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

[atyy]

I am thinking specifically of section 2 of http://relativity.livingreviews.org/Articles/lrr-2008-5/ . As you know, I believe LQG to be completely wrong here - I would side resolutely with what he calls the particle physicist approach - which could find LQG interesting despite his wrong motivation - in that sense LQG is faithful to Einstein who was conceptually confused about general covariance and background independence and lived in an age before Wilson (wow, as if he's Jesus Christ ).

If there is any hope for convergence between LQG and AS, I would look to KKL and to Dittrich (I'm not sure it isn't a coincidence, but Bahr has worked with both of them). I believe GFT is pointing away from AS of pure gravity.

A very happy 2011 to you too!

 

[Fra]

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.

I think it's worth to stay on this topic for a little while and elaborate. I think it's very easy to go too fast here. Ie. to just say that the lesson of GR is BI and then suggest that the observables where to apply QM must be the invariants.

There is apparently no clear consensus even on what the CORE lessons of QM and GR are. I mean is it the equations or the constructing principles?

Here I'd like to quote an insight of E.T Jaynes commenting on analogies between shannons information theory and statistical physics what I think has a universal validity.

"the essential content of both statistical mechanics and communication theory, of course, does not lie in the equations; it lies in the ideas that lead to those equations."
-- "Probability Theory in Science and Engineering", 1956

It's in this spirit, I think Rovelli's assumption to assume the full QM formalism as it stands, without questioning wether the IDEAS that lead to QM; would lead to something different if the IDEAS that lead to GR would have been taken seriously? And of course - vice versa.

I think what Marcus says that sometimes incremental progress is the way to go is sound. But what worries me here is wether we are discussing how to make plumbing on the penthouse floor when the building is standing on unprobed soil. So I'm not saying we should do all at once, just that things should be done in a certain order in order to not misguide our efforts.

So what are the CORE ideas of GR - ie the ones that SHOULD keep?
Similarly what are the CORE ideas of QM?

How can we reform a common set of CORE ideas that is the union of these?

Edit: I'll let Marcus continue as he wish here, but one suggestion is that just for the case of constructiveness and interesting discussion we could focus in discussing the constructing principles of GR - in particular it's background independene, ie. to reconsider that arguments that lead to it, but now with the additional bonus of keeping in mind the measurement perspective. And see what we could up with?

Ie. what are the reasons and ideas that does indeed lead to BI? And how does that construction come out if we try to do it in terms of the interaction ~ measurement ~ communication that Rovelli himself puts forward in his RQM paper?

/Fredrik

 

[ConradDJ]

So what are the CORE ideas of GR - IE the ones that SHOULD keep?
Similarly what are the CORE ideas of QM?

How can we reform a common set of CORE ideas that is the union of these?

I.e. what are the reasons and ideas that does indeed lead to BI? And how does that construction come out if we try to do it in terms of the interaction ~ measurement ~ communication that Rovelli himself puts forward in his RQM paper?

The idea that leads to background independence is just that there is no given, absolute spacetime background. Another way of saying it is that spacetime measurements have no meaning in themselves, but only in relation to other spacetime measurements.

The reason this idea seems powerful is that it’s not setting up some arbitrary given fact – like Newtonian gravity – that we just have to accept without any justification. On the contrary, just because nature doesn’t have a fixed and given spacetime structure, any possible laws of nature have to be defined “relativistically”. And out of that we get gravity, without ad hoc assumptions.

This is the logic Relativity began with – that is, instead of postulating a background “ether” to which all velocities are referred, we ask how the laws of physics have to be defined if there is no single universal reference-frame?

Rovelli’s main point in his RQM paper was that there is an exact parallel to this logic in QM. That is, if we just eliminate the assumption that physical systems have absolute, given properties “in themselves”, then (he suggests, without quite proving it) that any possible laws of physics have to be formulated like Quantum theory.

The strength of these ideas is that in any case, no one can ever measure anything by reference to “spacetime” – only by comparing measurements with other measurements. Nor do properties of systems have any meaning apart from physical measurement-contexts. So by eliminating the spacetime “background” or the intrinsic “hidden reality” of things, we are only dispensing with metaphysical notions that are empirically shown to be helpful only in certain regimes. What physics actually describes is in any case a world of measured and communicated information.

