Lubos Motl
May30-04, 09:50 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Dear John (from sci.physics.research),\n\n> It was good to see old friends and talk about quantum gravity near\n> the "Calanques" - the rugged limestone cliffs lining the Mediterranean\n> coastline...\n\nthat\'s beautiful.\n\n> It was good to meet lots of young people who have recently\n> entered this difficult field: about 100 people attended, considerably\n> more than at any previous meeting.\n\nCongratulations. Maybe we will soon be forced to correct the Wikipedia\'s\nestimated ratio 10:1 between the size of the stringy and loopy\ncommunities. It would be even better for LQG to improve the 50:1 ratio of\nthe numbers of publications.\n\n> Can we get the 4-dimensional spacetime we know and love, whose geometry\n> is described by general relativity, to emerge from some theory that takes\n> quantum physics into account? And can we do it *nonperturbatively*?\n\nThis used to be a big dream in string theory, but it has been more or less\nsolved, at least for some particular backgrounds. You can put N=4 d=4\nYang-Mills on some sort of lattice - e.g. using deconstruction - to define\nthis theory non-perturbatively (much like QCD), and then you obtain\nnon-perturbative results about quantum gravity in the AdS space.\nSimilarly, Matrix theory gives you non-perturbative answers about\ngravitational physics in flat space with many large dimensions.\n\nThe difficult task in string theory today is to have a set of "equations"\nthat allow you *both* to go to larger values of coupling, as well as to\nvery different geometries than the geometry you start with.\n\n> In other words, can we do quantum physics without choosing some fixed\n> spacetime geometry from the start, a "background" on which small\n> perturbations move like tiny quantum ripples on a calm pre-established\n> lake?\n\nJust to be sure: do you agree that the correct answer may be "No, it is in\nprinciple impossible", or do you prefer to ask rhetorical questions only?\n\n> A background geometry is convenient: it lets us keep track of\n> times and distances. It\'s like having a fixed stage on which the actors -\n> gravitons, strings, branes, or whatever - cavort and dance.\n\nThat\'s, indeed, the conventional particle physics framework to do almost\nall calculations - one that is applied in string theory most of the times.\nMost successful calculations are done in this way, and it is conceivable\nthat we won\'t have anything better in the next decades - maybe never.\n\n> But, the main lesson of general relativity is that spacetime is *not*\n> a fixed stage: it\'s a lively, dynamical entity!\n\nIt\'s even more lively in string theory. Not only that geometry can be\ncurved and it not only affects the matter, but it is also affected by\nobjects immersed in spacetime; it can be transmuted into non-geometric\nphysics; its topology can change (once wrapped branes are condensed),\nunlike the case of classical GR (and most interpretations of LQG); two\ndifferent geometries can lead to identical physics (by T-duality or mirror\nsymmetry); K3 manifolds with one theory can be equivalent to tori with\nanother (heterotic) theory; charges get continuously transmuted to momenta\nand vice versa; black holes become elementary particles (vibrating\nstrings) and vice versa; timelike singularities can be resolved.\n\nString theory offers much more flexibility and mutual interrelations\nbetween the different players than Einstein could have ever dreamed of.\nAnd LQG reproduces Einstein (with some observables quantized), with a\ntypically Einsteinian hope that quantum physics won\'t modify anything\nessential; it can be just added and ignored.\n\nAll of us would be happy to have a framework that would describe all these\npossible transmutations of the players (in string/M-theory) into each\nother in a unified framework - a framework that allows us to see all such\npossibilities - but on the other hand, it is a philosophical and\naesthetical desire (which, we expect, could have big technical\nimplications), not a proved physical necessity. It can be used as a\nmotivation for a physicist to direct her research, but not as a convincing\nscientific argument.\n\n> There\'s no good way to separate the ripples from the lake.\n\nThat\'s right, and string theory allows us to prove - at least\nperturbatively, or also in effective field description of nonperturbative\nphysics - that physics of (a coherent state of) ripples is exactly\n*equivalent* to a modified lake. But string theory claims much more:\nthere is no good and universal way to separate the ripples and the lake\n(gravity) from other particles (matter). All of them inevitably arise\nfrom the same ingredient - a vibrating string - or more precisely\n(nonperturbatively) from "M" whatever it is. ;-) String theory has\nalready taught us more far-reaching lessons that go beyond the lessons\nfrom 1915 that you keep on repeating with such a respect - lessons that I\nalso like, but that are far from being everything!\n\n> So, we should learn to make do without a background when studying quantum\n> gravity. But it\'s tough!\n\nYes, it is, and it is by no means guaranteed that it is possible. Let me\nsay a more trivial example. The electroweak theory can be written in\nunitary gauge, and the SU(2) x U(1) symmetry is then obscured. We also\nknow that there is a formulation that makes the (spontaneously broken)\nsymmetry manifest. But is it necessarily true that there exists a\nformulation that makes *all* interesting features and relations of the\ntheory of everything manifest? I hope so, but once again, no one can\nguarantee it!\n\n> There are knotty conceptual issues like the "problem of time": how do\n> we describe time evolution without using a fixed background to measure\n> the passage of time? There are also practical problems: in most\n> attempts to describe spacetime from the ground up in a quantum way,\n> all hell breaks loose!\n\nRight. It is very hard to maintain the existence of some exact objects\nonce we sacrifice the existence of the spacetime arena itself; I think\nthat Brian Greene in Chapter 15 of the Elegant Universe, as well as in the\nnew The Fabric of the Cosmos, describes these dreams and the difficult\nsituation very well.\n\n> We can easily get spacetimes that crumple up into a tiny blob... or\n> spacetimes that form endlessly branching fractal "polymers" of Hausdorff\n> dimension 2... but it seems hard to get reasonably smooth spacetimes of\n> dimension 4. It\'s even hard to get spacetimes of dimension 10 or 11...\n> or *anything* remotely interesting!\n\nToday, you can almost certainly get 4 out of 10 or 11 because people now\nclaim to have the compactification and the stabilization of all moduli\nunder full control. Because string theory knows how to get 10 or 11, it\ncan obtain 4, too. This specific problem also belongs to the past, in a\nway. What we really need to understand today are the laws that govern\ntime-dependent backgrounds, string cosmology, and such - those may play a\nvery important role in organizing the jungle (landscape); some people\nbelieve that these problems can be attacked directly and they try to do\nso. It is often good to try at least something - well, even though one\noften fails.\n\n> It almost seems as if we need a solid background as a bed frame to keep\n> the mattress of spacetime from rolling up or otherwise misbehaving.\n> Unfortunately, even *with* a background there are serious problems: we\n> can use perturbation theory to write the answers to physics questions as\n> power series, but these series diverge and nobody knows how to resum them.\n\nThey are asymptotic expansions, and the error that we introduce when we\ntry to resum them "optimally" (up to the minimal term) is O(exp(C/g)) -\ncomparable to the size of the first nonperturbative corrections (from\nD-branes whose action scales like 1/g). Once again, Matrix theory and\nAdS/CFT can give you, at least in principle, the full answer for finite\nvalue of "g" and it is probably just a matter of technical difficulty if\nsome of these results have not been calculated (usually, the\nsupersymmetry-protected ones only are known exactly, but there are also\nexamples where we know more). The only way how these problems could be\nmore than technical is the possibility that the large N limits of AdS/CFT\nor Matrix theory don\'t exist - an option that is strongly disfavored by\nthe calculations that have already been done.\n\n> String theorists are pragmatic in a certain sense:\n\n.... probably in many senses ... That\'s the difference between theoretical\nphysics and mathematical physics; theoretical physics prefers common sense\nand pragmatism - and a long-term vision how to agree with experiments -\nwhile mathematical physics always prefers rigor (it often prefers to be\npicky about details).\n\n> they don\'t mind using a background, and they don\'t mind doing what\n> physicists always do:\n\nThe reason why they don\'t mind using a background is because they know\nthat they should be ready to do anything if it turns out to describe\nphysics well yet consistently, and philosophical prejudices are the things\nthat must be always sacrificed once they\'re proved unsuccessful in leading\nto the right physical theory.\n\nWhat is more important, however, is that *physics* of string theory does\nnot treat the background as something that is separated from its\nexcitations - and we can easily prove it.\n\n> approximating a divergent series by the sum of the first couple of terms.\n> But this attitude doesn\'t solve everything, because right now in string\n> theory there is an enormous "landscape" of different backgrounds, with no\n> firm principle for choosing one.