[SOLVED] This Week's Finds in Mathematical Physics (Week 206) [Archive]

John Baez

May11-04, 08:04 AM

<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>\n\nAlso available at http://math.ucr.edu/home/baez/week206.html\n\nMay 10, 2004\nThis Week\'s Finds in Mathematical Physics - Week 206\nJohn Baez\n\nI just got back from Marseille, where Carlo Rovelli, Laurent Freidel\nand Phillipe Roche held the first really big conference on loop quantum\ngravity and spin foams since the 2nd Warsaw workshop run by Jerzy\nLewandowski back in 1997:\n\n1) Non Perturbative Quantum Gravity: Loops and Spin Foams,\n3-7 May 2004, CIRM, Luminy, Marseille, France,\nhttp://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/\n\nIt was good to see old friends and talk about quantum gravity near\nthe "Calanques" - the rugged limestone cliffs lining the Mediterranean\ncoastline. It was good to meet lots of young people who have recently\nentered this difficult field: about 100 people attended, considerably\nmore than at any previous meeting. But most of all, it was good to\nsee some progress on the tough problem of understanding dynamics in\nnonperturbative quantum gravity.\n\nCan we get the 4-dimensional spacetime we know and love, whose geometry\nis described by general relativity, to emerge from some theory that takes\nquantum physics into account? And can we do it *nonperturbatively*?\n\nIn other words, can we do quantum physics without choosing some fixed\nspacetime geometry from the start, a "background" on which small\nperturbations move like tiny quantum ripples on a calm pre-established\nlake? A background geometry is convenient: it lets us keep track of\ntimes and distances. It\'s like having a fixed stage on which the actors -\ngravitons, strings, branes, or whatever - cavort and dance. But, the\nmain lesson of general relativity is that spacetime is *not* a fixed\nstage: it\'s a lively, dynamical entity! There\'s no good way to separate\nthe ripples from the lake. This distinction is no more than a convenient\napproximation - and a dangerous one at that.\n\nSo, we should learn to make do without a background when studying quantum\ngravity. But it\'s tough! There are knotty conceptual issues like the\n"problem of time": how do we describe time evolution without using a fixed\nbackground to measure the passage of time? There are also practical\nproblems: in most attempts to describe spacetime from the ground up in\na quantum way, all hell breaks loose!\n\nWe can easily get spacetimes that crumple up into a tiny blob... or\nspacetimes that form endlessly branching fractal "polymers" of Hausdorff\ndimension 2... but it seems hard to get reasonably smooth spacetimes of\ndimension 4. It\'s even hard to get spacetimes of dimension 10 or 11...\nor *anything* remotely interesting!\n\nIt almost seems as if we need a solid background as a bed frame to keep\nthe mattress of spacetime from rolling up or otherwise misbehaving.\nUnfortunately, even *with* a background there are serious problems: we\ncan use perturbation theory to write the answers to physics questions as\npower series, but these series diverge and nobody knows how to resum them.\n\nString theorists are pragmatic in a certain sense: they don\'t mind using\na background, and they don\'t mind doing what physicists always do:\napproximating a divergent series by the sum of the first couple of terms.\nBut this attitude doesn\'t solve everything, because right now in string\ntheory there is an enormous "landscape" of different backgrounds, with no\nfirm principle for choosing one. Some estimates guess there are over\n10^{100}. Leonard Susskind guesses there are 10^{500}, and argues that\nwe\'ll need the anthropic principle to choose the one describing our\nworld:\n\n2) Leonard Susskind, The Landscape, article and interview on John\nBrockman\'s "EDGE" website,\nhttp://www.edge.org/3rd_culture/susskind03/susskind_index.html\n\nThis position is highly controversial, but my point here shouldn\'t be:\ndeveloping a background-free theory of quantum gravity is tough, but\nworking *with* a background has its own difficulties. And let\'s face\nit: we haven\'t spent nearly as much time thinking about background-free\nor nonperturbative physics as we\'ve spent on background-dependent\nor perturbative physics. So, it\'s quite possible that our failures\nwith the former are just a matter of inexperience.\n\nGiven all this, I\'m delighted to see some real progress on getting 4d\nspacetime to emerge from nonperturbative quantum gravity:\n\n3) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world\nfrom causal quantum gravity, available as hep-th/0404156.\n\nThis trio of researchers have revitalized an approach called "dynamical\ntriangulations" where we calculate path integrals in quantum gravity by\nsumming over different ways of building spacetime out of little 4-simplices.