tag:blogger.com,1999:blog-2381900080106522441.comments2017-09-15T08:29:22.247+02:00relatively quantumNorberthttp://www.blogger.com/profile/04965554394207041308noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-2381900080106522441.post-70996111797231351522017-04-07T09:25:41.946+02:002017-04-07T09:25:41.946+02:00Excellent advice, I know about this not by hearsay...Excellent advice, I know about this not by hearsay, it's a real experience of many years of work. I have been making presentations on various topics and products for a long time. Especially useful for beginners, who do not fully understand why this is done so scrupulously and accurately. If you like to work with Google tools, this will help you <a href="https://poweredtemplate.com/google-slides-themes/" rel="nofollow">https://poweredtemplate.com/google-slides-themes/</a> to diversify your work and add unique features.Kenneth Franzhttps://www.blogger.com/profile/05888858156254081041noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-46172755204989392982016-06-24T10:49:14.408+02:002016-06-24T10:49:14.408+02:00In order to establish a connection between LQG and...In order to establish a connection between LQG and string theory one needs an effective field theory approximation to LQG whith matter, where the matter is represented by special loops embedded in a spin network.<br /><br />As far as the pure LQG is concerned, the first step towards an effective field approximation is an effective action for the corresponding spin-foam model. This formalisam was developed in a series of papers by M. Vojinovic and myself four years ago.A. Mikovichttps://www.blogger.com/profile/03175906801121515444noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-29256122970216975282016-04-28T08:51:40.126+02:002016-04-28T08:51:40.126+02:00Matter propagates in a spin foam according to the ...Matter propagates in a spin foam according to the discretized form of the corresponding matter-field action. In the case of fermions there is a problem to formulate such an action because the fermions couple to the tetrads, and the tetrads are not well-defined in a spin-foam geometry. That was the reason to propose a spin-cube formulation, which is a generalization of the spin-foam formulation, based on the substitution of the spin-foam group by a 2-group (in the QG case the Lorentz group is replaced by the Poincare 2-group). The consequence is that the tetrads enter the formalism explicitely, through the edge lengths, so that a spin foam (a colored 2-complex) is replaced by a spin cube, which is a colored 3-complex. Hence in a spin cube the edges carry the 2-group irreps, the triangles carry the corresponding 1-intertwiners and the tetrahedrons carry the corresponding 2-intertwiners as oposed to a spin foam where the triangles carry the group irreps and the tetrahedrons carry the corresponding intertwiners.A. Mikovichttps://www.blogger.com/profile/03175906801121515444noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-22811942066855870582016-04-27T11:45:40.255+02:002016-04-27T11:45:40.255+02:00Thank you for the clarification. It still seems to...Thank you for the clarification. It still seems to me that the notion of local Lorentz invariance that you refer to is not what one means when one asks whether LQG is locally Lorentz invariant from a phenomenological point of view. There, the question of how matter propagates, morally from 4-simplex to 4-simplex, is the relevant one. Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-7067440309221112032016-04-26T14:52:53.431+02:002016-04-26T14:52:53.431+02:00In canonical LQG the local Lorentz invariance can ...In canonical LQG the local Lorentz invariance can be established by constructing the generators of local Lorentz rotations from holonomy and flux operators (if there is fermionic matter one has to add the matter contributions to the generators) and then verify that the algebra closes. This is a difficult task and anomalies may appear. In the spin-foam case, the analog of the local Lorentz transformations would be the Lorentz transformations that preserve the flat metric in each 4-simplex (provided that such a metric exists in every 4-simplex).A. Mikovichttps://www.blogger.com/profile/03175906801121515444noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-35822346223921822432016-04-25T11:38:02.938+02:002016-04-25T11:38:02.938+02:00Thank