Two recent interesting conferences that have some materials available on-line:
Last week the Perimeter Institute held a workshop on Emergence of Spacetime. Some of the talks are available at the Perimeter streaming video site (scroll to the bottom of the list for the Emergence of Spacetime workshop). The first day talks which are available online cover a very wide variety of points of view, including Petr Horava on string theory, Renate Loll on causal dynamical triangulations and Seth Lloyd on “Computing the Universe”.
Earlier this month there was a program in Lisbon on Algebraic Geometry and Topological Strings. The program included mini-courses by Jim Bryan, Marcos Marino, Albrecht Klemm and Rahul Pandharipande.
that link doesnt get to it either
at least this should work to get the program of the workshop, with its schedule of talks:
http://perimeterinstitute.ca/activities/scientific/PI-WORK-5/schedule.php
to download the slides and recording you probably do have to
go thru the steps Peter mentioned, scrolling down the menu and all.
Xiao-Gang Wen has collected the papers most closely related to the ideas presented at the PI workshop on this page.
I just finished watching the presentations by Markopoulou and Seth Lloyd. The latter summarizes his quant-ph/0501135, which was submitted to Science, and also touches upon the subject matter of quant-ph/0505064.
In case you haven’t read much of or about Lloyd’s work, it can be very briefly summarized as follows:
He starts by setting the problem (after an introduction by Lee Smolin). Forget trying to arrive at a quantum theory of gravity by quantizing the classical theory in some fashion. Instead, make a guess at a quantum theory that (one hopes) captures essential features of general relativity (as geometrodynamics!), and see how much headway can be made. So what’s the quantum theory? It’s a system consisting of simple two-way quantum gates — two inputs and two outputs. Feed an output of one gate into an input of another, constructing a simplicial lattice and a causal order. As in causal set theory one relies on the fact that the causal order determines the metric structure of spacetime up to a conformal factor. Getting this to work with two-way gates constrains the dimensionality of the spacetime to 4. (Lloyd spent some time on this in his talk.) The structure of system — the quantum computation — contains more information however, and this makes it possible to formulate an analog of spacetime’s energy-momentum content as well as a Regge-calculus-like construction and reproduce Einstein’s field equation.
Of course there is fine print. In particular he makes the point that the computational universality of even such a simple system is a problem — his version of the string theory landscape, as it were. (He mentioned this; I’m not just throwing it in.) It can simulate too much; we would like to identify a principle that constrains the simulation to something closely approximating the Standard Model in a classical spacetime governed by Gμν = 8πTμν.
Markopoulou’s talk complements Lloyd’s in some respects, and she makes the connection explicitly; she also employs ideas from quantum information theory, with emphasis on the ramifications of coarse-graining procedures applied to a quantum computational “pre-geometry”.* Furthermore there are strong connections between spin networks as employed in LQG and string-nets as employed by Wen and, more generally, several points of contact with condensed matter models of fundamental physics, which is what led the organizers to invite Xiao-Gang Wen and G. E. Volovik to this workshop.
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* Remember John Wheeler’s “pregeometry as the calculus of propositions” in Chapter 44 of Gravitation?
Also compare with the ideas outlined in physics/0505040.
Chris W.,
interesting post about an interesting idea. Other people (e.g. Finkelstein) have made similar proposals and the difficulty is always to get GR in a classical continuum limit. Lloyd tries to use Regge calculus to do this, but the devil is in the details as you have noticed. In particular the details of the ‘microscopic elements’ of the quantum network; There sems to be an infinite number of possibilities how such an element could look like.
But perhaps we are lucky and the ‘simplest element’ can reproduce our world (and nothing more).
CDT is a very interesting theory also. However there is something that puzzles me. You are in a 4 d world, but you can show that at short scale it is 2 dimensional. Now you use 4 d building blocks to prove this. But suppose you were living at the 2 d scale : you would never think of using 4 d building blocks, you would use 2 d blocks instead. But now I think I remember from a paper of Loll et al that if you use 2 d blocks you get degenerate geometries, and anyway you don’t get 4 d at large scale. I think this is problem. You should be allowed to use 2 d building blocks if the short scale effective dimension is really 2. It’s a bit like supposing you have an acid solution and finding that the pH is 8. Now it’s an effective dimension, and maybe this is why I’m mistaken. Does Loll address this question in the conference ? I watched the loops 2005 one but unfortunately the sound was too bad in the part where she talked about this dimension issue.