\nThey showed that if we restrict this sum to spacetimes with a well-behaved\nconcept of causality, we get good results. This is a bit startling,\nbecause after decades of work, most researchers had despaired of getting\ngeneral relativity to emerge at large distances starting from the dynamical\ntriangulations approach. But, these people hadn\'t noticed a certain flaw\nin the approach... a flaw which Loll and collaborators noticed and fixed!\n\nIf you don\'t know what a path integral is, don\'t worry: it\'s pretty\nsimple. Basically, in quantum physics we can calculate the expected value\nof any physical quantity by doing an average over all possible histories\nof the system in question, with each history weighted by a complex number\ncalled its "amplitude". For a particle, a history is just a path in\nspace; to average over all histories is to integrate over all paths -\nhence the term "path integral". But in quantum gravity, a history is\nnothing other than a SPACETIME.\n\nMathematically, a "spacetime" is something like a 4-dimensional manifold\nequipped with a Lorentzian metric. But it\'s hard to integrate over all\nof these - there are just too darn many. So, sometimes people instead\ntreat spacetime as made of little discrete building blocks, turning\nthe path integral into a sum. You can either take this seriously or treat\nit as a kind of approximation. Luckily, the calculations work the same\neither way!\n\nIf you\'re looking to build spacetime out of some sort of discrete building\nblock, a handy candidate is the "4-simplex": the 4-dimensional analogue\nof a tetrahedron. This shape is rigid once you fix the lengths of its 10\nedges, which correspond to the 10 components of the metric tensor in\ngeneral relativity.\n\nThere are lots of approaches to the path integrals in quantum gravity\nthat start by chopping spacetime into 4-simplices. The weird special\nthing about dynamical triangulations is that here we usually assume\nevery 4-simplex in spacetime has the same shape. The different spacetimes\narise solely from different ways of sticking the 4-simplices together.\n\nWhy such a drastic simplifying assumption? To make calculations quick\nand easy! The goal is get models where you can simulate quantum geometry\non your laptop - or at least a supercomputer. The hope is that simplifying\nassumptions about physics at the Planck scale will wash out and not make\nmuch difference on large length scales.\n\nComputations using the so-called "renormalization group flow" suggest\nthat this hope is true *IF* the path integral is dominated by spacetimes\nthat look, when viewed from afar, almost like 4d manifolds with smooth\nmetrics. Given this, it seems we\'re bound to get general relativity at\nlarge distance scales - perhaps with a nonzero cosmological constant, and\nperhaps including various forms of matter.\n\nUnfortunately, in all previous dynamical triangulation models, the path\nintegral was *NOT* dominated by spacetimes that look like nice 4d manifolds\nfrom afar! Depending on the details, one either got a "crumpled phase"\ndominated by spacetimes where almost all the 4-simplices touch each other,\nor a "branched polymer phase" dominated by spacetimes where the 4-simplices\nform treelike structures. There\'s a transition between these two phases,\nbut unfortunately it seems to be a 1st-order phase transition - not the\nsort we can get anything useful out of. For a nice review of these\ncalculations, see:\n\n4) Renate Loll, Discrete approaches to quantum gravity in four dimensions,\navailable as gr-qc/9805049 or as a website at Living Reviews in Relativity,\nhttp://www.livingreviews.org/Articles/Volume1/1998-13loll/\n\nLuckily, all these calculations shared a common flaw!\n\nComputer calculations of path integrals become a lot easier if instead of\nassigning a complex "amplitude" to each history, we assign it a positive\nreal number: a "relative probability". The basic reason is that unlike\npositive real numbers, complex numbers can cancel out when you sum them!\n\nWhen we have relative probabilities, it\'s the *highly probable* histories\nthat contribute most to the expected value of any physical quantity. We\ncan use something called the "Metropolis algorithm" to spot these highly\nprobable histories and spend most of our time worrying about them.\n\nThis doesn\'t work when we have complex amplitudes, since even a history\nwith a big amplitude can be canceled out by a nearby history with the\nopposite big amplitude! Indeed, this happens all the time. So, instead\nof histories with big amplitudes, it\'s the *bunches of histories that\nhappen not to completely cancel out* that really matter. Nobody knows an\nefficient general-purpose algorithm to deal with this!\n\nFor this reason, physicists often use a trick called "Wick rotation"\nthat converts amplitudes to relative probabilities. To do this trick, we\njust replace time by imaginary time! In other words, wherever we see the\nvariable "t" for time in any formula, we replace it by "it". Magically,\nthis often does the job: our amplitudes turn into relative probabilities!