\n\nThe landscape is a totally different question; I don\'t understand why you\nmix it with the question whether the calculations are perturbative. The\nstatements that there exist very many vacua is (claimed to be)\nnon-perturbative statements, and they are true, we must simply accept it\nregardless of the type of approximations that we prefer. There are still\nmany potential (e.g. cosmological) mechanisms to organize this "landscape"\nor to make most of it irrelevant, but once a result is established, it\nmust be treated seriously.\n\nI personally don\'t think that focusing on "generic" vacua (that have very\nmany sibblings, i.e. those as un-predictive about the details as possible)\nis a reasonable or scientific thing to do - and my belief is that true\nphysical mechanisms will always choose some "priviliged", "simple" or\n"canonical" vacua, whatever it means (our world, as described by the\nStandard Model, is much more "simple" than what we could have thought\ncenturies ago) - but it does not change the fact that if string theory\nteaches us about something, we should listen. By doing so, we have already\nlearned about plenty of wrong prejudices we had; we have learned that many\nunproved "no-go theorems" have been wrong. Many things are possible even\nin a controllable framework.\n\nHowever, now it is not clear to me and others whether string theory is\ntrying to teach us that we should work with a huge landscape where the\nchances to predict something new are small. Landscape is not like\ndualities; with dualities, everything fits together and we can check\nhundreds of explicit quantitative formulae - and they agree. The landscape\nis still just a vague and qualitative statement based on a philosophical\nprejudice. I am afraid that it will always be. The landscape is inherently\nun-improvable concept unless we become bullish again and try to pinpoint\nthe right point on the map.\n\n> This position is highly controversial, but my point here shouldn\'t be:\n> developing a background-free theory of quantum gravity is tough, but\n> working *with* a background has its own difficulties.\n\nYou seem to misunderstand what the word "background" or "landscape" means\nin string theory. The individual vacua are stationary points of the\npotential in the landscape, roughly speaking. They generate superselection\nsectors; sectors of different states in the same (string/M) theory.\n\nOnce a correct argument claiming that a large number of such stationary\npoints exists (and let me now assume that KKLT are correct, for example),\nit is simply there. If we had a totally background-independent formulation\nof string theory, the conclusion would have to be identical!\n\nA background-independent formulation of string theory is like an airplane\nor a rocket - something that could allow us to see the whole landscape as\na single entity. But even without an airplane, if we see from Mount\nEverest that there also exists K2 and K3, an airplane cannot change\nanything about it!\n\nYou seem to be confusing language and physics. We might want to find a\nmanifestly background-independent *language* in string theory, but I think\nthat no string theorist really wants or expects to change the physics that\nhas already been calculated. Assuming that we are not completely wrong, we\nalready have the correct *theory*. We just want better tools to study the\nsame theory. String theory is a well-defined and unique theory and what we\nhave learned is reliable - at least the non-cosmological questions - and\nany better language in the future must confirm it! Be sure that if another\nframework would show that the gauge group of type I string theory must be\nSO(3200) instead of SO(32), the whole structure would certainly break\ndown. Well, the whole mathematics could then break down :-) because some\nconclusions have been simply rigorously derived. There is no way to undo\nthese insights!\n\n> And let\'s face it: we haven\'t spent nearly as much time thinking about\n> background-free or nonperturbative physics as we\'ve spent on\n> background-dependent or perturbative physics.\n\nI think that you have, and I have done the same thing.\n\n> So, it\'s quite possible that our failures\n> with the former are just a matter of inexperience.\n\nIt\'s also possible that the reason is different - namely that explicit\nconstructions that don\'t care whether all beauties are manifest are simply\nthe right paths to go.\n\n> 3) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world\n> from causal quantum gravity, available as hep-th/0404156.\n\nObviously, I will have to comment on these evergreens again.\n\n> If you\'re looking to build spacetime out of some sort of discrete building\n> block, ...\n\n.... then the vacuum itself will have a very complicated and slightly\nchaotic and disordered structure. All conceivable similar microstates (or\nmicrohistories) will contribute; the entropy density is essentially\nPlanckian. Such a sum over non-equivalent spin foams gives qualitatively\nthe same results as a thermal path integral with a Planckian temperature\nbecause the "vacuum" (spin foam) really behaves as a sort of liquid.\n\nThis Planckian temperature - counting all similar microstates that can\ndiffer in all these details at the Planck scale - is in fact the maximal\ntemperature we can have. Because any temperature breaks Lorentz\ninvariance, such a sum over discrete histories will break the Lorentz\ninvariance by the highest possible amount, which is more than enough to be\nruled out experimentally.\n\nAny theory in which the vacuum is built as a chaotic arrangement of\ndiscrete elementary blocks is a modern version of the theory of\nluminiferous aether. Unless the vacuum state can be proved unique, it will\ngenerate a Planckian entropy density, and therefore the "vacuum" will\nbehave as an object/phase/liquid with a Planckian energy density (even if\nthe cosmological constant is cancelled) - which is not quite what we want.\n\nVacuum must be empty, and its structure must therefore be unique.\n\n> Why such a drastic simplifying assumption? To make calculations quick\n> and easy!\n\nThis is another major type of assumption that I could never agree with.\nNature does not care whether a calculation will be hard or easy for us! We\nmay often choose an easy type of calculation which is great if it can give\nus testable & new results that are then confirmed experimentally or by\nother means. Unfortunately, this is not the case of loop quantum gravity\nbecause no such verifiable (or verified) calculations - that would justify\nany of the simple approaches - have been made so far.\n\nConcerning the difficult calculations, let me mention another example.\n\nQCD is easy to calculate perturbatively - and people had to realize that\nthese simple perturbative calculations are increasingly useful at ever\nlarger energies because of asymptotic freedom. It does not change anything\nabout the fact that at low energies, QCD is strongly coupled and confining\nand it is *not* easy to calculate the spectrum of baryons, for example.\nPeople had to respect Nature and find the right regime where the\ncalculations can be done and compared; it turned out that very high\nenergies were simpler. It would have been very incorrect if they decided\nin advance that low energy nuclear physics must be simple to calculate,\nand then they tried to force Nature to behave according to this\nassumption. Such an approach would be very unlikely to lead to the correct\ntheory (unless they would find the correct AdS/CFT dual and described pure\nQCD by a string theory - which we\'re not still quite able to do even\ntoday).\n\nIt seems to me that you are doing these manipulations based on randomly\nchosen simple rules because you still want to argue that they are, at\nleast in some sense, true. This is not how it works in particle physics.\nIn particle physics, we can either find a simple enough theory - such as\nthe Standard Model - and claim that it is true once it agrees with the\navailable experiments, or we can construct a theory that goes beyond the\ndoable experiments. In the latter case, however, we can only argue that it\nis probably correct and worth studying in most of our time if it is the\nunique theory.\n\nString theory is, we think, the unique theory of that type, and this is\nthe only real reason why such a large percentage of people focus on it (as\nopposed to something else one could a priori imagine). It is not because\nit would simplify some of our calculations; indeed, string theory is\ncomplex enough and it requires a lot of advanced math. Also, it has many\nscenarios how the real Universe can occur in it. Because the scenario\nwithin string theory is *not* unique, we must admit that we don\'t know\nwhich one is correct, and different pheno-people work on different\npossibilities.\n\n> The goal is get models where you can simulate quantum geometry on your\n> laptop - or at least a supercomputer.\n\nI don\'t quite understand how can you call a randomly chosen simple\ndiscrete model "quantum geometry". Should any model of some elementary\n"atoms" and "links" between them that we can invent - be called "quantum\ngeometry"? What about quantum LEGO?\n\nI only call "quantum geometry" a generalization of the usual concepts of\ngeometry that reconciles them with the postulates of quantum physics. It\nmeans that *first* we must show that the union is consistent and that it\nreduces to the usual geometry in the appropriate limit, and only\n*afterwards* we can call it quantum geometry.\n\n> The hope is that simplifying\n> assumptions about physics at the Planck scale will wash out and not make\n> much difference on large length scales.