Fabien,
the fractal dimension of 2d euclidean dynamical triangulation is 4
or very close to it. It seems to work in both directions.
At this point I would emphasize “it seems”.
Fabien, to respond without being able to give more than my own interpretation:
I think one has to make a sharp mental distinction between the simplex dimension (a feature of the regularization) and the quantum observable which is the observed dimensionality at a given scale.
I think the simplex dimension is a combinatorial formality that helps to determine the network in which the blocks are assembled and how to shuffle and permute their interconnections, and the form of the Lagrangian.
the simplex dimension has no direct tie to the resulting spacetime dimension—–indeed prior to 1998, when they used plain DT, they found that when they used 2D and 3D simplices the resulting dimensionality was usually wrong. It would either be unbounded—essentially infinite—or too small. the resulting dimension was always too big (much too big) or too small.
in 1998 they started doing CDT and by 2003 they had found that in the case of using 2D and 3D simplexes the resulting expectation value of the largescale dimensionality was CORRECT. Actually the pathological behavior of too large or too small dimensionality can occur, but it has vanishing probability.
It took several years to do the computer simulations for the 2D and 3D case, so only in 2004 they got around to the 4D case.
I think in the CDT approach they do not pretend that the simplexes actually exist—they are just a combinatorial formalism that provides a framework for the dynamics and a regularization for the path integral.
When the model is compared to physical scale my understanding is that it is assumed the size of the simplexes is much smaller than planck length, the idea is that the size of the simplexes should go ideally to zero.
So I think of these simplexes as an imaginary formality, for performing the random Monte Carlo moves that implement the spacetime dynamics and for computing the path integral and expectation values of various things. I try to detach the idea of the simplex dimension from my expectations about the real spacetime dimension observed at various scales.
The result is that although I find your questions intriguing I nevertheless disagree when you say: “You should be allowed to use 2D building blocks if the short scale effective dimension is really 2.”
You could be right though. I can’t speak with any assurance and what you are pointing to does seem paradoxical. No time right now to try to shorten or clarify this post so have to leave it confused. maybe someone else can clarify.
I’m visiting Duke this week, and they have this talk:
String Theory Seminar
2:45pm, 120 Physics Building (DUKE)
Katrin Wendland (University of North Carolina, Chapel Hill)
“Z_4 orbifold limits of K3 and a family of smooth quartic K3s: A
nonclassical duality”
Smells like bullshit to me… but perhaps someone can explain what the title means?
Steven,
Not clear why you think Wendland’s talk is any more “bullshit” than any other. She works on conformal field theories with target space a complex surface (i.e. 2 complex dimensions, 4 real dimensions). A K3 is such a surface, they come in families.
I think it’s hard to make the case this is interesting for physicists. It seems to me to be the kind of thing many physicists have in mind when they say it belongs in math departments, not physics departments. Wendland does work in a math department, so physicists can’t complain. There’s a lot of interesting math involved here: conformal field theory and algebraic geometry. I don’t know any particular reason to be interested in the specific geometry and models she is studying, presumably experts in this are could tell you more of the motivation.
New paper (25 Nov 2005) by Lauscher and Reuter reviewing their recent work and the similiarity of its conclusions to those of the recent work in CDT:
Asymptotic Safety in Quantum Einstein Gravity: nonperturbative renormalizability and fractal spacetime structure (hep-th/0511260)
Wolfang :
>the fractal dimension of 2d euclidean dynamical triangulation is 4
This is very interesting. Can you tell me in which paper do they speak about this ? I could not find it. It is strange that such a consistency result is not more emphasized.
Who :
>So I think of these simplexes as an imaginary formality
Yes, this is precisely why it is important to prove it. In fact you seem to think about an even more stringent consistency condition : that the building blocks topology (and in particular dimension) have no importance whatsoever. I don’t think that something that strong could be true, but maybe I’m wrong.
