start from a complete vacuum. They are probably different ways of tackling the problems encounter in the first efforts.

For example, as I understand it, the first effort was to simply put the Hilbert-Einstein action in the path integral in order to quantize gravity. When that proved difficult (non-renormalizable?), they reformulated it with ADM's effort. Then used Ashtekar variable, etc. And then somewhere someone recognized spin networks in this formulation. And LQG was born. I'm guessing here. Maybe someone can give us a better idea of how it developed.

 

[marcus]

To get a better idea of the conceptual foundation of various research programs, it might be helpful to consider the history of the Quantum Gravity effort and where the programs start to diverge...

Rovelli's 2004 book has a chapter on the history of QG going back to (if I remember right) the 1930s.

The 2003 draft is available free online. Do you need the link?

Since 2007 there has been a strong movement towards convergence.

There used to be canonical (or hamiltonian) LQG
different from spinfoam
different from LQC (cosmology)

Now they are practically merged. Many of the papers you see in 2009-2010 are engaged in this process of bridging gaps, eliminating differences, showing equivalences.

Some minor programs like CDT and Causal Sets seem to have lost steam. Less written now than, say, 2005-2006.
Loll in CDT brought up a bunch of PhDs and postdocs but they mostly kind of leaked out of CDT, many into Loop-related research.

Some major non-Loop programs are Noncommutative Geometry, Group Field Theory, AsymSafe gravity. What is interesting is to watch the signs of convergence there!

The March 2011 Zakopane LQG school and workshop looks like about half NG! Rovelli has gotten a NG guy (Krajewski) on his Marseille team as a permanent. Last year there was a Oberwolfach workshop on NG and Spinfoam. Many people investigating how to connect NG and noncommutative field theory with LQG. John Barrett a leader here.

Also Group Field Theory and LQG. A lot of overlap of the communities. Krajewski. Oriti. Fairbairn too if I remember. The new formulation of LQG is actually based on GFT.

So far the major program most distinct from LQG I think would be AsymSafe gravity. But even there just this month we got Reuter's paper on doing AS with the Holst action (the GR action that spinfoam is based on).

The rate of convergence of the various nonstring QG approaches is fast enough that any attempt to highlight differences is likely to be out of date soon.
=============

But if you want a history of the various pre-2004 QG attempts, there is that history chapter in Rovelli's book, or maybe it is an appendix at the end. I will get the link. Here it is:
www.cpt.univ-mrs.fr/~rovelli/book.pdf

Perhaps you can get a different perspective on this business of divergence-or-convergence from Atyy. He has said things that suggest to me that he sees the LQG lines of investigation as diverging. I don't see that at all, especially in light of NG and GFT people working with LQG, and in light of papers like Ding Han Rovelli "Generalized Spinfoams" and Lewandowski et al "Spinfoams for All LQG". They are actively engaged in working out differences between various groups research.

It's always been a bunch of individualists, of course, but the divisions never seem to harden into permanent split. So I try to maintain an overall unified picture of how things are progressing.

 

[inflector]

marcus, I hate it when that happens.

I should have pointed out that I was trying to state what I believed were the assumptions in Rovelli's approach that are not necessarily a given in the spirit of what I thought you were trying to accomplish with this thread.

And you have to look at the people---physics is a human (even social) endeavor.

Perhaps one of the wisest comments I've seen here on PF. And relevant to how I attempt to put all these pieces together in my own head.

As physics is indeed a social endeavor, the group dynamics are important too. You need a few smart crazy people just to keep the ideas flowing, and you need a lot of slow steady progress to make apparent what works and where the actual roadblocks exist.

Sometimes I think Fra wants to reform everything at once Your quotes of Fra reminded me of that. Personally I'm pragmatic, let's see how Rovelli's gradualist approach works. (right now if you follow the papers it is going ahead very fast, working well.)

There may be times when a radical total-reform style is appropriate, and other times when a conservative style is.

Science seems to ebb and flow in each respective discipline as fresh ideas come like QM and GR in the 1920s, and experimental results that no longer fit science require a rethinking of the status quo.

I believe that all would agree that both approaches have merit and science needs both to advance.

Smolin is brilliant and has lots of original ideas but he has not worked in LQG proper for, I guess, over 5 years. He has not brought up any PhD students who are active in LQG. What he contributes is valuable in itself, but not central or typical. He explores related areas and ideas---like a scout or outrider if you can put up with a colorful image like that.

A scout sounds about right.

-------------------------------

I unintentionally diverted the conversation from this interesting thread on the conceptual basis for the idea of the path integral.

If you want to understand the dynamics of as Rovelli puts it:

a “quantum spacetime” formed by “quanta of space” evolving probabilistically, and allowing “quantum superposition of spaces”

then it seems like you need to have some approach for dealing with the resulting set of possibilities akin to the path integral approach in QM.