\n\nThere may exist many hopes, but nevertheless the detailed values of the\ntheory and its parameters in the short distance regime is totally\nessential for determining where the theory will flow in the infrared (if\nthere is any infrared at all). Free massless spin 2 particles is a fixed\npoint, of course, but GR with the interactions added is *not* a fixed\npoint in any technical sense we know of. ;-)\n\nGenerically, there is no reason to think that a generic UV theory should\nflow to GR that admits small ripples around a flat space, for example. A\n*generic* discrete model is not gonna self-organize into a 4-dimensional\nGR. There is also no reason to think that a theory that is\nnon-relativistic (Lorentz breaking) at the Planck scale will suddenly or\nautomatically flow to a Lorentz invariant theory at long distances. All\nsuch things must have a reason.\n\nIt just seems to me that you are assuming too many things that are too\nunlikely, and if you multiply the probabilities, it seems that the\nprobability that LQG is a working theory of quantum geometry might be\nsomething like 10^{-1600}. There are sort of no non-trivial checks and\nconfirmations, no nice surprises, nothing that would justify the\nassumptions.\n\n> Computations using the so-called "renormalization group flow" suggest\n> that this hope is true *IF* the path integral is dominated by spacetimes\n> that look, when viewed from afar, almost like 4d manifolds with smooth\n> metrics.\n\nRight. You just wrote that unless the flat space "phase" is incorporated\nand guaranteed, it will almost never appear "for free".\n\n> Unfortunately, in all previous dynamical triangulation models, the path\n> integral was *NOT* dominated by spacetimes that look like nice 4d manifolds\n> from afar!\n\nRight.\n\n> This doesn\'t work when we have complex amplitudes, since even a history\n> with a big amplitude can be canceled out by a nearby history with the\n> opposite big amplitude! Indeed, this happens all the time. So, instead\n> of histories with big amplitudes, it\'s the *bunches of histories that\n> happen not to completely cancel out* that really matter. Nobody knows an\n> efficient general-purpose algorithm to deal with this!\n\nThe usual algorithm to extract these histories is to follow the standard\nperturbation rules where the path integral is dominated by the stationary\npoints of the action, regardless of the signature you work with, and then\ncomputing the effects around these stationary points as Taylor expansion\nin a small parameter. This can be tried for gravity, even without any\ndiscretization, and it leads to a non-renormalizable theory. A correctly\ndone discretization is just a different way to reorganize these\ndivergences and problems, but if it is done correctly, it should not\nchange the conclusions about the 2-loop effective action, for example.\n\n> The new work by Ambjorn, Jurkiewiecz and Loll deals with this by\n> restricting to spacetimes that *do* have a time coordinate.\n\nThis is a kind of twisting the original rules because the correct path\nintegral should sum over everything. Let me paraphrase what they\'re doing.\nIt is not surprising that if we restrict a path integral to contain only\nthe configurations that look almost exactly like an elephant\n(equivalently, the action is re-defined to be i.infinity for non-elephant\nconfigurations), we will get a path integral dominated by an elephant.\nBut in that case, we cannot claim that we have derived an elephant from a\ndeeper theory! ;-) Simply speaking, I have no idea what you can be excited\nabout because the reason of this success (?) seems pretty manifest, and\nthe output is again exactly equal to the input.\n\nIt\'s like with the LQG "calculation" of the black hole entropy. The only\ngood thing that comes out of it - the entropy proportional to the area -\nwas inserted as input because the interior was artificially (and\ncontroversially) removed by hand, and the calculation only focused on the\narea of the horizon and defined a local theory on it, so that its entropy\nhad to be proportional to the area. The only nice thing that such a\ncalculation could give is the proportionality factor - but unforunately it\ndoes not come out correctly and there exists no improved way that could\npredict the correct proportionality factor.\n\nThis requirement that a physicist must be very careful to compare the\noutputs and inputs of her theory - and only be excited if the number of\noutputs exceeds the inputs - is an important lesson that many physicists\nsuch as Feynman repeated many times, and I find it very important, too.\nUsing this counting, it just seems that the difference output-input for\nLQG vanishes.\n\n> When they do this, they get convincing good evidence that the spacetimes\n> which dominate the path integral look approximately like nice smooth\n> 4-dimensional manifolds at large distances!\n\nBut they can\'t look like a spacetime from GR simply because there is no\nelephant that is locally Lorentz-invariant. It\'s just impossible to create\na correct long-distance spacetime from any discrete blocks that have this\nhuge sort of ambiguity - this "Planckian entropy density". If a path\nintegral is required to lead to Lorentz-invariant results, all\nconfigurations that are Lorentz transforms of each other should be counted\nwith the same weight (amplitude). But if the individual configurations\nlook like discrete "spin foams" with some edges and triangles, it is clear\nthat by averaging over the Lorentz group (or approximate averaging over\nmost of this group), which is the only way to get (approximately)\nLorentz-invariant results, we will inevitably make the path integral\ndominated by singular spin foams where the edges are boosted by infinite\n(or huge) boosts and therefore the edges have infinite (or huge)\ncoordinate length - simply because the Lorentz group is non-compact and\n"most" of its elements are infinite boosts that will stretch every link in\nthe spin foam to infinite coordinate distance. Do you see some bug in this\nargument? It seems so obvious to me that one can\'t get an approximately\nLorentz-invariant theory from a path integral dominated by non-singular\nspin foams.\n\nIt might be useful if Loll et al. tried to think about this argument\ninstead of working on 50 new similar papers about the same thing that\nprobably can never work.\n\n> Any physicist worth his salt who hears this modification of Newton\'s law\n> should be overcome with a feeling of revulsion! There just *aren\'t* laws\n> of physics that split a situation in two cases and say "if this is bigger\n> than that, then do X, but if it\'s smaller, then do Y."\n\nExactly. For example, there aren\'t laws of physics that would tell you\nthat your path integral should not count spin foams whose global curvature\nis too large so that a coordinate cannot be globally defined. The only\nrule that tells you to omit these contributions is the rule of LQG that a\ntheory satisfying the "right" dogmas must be studied and promoted even\nafter it is proved inconsistent. Pure GR has real UV problems, and any\nfaithful description of it will confirm their existence. One can try to\nhide these problems - for example by erasing all terms from the path\nintegral that are identified as those responsible for the problems - but\none cannot get a working & consistent theory based on these tricks.\n\nOnce again, pure GR simply has these UV problems, and they show that there\nis new physics at short distances that regulates them.\n\n> So, MOND should instantly make any decent physicist cringe. Esthetics\n> alone would be enough to rule it out, except for one slight problem: it\n> seems to fit the data!\n\nYes, I can also imagine the rough form of nice "holographic" laws that\nwould approximately lead to this strange modification of Newton\'s laws.\nFor example, if the acceleration is smaller than the inverse radius of the\nUniverse, the 2+1D hologram of the accelerating object might be too\ncoherent: it might not contain enough maxima and minima from the\nself-interference - and the large number of interference patterns is what\nis necessary in a hologram to create the extra dimension. Consequently,\nthe local 3+1D physics might break down, and the 1/r^2 law might be\nreplaced by a 1/r law, because these "very slowly accelerating objects"\nmight "really" live in 2+1 dimensions of the hologram. What do you think\nabout this idea?\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Dear John (from sci.physics.research),
> It was good to see old friends and talk about quantum gravity near
> the "Calanques" - the rugged limestone cliffs lining the Mediterranean
> coastline...
that's beautiful.
> It was good to meet lots of young people who have recently
> entered this difficult field: about 100 people attended, considerably
> more than at any previous meeting.
Congratulations. Maybe we will soon be forced to correct the Wikipedia's
estimated ratio 10:1 between the size of the stringy and loopy
communities. It would be even better for LQG to improve the 50:1 ratio of
the numbers of publications.
> Can we get the 4-dimensional spacetime we know and love, whose geometry
> is described by general relativity, to emerge from some theory that takes
> quantum physics into account? And can we do it *nonperturbatively*?
This used to be a big dream in string theory, but it has been more or less
solved, at least for some particular backgrounds. You can put N=4 d=4
Yang-Mills on some sort of lattice - e.g. using deconstruction - to define
this theory non-perturbatively (much like QCD), and then you obtain
non-perturbative results about quantum gravity in the AdS space.
Similarly, Matrix theory gives you non-perturbative answers about
gravitational physics in flat space with many large dimensions.
The difficult task in string theory today is to have a set of "equations"
that allow you *both* to go to larger values of coupling, as well as to
very different geometries than the geometry you start with.