There are two big problems with this. One is that we’ve been used to the notion of a given, absolute reality for well over 2,000 years. So it still seems more plausible to many of us to imagine spacetime as a new “ether” that exists in itself with a certain intrinsic (though twisty and maybe superposed) metric. The other problem is that describing how measurements are actually made and how information is actually communicated requires a different kind of analysis from what we’re used to, because every kind of information can only be defined in a context of other kinds of information.

I think the paper in which Rovelli went furthest in exploring this kind of idea was his 1997 http://philpapers.org/rec/ROVHTT" – I don’t know of a freely accessible version of this, unfortunately. But since then, the whole issue of “the observer” seems to have dropped out of his work in LQG.

 

[friend]

The idea that leads to background independence is just that there is no given, absolute spacetime background. Another way of saying it is that spacetime measurements have no meaning in themselves, but only in relation to other spacetime measurements.

This is the logic Relativity began with – that is, instead of postulating a background “ether” to which all velocities are referred, we ask how the laws of physics have to be defined if there is no single universal reference-frame?

How can there be discrete quanta of area and volume of something that does not exist? And how would we measure the area and volume of something that has no physical meaning?

 

[ConradDJ]

How can there be discrete quanta of area and volume of something that does not exist? And how would we measure the area and volume of something that has no physical meaning?

The idea isn't that space and time don't exist, or that they have no physical meaning. That would be nonsense. Evidently there's something about the structure of all this information that's getting communicated between things that makes space and time meaningful and measurable.

In classical physics we have the great convenience of imagining space and time as existing in an absolute sense, and we can just say, "this object weighs Xkg and moves with velocity Ymph in direction Z."

But in principle it must be possible to interpret physical information by reference to other physical information (because that's all we have), rather than by reference to "space and time" per se. And both GR and QM seem to be telling us that we need to do something like that to see what's going on at the fundamental level. Not necessarily to translate everything into "operational" language, but at least to see what's required in the structure of physics to make things observable to each other.

As to your question about quanta of area and volume, I don't know. Apparently that means that instead of a background-continuum, there's a different kind of base-level structure that I don't know how to envision. If we imagine tiny chunks of spacetime as existing all by themselves with certain properties -- that may or may not prove to be a helpful metaphor. But as with any physical theory, ultimately the question will be -- what is actually observed about the world that makes these concepts meaningful?

 

[inflector]

There is apparently no clear consensus even on what the CORE lessons of QM and GR are. I mean is it the equations or the constructing principles?

Here I'd like to quote an insight of E.T Jaynes commenting on analogies between shannons information theory and statistical physics what I think has a universal validity.

"the essential content of both statistical mechanics and communication theory, of course, does not lie in the equations; it lies in the ideas that lead to those equations."
-- "Probability Theory in Science and Engineering", 1956

It's in this spirit, I think Rovelli's assumption to assume the full QM formalism as it stands, without questioning wether the IDEAS that lead to QM; would lead to something different if the IDEAS that lead to GR would have been taken seriously? And of course - vice versa.

(emphasis Fra's)

Illustrating one example of Fra's distinction between ideas that lead to GR and QM and the formalisms they embody, I note a difference in Rovelli's characterization of the lessons of QM and a hint at the ideas that lead to QM in http://arxiv.org/abs/gr-qc/0604045" where he says:

we learn from QM that all dynamical field are quantized

and http://relativity.livingreviews.org/Articles/lrr-2008-5/" :

General relativity has taught us not only that space and time share the property of being dynamical with the rest of the physical entities, but also – more crucially – that spacetime location is relational (see Section 5.3). Quantum mechanics has taught us that any dynamical entity is subject to Heisenberg’s uncertainty at small scale. Therefore, we need a relational notion of a quantum spacetime in order to understand Planck-scale physics.