you for pointing out these differences betwe...Thank you for pointing out these differences between canonical LQG and the spinfoam formulation. I didn’t include them in my post, because I thought that they would distract too much from the core issues. <br /><br />About Lorentz invariance: I am not sure if we speak about the same thing. As emphasised in the post, the notion of “Lorentz invariance” appears in LQG both when choosing the internal gauge group (which can be the Lorentz group), and in the context of the question how the quantum geometry described by your physical state behaves (e.g. how matter fields propagate on it). While there are spinfoam models which are “Lorentz invariant” w.r.t. the the former notion, this is not clear for the second one, and thus for what people usually mean by Lorentz invariance. Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-19602610209561224622016-04-24T12:28:04.800+02:002016-04-24T12:28:04.800+02:00In order to better understand the theory called LQ...In order to better understand the theory called LQG, it is necessary to make the distinction between the spin-foam (covariant) and the canonical formulation. Although many people beleive that these two are the same theory, they are really two different theories. In the canonical LQG<br />the spacetime is topologically Sx[a,b] and there are colored graphs (i.e. spin networks) embedded in a smooth 3-manifold S. A physical state is a linear combination of the spin-network states such that it satisfies the hamiltonian constraint. The classical limit in this case is<br />defined by veryfying whether (hbar)Im(log Psi(A)) satisfies the Hamilton-Jacobi equation for the canonical GR in the limit hbar --> 0 and A is the Ashtekar-Barbero connection on S. This is a very difficult task, so that one uses the spin-foam formulation. In the spin-foam formulation, the theory is formulated on a triangulation of Sx[a,b], which is not the same as the smooth manifold Sx[a,b]. Hence obtaining the classical limit requires performing 2 limits, as you point out, i.e. the limit hbar --> 0, or equivalently j(triangle) --> infinity, and the smooth limit, i.e. N --> infinity, where N is the number of 4-simplices in T(Sx[a,b]). The easiest way to study these two limits is to use the effective action formalism. One then obtains that the first limit gives the area-Regge action. This is a problem, because area-Regge theory does not define always a metric geometry, so it is not equivalent to the usual Regge discretization of GR. Hence one needs to modify the usual spin-foam formulation in order to implement the constraints which reduce the area-Regge theory to the length-Regge theory. <br /><br />As far as the Lorentz invariance is concerned, it is not problematic for the spin-foam formulation, because the unitary irreps of the Lorentz group are (j,p) where j is an SU(2) spin and p is a real number. Also one can assume that the area of a triangle in a spacetime triangulation is determined by the flat metric in a 4-simplex which contains that triangle. The Lorentz invariance is more problematic in the canonical case, because it is not manifest.<br />A. Mikovichttps://www.blogger.com/profile/03175906801121515444noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-26351971533305893282016-04-15T12:14:41.739+02:002016-04-15T12:14:41.739+02:00Nice review! I would like to point out that the de...Nice review! I would like to point out that the described approaches are all based on the assumption that the short-distance topological structure of the spacetime is given by a smooth manifold. This is a logical possibility, but somehow I find it difficult to believe. Note that the approaches you refer to as "smaller" are precisely those where the smooth manifold structure is abandoned and one uses a non-commutative manifold, or a discrete set, or a piecewise linear manifold, etc ... Even in the case of CDT, although the theory is defined in the picewise linear manifold case (a triangulation), the goal is to obtain the smooth-manifold limit. More than 20 years ago Chris Isham has described this problem in one of his QG reviews: one starts with a smooth manifold M and a metric g, so the simplest thing is to replace (M,g) with (M,g*), where g* is an operator. A more general quantization is to replace (M,g) with (M*,g*) where M* and g* are some quantum generalizations of M and g.A. Mikovichttps://www.blogger.com/profile/03175906801121515444noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-81717218494102153982016-04-13T11:12:50.517+02:002016-04-13T11:12:50.517+02:00Hi Vedran,