Fabien,
http://xxx.lanl.gov/abs/hep-th/9806241
Already in the abstract they state that:
“the intrinsic Hausdorff dimension of usual 2d Euclidean quantum gravity is four, and not two. However, certain aspects of quantum space-time remain two-dimensional, exemplified by the fact that its so-called spectral dimension is equal to two”
The paper discusses the relationship between 2d Euclidean and Lorentzian dynamical triangulation and may shed some light on your question.
Thanks a lot, Wolfgang. It seems a very interesting and important result, although I still don’t understand why the spectral dimension would remain equal to two. I’ll have to read and see.
By the way —
From hep-th/0505113; Ambjorn, Jurkiewicz, Loll; June 2005 (abstract):
Compare with gr-qc/9310026; G. ‘t Hooft; October 1993 (abstract):
I think that I have good reasons to hope that this comment might not be classified as off topic but still I have unpleasant feeling in my gut(;-).
The effective 2-dimensionality is an interesting phenomenon which appears also in TGD framework. Apart from vacuum functional which carries information about 3-surface or equivalently about corresponding 4-surface analogous to Bohr orbit (exponent of Kahler function in the configuration space of 3-surfaces, the “world of classical worlds”), the quantum state carries only information about certain rather special 2-dimensional sub-manifols of 3-surface having interpretation as partons.
These partonic 2-surfaces represent cross sections of 3-D lightlike causal horizons of 4-surface meaning that partons are analogs of shock waves. It is not difficult to guess that a generalization of super-conformal invariance so that it applies to metrically 2-dimensional but topologically 3-dimensional lightlike causal horizons is involved. This superconformal invariance is present only for 4-dimensional space-time surfaces so that the theory predicts space-time dimension correctly from the requirement of generalized super-conformal invariance alone.
Matti
Off-topic, but did anyone else see Brian Greene on The Colbert Report last night?
Brian’s heart just didn’t seem in it. He trotted out the usual talking points though anyway. I really wish that string theorists wouldn’t always immediately think in terms of strings when addressing unification. Don’t they see a need to introduce the problem first and then say why strings are nice? From the interview you didn’t get really any idea of why quantum theory and gravity were so hard to put together. Brian just said that there’s this great theory out there called Superstring theory that may be the final theory that describes everything. I would’ve far preferred Brian giving a physical basis for why unifying gravity and quantum mechanics is so hard. And not one based on non-singular, stringy Feynman diagrams, please. (I realize that Colbert’s Q&A sessions can be a bit daunting, but that’s all the more reason to really figure out what it is you want to say beforehand.)
Case in point: I attended a talk by Seth Lloyd this week where he described a very conceptual approach to quantum gravity. His springboard was the GPS system. Satellites with clocks all tracking one another and mapping out spacetime. That kind of explanation could capture the imagination of the public much more than non-singular Feyman diagrams or extra dimensions.
To string theorists, I say, please step back a little bit when addressing the public before launching into your talking points.
god, ali, string theorists like that should be strung up…
Anonymous,
Please stop with the content-free abuse of string theorists, both ones who are my colleagues and ones who aren’t. It has been justifiably pointed out to me recently that there’s sometimes a Motlesque tone to many of the comments here, which is not a good thing. Leave the personal abuse tactic to Lubos and colleagues since it’s often the only argument they have.
” Leave the personal abuse tactic to Lubos …”
Amen to that. Self-defeating.
BTW of course like everyone else, I would imagine, I have have the highest respect for Frank Wilczek, but I was disappointed by parts of his article with Tegmark and others
http://arxiv.org/astro-ph/0511774
“Dimensionless constants, cosmology and other dark matters”
the reasoning involving the “prior” probability distribution on the vector of 31 dimensionless constants seemed nebulous or fishy.
the assumption of a particular eternal multibubble inflation to give a prior. Bayesian reasoning can be a very good thing but unexamined foundations here could be rotten. wonder if anyone else felt worried by this paper
however nothing adhominem—only highest respect for Wilczek and his fellow authors.
“Case in point: I attended a talk by Seth Lloyd this week where he described a very conceptual approach to quantum gravity.”
