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

[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.

 

[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.

 

[Fra]

So what about the core principles of QM?

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."

I personally think this is too fast to see the steps.

I'd like to propose that the core principles, is the content of Bohrs mantra that essentially says that the laws of physics doesn't encode what nature is or does, it encodes what we can say about nature and how it behaves. This summarizes almost the essence of science, namely that we infer/abduct from experiment (OBSERVATION) what nature SEEMS to be and how it SEEMS to behave.

Thus we arrive at an effective undertanding in a good scientific spirit, and all we have is our rational scientific expectations. There just IS no such thing as "real reality". It serves no purpose in the scientific process.

But as with the GR, there seems even here multiple ways to understand and extrapolate this.

I read it in a more explicit way so that the laws of physics encode the the observers expectation of nature as a function of their state of knowledge.

It seems like Rovelli's conclusion is that since he considers the equivalence class of observers as the physical core, he thinks that QM says that the laws of "quantized" physics, encodes expectations of equivalence classes of observations. In this view, he doesn't consider the quantum laws themselves subject to Bohrs mantra. It apparently enters as a realist element.

The alternative, quite similar to GR, is to think that combining this with the "observer democracy" rather suggest that physical law itself - including "quantum laws" are rather intrinsically observer dependent and that instead the problem becomes how to understand how the effective objectivity that we de facto see is a result of a democratic process (which of course would be purely physical to its nature).

/Fredrik

 

[inflector]

If we would start where you suggest (with e.g. the idea of "quanta of space")

(snip)

Area and volume are quantized as part of how nature responds to measurement. It is like what Niels Bohr said. "Physics is not about what Nature IS, but rather what we can SAY about Nature." So it is about information---initial and final information about an experiment, transition amplitudes. Or so I think.

Returning to the idea of quantization itself...

It seems clear to me that taking GR and quantizing it is a strategy that makes a decision.

We know that measurement is quantized through large quantities of actual experiment. But it seems to me that this quantization could come from two places:

1) That geometry itself is quantized

2) That there is an interaction in the process of measurement between the device doing the measuring and the object being measured that results in a quantization

All of the quantization of GR approaches seem to be deciding that 1) is more likely than 2). Is there some reason? Has this issue been specifically addressed?

For example, let's go back to the first concrete quantum weirdness experiment (at least that I know of), Stern-Gerlach. In that experiment, some of the silver ions were diverted up and some were diverted down and the classically expected smooth distribution did not occur. But it may be that the process of measurement is what does the quantization, right? Depending on your favorite interpretation of QM you might look at this in various ways but it comes down to the process of measuring resulting in two distinct values, up and down.

We also know through various experiments with http://en.wikipedia.org/wiki/Stern–Gerlach_experiment#Sequential_experiments" and light polarization that the measuring apparatus also changes the state of the objects being tested, whether ions or photons. So clearly there is a significant interaction between the measurement device and the object being measured.

So what says that it is not the process of measuring that results in the quantization rather than that geometry itself is quantized? Strategies that quantize the geometry seem—to me anyway—to assume that it is not the measurement that causes the quantization. They seem to assume that the objects exist in a state that is probabilistically quantized because the geometry itself is probabilistically quantized.

On the other hand, experimental quantum theory itself seems agnostic on this issue. Some interpretations refer to collapses of the wave function during measurement, but quantum theory itself doesn't say why the collapsing happens only that the measurements end up being quantized.

Am I missing something? Or is it fair to say that my points 1) and 2) above characterize two equally valid points of view, but that LQG and other quantize-GR theories assume 1) and NOT 2).

 

[friend]

So what says that it is not the process of measuring that results in the quantization rather than that geometry itself is quantized? Strategies that quantize the geometry seem—to me anyway—to assume that it is not the measurement that causes the quantization. They seem to assume that the objects exist in a state that is probabilistically quantized because the geometry itself is probabilistically quantized.

To add to this question, since it will take particles to measure the quantization of space, how would we know it is not just a further quantization of particles that we are measuring?

Also, aren't there quantum variables that can be measured in a continuous spectrum? For example, position and momentum of free particles can be measured anywhere, right? How would spacetime be in a bound state so that its has a discrete spectrum? What is the boundary of spacetime? Maybe it's the particles used to measure space that form the boundary of space, making it have a discrete spectrum.

 

[Fra]

I for one think that it's quite established that the issues of exactly what quantization means is NOT sufficiently addressed by Rovelli. He doesn't even try very hard.

Somehow that settles the issue. But he has also declared that this isn't his ambition.

To me the CORE essence of quantization, in despite of the name has nothing to do with wether something ends up literally quantized (in chunks), it's more the constraint that is applied be requireing "observability" or "inferrability". This I picture achieved by requiring the the predictions to be cast in terms of "expectations", computer from initial information that must originate from prior measurements.

So I think you are right to not ignore these things.