(emphasis mine)

In this second article note how Rovelli presents the lesson of QM as "any dynamical entity is subject to Heisenberg's uncertainty at small scale" which is different from the "all dynamical fields are quantized of his earlier Quantum Gravity book's introductory chapter."

The first presents an idea that we've seen verified by direct experiment. The second implies a formalism and indeed it is evident from Rovelli's next sentence where he uses the word "therefore" that he believes quantizing spacetime is the only reasonable means to bring the ideas of GR and QM together.

Which leads to ConradDJ's point:

Rovelli’s main point in his RQM paper was that there is an exact parallel to this logic in QM. That is, if we just eliminate the assumption that physical systems have absolute, given properties “in themselves”, then (he suggests, without quite proving it) that any possible laws of physics have to be formulated like Quantum theory.

(snip)

There are two big problems with this. One is that we’ve been used to the notion of a given, absolute reality for well over 2,000 years. So it still seems more plausible to many of us to imagine spacetime as a new “ether” that exists in itself with a certain intrinsic (though twisty and maybe superposed) metric.

Rovelli's conclusion completely rules out the possibility that there could be a realistic "twisty and maybe superimposed" spacetime where the the observations of the idea behind QM—namely that "any dynamical entity is subject to Heisenberg’s uncertainty at small scale"—come out as an emergent phenomenon.

I'm not saying Rovelli is wrong to draw this conclusion. I do, however, agree with ConradDJ that there are other plausible alternatives like: "a new 'ether' that exists in itself with a certain intrinsic (though twisty and maybe superposed) metric."

These sorts of ideas have seen relatively little work by comparison. Are there any serious QG scientists whose conceptual thoughts are relevant to this idea that we haven't yet considered?

All of the quantum gravity research I've seen—other than the odd paper here or there by someone like t' Hooft, who is not working on QG fulltime or like Koch who is new and relativly unknown—takes Rovelli's assumption as a starting point. There does not seem to be a serious research program that is not trying to quantize spacetime as far as I can see.

This is in opposition to the other possibility, that of trying to look at the potential ways that one could get QM behavior out of something inherently relational like ConradDJ's new "ether."

 

[marcus]

How can there be discrete quanta of area and volume of something that does not exist?

Nobody has said this, have they? As I recall in his book Rovelli talks about the area of a desk.
A desk exists. You have to want to understand and learn. You have to read. Isn't it inefficient to just sit around misinterpreting what people say and snapping at tidbits.

And how would we measure the area and volume of something that has no physical meaning?

Nobody said this (Desks have physical meaning, don't they? you sound like you are playing wordgames...intentionally misinterpreting so as to get apparent contradiction.)

OK here is another tidbit. Space is not what has area and volume. Things do. Einstein already said in 1915 that space has no objective reality, no physical existence, so it is not represented by a mathematical object in LQG.

You can say that geometry (finitized as a spinnetwork) gives things area and volume. The area of the desktop depends on how many links it cuts---each link contributes a quantum of area.

We are describing the potential results of measuring something. This is about information and the setup used to represent and correlate and predict it---that is: a mathematical setup used to correlate and predict responses to measurement.

The volume of the desk depends on how many nodes it surrounds.

What you see here is, I think, minimalist: it does the least one can ask of a math object representing of geometry. With the least extra baggage of additional assumptions. The cleanest, or most Occam, if you want to think of it that way.

Conrad may know this stuff better than I do. I'll try not to get in his way and try to listen more.

 

[inflector]

We are describing the potential results of measuring something. This is about information and the setup used to represent and correlate and predict it---that is: a mathematical setup used to correlate and predict responses to measurement.

I think what you said earlier was a good distinction that may be lost to those who are new to LQG or QG in general:

Anyway to build on your mention of discreteness, in case others might read this thread: I think everyone here realizes that Lqg does not depict space as "made of little grains". Geometric information is quantized the way, in other branches of theory, spin and energy are quantized: in response to measurement. Just as spin was not created in the form of "little bits of spin", so area and volume do not exist as little granules of area and volume. Area and volume are quantized as part of how nature responds to measurement.