So bringing back together a few of the prior comments:

My reaction when I read your post was simply "first off, how do you define an integration measure on the space of metrics?"

(snip)

I don't offhand see any way to get a finite integral, or even a well-defined measure.

I remember reading stuff on how the Feynman Path Integral was not well defined; problems arose on defining a measure on the space of paths. I think they were able to get a well defined path integral using the Wiener measure that include the exponential as part of the measure. But then once a complex action was introduced, I'm not sure that did not introduce further complications. So when you start talking about measures on even more complicated spaces as space of metrics, etc. I really have to wonder if that has been well defined.

The last posts has focused on the PI over the space of gravitational fields. From a technical perspective this integral seems to be a natural focal point between QM and GR as it seems simple, yet confusing. As everyone usually points out when talking about this is that the PI is not really something well defined. It's just a symbols that looks like mathematics but which merely rather is a statement of intent. It expresses an IDEA of what logic to apply, but the exact details are missing.

That's my take on it too. I keep reading in papers about "taking the path integral" but it is not at all clear to me that there can be any formal mechanism for doing any such thing with the space quanta for any given theory. So it sure seems to me to be a placeholder for a "statement of intent," as Fra puts it.

The idea is to use the QM principles for computing an expectations; you simply ADD all possibilities according to their COUNTS, where the ADDITION is made according to quantum logic and superposition principles.

(snip)

But I think it's fair to say that this procedure is not well understood even before trying to put in GR. It's gets more ill behaved when putting in GR.

It may be just my limited math skills, but this seems to me to be the biggest conceptual hurdle that I haven't seen resolved in any ways that make sense to me yet.

So in many respects, it seems like quantum gravity theories start with this idea in mind: "What types of spacetime quanta are sufficiently defined so as to allow one to compute a path integral?" That defines potential quanta which can serve as the basis for the theory.

This is one of the reasons that Causal Dynamical Triangulation is interesting and generated some concrete results a few years back. In that approach, it is much easier to understand how one could perform a valid path integral, especially when computed as part of a Monte Carlo simulation. You can get the empirical data you need during the simulation to compute the path integrals.

In the spirit of the thread and the process of delineating the conceptual analysis of the QG scientists, is there some consensus among the LQG community for the computation of the Path Integral? Or does the approach to computing one differ from specific LQG theory to theory, i.e. spinfoam theories have one way, CDT has another, Causal Sets have another Non-Commutative Gravity has another? (my guess is that it must be the latter)

 

[atyy]

versus? The LQG program's repeatedly stated goal is a "general covariant quantum field theory" or a "background independent quantum field theory".

That was how he described the overall goal of the program when talking at Strings 2008. And in every major overview paper where he boils it down to one goal. You shouldn't need references but i bet i could find 3 or 4 recent instances.

In other words, no 'versus' or conflict. The main aim is to take seriously lessons learned from GR and carry those lessons over to QFT.

Presumably one of the first aims is to formulate geometry as a (background indep.) quantum field theory. Since matter fields live in geometry it seems reasonable that the first item on the agenda would be QG. Geometry would be the first field to quantize. Then start including matter (like in the recent paper "Spinfoam Fermions".)

The overall (explicitly consistently repeatedly stated) goal is QFT.
=====================

The tension you are thinking of is probably not with QFT per se, but with the outlook of those among today's (or anyway yesterday's) particle physicists who habitually think in terms of a fixed geometric background. A lot of inertia there, deeply engrained habit of viewing the world as fields living on a manifold with fixed geometry.

I think it may no longer be so widely shared among particle physicists. But even so you might call it the (traditional) particle physics perspective. If relativists are in conflict with something it is more apt to be with that fixed-geometry picture of the world. Not in conflict with the goal of a a general relativistic QFT!

Yes, to be more accurate: *practioners* of QFT versus GR. I said the inaccurate thing because I couldn't bring myself to write it, but unfortunately, that is what Rovelli writes.

 

[marcus]

Yes, to be more accurate: *practioners* of QFT versus GR. I said the inaccurate thing because I couldn't bring myself to write it, but unfortunately, that is what Rovelli writes.

As R has made clear, Loopsters aspire above all to be practitioners of QFT that being a general relativistic quantum field theory, in the sense of B.I.
That's how the main goal of the program is stated when he or anybody has to boil down. A background independent QFT. One that reflects GR's general covariance.

What I bolded are the exact words from R. presentation to Strings 2008. A serious effort to communicate. In other words you can say that a modern QFT is the holy grail of the LQG program.

Sometimes you hear relativists characterize a "particle theorists' viewpoint" as distinct from theirs. I don't know what you are quoting, or whether the context makes clear that he is talking about the viewpoint of particle theorists.

Have to go. Happy New! Hope to continue conversation tomorrow or before.