> In other words, can we do quantum physics without choosing some fixed
> spacetime geometry from the start, a "background" on which small
> perturbations move like tiny quantum ripples on a calm pre-established
> lake?
Just to be sure: do you agree that the correct answer may be "No, it is in
principle impossible", or do you prefer to ask rhetorical questions only?
> A background geometry is convenient: it lets us keep track of
> times and distances. It's like having a fixed stage on which the actors -
> gravitons, strings, branes, or whatever - cavort and dance.
That's, indeed, the conventional particle physics framework to do almost
all calculations - one that is applied in string theory most of the times.
Most successful calculations are done in this way, and it is conceivable
that we won't have anything better in the next decades - maybe never.
> But, the main lesson of general relativity is that spacetime is *not*
> a fixed stage: it's a lively, dynamical entity!
It's even more lively in string theory. Not only that geometry can be
curved and it not only affects the matter, but it is also affected by
objects immersed in spacetime; it can be transmuted into non-geometric
physics; its topology can change (once wrapped branes are condensed),
unlike the case of classical GR (and most interpretations of LQG); two
different geometries can lead to identical physics (by T-duality or mirror
symmetry); K3 manifolds with one theory can be equivalent to tori with
another (heterotic) theory; charges get continuously transmuted to momenta
and vice versa; black holes become elementary particles (vibrating
strings) and vice versa; timelike singularities can be resolved.
String theory offers much more flexibility and mutual interrelations
between the different players than Einstein could have ever dreamed of.
And LQG reproduces Einstein (with some observables quantized), with a
typically Einsteinian hope that quantum physics won't modify anything
essential; it can be just added and ignored.
All of us would be happy to have a framework that would describe all these
possible transmutations of the players (in string/M-theory) into each
other in a unified framework - a framework that allows us to see all such
possibilities - but on the other hand, it is a philosophical and
aesthetical desire (which, we expect, could have big technical
implications), not a proved physical necessity. It can be used as a
motivation for a physicist to direct her research, but not as a convincing
scientific argument.
> There's no good way to separate the ripples from the lake.
That's right, and string theory allows us to prove - at least
perturbatively, or also in effective field description of nonperturbative
physics - that physics of (a coherent state of) ripples is exactly
*equivalent* to a modified lake. But string theory claims much more:
there is no good and universal way to separate the ripples and the lake
(gravity) from other particles (matter). All of them inevitably arise
from the same ingredient - a vibrating string - or more precisely
(nonperturbatively) from "M" whatever it is. ;-) String theory has
already taught us more far-reaching lessons that go beyond the lessons
from 1915 that you keep on repeating with such a respect - lessons that I
also like, but that are far from being everything!
> So, we should learn to make do without a background when studying quantum
> gravity. But it's tough!
Yes, it is, and it is by no means guaranteed that it is possible. Let me
say a more trivial example. The electroweak theory can be written in
unitary gauge, and the SU(2) x U(1) symmetry is then obscured. We also
know that there is a formulation that makes the (spontaneously broken)
symmetry manifest. But is it necessarily true that there exists a
formulation that makes *all* interesting features and relations of the
theory of everything manifest? I hope so, but once again, no one can
guarantee it!
> There are knotty conceptual issues like the "problem of time": how do
> we describe time evolution without using a fixed background to measure
> the passage of time? There are also practical problems: in most
> attempts to describe spacetime from the ground up in a quantum way,
> all hell breaks loose!
Right. It is very hard to maintain the existence of some exact objects
once we sacrifice the existence of the spacetime arena itself; I think
that Brian Greene in Chapter 15 of the Elegant Universe, as well as in the
new The Fabric of the Cosmos, describes these dreams and the difficult
situation very well.
> We can easily get spacetimes that crumple up into a tiny blob... or
> spacetimes that form endlessly branching fractal "polymers" of Hausdorff
> dimension 2... but it seems hard to get reasonably smooth spacetimes of
> dimension 4. It's even hard to get spacetimes of dimension 10 or 11...
> or *anything* remotely interesting!
Today, you can almost certainly get 4 out of 10 or 11 because people now
claim to have the compactification and the stabilization of all moduli
under full control. Because string theory knows how to get 10 or 11, it
can obtain 4, too. This specific problem also belongs to the past, in a
way. What we really need to understand today are the laws that govern
time-dependent backgrounds, string cosmology, and such - those may play a
very important role in organizing the jungle (landscape); some people
believe that these problems can be attacked directly and they try to do
so. It is often good to try at least something - well, even though one
often fails.
> It almost seems as if we need a solid background as a bed frame to keep
> the mattress of spacetime from rolling up or otherwise misbehaving.
> Unfortunately, even *with* a background there are serious problems: we
> can use perturbation theory to write the answers to physics questions as
> power series, but these series diverge and nobody knows how to resum them.
They are asymptotic expansions, and the error that we introduce when we
try to resum them "optimally" (up to the minimal term) is O(\exp(C/g)) -
comparable to the size of the first nonperturbative corrections (from
D-branes whose action scales like 1/g). Once again, Matrix theory and
AdS/CFT can give you, at least in principle, the full answer for finite
value of "g" and it is probably just a matter of technical difficulty if
some of these results have not been calculated (usually, the
supersymmetry-protected ones only are known exactly, but there are also
examples where we know more). The only way how these problems could be
more than technical is the possibility that the large N limits of AdS/CFT
or Matrix theory don't exist - an option that is strongly disfavored by
the calculations that have already been done.
> String theorists are pragmatic in a certain sense:
.... probably in many senses ... That's the difference between theoretical
physics and mathematical physics; theoretical physics prefers common sense
and pragmatism - and a long-term vision how to agree with experiments -
while mathematical physics always prefers rigor (it often prefers to be
picky about details).
> they don't mind using a background, and they don't mind doing what
> physicists always do:
The reason why they don't mind using a background is because they know
that they should be ready to do anything if it turns out to describe
physics well yet consistently, and philosophical prejudices are the things
that must be always sacrificed once they're proved unsuccessful in leading
to the right physical theory.
What is more important, however, is that *physics* of string theory does
not treat the background as something that is separated from its
excitations - and we can easily prove it.
> approximating a divergent series by the sum of the first couple of terms.
> But this attitude doesn't solve everything, because right now in string
> theory there is an enormous "landscape" of different backgrounds, with no
> firm principle for choosing one.
The landscape is a totally different question; I don't understand why you
mix it with the question whether the calculations are perturbative. The
statements that there exist very many vacua is (claimed to be)
non-perturbative statements, and they are true, we must simply accept it
regardless of the type of approximations that we prefer. There are still
many potential (e.g. cosmological) mechanisms to organize this "landscape"
or to make most of it irrelevant, but once a result is established, it
must be treated seriously.
I personally don't think that focusing on "generic" vacua (that have very
many sibblings, i.e. those as un-predictive about the details as possible)
is a reasonable or scientific thing to do - and my belief is that true
physical mechanisms will always choose some "priviliged", "simple" or
"canonical" vacua, whatever it means (our world, as described by the
Standard Model, is much more "simple" than what we could have thought
centuries ago) - but it does not change the fact that if string theory
teaches us about something, we should listen. By doing so, we have already
learned about plenty of wrong prejudices we had; we have learned that many
unproved "no-go theorems" have been wrong. Many things are possible even
in a controllable framework.
However, now it is not clear to me and others whether string theory is
trying to teach us that we should work with a huge landscape where the
chances to predict something new are small. Landscape is not like
dualities; with dualities, everything fits together and we can check
hundreds of explicit quantitative formulae - and they agree. The landscape
is still just a vague and qualitative statement based on a philosophical
prejudice. I am afraid that it will always be. The landscape is inherently
un-improvable concept unless we become bullish again and try to pinpoint
the right point on the map.
> This position is highly controversial, but my point here shouldn't be:
> developing a background-free theory of quantum gravity is tough, but
> working *with* a background has its own difficulties.
You seem to misunderstand what the word "background" or "landscape" means
in string theory. The individual vacua are stationary points of the
potential in the landscape, roughly speaking. They generate superselection
sectors; sectors of different states in the same (string/M) theory.
Once a correct argument claiming that a large number of such stationary
points exists (and let me now assume that KKLT are correct, for example),
it is simply there. If we had a totally background-independent formulation
of string theory, the conclusion would have to be identical!