(emphasis mine)

Which correlates very nicely with Rovelli's logical transition from "Heisenberg uncertainty in measurement at the small scale" as the underlying idea to quantizing spacetime as the specific mechanism. It seems to me that LQG, through the formalism of quantizing spacetime is building into spacetime itself the idea that measurement involves uncertainty.

 

[marcus]

...
There are two big problems with this. One is that we’ve been used to the notion of a given, absolute reality for well over 2,000 years. So it still seems more plausible to many of us to imagine spacetime as a new “ether” that exists in itself with a certain intrinsic (though twisty and maybe superposed) metric. The other problem is that describing how measurements are actually made and how information is actually communicated requires a different kind of analysis from what we’re used to, because every kind of information can only be defined in a context of other kinds of information.
...

The two problems you mention are not AFAICS problems with the theory, they are difficulties experienced by those "many of us" whose expectations are conditioned by past history and who are "not used to" the math tools or kind of analysis. They don't hurt the theory, just slow down its acceptance.

In a sense this is why I find the quantum theory of geometry interesting. It necessarily involves new (manifoldless) geometry, fundamentally new mathematics not just more and more elaborate (manifoldy) differential geometry. That it also slows down the rate at which awareness percolates into the physics community at large is not necessarily bad! The theory (and its application to cosmology) have changed substantially in the past 5 years. There are advantages to gradual seepage into the "market".

One big obstacle to understanding I've noticed is that many people have not gotten used to the 1986 Ashtekar introduction of connection rather than metric representation of geometry. So they don't see spinnetworks as a natural construct. Connection means parallel transport.
Geometry can be described by how stuff parallel transports along loops---a network is just a generalization of a loop. So a network can be a function defined on the connections. Like a quantum state or wave function defined on the configurations of a simpler system.
The spin network is a natural math object to serve as a state of geometry.
But it only seems natural after the Ashtekar "new variables" of 1986.

While we are on the subject of drawbacks, I should mention those I see:
1. the theory could be wrong.
Every application of LQG to cosmology seems to predict a bounce---a pre-bang contraction phase. That should show up. If it doesn't then the theory is wrong. Also concentric circles like Penrose thinks he sees should NOT show up. If they are really there, not just random coincidence mirage patterns, then AFAICS the theory is wrong.

2. the theory is still evolving rapidly. 2010 was a year of enormous changes---Rovelli posted 15 papers, that gives some indication. But so also were 2008 and 2009. Being in flux probably makes it harder for newcomers to understand, you have to work a little to keep up.

3. no one has done a Greene-ish popularization. As far as I know there is no popular book that gives a reasonably accurate layman's notion of what LQG is, e.g. how spinfoam dynamics gives transition amplitudes between initial and final quantum states of geometry.

the idea of a quantum state of geometry (the spin network) is potentially fairly intuitive---an abstraction corresponding to the finite set of geometric measurements available to us---what we know and can say about current geometry, or the geometric conditions surrounding an experiment

the idea of a transition amplitude based on a kind of path integral average over all the ways of getting from initial to final---that could also be intuitive.

but there is no layman's introduction that discusses those things. that I know of. No "Brian Greene" treatment.

That's why I always list the three (very hard, but well written) survey papers Rovelli wrote this year. They are truthful and fairly complete, they communicate, but not at lay-level. They are not introductions in that sense. They are introductions at the advanced PhD student and postdoc level---people wanting into the research community. I list them because they are all I know to mention that is truthful. It's tough.

Anyway here are the references again:
April 1780
http://arxiv.org/abs/1004.1780
October 1939
December 4707

 

[friend]

Nobody has said this, have they?

I'm sorry, but I was not able to derive anything useful from your previous comment.

I thought I was bringing up a valid point concerning conceptual foundations. But perhaps I was a little too brief. And you may have mistakenly assumed I was expressing any confusion I may have had as opposed to my commenting on how the previous poster worded his ideas. I guess I meant to ask what it means that GR considers any spacetime background not to have any physical meaning. Obviously, there is no preferred units of measure or reference frame, but is there more to it than that? This probably gets into the difference between background independence, diffeomorphism invariance and general covariance. It also seems obvious that spacetime in itself inherently has some physical existence. For otherwise it would be impossible for information to propagate through nothing.