Strategies that quantize the geometry seem—to me anyway—to assume that it is not the measurement that causes the quantization. They seem to assume that the objects exist in a state that is probabilistically quantized because the geometry itself is probabilistically quantized.

I'm not sure I would agree with your two options. But I do agree that this is generally under-analysed.

Expectations of course exist in classical logic as well, and clasical probability. I think that what "causes" the quantum logic (or cause quantization as you phrase it) is that if we take seriously how information is encoded by the observer, and consider fitness of this code as an interacting one, then it seems a plausible conjecture that non-commutative structure in the code would have higher fitness and that the evolutionary selection of these "non-commutative histories" is the original of quantization.

I'd claim that an expectation (genereally inductive, probabilistic) is the essence of QM.

Classically we don't have expectations, we have laws that given initial conditions DEDUCES what WILL happen, in an objective sense.

QM expectations is in the form of deductive probability, QM DEDUCES what the probabilities are that certain things will happen. Thus the expectations encodes, in line woth Bohrs mantra, not what WILL happen, but what we can SAY about what will happen; ie what we EXPECT to happen.

So I see construction of the expectations as a key construct. So, we need to construct geometrical notions interms of expectations. Here Rovelli is possibly missing a point becase geometry is defined be relations between observations, and observers. So it may mean that geometry in the GR sense is not observable in the sense of QM, beucase it takes a collection of interacting observerations to observe it. (The democratic view).

Rovelli sometimes seems to assume that geometry exists, and doesn't even try to reconstruct it in terms of realistic measuremnts from the point of view of a single observer. So I basically question his choice of what's observable and what's not. Clearly IMHO at least, observer invariants are not what should be subjecto "quantization" for me that is a likely abuse of QM.

/Fredrik

 

[Fra]

What is the boundary of spacetime? Maybe it's the particles used to measure space that form the boundary of space

Mathematically we can picture an empty space without boundaries, but physically and in particular when constrained by the observability criterion that QM teaches us, the boundary of spacetime is obviously matter.

Anything else is just something that lacks physical basis IMO.

So I think your on the right track. For me, I've always associated matter with the observer. Gravity without matter is like a quantum theory without observers. Also in all experiments on "empty space" such as casimir effects, the boundary is critical. You can't observer an empty space without inserting a boundary.

To take it a step further, I think there has to be a theory living on the boundary (or more exactly, encoded in them matter) that somehow interacts and mirrors whatever is going on on in the extenral bulk. It's a vauge form of holography.But it's not necessarily exact, the holographic conection is more likely IMO to correspond to an equilibrium point. This is why maybe we need further understanding og this. because it may not be right to use an equilibrium condition as constraint, we may be missing out on physics.

Edit: I insinuated in another thread, but I think that this holographic connection (to be understood) can also be seen dual to the problem of understanding the more general theory mapping. If you consider a generalisation of RG, where you consider the theory space to include a larger set of observers, not just observational scales that you arrive at by changing energy scale, but observers with completely different topology and complexity, then it seems that the holographic duality is like a connection between two different points in theory space with are communicating. It seems to me that the RG space itself must evolve, as this itself should also be subject to observabiltiy constraints.

So it seems like QM + GR must be something like an evolving theory space at where at each "instant" the state of the space (I don't thikn it's a continuous manifold) it defines "connections" between expectations... like the "quantum version" of a GR connection which is not the same as a quantized connection. It seems to be something hairy where certainly the EH action itself is emergent, rather than put in by hand.

So the QG replacement of the GR state space must be something far more hairy, something like a theory space. And here, matter (or what corresponds to it) must be included from constructing principles. It wouldn't make sense otherwise.

/Fredrik

 

[cutbait]

IMO the first place to look would be the Dirac Sea. Electron and positrons that disappear and then can magically reappear from absolutely nothing. I have issues with any theory that claims to be based on math, but is really based on magic. What if the electrons and positrons did not annihilate, but are instead sitting at an immeasurable zero spin state. In addition, when energy is added they would spilt apart, and then come back into our measurable existence. Bosons are then not required to satisfy the math requirement for a zero spin state.

An electron's probability orbit around an atom could be nothing more then measurement error. Similar to how moths and bugs appear as "flying rods", to cameras that are not able to capture or measure at a fast enough rate. It is a shame we do not have something smaller then an electron or positron in which to measure with, but it would then be the same problem just the particle would have a different name.

Time is nothing more then the rate at which processes run at or complete in. If matter uses electrons and positrons to measure time with how do electrons and positrons measure time? Could energy and matter not experience time at a different rate? How could we measure the time that energy experiences? We cannot.

Quantization is due to having to measure things with matter. All current sensors and measurement devices are composed of matter. We are limited in measuring to what is happening at the transmitter and what is happening at the receiver or sensor. We cannot take a CRT and label an electron as it leaves the gun. To prove that it was the electron that actually hit the screen, and knocked an electron in the screen matter to a higher energy state.