
#37
Jan1412, 03:19 PM

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The other attractive view to take spin foams as really discrete is Barrett's http://arxiv.org/abs/1101.6078.
"This is done by generalising Sakharov’s idea of induced gravity ... For this idea to work, it is necessary for the spacetime geometry to exhibit discreteness at the Planck scale ..." "Although the state sum models are discrete in nature, it is envisaged that an approximate continuum description should emerge at energies below the Planck scale. Therefore state sum models are constructed with this limit in mind  it guides the expectations of the physical content of the model." "The wishlist of properties for a state sum model is • It defines a diffeomorphisminvariant quantum field theory on each 4manifold • The state sum can be interpreted as a sum over geometries • Each geometry is discrete on the Planck scale • The coupling to matter fields can be defined • Matter modes are cut off at the Planck scale • The action can include a cosmological constant Diffeomorphism invariance here actually means invariance under piecewiselinear homeomorphisms, but this is essentially equivalent. The piecewiselinear homeomorphisms are maps which are linear if the triangulations aresubdivided sufficiently and play the same role as diffeomorphisms in a theory with smooth manifolds. This invariance is seen in the CraneYetter model and also in the 3d gravity models, the PonzanoRegge model and the TuraevViro model, the latter having a cosmological constant. The 3d gravity models can be interpreted as a sum over geometries, a feature which is carried over to the fourdimensional gravity models [BC, EPRL, FK], which however do not respect diffeomorphism invariance." 



#38
Jan1612, 03:57 AM

P: 216

"Highenergy gamma rays should show marked differences in polarization from their lowerenergy counterparts. Yet studying the difference in polarization between the two types of gamma rays, Philippe Laurent of CEA Saclay and his collaborators found no differences in polarization to the accuracy limits of the data.
Theories have suggested that the quantum nature of space should become apparent at the Planck scale: 10^35 of a meter. But the Integral observations are 10,000 times more accurate than any previous measurements and show that if quantum graininess exists, it must occur at a level of at least 10^48 m or smaller." http://www.centauridreams.org/?p=18718 The above is true if the spacetime would be built of the physical particlesantiparticles interacting with the photons. I suppose the spacetime is nothing more but a topology constructed by a relation between the nonmaterial information like wave functions of the Schroendiger equation. If the information of the wavefunctions might be nonlocal they may create relations everywhere due their probability and create the spacetime. Another supposition is that each relation of the nonlocal wavefunction encodes a Planck time dilation and it causes the sequence of the events and time flow. I think, each theory has to include information conservation, superposition and nonlocality. It suggests that even the smooth information has to be observed as a discrete after each relation. 



#39
Jan1612, 04:21 AM

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P: 5,307

not every theory based on a "discrete structure of spacetime" does indeed predict Lorentz invariance violations, anomalous dispersion relations etc.; so not all these theories have been rules out, especially not LQG which can be formulated in a Lorentzcovariant manner and from which no Lorentz violation has been derived so far.




#40
Jan1612, 08:03 AM

P: 5,634

CZES posts:




#41
Jan1612, 08:32 AM

P: 216





#42
Jan1712, 12:16 PM

Astronomy
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PF Gold
P: 22,800

Angular momentum appears discrete when one measures but does not consist of permanent lumps. An atom's energy appears in discrete levels but energy itself is not divided into fixed lumps. So geometric measurements of continuous media can have discrete spectra (angle, area, volume...). I guess one can regard this as analogous to the waveparticle duality. Perhaps these dualities are different faces of the same core fact about nature. 



#43
Jan1712, 12:47 PM

Astronomy
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PF Gold
P: 22,800

Czes linked to a misleading popularization in a blog whose main focus seems to be spacetravel. The actual scientific paper by Philippe Laurent et al did not directly mention LQG or draw any explicit connection. It is here: http://arxiv.org/abs/1106.1068 Constraints on Lorentz Invariance Violation using INTEGRAL/IBIS observations of GRB041219A The June 2011 paper is based on this earlier analysis by Götz et al http://arxiv.org/abs/1103.3663 After the June 2011 paper appeared, Philippe Laurent was quoted in popular newsmedia making some loose unqualified claims that their paper applied to some unspecified version of string theory and some unspecified version of LQG. He may have had something definite in mind. LQG has evolved quite a bit over the past decade and if you go back into earlier versions say from the 1990s you can undoubtably find a lot of variety. Or even before 2007. But he didn't give any footnotes or pointers to actual research literature so it was not clear what he was talking about. 