And then there's the question of how one would measure quanta of spacetime. It was mentioned that we can only measure the distance between things. So theories that don't include particles to measure distance between seem doomed from the start. Are we really describing a testible theory about spacetime if it does not include particles that enable us to measure its predictions?

 

[MTd2]

Anyway to build on your mention of discreteness, in case others might read this thread: I think everyone here realizes that Lqg does not depict space as "made of little grains".

Actually it DOES depict space as "made of little grains", but ONLY when there is a measurement, because "little grains" is the generic eigenstate. The wave function is a complex superposition of all possible configurations of "little grains".

So, "little grains" is the particle part of the wave/particle duality of quantum mechanics.

 

[friend]

One big obstacle to understanding I've noticed is that many people have not gotten used to the 1986 Ashtekar introduction of connection rather than metric representation of geometry. So they don't see spinnetworks as a natural construct. Connection means parallel transport.

This is precisely the case (at least for me). I can't envision geometry without a metric. For me the two words are synonomous. I can understand how one might be preferred is some description over the other. But I can't see how geometry can have meaning without a metric being implied somewhere. But if you were able to explain that to me. The next step would be to show me how these spin networks have anything to do with these Ashtekar variable.

 

[marcus]

Which correlates very nicely with Rovelli's logical transition from "Heisenberg uncertainty in measurement at the small scale" as the underlying idea to quantizing spacetime as the specific mechanism. It seems to me that LQG, through the formalism of quantizing spacetime is building into spacetime itself the idea that measurement involves uncertainty.

Yes! Nice clarification.

 

[MTd2]

This is precisely the case (at least for me). I can't envision geometry without a metric.

This is because it depends on the definition of geometry. If you think geometry as a topological space, sometimes you won't even have the possibility of having a metric space.

Here's an example:

http://en.wikipedia.org/wiki/E8_manifold

 

[friend]

This is because it depends on the definition of geometry. If you think geometry as a topological space, sometimes you won't even have the possibility of having a metric space.

As I'm understanding it so far, if you redefine GR in terms of Ashtekar variable and then define spin networks on that, you don't lose the underlying math of GR. I thought the whole point was to continue Einstein's work.

 

[MTd2]

The classical solutions of GR involves metrics that spans the whole space. The point is, Einstein Equation is a differential equation, so it is about local differentiability. So, geometry ends up being the union of differential patches of geometry. In 4 dimensions, it has crazy consequences such as infinite non diffeomorphic metrics sharing the same topology or no metric at all despite the existence of a well defined topology.

 

[marcus]

As I'm understanding it so far, if you redefine GR in terms of Ashtekar variable and then define spin networks on that, you don't lose the underlying math of GR. I thought the whole point was to continue Einstein's work.

I don't understand what you mean by "I thought the whole point.." Is there any doubt about this as a continuation?

Ashtekar variables are a classical formulation of GR. There are a half dozen different reformulations of GR. They are a continuation of Einstein's work because they are mathematically interesting different ways to look at GR. Alternative reformulation is part of science and can contribute to progress.

Some reformulations are Palatini, Holst, Arnowitt-Deser-Misner (ADM), constrained BF theory, I won't try to be complete. Often the reformulations do not involve a metric. A metric does not appear in the mathematics.

So the point is to continue developing GR, and the Ashtekar variables DO that. If you thought it was a continuation, you were right.

But they are still classical. Not quantum yet. They just happen to afford a convenient opportunity to move to quantum theory.

There are other routes as well. (Holst, BF-theory, Regge-like?) What we are now seeing is a convergence of quantum theories of geometry that have gone up the mountain by different routes.

I'm not sure you can say Ashtekar variables are the ONLY way to go. But they played an important historical role. For one thing, the Immirzi parameter came in that way (as a modification of Ashtekar's original variables.)

If I'm off on any details I'd welcome correction. Some readers are surely more knowledgeable about some of the details here. Also I haven't checked the 1986 date here, it is just what comes to mind.