A background-independent formulation of string theory is like an airplane
or a rocket - something that could allow us to see the whole landscape as
a single entity. But even without an airplane, if we see from Mount
Everest that there also exists K2 and K3, an airplane cannot change
anything about it!
You seem to be confusing language and physics. We might want to find a
manifestly background-independent *language* in string theory, but I think
that no string theorist really wants or expects to change the physics that
has already been calculated. Assuming that we are not completely wrong, we
already have the correct *theory*. We just want better tools to study the
same theory. String theory is a well-defined and unique theory and what we
have learned is reliable - at least the non-cosmological questions - and
any better language in the future must confirm it! Be sure that if another
framework would show that the gauge group of type I string theory must be
SO(3200) instead of SO(32), the whole structure would certainly break
down. Well, the whole mathematics could then break down :-) because some
conclusions have been simply rigorously derived. There is no way to undo
these insights!
> And let's face it: we haven't spent nearly as much time thinking about
> background-free or nonperturbative physics as we've spent on
> background-dependent or perturbative physics.
I think that you have, and I have done the same thing.
> So, it's quite possible that our failures
> with the former are just a matter of inexperience.
It's also possible that the reason is different - namely that explicit
constructions that don't care whether all beauties are manifest are simply
the right paths to go.
> 3) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world
> from causal quantum gravity, available as http://www.arxiv.org/abs/hep-th/0404156.
Obviously, I will have to comment on these evergreens again.
> If you're looking to build spacetime out of some sort of discrete building
> block, ...
.... then the vacuum itself will have a very complicated and slightly
chaotic and disordered structure. All conceivable similar microstates (or
microhistories) will contribute; the entropy density is essentially
Planckian. Such a sum over non-equivalent spin foams gives qualitatively
the same results as a thermal path integral with a Planckian temperature
because the "vacuum" (spin foam) really behaves as a sort of liquid.
This Planckian temperature - counting all similar microstates that can
differ in all these details at the Planck scale - is in fact the maximal
temperature we can have. Because any temperature breaks Lorentz
invariance, such a sum over discrete histories will break the Lorentz
invariance by the highest possible amount, which is more than enough to be
ruled out experimentally.
Any theory in which the vacuum is built as a chaotic arrangement of
discrete elementary blocks is a modern version of the theory of
luminiferous aether. Unless the vacuum state can be proved unique, it will
generate a Planckian entropy density, and therefore the "vacuum" will
behave as an object/phase/liquid with a Planckian energy density (even if
the cosmological constant is cancelled) - which is not quite what we want.
Vacuum must be empty, and its structure must therefore be unique.
> Why such a drastic simplifying assumption? To make calculations quick
> and easy!
This is another major type of assumption that I could never agree with.
Nature does not care whether a calculation will be hard or easy for us! We
may often choose an easy type of calculation which is great if it can give
us testable & new results that are then confirmed experimentally or by
other means. Unfortunately, this is not the case of loop quantum gravity
because no such verifiable (or verified) calculations - that would justify
any of the simple approaches - have been made so far.
Concerning the difficult calculations, let me mention another example.
QCD is easy to calculate perturbatively - and people had to realize that
these simple perturbative calculations are increasingly useful at ever
larger energies because of asymptotic freedom. It does not change anything
about the fact that at low energies, QCD is strongly coupled and confining
and it is *not* easy to calculate the spectrum of baryons, for example.
People had to respect Nature and find the right regime where the
calculations can be done and compared; it turned out that very high
energies were simpler. It would have been very incorrect if they decided
in advance that low energy nuclear physics must be simple to calculate,
and then they tried to force Nature to behave according to this
assumption. Such an approach would be very unlikely to lead to the correct
theory (unless they would find the correct AdS/CFT dual and described pure
QCD by a string theory - which we're not still quite able to do even
today).
It seems to me that you are doing these manipulations based on randomly
chosen simple rules because you still want to argue that they are, at
least in some sense, true. This is not how it works in particle physics.
In particle physics, we can either find a simple enough theory - such as
the Standard Model - and claim that it is true once it agrees with the
available experiments, or we can construct a theory that goes beyond the
doable experiments. In the latter case, however, we can only argue that it
is probably correct and worth studying in most of our time if it is the
unique theory.
String theory is, we think, the unique theory of that type, and this is
the only real reason why such a large percentage of people focus on it (as
opposed to something else one could a priori imagine). It is not because
it would simplify some of our calculations; indeed, string theory is
complex enough and it requires a lot of advanced math. Also, it has many
scenarios how the real Universe can occur in it. Because the scenario
within string theory is *not* unique, we must admit that we don't know
which one is correct, and different pheno-people work on different
possibilities.
> The goal is get models where you can simulate quantum geometry on your
> laptop - or at least a supercomputer.
I don't quite understand how can you call a randomly chosen simple
discrete model "quantum geometry". Should any model of some elementary
"atoms" and "links" between them that we can invent - be called "quantum
geometry"? What about quantum LEGO?
I only call "quantum geometry" a generalization of the usual concepts of
geometry that reconciles them with the postulates of quantum physics. It
means that *first* we must show that the union is consistent and that it
reduces to the usual geometry in the appropriate limit, and only
*afterwards* we can call it quantum geometry.
> The hope is that simplifying
> assumptions about physics at the Planck scale will wash out and not make
> much difference on large length scales.
There may exist many hopes, but nevertheless the detailed values of the
theory and its parameters in the short distance regime is totally
essential for determining where the theory will flow in the infrared (if
there is any infrared at all). Free massless spin 2 particles is a fixed
point, of course, but GR with the interactions added is *not* a fixed
point in any technical sense we know of. ;-)
Generically, there is no reason to think that a generic UV theory should
flow to GR that admits small ripples around a flat space, for example. A
*generic* discrete model is not gonna self-organize into a 4-dimensional
GR. There is also no reason to think that a theory that is
non-relativistic (Lorentz breaking) at the Planck scale will suddenly or
automatically flow to a Lorentz invariant theory at long distances. All
such things must have a reason.
It just seems to me that you are assuming too many things that are too
unlikely, and if you multiply the probabilities, it seems that the
probability that LQG is a working theory of quantum geometry might be
something like 10^{-1600}. There are sort of no non-trivial checks and
confirmations, no nice surprises, nothing that would justify the
assumptions.
> Computations using the so-called "renormalization group flow" suggest
> that this hope is true *IF* the path integral is dominated by spacetimes
> that look, when viewed from afar, almost like 4d manifolds with smooth
> metrics.
Right. You just wrote that unless the flat space "phase" is incorporated
and guaranteed, it will almost never appear "for free".
> Unfortunately, in all previous dynamical triangulation models, the path
> integral was *NOT* dominated by spacetimes that look like nice 4d manifolds
> from afar!
Right.
> This doesn't work when we have complex amplitudes, since even a history
> with a big amplitude can be canceled out by a nearby history with the
> opposite big amplitude! Indeed, this happens all the time. So, instead
> of histories with big amplitudes, it's the *bunches of histories that
> happen not to completely cancel out* that really matter. Nobody knows an
> efficient general-purpose algorithm to deal with this!
The usual algorithm to extract these histories is to follow the standard
perturbation rules where the path integral is dominated by the stationary
points of the action, regardless of the signature you work with, and then
computing the effects around these stationary points as Taylor expansion
in a small parameter. This can be tried for gravity, even without any
discretization, and it leads to a non-renormalizable theory. A correctly
done discretization is just a different way to reorganize these
divergences and problems, but if it is done correctly, it should not
change the conclusions about the 2-loop effective action, for example.
> The new work by Ambjorn, Jurkiewiecz and Loll deals with this by
> restricting to spacetimes that *do* have a time coordinate.
This is a kind of twisting the original rules because the correct path
integral should sum over everything. Let me paraphrase what they're doing.
It is not surprising that if we restrict a path integral to contain only
the configurations that look almost exactly like an elephant
(equivalently, the action is re-defined to be i.infinity for non-elephant
configurations), we will get a path integral dominated by an elephant.
But in that case, we cannot claim that we have derived an elephant from a
deeper theory! ;-) Simply speaking, I have no idea what you can be excited
about because the reason of this success (?) seems pretty manifest, and
the output is again exactly equal to the input.
