Using Verlinde's argument, Smolin shows Loop implies Newton's law of gravity in the appropriate limit. Verlinde's recent paper has thus supplied LQG with a missing piece of the puzzle. Smolin's paper presents his perspective on the significance of the Jacobson 1995 paper and of Verlinde's recent contribution---the basing of spacetime geometry on thermodynamics (basing gravity on entropy.) http://arxiv.org/abs/1001.3668 Newtonian gravity in loop quantum gravity Lee Smolin 16 pages (Submitted on 20 Jan 2010) "We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime."
Compton wave length? Do you mean the the radius for a Newtonian gravitational orbit around a body of mass M to sweep one Planck Area in one unit of Planck time? :tongue2:
"The proportionality is given by a fudge factor f, which we adjust to make m exactly into the passive gravitational mass". "It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of gravity is necessarily satisfied."
Inertial mass and gravitational mass are two different things. I suppose in any theory where the two arise and are shown to be proportional, one has the choice of setting them equal. The issue about splitting the universe into two regions is more interesting, I think. There is a school of thought which holds that Quantum Mechanics is inherently about information which a classical observer has about a quantum system. It only applies where the observer is OUTSIDE the experimental setup, or system. The Hilbert space is in essence a property of the boundary: the box containing the experiment, the interface through or across which observations are made. According to that view, one cannot have a comprehensive QM that embraces the whole universe, because it would not have room for the outside observer. One has to divide the universe into two parts: a box containing what is to be observed and studied, and a classical outside. At least that is a simplified sketch. Does it fit with any views of QM that you have encountered? I recall Smolin stressing this and related foundational issues in a couple of PIRSA video talks, I can get the links if anyone is interested.
Hmmm, I finally succumbed and glanced at Verlinde's paper! So if you assume that entropy scales with area, you get gravity? So any gravity here: http://arxiv.org/abs/0704.3906 ? Interestingly that is cited by http://arxiv.org/abs/0907.2939 , which does reference Crane, Rovelli, Smolin and Markopoulou "The mathematical structure that we observe in section 2 shares some features with an approach to quantum gravity called “relational quantum cosmology” [11]".
Just a thinking. Set [c]=1. Then [itex][G]=L / M [/itex] and [itex][h]=L . M [/itex] So a lot of relationships can be just naive dimensional analisis when M=1 or when you can somehow disregard masses or lenghts. This is a peril in this kind of papers, and so they are more careful than usual about doing all the steps explicit. Related question: if we were to live in an universe with more than 3 spatial dimensions, which should be the shape of Newton's Gravity Formula? which the units of [G]? I got worried because Smolin seems to say that his paper does not depend of the number of dimensions.
I am starting to feel that there is good hope for substantial progress, when good questions appear from many directions. I think the dark ages are soon over and unavoidable conclusions await us. The point marcus raises is a key one to me as well. But I do not feel it's necessary to consider one side to be "classical". The abstraction should works even when the observer side is non-classical with respect to a second observer. It's just IMO a matter of conditional probabilities, and it doesn't matter as I see it wether the prior condition is classical or quantum. The action of the observing system is I think _as if_ it was classical. It's somewhat analogous to the action of a player, where the action is executed from the point of view of the player with the full confidence in that the observed expectation is correct - even if it's wrong! Yet this is completely rational. This IMO also relates to a question Dmitry raised some time ago about the role of "false information"; in my view/interpretation at least the observer can not have an independent view of wether it's own expectations is right or wrong, so from the point of view of intrinsic action, right or wrong doesn't matter. Wether it matters to another observer, is a completely different question and relates to the action of that observer. I think this deeper connection that everbody, smoling, bekenstein and verlinde are now fishing for is going to take us yet on entire level away from realism. I think we will eventually think of "hilbert space" as about as up to date as we once thought of newtons absolut spacetime /Fredrik
Well, to make gauss law work, you should need that the power law fell with the inverse the number of dimensions minus one... So, in 10 dimensions it would be 1/r^9. Edit: Hmm, he meant the method is valid. Because at least in the citation he gave, it looks like so. http://arxiv.org/abs/hep-th/9901069 I guess it was just an unfortunate choice of words.