#44
Jan1812, 01:01 PM

Astronomy
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PF Gold
P: 22,800

It seems that what Czes was saying about "graininess" and last June's Philippe Laurent paper about a gammaray burst is not relevant to Loop/Spinfoam QG, so does not apply to what we are discussing in this thread.
But Atyy's post #37 (just a bit earlier) was interesting. BTW the quote from Barrett points out that (quantum states of) geometry can be discrete while the underlying manifold is continuous. ==quote Atyy http://physicsforums.com/showthread.php?p=3710407 == The other attractive view to take spin foams as really discrete is Barrett's http://arxiv.org/abs/1101.6078. "This is done by generalising Sakharov’s idea of induced gravity ... For this idea to work, it is necessary for the spacetime geometry to exhibit discreteness at the Planck scale ..." "Although the state sum models are discrete in nature, it is envisaged that an approximate continuum description should emerge at energies below the Planck scale. Therefore state sum models are constructed with this limit in mind  it guides the expectations of the physical content of the model." "The wishlist of properties for a state sum model is • It defines a diffeomorphisminvariant quantum field theory on each 4manifold • The state sum can be interpreted as a sum over geometries • Each geometry is discrete on the Planck scale • The coupling to matter fields can be defined • Matter modes are cut off at the Planck scale • The action can include a cosmological constant Diffeomorphism invariance here actually means invariance under piecewiselinear homeomorphisms, but this is essentially equivalent. The piecewiselinear homeomorphisms are maps which are linear if the triangulations aresubdivided sufficiently and play the same role as diffeomorphisms in a theory with smooth manifolds. This invariance is seen in the CraneYetter model and also in the 3d gravity models, the PonzanoRegge model and the TuraevViro model, the latter having a cosmological constant. The 3d gravity models can be interpreted as a sum over geometries, a feature which is carried over to the fourdimensional gravity models [BC, EPRL, FK], which however do not respect diffeomorphism invariance." The red is a serious issue. Loop/Spinfoam QG should respect diffeo invariance. I am not convinced that what Barrett said in this case is right. The issue may now have been addressed by the Freidel Geiller Ziprick paper: http://arxiv.org/abs/1110.4833 Continuous formulation of the Loop Quantum Gravity phase space Laurent Freidel, Marc Geiller, Jonathan Ziprick (Submitted on 21 Oct 2011) In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomyflux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomyflux variables. Our construction shows that the fluxes depend on the threegeometry, but also explicitly on the connection, explaining their non commutativity. It also clearly shows that the flux variables do not label a unique geometry, but rather a class of gaugeequivalent geometries. This allows us to resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since we establish that both geometries belong to the same equivalence class. This finally gives us a clear understanding of the relationship between the piecewise flat spin foam geometries and Regge geometries, which are only piecewiselinear flat: While Regge geometry corresponds to metrics whose curvature is concentrated around straight edges, the loop gravity geometry correspond to metrics whose curvature is concentrated around not necessarily straight edges. 27 pages 



#45
Jan1812, 01:12 PM

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#46
Jan1812, 08:45 PM

Astronomy
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PF Gold
P: 22,800

"Loops 2004" was called something else but it got the series of conferences started. Anyway there was already that idea of quantum gravity having something to do with different PL structures, or not PL but smooth, that can live on the same topology. Or so I recall. I should get the link to make sure. Here it is. I recall being impressed. But I cannot confidently answer your question could it play a role. http://arxiv.org/abs/grqc/0404088 Quantum general relativity and the classification of smooth manifolds Hendryk Pfeiffer (Submitted on 21 Apr 2004) The gauge symmetry of classical general relativity under spacetime diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over spacetime geometries, gives rise to a formal invariant of smooth manifolds. This is an opportunity to review results on the classification of smooth, piecewiselinear and topological manifolds. It turns out that differential topology distinguishes the spacetime dimension d=3+1 from any other lower or higher dimension and relates the soughtafter path integral quantization of general relativity in d=3+1 with an open problem in topology, namely to construct nontrivial invariants of smooth manifolds using their piecewiselinear structure. In any dimension d<=5+1, the classification results provide us with triangulations of spacetime which are not merely approximations nor introduce any physical cutoff, but which rather capture the full information about smooth manifolds up to diffeomorphism. Conditions on refinements of these triangulations reveal what replaces blockspin renormalization group transformations in theories with dynamical geometry. The classification results finally suggest that it is spacetime dimension rather than absence of gravitons that renders pure gravity in d=2+1 a `topological' theory. 41 pages Yes, he does cite a 1990 paper of Donaldson. And also incidentally a 2002 paper by Torsten AM, whom we know from discussions here! 



#47
Jan1912, 12:09 AM

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P: 5,307

I can't find the thread but sometimes ago I posted the idea that exactly these inequivalent smooth structures in dim=4 singles out dim=4. Suppose you could write down a PI summing over all nondiffeomorphic smooth manifolds in all dimensions. Then the probability for a 4dim. manifold in the PI is 1, b/c there are uncountably many inequivalent 4dim. smooth manifolds, whereas for all other dimensions there are only countably many. So dim=4 is explained exactly by diff. inv.




#48
Jan1912, 02:24 AM

Astronomy
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PF Gold
P: 22,800

I am interested by it and was impressed by Pfeiffer's paper back in 2004 but I don't understand it well enough to make a guess as to whether it is a good idea or not. Actually I have the same problem with Louis Crane's paper here. I would like to hear other people's opinions because I am not able to confidently evaluate. You know how some people do "numerology" and find amazing coincidences of numbers. Could it be that Louis Crane has fallen prey to "groupology" and has found an accidental appearance of the alternating group on 4 letters, namely A_{4}. And could he be overinterpreting or overreacting to this? On the other hand could it be that the paper is an important opening to new territory that deserves to be explored? (whether or not eventually leading to success.) He says he is going to follow it up with a longer paper. At the bottom of page 3 he says "A more detailed study of the structure will follow." That is right after he states a conjecture. ==quote== CONJECTURE: The EPRL model coupled to the tetron field gives a unified model which breaks to give the standard model. ==endquote== It's a bold interesting conjecture and I have to take something like that seriously, as potentially important, unless there is a good reason to dismiss it. 



#49
Jan1912, 04:08 AM

P: 216




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