Seth Lloyd’s “theory of quantum
gravity” has much less predictive value than String Theory, and very little original content (it consists mainly of the ancient Regge ideas). For all his faults, Lubos has given a very intelligent assessment of Lloyd’s extremely naive, wishful thinking ideas about quantum gravity. It’s sad that some of the people (not Woit or Wolfgang) commenting in this blog seem to think that Lloyd’s ideas are a respectable alternative to string theory or even a serious foundation for a theory of quantum gravity. I’m afraid that those highly gullible people are guilty of judging a book by its cover, in this case judging Lloyd by the fact that he works at MIT.
Even within quantum computing, Lloyd’s contributions have been minimal. (if you disagree, please tell me what they are). If somebody asked me who is the quantum computation counterpart of Michio Kaku, I would say Seth Loyd. Lately, Seth has decided to make a foray into quantum gravity, and he is way out of his depth.
What I do not understand about Lloyd’s approach is that at some point he ad hoc introduces a continuous manifold in which he embeds his QC-graph. What is the motivation for this and “where” does the manifold come from? It does not seem to be a truly “emerging spacetime” concept.
anon,
It might help others in assessing Lubos Motl’s comments if you could point to some approaches to quantum gravity — other than string theory of course — that he has not dismissed as a naive product of wishful thinking and half-baked speculation, or a reasonably well developed but conclusive failure. “String theory is the only game in town and everything else is a waste of time, talent, and research funding” doesn’t cut it.
After watching his antics for more than a year and a half I find it difficult to care about anything Motl says anymore. If I want a usefully critical perspective on any idea I happen to find interesting there are plenty of other places I can find it.
anon,
the proposal of Seth Lloyd is an interesting idea, just ‘some details’ need to be worked out; as in the story of Pauli who claimed that he can paint like Tizian once he has worked out ‘some details’.
By the way there are many other great ideas which just need ‘some details’ be worked out (LQG, causal sets, etc.)
With superstring theory it is almost the other way around. A lot of details have been worked out and it all looks very promising.
I am just not convinced it is such a great idea 😎
But what do I know…
By the way, there is a fresh paper related to this discussion:
“Spin networks, quantum automata and link invariants”
http://xxx.lanl.gov/abs/gr-qc/0511161
The aforementioned paper is one of several included in the proceedings of QG05 (September ’05). The list of participants is impressive, and many of the abstracts are very interesting and relevant to this post.
I happened to be in Seth Lloyd’s first ever quantum computing class, and in the last lecture, he presented some of his first ideas about quantum gravity. To me, they seemed hopelessly naive, built almost entirely on dimensional analysis (something that is not necessarily useful in nonperturbative GR, which was what he wanted to talk about). His ideas have gotten a little more sophisticated since then, but they are still quite unimpressive.
Peter (and others) what do you people think about Finkstein’s aproach to
quantum gravity based on plexors ? sometime back I remember reading
on usenet that his work (though heroic) has received very little attention.
I don’t recall it discussed even once here or on cosmicvariance
As good as the talk by Lloyd was, PI emergence of spacetime, I was not surprised that during this talk he admitted he was at the same “car-salesman” seminar as detailed here:
http://www.physicsforums.com/showthread.php?t=89240
in the early eighties!
This San Francisco seminar series of the early eighties, has really a lot of explinations for the emergence of String Theory and Anthropic Rationale.
Personally I cannot take seriously the discretization of space-time continuum. A much more elegant manner to introduce
dicreteness at the basic level consistent with basic ideas fo algebraic geometry emerges if one accepts all number fields, also p-adic number fields and their extensions as building blocks of physics.
This more or less forces the view that real and various p-adic physics (possibly representing physical correlates for intention and cognition) are obtained by analytical continuation from rational physics both at classical spacetime level and quantum level.
A possible application is the definition of fermionic determinant playing fundamental role in QFT:s and also in TGD and being plagued by divergences. The idea is that the restriction to rational eigenvalues of the appropriate Dirac operator could make the determinant finite. Entire hierarchy of determinants corresponding to various algebraic extrensions of rationals emerges perhaps defining a hierarchy of finite Dirac determinants. This hierarchy would not be a calculational trick in TGD Universe but represent an actual physical hierarchy having natural identification in many-sheeted space-time of TGD Universe.
Matti Pitkanen