 

[marcus]

I found a much more introductory paper, which both gives a conceptual overview and a simple sketch of the mathematical elements of Lqg as it was in 1999. Not a bad way to begin. You get the more philosophical reflective side in conjunction with the math as it was at an earlier stage of development.

http://arxiv.org/abs/hep-th/9910131
The century of the incomplete revolution: searching for general relativistic quantum field theory
Carlo Rovelli
(Submitted on 17 Oct 1999)
In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have been revealed by these two ``first pieces of a conceptual revolution''. I discuss the general requirements on the mathematics and some specific developments towards the construction of such a framework. Examples of covariant constructions of (simple) generally relativistic quantum field theories have been obtained as topological quantum field theories, in nonperturbative zero-dimensional string theory and its higher dimensional generalizations, and as spin foam models. A canonical construction of a general relativistic quantum field theory is provided by loop quantum gravity. Remarkably, all these diverse approaches have turn out to be related, suggesting an intriguing general picture of general relativistic quantum physics.
Comments: To appear in the Journal of Mathematical Physics 2000 Special Issue

 

[marcus]

The first two paragraphs of that 1999 paper just happen to make the main points being discussed in this thread.
==quote from the 1999 "search for general relativistic QFT" paper==

In fundamental physics, the first part of the twentieth century has been characterized by two important steps towards a major conceptual revolution: quantum mechanics and general relativity. Each of these two theories has profoundly modified some key part of our understanding of the physical world. Quantum mechanics has changed what we mean by matter and by causality and general relativity has changed what we mean by “where” and “when”. ... framework, capable of replacing ... Lacking a better expression, we can loosely denote a theoretical framework capable of doing so as a “background independent theory”, or, more accurately, “general relativistic quantum field theory”.

The mathematics needed to construct such a theory must depart from the one employed in general relativity – differentiable manifolds and Riemannian geometry– to describe classical spacetime, as well as from the one employed in conventional quantum field theory –algebras of local field operators, Fock spaces, Gaussian measures ...– to describe quantum fields. Indeed, the first is incapable of accounting for the quantum features of spacetime; the second is incapable of dealing with the absence of a fixed background spatiotemporal structure. The new mathematics should be capable to describe the quantum aspects of the geometry of spacetime. For instance, it should be able to describe physical phenomena such as the quantum superposition of two distinct spacetime geometries, and it should provide us with a physical understanding of quantum spacetime at the Planck scale and of the “foamy” structure we strongly suspect it to have.

Here, I wish to emphasize that what we have learned in this century on the physical world –with quantum mechanics and general relativity– represents a rich body of knowledge which strongly constraints the form of the general theory we are searching. If we disregard one or the other of these constraints for too long, we just delay the confrontation with the hard problems...
==enquote==

 

[inflector]

This is for the relative beginners trying to follow this thread who get bogged down (like me) in the reference to "(active) diffeomorphism invariance" in the paper that marcus just referenced in post #78 because you didn't have a clear understanding of the meaning of active versus passive diffeomorphism invariance as used by Rovelli.

I found the paper by Gaul and Rovelli, http://arXiv.org/abs/gr-qc/9910079v2" , under Section 4.1 entitled: "Passive and Active Diffeomorphism Invariance," to be quite easy to comprehend and a very clear description of the difference between active and passive diffeomorphism invariance. It made reading the paper from post #78 much easier.

Since active diffeomorphism invariance is one of the explicit lessons of GR that Rovelli claims, it seemed useful to have a very precise definition of what that means. Section 4.1 provides just one such definition.

 

[friend]

I don't understand what you mean by "I thought the whole point.." Is there any doubt about this as a continuation?

Yes, I know I have to catch up on some of the reading. I hope I'm presenting relevant questions to keep in mind as I read. I think I may start with John Baze's book, "Gauge fields, Knots and Gravity", starting from chapter 3. It seems to include everything to get me to Ashtekar variables.