*shrug* Some people say this has already been shown. Note that Smolin did not say that the correct largescale limit had not been shown. He said that using his particular thermodynamics argument he did not show it. You could write a simple email letter to two people: Lee Smolin and his associate at Perimeter, Laurent Freidel. You could ask: "Has it been shown that classical spacetime emerges from LQG?" I don't know what they would answer. They might both say Yes, or they might both say No, or they might hold different opinions. I wonder. They are both busy people. It would not be fair to ask for more than a Yes/No answer. One would have to be courteous and keep it simple.
He could revise his paper by stating "classical spacetime in LQG has been shown in this paper" and cite reference. i.e Ashketar Friedal 2009.
I see no reason for anyone to do what you suggest. In this paper Smolin is not discussing who else has proved what. He is not giving a status report! For his purposes all he needs to do is to point out the facts about his own proof, namely that his particular proof has such and such assumptions. Proves this and not that. He has to tell the reader clearly what HE is doing. It would be great if someone well versed in the current situation would write a review paper this year, saying who has proven what. In what cases, with what assumptions. In which versions of Lqg and so on. Review papers are different from research papers. Last year Laurent Freidel gave a review talk (about the semiclassical limit) at the Marcel Grossmann meeting in Paris. It's a lot of work to prepare a review talk or review paper. You don't expect every individual research paper to provide a review
Given Smolin writes ""It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of gravity is necessarily satisfied." Does classical spacetime emerge from LQG?
So do I. Here are some off-the-wall remarks: Both Verlinde and Smolin seem to distinguish quite sharply between the macroscopic and the microscopic --- the macroscopic milieu that we live in, where spacetime has emerged and gravity rules as an entropic force arising from happenings inside surfaces enclosing the microscopic quantum milieu. On such separating surfaces, they propose, holographic information exists about the microscopic milieu; details about the microscopic degrees of freedom (in principle including gravity itself?) are not needed to derive Newton’s law of gravity. Our familiar Newtonian gravity is thus suggested to be a consequence of this proposed distinction. It seems to me that the only way one can quantitatively distinguish between the microscopic and macroscopic domains is via Planck’s constant, h, by choosing a scale based on a length defined by h, like the Compton wavelength of an object. But Verlinde argues that: If this means that the macroscopic-microscopic distinction is a movable feast, as it were, which can be done away with once it has been used to derive Newton’s gravity, it makes me wonder if said gravity might not be MONDified by the heirarchical inhomogeneity of our universe (strings-quarks-baryons-atoms-fluids-planets-stars-galaxies- voids and sheets).