thanks a lot for your input. I incorp...Hi Vedran, <br /><br />thanks a lot for your input. I incorporated it in the post. <br />Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-55562607441219592862016-04-12T22:45:45.288+02:002016-04-12T22:45:45.288+02:00Hi,
CDT was misspelled as "casual" DT i...Hi,<br /><br />CDT was misspelled as "casual" DT instead of "causal".<br /><br />Also in asymptotic safety you (almost) always go Euclidean.<br /><br />Finally, in asympt. safety spectral dimension apparently goes to 3/2, and not 2 as previously thought. This was confirmed in CDT and very recently Euclidean Dynamical Triangulations (EDT). Note that this result is relevant as it bypasses one usual apriori counterargument against QFTs of gravity.Vedranhttps://www.blogger.com/profile/02194339965441762137noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-27375307889079912012016-04-12T17:30:05.880+02:002016-04-12T17:30:05.880+02:00Dear Jakob,
thanks a lot for your comment. I fix...Dear Jakob, <br /><br />thanks a lot for your comment. I fixed the typo and added a brief explanation for the origins of the name. It originated in the time before it was realised that one needs to go beyond Wilson-loops to have non-vanishing volumes, i.e. to Wilson-"graphs", but it got stuck. Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-33796708684607819112016-04-12T17:05:37.183+02:002016-04-12T17:05:37.183+02:00Nice review! In the last section an "of"...Nice review! In the last section an "of" is missing in the sentence "The application the main technical and conceptual ideas". In addition, I think a short explanation is missing on why loop quantum gravity is called LOOP quantum gravity at all.<br /><br />Best wishes,<br /><br />Jakob<br />http://JakobSchwichtenberg.com/Jakob Schwichtenberghttps://www.blogger.com/profile/10458230617292717089noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-34567936851932301202016-03-29T14:15:08.988+02:002016-03-29T14:15:08.988+02:00In his introductory article, Ashketar asks the que...In his introductory article, Ashketar asks the question, "Can one construct a framework that cures the short-distance difficulties faced by the classical theory near singularities, while maintaining an agreement with it at large scales?”’<br />I have suggested that Einstein’s field equations are slightly wrong (because the equivalence principle is completely false for dark matter and even very slightly wrong for ordinary matter) — I have also suggested that Maxwell's equations are slightly wrong. By correcting Einstein's field equations and Maxwell's equations, most problems with singularities might be resolved.<br />Renormalization in quantum electrodynamics deals with infinite integrals that arise in perturbation theory. Such infinite integral might arise merely because Maxwell’s equations are incorrect at the Planck scale. Assume that leptons have structure at the Planck scale. I conjecture that, EVEN AFTER QUANTUM AVERAGING, Maxwell’s equations might be false at the Planck scale, because leptons have structure at the Planck scale. Let ρ represent the electric charge density (charge per unit volume). I conjecture that, in equation (19b) on page 23 of Einstein’s “The Meaning of Relativity” (5th edition), ρ should be replaced by the expression ρ/ (1 – (ρ^2 / (ρ(max))^2))^(1/2), where ρ(max) is the maximum of the absolute value of the electric charge density in the physical universe.<br />The preceding hypothesis makes the qualitative prediction that electromagnetic radiation emanating from sources near black holes might be unexpectedly large. M82 X-2 might be worth considering in this regard.<br /><a href="https://en.wikipedia.org/wiki/M82_X-2" rel="nofollow">M82 X-2, en.wikipedia</a>David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-49405531893849562162016-03-25T12:40:54.648+01:002016-03-25T12:40:54.648+01:00David, thanks for your comment.