But perhaps you already know the answer to the following question: It seems that putting the Hilbert-Einstein action in the path integral was the first attempt to quantize gravity. It proved non-renormalizable but still made confirmed predictions in the low energy limit. Then there was a change to Astekar variables which seemed to provide a better way to quantize gravity. My question is can the later version be reduced to the former version? If so, then the first version IS renormalizable. If not, then how can we be sure we are even quantizing in the correct way? Thanks.

 

[Fra]

The idea that leads to background independence is just that there is no given, absolute spacetime background. Another way of saying it is that spacetime measurements have no meaning in themselves, but only in relation to other spacetime measurements.

Yes! But before we run into conclusions, let's go slower:

In special as well as general relativity, "spacetimes" are associated to reference frames and observers. The spacetime points simply indexs events relative to this observer.

So to rephrase this slightly, the idea that leads to BI is that there are no preferred observers.

Now, does this imply that observers or spacetime are devoid of physical basis and that the laws of physics must be observer invariant? And that somehow the laws of physics must be a statement of the transformations between spacetimes that manifests that allows for a invariant formulation?

IMO No. It is however a very plausible possibility. It's also the possibility that comes naturally with structural realism, but it's not the only possibility.

The alternative to EQUIVALENCE of observers is DEMOCRACY of observers.

Note that the latter is fully consistent with "the no preferred observer" constructing principles. The difference is that equivalence of observers is to a higher degree a realist construct. In the democracy of observer view the equivalence of observers corresponds to a special case where ALL observers are in perfect consistency. A possible equiblirium point.

So I think the constructing principle of GR, does NOT imply by necessity that the observers are in perfect consistency. It is merely a possibility. But it's admittedly the single most probably possibility! But I think of ot analogous to an "on shell" possibility, where the off shell possibilities are important.

Alterantively one can say that the constructing principle of relativity is that the laws of physics must be observer invariant. However this is a structural REALIST version that may or many not be suitable for merging with QM.

So I think a more neutral version is not "background independence" but rather "background democracy". And the difference is what I tried to describe.

Rovelli as I see it, tries to enforce the background independence by hard constraints, rather than let it be the result of a democratic process. The end result at equilibrium may be very similar but the understanding is quite different.

/Fredrik

 

[atyy]

Yes, I know I have to catch up on some of the reading. I hope I'm presenting relevant questions to keep in mind as I read. I think I may start with John Baze's book, "Gauge fields, Knots and Gravity", starting from chapter 3. It seems to include everything to get me to Ashtekar variables.

But perhaps you already know the answer to the following question: It seems that putting the Hilbert-Einstein action in the path integral was the first attempt to quantize gravity. It proved non-renormalizable but still made confirmed predictions in the low energy limit. Then there was a change to Astekar variables which seemed to provide a better way to quantize gravity. My question is can the later version be reduced to the former version? If so, then the first version IS renormalizable. If not, then how can we be sure we are even quantizing in the correct way? Thanks.

Although different classes of action may have the same classical equations of motion, they are not necessarily equivalent when treated as quantum theories. Within LQG itself, the Immirzi parameter is such an example. In AS, this means that we do not know if eg. there is no UV fixed point in the generalizations of the Hilbert action, that there is also no UV fixed point in the generalizations of the Holst action (by generalization I mean including all terms compatible with the symmetry of the action).

 

[friend]

Although different classes of action may have the same classical equations of motion, they are not necessarily equivalent when treated as quantum theories. Within LQG itself, the Immirzi parameter is such an example. In AS, this means that we do not know if eg. there is no UV fixed point in the generalizations of the Hilbert action, that there is also no UV fixed point in the generalizations of the Holst action (by generalization I mean including all terms compatible with the symmetry of the action).

Yes, I suppose this is what happens with the bottom up approach, where you try to quantize classical equations of motion. But the question still remains: How do we know we have the right quantization procedure?

 

[atyy]

Yes, I suppose this is what happens with the bottom up approach, where you try to quantize classical equations of motion. But the question still remains: How do we know we have the right quantization procedure?

Right in the sense of UV complete can be determined purely mathematically.

Right in the sense of describing reality is determined by observation.

 

[friend]

Right in the sense of UV complete can be determined purely mathematically.