It's like with the LQG "calculation" of the black hole entropy. The only
good thing that comes out of it - the entropy proportional to the area -
was inserted as input because the interior was artificially (and
controversially) removed by hand, and the calculation only focused on the
area of the horizon and defined a local theory on it, so that its entropy
had to be proportional to the area. The only nice thing that such a
calculation could give is the proportionality factor - but unforunately it
does not come out correctly and there exists no improved way that could
predict the correct proportionality factor.
This requirement that a physicist must be very careful to compare the
outputs and inputs of her theory - and only be excited if the number of
outputs exceeds the inputs - is an important lesson that many physicists
such as Feynman repeated many times, and I find it very important, too.
Using this counting, it just seems that the difference output-input for
LQG vanishes.
> When they do this, they get convincing good evidence that the spacetimes
> which dominate the path integral look approximately like nice smooth
> 4-dimensional manifolds at large distances!
But they can't look like a spacetime from GR simply because there is no
elephant that is locally Lorentz-invariant. It's just impossible to create
a correct long-distance spacetime from any discrete blocks that have this
huge sort of ambiguity - this "Planckian entropy density". If a path
integral is required to lead to Lorentz-invariant results, all
configurations that are Lorentz transforms of each other should be counted
with the same weight (amplitude). But if the individual configurations
look like discrete "spin foams" with some edges and triangles, it is clear
that by averaging over the Lorentz group (or approximate averaging over
most of this group), which is the only way to get (approximately)
Lorentz-invariant results, we will inevitably make the path integral
dominated by singular spin foams where the edges are boosted by infinite
(or huge) boosts and therefore the edges have infinite (or huge)
coordinate length - simply because the Lorentz group is non-compact and
"most" of its elements are infinite boosts that will stretch every link in
the spin foam to infinite coordinate distance. Do you see some bug in this
argument? It seems so obvious to me that one can't get an approximately
Lorentz-invariant theory from a path integral dominated by non-singular
spin foams.
It might be useful if Loll et al. tried to think about this argument
instead of working on 50 new similar papers about the same thing that
probably can never work.
> Any physicist worth his salt who hears this modification of Newton's law
> should be overcome with a feeling of revulsion! There just *aren't* laws
> of physics that split a situation in two cases and say "if this is bigger
> than that, then do X, but if it's smaller, then do Y."
Exactly. For example, there aren't laws of physics that would tell you
that your path integral should not count spin foams whose global curvature
is too large so that a coordinate cannot be globally defined. The only
rule that tells you to omit these contributions is the rule of LQG that a
theory satisfying the "right" dogmas must be studied and promoted even
after it is proved inconsistent. Pure GR has real UV problems, and any
faithful description of it will confirm their existence. One can try to
hide these problems - for example by erasing all terms from the path
integral that are identified as those responsible for the problems - but
one cannot get a working & consistent theory based on these tricks.
Once again, pure GR simply has these UV problems, and they show that there
is new physics at short distances that regulates them.
> So, MOND should instantly make any decent physicist cringe. Esthetics
> alone would be enough to rule it out, except for one slight problem: it
> seems to fit the data!
Yes, I can also imagine the rough form of nice "holographic" laws that
would approximately lead to this strange modification of Newton's laws.
For example, if the acceleration is smaller than the inverse radius of the
Universe, the 2+1D hologram of the accelerating object might be too
coherent: it might not contain enough maxima and minima from the
self-interference - and the large number of interference patterns is what
is necessary in a hologram to create the extra dimension. Consequently,
the local 3+1D physics might break down, and the 1/r^2 law might be
replaced by a 1/r law, because these "very slowly accelerating objects"
might "really" live in 2+1 dimensions of the hologram. What do you think
about this idea?
All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> It was good to see old friends and talk about quantum gravity near
> the "Calanques" - the rugged limestone cliffs lining the Mediterranean
> coastline...
that's beautiful.
> It was good to meet lots of young people who have recently
> entered this difficult field: about 100 people attended, considerably
> more than at any previous meeting.
Congratulations. Maybe we will soon be forced to correct the Wikipedia's
estimated ratio 10:1 between the size of the stringy and loopy
communities. It would be even better for LQG to improve the 50:1 ratio of
the numbers of publications.
> Can we get the 4-dimensional spacetime we know and love, whose geometry
> is described by general relativity, to emerge from some theory that takes
> quantum physics into account? And can we do it *nonperturbatively*?
This used to be a big dream in string theory, but it has been more or less
solved, at least for some particular backgrounds. You can put N=4 d=4
Yang-Mills on some sort of lattice - e.g. using deconstruction - to define
this theory non-perturbatively (much like QCD), and then you obtain
non-perturbative results about quantum gravity in the AdS space.
Similarly, Matrix theory gives you non-perturbative answers about
gravitational physics in flat space with many large dimensions.
The difficult task in string theory today is to have a set of "equations"
that allow you *both* to go to larger values of coupling, as well as to
very different geometries than the geometry you start with.
> In other words, can we do quantum physics without choosing some fixed
> spacetime geometry from the start, a "background" on which small
> perturbations move like tiny quantum ripples on a calm pre-established
> lake?
Just to be sure: do you agree that the correct answer may be "No, it is in
principle impossible", or do you prefer to ask rhetorical questions only?
> A background geometry is convenient: it lets us keep track of
> times and distances. It's like having a fixed stage on which the actors -
> gravitons, strings, branes, or whatever - cavort and dance.
That's, indeed, the conventional particle physics framework to do almost
all calculations - one that is applied in string theory most of the times.
Most successful calculations are done in this way, and it is conceivable
that we won't have anything better in the next decades - maybe never.
> But, the main lesson of general relativity is that spacetime is *not*
> a fixed stage: it's a lively, dynamical entity!
It's even more lively in string theory. Not only that geometry can be
curved and it not only affects the matter, but it is also affected by
objects immersed in spacetime; it can be transmuted into non-geometric
physics; its topology can change (once wrapped branes are condensed),
unlike the case of classical GR (and most interpretations of LQG); two
different geometries can lead to identical physics (by T-duality or mirror
symmetry); K3 manifolds with one theory can be equivalent to tori with
another (heterotic) theory; charges get continuously transmuted to momenta
and vice versa; black holes become elementary particles (vibrating
strings) and vice versa; timelike singularities can be resolved.
String theory offers much more flexibility and mutual interrelations
between the different players than Einstein could have ever dreamed of.
And LQG reproduces Einstein (with some observables quantized), with a
typically Einsteinian hope that quantum physics won't modify anything
essential; it can be just added and ignored.
All of us would be happy to have a framework that would describe all these
possible transmutations of the players (in string/M-theory) into each
other in a unified framework - a framework that allows us to see all such
possibilities - but on the other hand, it is a philosophical and
aesthetical desire (which, we expect, could have big technical
implications), not a proved physical necessity. It can be used as a
motivation for a physicist to direct her research, but not as a convincing
scientific argument.
> There's no good way to separate the ripples from the lake.
That's right, and string theory allows us to prove - at least
perturbatively, or also in effective field description of nonperturbative
physics - that physics of (a coherent state of) ripples is exactly
*equivalent* to a modified lake. But string theory claims much more:
there is no good and universal way to separate the ripples and the lake
(gravity) from other particles (matter). All of them inevitably arise
from the same ingredient - a vibrating string - or more precisely
(nonperturbatively) from "M" whatever it is. ;-) String theory has
already taught us more far-reaching lessons that go beyond the lessons
from 1915 that you keep on repeating with such a respect - lessons that I
also like, but that are far from being everything!
> So, we should learn to make do without a background when studying quantum
> gravity. But it's tough!
Yes, it is, and it is by no means guaranteed that it is possible. Let me
say a more trivial example. The electroweak theory can be written in
unitary gauge, and the SU(2) x U(1) symmetry is then obscured. We also
know that there is a formulation that makes the (spontaneously broken)
symmetry manifest. But is it necessarily true that there exists a
formulation that makes *all* interesting features and relations of the
theory of everything manifest? I hope so, but once again, no one can
guarantee it!
> There are knotty conceptual issues like the "problem of time": how do
> we describe time evolution without using a fixed background to measure
> the passage of time? There are also practical problems: in most
> attempts to describe spacetime from the ground up in a quantum way,
> all hell breaks loose!
Right. It is very hard to maintain the existence of some exact objects
once we sacrifice the existence of the spacetime arena itself; I think
that Brian Greene in Chapter 15 of the Elegant Universe, as well as in the
new The Fabric of the Cosmos, describes these dreams and the difficult
situation very well.