We can divide th...David, thanks for your comment. <br /><br />We can divide the ambiguities discussed here in two classes: the first class is coming from the choice of observables. This choice is however related to a physical choice about how you prepare your experiment. Different observable constructions refer to different ways of defining which area you mean, i.e. with respect to what other structure you locate this area. In general, it is hard, if not impossible, to unambiguously translate questions between such preferred elementary sets of observables. For predictions, I would then trust always those observables where we have an unambiguous quantum analog of the classical function. <br /><br />This leaves the freedom of rescaling the metric by a constant parameter $\beta$. Concerning this, there has been some development in the literature recently pointing towards the self-dual value $\beta = i$ being preferred, see the links below. As a little background: the original Ashtekar variables in which the classical theory simplifies the most are obtained by the choice $\beta = i$. However, people were not successful in constructing a Hilbert space for this choice of variables (we are lacking an inner product implementing the rather complicated reality conditions). On the other hand, the Hilbert space can be rigorously constructed for real $\beta$. The attitude that I would now take is to check whether a certain value of $\beta$ is preferred in the quantum theory. As discussed in the references, there are several hints now for $\beta = i$, obtained from analytically continuing results for real $\beta$. If this turns out to be way to go, then this would solve the problem of this ambiguity. <br /><br />More answers to the other criticism you cited are scattered in the literature. I am planning to come back to them at some point in the future. <br /><br />http://arxiv.org/abs/1212.4060<br />http://arxiv.org/abs/1303.4752<br />http://arxiv.org/abs/1305.6714<br />http://arxiv.org/abs/1402.4138Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-44454731436342217002016-03-24T09:55:06.944+01:002016-03-24T09:55:06.944+01:00"... the reason for the ambiguity in the geom..."... the reason for the ambiguity in the geometric operators in loop quantum gravity is the freedom in choosing a metric on which the connection variables are based." From the point of view of making predictions, I would say that such freedom is a flaw in loop quantum gravity.<br />It might be helpful for someone to give a critique of Motl's critique of loop quantum gravity.<br /><a href="http://motls.blogspot.com/2004/10/objections-to-loop-quantum-gravity.html" rel="nofollow">objections-to-loop-quantum-gravity.html, Motl's blog, 2004</a>David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-62114503367279664182016-03-14T15:25:44.141+01:002016-03-14T15:25:44.141+01:00With regard to "global problems in defining o...With regard to "global problems in defining observables", I noticed that the publication "Chaos, Dirac observables and constraint optimization" has no references to the work of Milgrom, McGaugh, Kroupa, or Pawlowski. I say that Milgrom is the Kepler of contemporary cosmology and that foundational investigations related to general relativity should take into account Milgrom's ideas.<br /><a href="https://www.youtube.com/watch?v=C0oZQpQbFx4" rel="nofollow">Dark Matter or Modified Gravity? - Stacy McGaugh, YouTube, 2015</a><br />David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-11222609711234699182016-03-12T12:52:54.498+01:002016-03-12T12:52:54.498+01:00Kartik, thanks for your comment!
Concerning a sim...Kartik, thanks for your comment!<br /><br />Concerning a similar ambiguity in Yang-Mills theory: <br />I am planning to write a post about that, since the discussion is a bit too lengthy for a reply here. <br /><br />Concerning the strategy of dealing with the gauge freedom: <br />There are several ways how one can try to implement the constraints, with the advantages and disadvantages summarised for example in the book of Henneaux and Teitelboim. Out of them, it seems that the BRST method is the most useful in the context of standard gauge theory. However, solving all the constraints at the quantum level has proven very difficult in the context of general relativity, which is why some people started to solve them classically and then quantise. If progress can be made along this route, it would already be very interesting and we should be able to draw some lessons from it. But I agree that the ultimate goal should be to solve the constraints at the quantum level (by BRST or some other method), in order to understand what general covariance means in a quantum spacetime, and if the Dirac algebra gets deformed in some way. Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-10464570589585420012016-03-10T19:46:39.708+01:002016-03-10T19:46:39.708+01:00I am curious as to why a similar problem of gauge-...I am curious as to why a similar problem of gauge-fixing and choice of variables does not arise in other gauge theories like Yang-Mills?<br /><br />Also, shouldn’t one not fix the gauge before quantisation and do a BRST/BV type quantisation?<br /><br />(original post: https://kartikprabhu.com/notes/re-lqg-spectra )Kartik Prabhuhttps://www.blogger.com/profile/08007323225438909082noreply@blogger.com