Right in the sense of describing reality is determined by observation.

So we're waiting for experiment to confirm that we have the right action in the path integral or the right conjugate variables in the commutator?

 

[marcus]

How do we know we have the right quantization procedure?

Right in the sense of UV complete can be determined purely mathematically.

Right in the sense of describing reality is determined by observation.

Just a comment, Atyy. You have actually answered the question how do we decide we have the right quantum theory. (not "quantization procedure".)

AFAIK there is no god-given correct "quantization procedure" and a quantum theory does not have to be the result of "quantizing" a classical theory. It should be thought of as an optional heuristic guide. As a practical matter one can choose to follow procedures which have often worked in the past.

One could, I imagine, come up with a quantum theory not based on any prior classical and not resulting from any "procedure"---that described some phenom. not yet studied classically or otherwise. And then one would check the correctness of that quantum theory exactly as you said in your post---mathematically and by observation.

 

[marcus]

So we're waiting for experiment to confirm that we have the right action in the path integral...

Right. Always. Right is as as right does. There is no other way according to the scientific method. Right?

But Friend, wouldn't you agree that theories (and mathematical models in particular) are never proven correct, only provisionally trusted as long as they pass empirical tests.

In the case of LQG some tests of the theory have been proposed recently by early universe phenomenologists, based on some possible observations of ancient light (CMB polarization). LQG cosmology rests ultimately on spinfoam dynamics or, if you want to think of it that way, on the Holst action. Spinfoam is a type of sum-over-histories analogous to path integral, but it is probably simpler and more accurate to consider that one would be testing the spinfoam model directly (rather than the Holst action).

So that is a case in point, any pattern seen in the CMB which indicates that the early universe did not result from the kind of bounce predicted by the theory would tend to cast serious doubt, and probably falsify the theory.

 

[friend]

Right. Always. Right is as as right does. There is no other way according to the scientific method. Right?

But Friend, wouldn't you agree that theories (and mathematical models in particular) are never proven correct, only provisionally trusted as long as they pass empirical tests.

The whole point of theorizing and model building is to predict or perhaps postdict nature. This means it must match up with exprerimental results and observations. If it fails to make correct predictions, then you don't have the right theory. I take issue, however, with the idea that we can only do this by producing mathematics to fit the data. I think there are means other than curve fitting the data. (I'm not saying that this is what you said or implied.) Afterall, what experimental proof did Einstein have that the speed of light is constant for all observers? There is mathematical consistency that serves as a guide. But when trying to understand the conceptual basis of someone's efforts, it helps to put them in terms of concepts that are already understood. That's why I ask about how spin networks are related to Ashtekar variable, and what quantum procedure they are using, etc.

 

[marcus]

The whole point of theorizing and model building is to predict or perhaps postdict nature. This means it must match up with exprerimental results and observations. If it fails to make correct predictions, then you don't have the right theory. I take issue, however, with the idea that we can only do this by producing mathematics to fit the data. I think there are means other than curve fitting the data. (I'm not saying that this is what you said or implied.) ...

That sounds pretty reasonable, especially if you get away from the idea of there being one rigid correct way to arrive at a quantum theory---one correct "quantization procedure".

I would agree entirely, with the proviso that theorists arrive at theories by various paths. Basic conceptual thinking---almost at the level of philosophical principles---can play a major role. So can working by analogy with other quantum theories!

And certainly classical theories. However you get there, the quantum theory has to have the right classical limit.

You are asking about LQG and in that case there are a handful of different convergent strands. Rovelli mentions them in the historical section of one of those three papers, I forget which. I think April 1780.

Quantizing the Ashtekar variables is only one of several heuristic paths that have led to the present theory. What he describes (in about a page or page and a half IIRC) is how various approaches have come together.

In another paper, I think October 1939, he brings out the analogies with QED and QCD. Clearly analogies with other quantum field theories have also helped guide the program to its present stage.

If you want to understand you do need to read some stuff. Not a lot, just find the right page or pages. Maybe I could give page references, instead of having to copy-paste stuff here.
Have to go for now. Back later.