> We can easily get spacetimes that crumple up into a tiny blob... or
> spacetimes that form endlessly branching fractal "polymers" of Hausdorff
> dimension 2... but it seems hard to get reasonably smooth spacetimes of
> dimension 4. It's even hard to get spacetimes of dimension 10 or 11...
> or *anything* remotely interesting!
Today, you can almost certainly get 4 out of 10 or 11 because people now
claim to have the compactification and the stabilization of all moduli
under full control. Because string theory knows how to get 10 or 11, it
can obtain 4, too. This specific problem also belongs to the past, in a
way. What we really need to understand today are the laws that govern
time-dependent backgrounds, string cosmology, and such - those may play a
very important role in organizing the jungle (landscape); some people
believe that these problems can be attacked directly and they try to do
so. It is often good to try at least something - well, even though one
often fails.
> It almost seems as if we need a solid background as a bed frame to keep
> the mattress of spacetime from rolling up or otherwise misbehaving.
> Unfortunately, even *with* a background there are serious problems: we
> can use perturbation theory to write the answers to physics questions as
> power series, but these series diverge and nobody knows how to resum them.
They are asymptotic expansions, and the error that we introduce when we
try to resum them "optimally" (up to the minimal term) is O(\exp(C/g)) -
comparable to the size of the first nonperturbative corrections (from
D-branes whose action scales like 1/g). Once again, Matrix theory and
AdS/CFT can give you, at least in principle, the full answer for finite
value of "g" and it is probably just a matter of technical difficulty if
some of these results have not been calculated (usually, the
supersymmetry-protected ones only are known exactly, but there are also
examples where we know more). The only way how these problems could be
more than technical is the possibility that the large N limits of AdS/CFT
or Matrix theory don't exist - an option that is strongly disfavored by
the calculations that have already been done.
> String theorists are pragmatic in a certain sense:
.... probably in many senses ... That's the difference between theoretical
physics and mathematical physics; theoretical physics prefers common sense
and pragmatism - and a long-term vision how to agree with experiments -
while mathematical physics always prefers rigor (it often prefers to be
picky about details).
> they don't mind using a background, and they don't mind doing what
> physicists always do:
The reason why they don't mind using a background is because they know
that they should be ready to do anything if it turns out to describe
physics well yet consistently, and philosophical prejudices are the things
that must be always sacrificed once they're proved unsuccessful in leading
to the right physical theory.
What is more important, however, is that *physics* of string theory does
not treat the background as something that is separated from its
excitations - and we can easily prove it.
> approximating a divergent series by the sum of the first couple of terms.
> But this attitude doesn't solve everything, because right now in string
> theory there is an enormous "landscape" of different backgrounds, with no
> firm principle for choosing one.
The landscape is a totally different question; I don't understand why you
mix it with the question whether the calculations are perturbative. The
statements that there exist very many vacua is (claimed to be)
non-perturbative statements, and they are true, we must simply accept it
regardless of the type of approximations that we prefer. There are still
many potential (e.g. cosmological) mechanisms to organize this "landscape"
or to make most of it irrelevant, but once a result is established, it
must be treated seriously.
I personally don't think that focusing on "generic" vacua (that have very
many sibblings, i.e. those as un-predictive about the details as possible)
is a reasonable or scientific thing to do - and my belief is that true
physical mechanisms will always choose some "priviliged", "simple" or
"canonical" vacua, whatever it means (our world, as described by the
Standard Model, is much more "simple" than what we could have thought
centuries ago) - but it does not change the fact that if string theory
teaches us about something, we should listen. By doing so, we have already
learned about plenty of wrong prejudices we had; we have learned that many
unproved "no-go theorems" have been wrong. Many things are possible even
in a controllable framework.
However, now it is not clear to me and others whether string theory is
trying to teach us that we should work with a huge landscape where the
chances to predict something new are small. Landscape is not like
dualities; with dualities, everything fits together and we can check
hundreds of explicit quantitative formulae - and they agree. The landscape
is still just a vague and qualitative statement based on a philosophical
prejudice. I am afraid that it will always be. The landscape is inherently
un-improvable concept unless we become bullish again and try to pinpoint
the right point on the map.
> This position is highly controversial, but my point here shouldn't be:
> developing a background-free theory of quantum gravity is tough, but
> working *with* a background has its own difficulties.
You seem to misunderstand what the word "background" or "landscape" means
in string theory. The individual vacua are stationary points of the
potential in the landscape, roughly speaking. They generate superselection
sectors; sectors of different states in the same (string/M) theory.
Once a correct argument claiming that a large number of such stationary
points exists (and let me now assume that KKLT are correct, for example),
it is simply there. If we had a totally background-independent formulation
of string theory, the conclusion would have to be identical!
A background-independent formulation of string theory is like an airplane
or a rocket - something that could allow us to see the whole landscape as
a single entity. But even without an airplane, if we see from Mount
Everest that there also exists K2 and K3, an airplane cannot change
anything about it!
You seem to be confusing language and physics. We might want to find a
manifestly background-independent *language* in string theory, but I think
that no string theorist really wants or expects to change the physics that
has already been calculated. Assuming that we are not completely wrong, we
already have the correct *theory*. We just want better tools to study the
same theory. String theory is a well-defined and unique theory and what we
have learned is reliable - at least the non-cosmological questions - and
any better language in the future must confirm it! Be sure that if another
framework would show that the gauge group of type I string theory must be
SO(3200) instead of SO(32), the whole structure would certainly break
down. Well, the whole mathematics could then break down :-) because some
conclusions have been simply rigorously derived. There is no way to undo
these insights!
> And let's face it: we haven't spent nearly as much time thinking about
> background-free or nonperturbative physics as we've spent on
> background-dependent or perturbative physics.
I think that you have, and I have done the same thing.
> So, it's quite possible that our failures
> with the former are just a matter of inexperience.
It's also possible that the reason is different - namely that explicit
constructions that don't care whether all beauties are manifest are simply
the right paths to go.
> 3) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world
> from causal quantum gravity, available as http://www.arxiv.org/abs/hep-th/0404156.
Obviously, I will have to comment on these evergreens again.
> If you're looking to build spacetime out of some sort of discrete building
> block, ...
.... then the vacuum itself will have a very complicated and slightly
chaotic and disordered structure. All conceivable similar microstates (or
microhistories) will contribute; the entropy density is essentially
Planckian. Such a sum over non-equivalent spin foams gives qualitatively
the same results as a thermal path integral with a Planckian temperature
because the "vacuum" (spin foam) really behaves as a sort of liquid.
This Planckian temperature - counting all similar microstates that can
differ in all these details at the Planck scale - is in fact the maximal
temperature we can have. Because any temperature breaks Lorentz
invariance, such a sum over discrete histories will break the Lorentz
invariance by the highest possible amount, which is more than enough to be
ruled out experimentally.
Any theory in which the vacuum is built as a chaotic arrangement of
discrete elementary blocks is a modern version of the theory of
luminiferous aether. Unless the vacuum state can be proved unique, it will
generate a Planckian entropy density, and therefore the "vacuum" will
behave as an object/phase/liquid with a Planckian energy density (even if
the cosmological constant is cancelled) - which is not quite what we want.
Vacuum must be empty, and its structure must therefore be unique.
> Why such a drastic simplifying assumption? To make calculations quick
> and easy!
This is another major type of assumption that I could never agree with.
Nature does not care whether a calculation will be hard or easy for us! We
may often choose an easy type of calculation which is great if it can give
us testable & new results that are then confirmed experimentally or by
other means. Unfortunately, this is not the case of loop quantum gravity
because no such verifiable (or verified) calculations - that would justify
any of the simple approaches - have been made so far.
Concerning the difficult calculations, let me mention another example.
QCD is easy to calculate perturbatively - and people had to realize that
these simple perturbative calculations are increasingly useful at ever
larger energies because of asymptotic freedom. It does not change anything
about the fact that at low energies, QCD is strongly coupled and confining
and it is *not* easy to calculate the spectrum of baryons, for example.
People had to respect Nature and find the right regime where the
calculations can be done and compared; it turned out that very high
energies were simpler. It would have been very incorrect if they decided
in advance that low energy nuclear physics must be simple to calculate,
and then they tried to force Nature to behave according to this
assumption. Such an approach would be very unlikely to lead to the correct
theory (unless they would find the correct AdS/CFT dual and described pure
QCD by a string theory - which we're not still quite able to do even
today).