associations Hmm... when I skimmed Smolins paper "Newtonian gravity in loop quantum gravity" as well as skimming his [38]"Holography in a quantum spacetime" http://arxiv.org/abs/hep-th/9910146 referenced to in the first paper during "Nonetheless, it is intriguing to wonder if the relationship between area and entropy is even more fundamental than the notion of geometry itself. Could there be a more fundamental picture, before spacetime emerges in which area has the fundamental meaning of the capacity of a quantum channel by which information flows[38]?" there is a touch of a new interpretation of LQG that remotely smells a little bit like what I thought it was, before I got rovelli's book and started to read. My original idea, that motivated me to look into rovelli's thinking and get the book, is that I originally associate the spin networks to microstructure of an observer. As such, a finite microstructure always has a boundary. The idea I had was that if this is true, then one can consider an interaction of two spin networks. Their interaction would eventually have to evolve a connection - connecting the two networks. In a similar sense eventually a whole environment would _emerge_ relations. But my impression of rovelli's reasoning from his book and old papers was that this was not really how He thought of it, and I felt I had to REinterpret everything to make sense out of, so I lost interest. But just like I see some angles to string theory that is promising (where string are emergent), this also sounds like one possible angle into LQG that might restore my interest. If what I envision work, I would also see no reason why LQG could not also unify all forces. There would probably be a more complex "network" that represents all degrees of freedom, not only space. /Fredrik
I haven't seen any paper claiming this has been achieved - but of course I cannot claim that I know all relevant papers :-) What I miss is a review paper on the new results from the last two years! Questions: 1) A propagator can somehow tell you a lot about long-distance limits, dimensionality etc., but it is not clear to me whether this sufficient. What happens to dimensionality in strong gravitational fields / inside a BH horizon but away from the "singularity"? 2) What does the "new-look-LQG" mean in terms of en emerging 4D spacetime? What does it mean in terms of Lorentz violation? (or - to be more precise - deformation)? What does it mean for light propagation, GZK cutoff, etc.? Are there already hints how to copmplete the canonical approach (the Hamiltonian)? I expected something like that from Thiemann's papers, but either this project is still incomplete, or I completely miss something. 3) What is the current status regarding the Immirzi-Parameter? What's its meaning (theta angle in LQG), what's it's value? Is it a field??? 4) What is the current status regarding q-deformation / framing of graphs (and braiding)? 5) Is the cc an input (as for q-deformation) or a result? A couple of years ago both Smolin and Ashtekar (and others) invested some time to present the current status in quite regular review papers. Unfortunately nothing like that has been done for the last years.
Indeed. The only conclusion I see is that there must be some rays going from a particle to another one in the other side of the universe instantly. I think I know what it is, but I can't tell you. Path integral gives a hint I guess , since a particle sniffs all of the universe as it moves,even tiny bit. maybe entropy is caused by gravity rays, entropy is an amount of change of state after all. so if entropy is due to gravity so time should be due to gravity( i.e. change of state), should'nt it?
I also am impatient to see a 2010 review paper. The most recent review paper for LQG is the May 2008 Rovelli, published online by the AEI in their Living Reviews series. ( http://relativity.livingreviews.org/Articles/lrr-2008-5/ ) This is a well-thought-out list of questions, IMHO. Thanks for compiling it: ==quote== Questions: 1) A propagator can somehow tell you a lot about long-distance limits, dimensionality etc., but it is not clear to me whether this sufficient. What happens to dimensionality in strong gravitational fields / inside a BH horizon but away from the "singularity"? 2) What does the "new-look-LQG" mean in terms of en emerging 4D spacetime? What does it mean in terms of Lorentz violation? (or - to be more precise - deformation)? What does it mean for light propagation, GZK cutoff, etc.? Are there already hints how to copmplete the canonical approach (the Hamiltonian)? I expected something like that from Thiemann's papers, but either this project is still incomplete, or I completely miss something. 3) What is the current status regarding the Immirzi-Parameter? What's its meaning (theta angle in LQG), what's it's value? Is it a field??? 4) What is the current status regarding q-deformation / framing of graphs (and braiding)? 5) Is the cc an input (as for q-deformation) or a result? ==endquote== I was motivated by your comment to look around for the LQG review papers that came before Rovelli 2008. I found 1. Ashtekar and Lewandowski 2004 ( http://arxiv.org/abs/gr-qc/0404018 ) 2. Smolin 2004 ( http://arxiv.org/abs/hep-th/0408048 , arxiv only. ) 3. Rovelli 1998 ( http://arxiv.org/abs/gr-qc/9803024 comparative survey of several qg incl. string) 4. Rovelli 1997 ( http://arxiv.org/abs/gr-qc/9705059 invited Living Reviews LQG article predecessor to current 2008 one) This doesn't count books---for example Thiemann's book would serve some of the same purposes as a review article. Also there was a conference talk by Ashtekar (to Marcel Grossmann 2006) that could serve at least in part as a review or status report ( http://arxiv.org/abs/0705.2222 ).
i'm not following this closely, but what about Padmanabhan's previous work? No citations or relations to it? Thanks.