\nWe then go ahead and calculate stuff. Then we take this stuff and go\nback and replace "it" everywhere by "t" to get our final answers.\n\nWhile the deep inner meaning of this trick is mysterious, it can be\njustified in a wide variety of contexts using the "Osterwalder-Schrader\ntheorem". Here\'s a pretty general version of this theorem, suitable\nfor quantum gravity:\n\n5) Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann,\nOsterwalder-Schrader reconstruction and diffeomorphism invariance,\npreprint available as quant-ph/9904094.\n\nPeople use Wick rotation in all work on dynamical triangulations.\nUnfortunately, this is *not* a context where you can justify this trick\nby appealing to the Osterwalder-Schrader theorem. The problem is that\nthere\'s no good notion of a time coordinate "t" on your typical\nspacetime built by sticking together a bunch of 4-simplices!\n\nThe new work by Ambjorn, Jurkiewiecz and Loll deals with this by\nrestricting to spacetimes that *do* have a time coordinate. More\nprecisely, they fix a 3-dimensional manifold and consider all possible\ntriangulations of this manifold by regular tetrahedra. These are the\nallowed "slices" of spacetime - they represent different possible\ngeometries of space at a given time. They then consider spacetimes\nhaving slices of this form joined together by 4-simplices in a few\nsimple ways.\n\nThe slicing gives a preferred time parameter "t". On the one hand this\ngoes against our desire in general relativity to avoid a preferred time\ncoordinate - but on the other hand, it allows Wick rotation. So, they\ncan use the Metropolis algorithm to compute things to their hearts\'\ncontent and then replace "it" by "t" at the end.\n\nWhen they do this, they get convincing good evidence that the spacetimes\nwhich dominate the path integral look approximately like nice smooth\n4-dimensional manifolds at large distances! Take a look at their graphs\nand pictures - a picture is worth a thousand words.\n\nNaturally, what *I\'d* like to do is use their work to develop some spin\nfoam models with better physical behavior than the ones we have so far.\nNow that Loll and her collaborators have gotten something that works,\nwe can try to fiddle around and make it more elegant while making sure it\nstill works. In particular, I\'m hoping we can get well-behaved models\nthat don\'t introduce a preferred time coordinate as long as they rule out\n"topology change" - that is, slicings where the topology of space changes.\nAfter all, the Osterwalder-Schrader theorem doesn\'t require a *preferred*\ntime coordinate, just *any* time coordinate together with good behavior\nunder change of time coordinate. For this we mainly need to rule out\ntopology change. Moreover, Loll and her collaborators have argued in 2d\ntoy models that topology change is one thing that makes models go bad: the\npath integral can get dominated by spacetimes where "baby universes" keep\nbranching off the main one:\n\n6) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative\nLorentzian quantum gravity, causality and topology change, Nucl. Phys.\nB536 (1998) 407-434. Also available as hep-th/9805108.\n\nRenate Loll and W. Westra, Space-time foam in 2d and the sum over\ntopologies, Acta Phys. Polon. B34 (2003) 4997-5008. Also available as\nhep-th/0309012.\n\nBy the way, it\'s also reading about their 3d model:\n\n7) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative 3d\nLorentzian quantum gravity, Phys.Rev. D64 (2001) 044011. Also available\nas hep-th/0011276.\n\nand for a general review, try this:\n\n8) Renate Loll, A discrete history of the Lorentzian path integral,\nLecture Notes in Physics 631, Springer, Berlin, 2003, pp. 137-171.\nAlso available as hep-th/0212340.\n\nAll this is great, but don\'t get me wrong - there were a lot of *other*\ncool talks at the conference besides Loll\'s. I\'ll just mention a few.\n\nLaurent Freidel spoke on his work on spin foam models. Especially\nexciting is how David Louapre and he have managed to "sum over\ntopologies" in 3d Riemannian quantum gravity with vanishing cosmological\nconstant - otherwise known as the Ponzano-Regge model He has to subtract\nout a counterterm that would otherwise lead to a bubble divergence, but\nthen he gets a beautiful theory where the sum over spin foams is Borel\nsummable:\n\n9) Laurent Freidel and David Louapre, Non-perturbative summation over\n3D discrete topologies, Phys.Rev. D68 (2003) 104004. Also available as\nhep-th/0211026.\n\nTheir work on gauge-fixing and the inclusion of spinning point particles\nin the Ponzano-Regge model is also very impressive, especially given how\nlong this model has been studied. It shows we have lots left to learn!\n\n10) Laurent Freidel and David Louapre, Ponzano-Regge model revisited I:\nGauge fixing, observables and interacting spinning particles, available\nas hep-th/0401076.\n\nThe title suggests we\'re in for more treats to come.