It seems to me that you are doing these manipulations based on randomly
chosen simple rules because you still want to argue that they are, at
least in some sense, true. This is not how it works in particle physics.
In particle physics, we can either find a simple enough theory - such as
the Standard Model - and claim that it is true once it agrees with the
available experiments, or we can construct a theory that goes beyond the
doable experiments. In the latter case, however, we can only argue that it
is probably correct and worth studying in most of our time if it is the
unique theory.
String theory is, we think, the unique theory of that type, and this is
the only real reason why such a large percentage of people focus on it (as
opposed to something else one could a priori imagine). It is not because
it would simplify some of our calculations; indeed, string theory is
complex enough and it requires a lot of advanced math. Also, it has many
scenarios how the real Universe can occur in it. Because the scenario
within string theory is *not* unique, we must admit that we don't know
which one is correct, and different pheno-people work on different
possibilities.
> The goal is get models where you can simulate quantum geometry on your
> laptop - or at least a supercomputer.
I don't quite understand how can you call a randomly chosen simple
discrete model "quantum geometry". Should any model of some elementary
"atoms" and "links" between them that we can invent - be called "quantum
geometry"? What about quantum LEGO?
I only call "quantum geometry" a generalization of the usual concepts of
geometry that reconciles them with the postulates of quantum physics. It
means that *first* we must show that the union is consistent and that it
reduces to the usual geometry in the appropriate limit, and only
*afterwards* we can call it quantum geometry.
> The hope is that simplifying
> assumptions about physics at the Planck scale will wash out and not make
> much difference on large length scales.
There may exist many hopes, but nevertheless the detailed values of the
theory and its parameters in the short distance regime is totally
essential for determining where the theory will flow in the infrared (if
there is any infrared at all). Free massless spin 2 particles is a fixed
point, of course, but GR with the interactions added is *not* a fixed
point in any technical sense we know of. ;-)
Generically, there is no reason to think that a generic UV theory should
flow to GR that admits small ripples around a flat space, for example. A
*generic* discrete model is not gonna self-organize into a 4-dimensional
GR. There is also no reason to think that a theory that is
non-relativistic (Lorentz breaking) at the Planck scale will suddenly or
automatically flow to a Lorentz invariant theory at long distances. All
such things must have a reason.
It just seems to me that you are assuming too many things that are too
unlikely, and if you multiply the probabilities, it seems that the
probability that LQG is a working theory of quantum geometry might be
something like 10^{-1600}. There are sort of no non-trivial checks and
confirmations, no nice surprises, nothing that would justify the
assumptions.
> Computations using the so-called "renormalization group flow" suggest
> that this hope is true *IF* the path integral is dominated by spacetimes
> that look, when viewed from afar, almost like 4d manifolds with smooth
> metrics.
Right. You just wrote that unless the flat space "phase" is incorporated
and guaranteed, it will almost never appear "for free".
> Unfortunately, in all previous dynamical triangulation models, the path
> integral was *NOT* dominated by spacetimes that look like nice 4d manifolds
> from afar!
Right.
> This doesn't work when we have complex amplitudes, since even a history
> with a big amplitude can be canceled out by a nearby history with the
> opposite big amplitude! Indeed, this happens all the time. So, instead
> of histories with big amplitudes, it's the *bunches of histories that
> happen not to completely cancel out* that really matter. Nobody knows an
> efficient general-purpose algorithm to deal with this!
The usual algorithm to extract these histories is to follow the standard
perturbation rules where the path integral is dominated by the stationary
points of the action, regardless of the signature you work with, and then
computing the effects around these stationary points as Taylor expansion
in a small parameter. This can be tried for gravity, even without any
discretization, and it leads to a non-renormalizable theory. A correctly
done discretization is just a different way to reorganize these
divergences and problems, but if it is done correctly, it should not
change the conclusions about the 2-loop effective action, for example.
> The new work by Ambjorn, Jurkiewiecz and Loll deals with this by
> restricting to spacetimes that *do* have a time coordinate.
This is a kind of twisting the original rules because the correct path
integral should sum over everything. Let me paraphrase what they're doing.
It is not surprising that if we restrict a path integral to contain only
the configurations that look almost exactly like an elephant
(equivalently, the action is re-defined to be i.infinity for non-elephant
configurations), we will get a path integral dominated by an elephant.
But in that case, we cannot claim that we have derived an elephant from a
deeper theory! ;-) Simply speaking, I have no idea what you can be excited
about because the reason of this success (?) seems pretty manifest, and
the output is again exactly equal to the input.
It's like with the LQG "calculation" of the black hole entropy. The only
good thing that comes out of it - the entropy proportional to the area -
was inserted as input because the interior was artificially (and
controversially) removed by hand, and the calculation only focused on the
area of the horizon and defined a local theory on it, so that its entropy
had to be proportional to the area. The only nice thing that such a
calculation could give is the proportionality factor - but unforunately it
does not come out correctly and there exists no improved way that could
predict the correct proportionality factor.
This requirement that a physicist must be very careful to compare the
outputs and inputs of her theory - and only be excited if the number of
outputs exceeds the inputs - is an important lesson that many physicists
such as Feynman repeated many times, and I find it very important, too.
Using this counting, it just seems that the difference output-input for
LQG vanishes.
> When they do this, they get convincing good evidence that the spacetimes
> which dominate the path integral look approximately like nice smooth
> 4-dimensional manifolds at large distances!
But they can't look like a spacetime from GR simply because there is no
elephant that is locally Lorentz-invariant. It's just impossible to create
a correct long-distance spacetime from any discrete blocks that have this
huge sort of ambiguity - this "Planckian entropy density". If a path
integral is required to lead to Lorentz-invariant results, all
configurations that are Lorentz transforms of each other should be counted
with the same weight (amplitude). But if the individual configurations
look like discrete "spin foams" with some edges and triangles, it is clear
that by averaging over the Lorentz group (or approximate averaging over
most of this group), which is the only way to get (approximately)
Lorentz-invariant results, we will inevitably make the path integral
dominated by singular spin foams where the edges are boosted by infinite
(or huge) boosts and therefore the edges have infinite (or huge)
coordinate length - simply because the Lorentz group is non-compact and
"most" of its elements are infinite boosts that will stretch every link in
the spin foam to infinite coordinate distance. Do you see some bug in this
argument? It seems so obvious to me that one can't get an approximately
Lorentz-invariant theory from a path integral dominated by non-singular
spin foams.
It might be useful if Loll et al. tried to think about this argument
instead of working on 50 new similar papers about the same thing that
probably can never work.
> Any physicist worth his salt who hears this modification of Newton's law
> should be overcome with a feeling of revulsion! There just *aren't* laws
> of physics that split a situation in two cases and say "if this is bigger
> than that, then do X, but if it's smaller, then do Y."
Exactly. For example, there aren't laws of physics that would tell you
that your path integral should not count spin foams whose global curvature
is too large so that a coordinate cannot be globally defined. The only
rule that tells you to omit these contributions is the rule of LQG that a
theory satisfying the "right" dogmas must be studied and promoted even
after it is proved inconsistent. Pure GR has real UV problems, and any
faithful description of it will confirm their existence. One can try to
hide these problems - for example by erasing all terms from the path
integral that are identified as those responsible for the problems - but
one cannot get a working & consistent theory based on these tricks.
Once again, pure GR simply has these UV problems, and they show that there
is new physics at short distances that regulates them.
> So, MOND should instantly make any decent physicist cringe. Esthetics
> alone would be enough to rule it out, except for one slight problem: it
> seems to fit the data!
Yes, I can also imagine the rough form of nice "holographic" laws that
would approximately lead to this strange modification of Newton's laws.
For example, if the acceleration is smaller than the inverse radius of the
Universe, the 2+1D hologram of the accelerating object might be too
coherent: it might not contain enough maxima and minima from the
self-interference - and the large number of interference patterns is what
is necessary in a hologram to create the extra dimension. Consequently,
the local 3+1D physics might break down, and the 1/r^2 law might be
replaced by a 1/r law, because these "very slowly accelerating objects"
might "really" live in 2+1 dimensions of the hologram. What do you think
about this idea?
All the best
Lubos
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