\n\nKirill Krasnov gave a talk entitled simple "ln(3)" - it was all about\nthe appearance of this constant in the work of Hod, Dreyer, Motl and\nNeitzke on black hole entropy and the ringing of black holes. I\'ve\ndiscussed all this at length in "week198", but Krasnov has given an elegant\nnew proof of Hod\'s conjecture using Riemann surface theory. One can\neven think of this as a "stringy" explanation of the quasinormal modes\nof black holes - but much remains mysterious here:\n\n11) Kirill Krasnov, Black hole thermodynamics and Riemann surfaces,\nClass. Quant. Grav. 20 (2003) 2235-2250. Also available as gr-qc/0302073.\n\nKirill Krasnov and Sergey N. Solodukhin, Effective stringy description\nof Schwarzschild black holes, available as hep-th/0403046.\n\nWhile I\'m at it, I can\'t resist mentioning Krasnov\'s work on including\npoint particles in 3d Lorentzian quantum gravity with negative\ncosmological constant, since it has close connections with that of\nFreidel and Louapre, though the context is a bit different:\n\n12) Kirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions I:\nquantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002)\n3977-3998. Also available as hep-th/0112164.\n\nKirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions II:\nblack hole creation by point particles, Class. Quant. Grav. 19 (2002)\n3999-4028. Also available as hep-th/0202117.\n\nIf I could duplicate myself, I\'d have one copy write a book on 3d quantum\ngravity that would synthesize all these wonderful results in a nice big\npicture. It\'s not realistic physics; it\'s just a toy model. But the\nmath is *so* nice, and so enlightening for real-world physics in some\nways, that it\'s hard to resist pondering it! TQFTs, Riemann surfaces,\nhyperbolic geometry, spinning point particles colliding and creating\nblack holes - a wonderful stew! Alas, I don\'t have time to savor it.\n\nThere were a lot of other interesting talks - but I don\'t have time to go\nthrough and describe all of them, either. So, I\'ll wrap up with something\nvery different!\n\nLee Smolin told me some neat stuff about MOND - that\'s "Modified\nNewtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\nthe strange behavior of galaxies without invoking dark matter. The basic\nproblem with galaxies is that the outer parts rotate faster than they\nshould given how much mass we actually see.\n\nIf you have a planet in a circular orbit about the Sun, Newton\'s laws\nsay its acceleration is proportional to 1/r^2, where r is its distance to\nthe Sun. Similarly, if almost all the mass in a galaxy were concentrated\nright at the center, a star orbiting in a circle at distance r from the\ncenter would have acceleration proportional to 1/r^2. Of course, not all\nthe mass is right at the center! So, the acceleration should drop off\nmore slowly than 1/r^2 as you go further out. And it does. But, the\nobserved acceleration drops off a lot more slowly than the acceleration\npeople calculate from the mass they see. It\'s not a small effect: it\'s a\nHUGE effect!\n\nOne solution is to say there\'s a lot of mass we don\'t see: "dark matter"\nof some sort. If you take this route, which most astronomers do, you\'re\nforced to say that *most* of the mass of galaxies is in the form of dark\nmatter.\n\nMilgrom\'s solution is to say that Newton\'s laws are messed up.\n\nOf course this is a drastic, dangerous step: the last guy who tried this\nwas named Einstein, and we all know what happened to him. Milgrom\'s theory\nisn\'t even based on deep reasoning and beautiful math like Einstein\'s!\nInstead, it\'s just a blatant attempt to fit the experimental data.\nAnd it\'s not even elegant. In fact, it\'s downright ugly.\n\nHere\'s what it says: the usual Newtonian formula for the acceleration\ndue to gravity is correct as long as the acceleration is bigger than\n\na = 2 x 10^{-10} m/sec^2\n\nBut, for accelerations less than this, you take the geometric mean\nof the acceleration Newton would predict and this constant a.\n\nIn other words, there\'s a certain value of acceleration such that above\nthis value, the Newtonian law of gravity works as usual, while below this\nvalue the law suddenly changes.\n\nAny physicist worth his salt who hears this modification of Newton\'s law\nshould be overcome with a feeling of revulsion! There just *aren\'t* laws\nof physics that split a situation in two cases and say "if this is bigger\nthan that, then do X, but if it\'s smaller, then do Y." Not in fundamental\nphysics, anyway! Sure, water is solid below 0 centigrade and fluid above\nthis, but that\'s not a fundamental law - it presumably follows from other\nstuff. Not that anyone has derived the melting point of ice from first\nprinciples, mind you. But we think we could if we were better at big\nmessy calculations.\n\nFurthermore, you can\'t easily invent a Lagrangian for gravity that makes\nit fall off more *slowly* than 1/r^2. It\'s easy to get it to fall off\n*faster* - just give the graviton a mass, for example! But not more\nslowly. It turns out you can do it - Bekenstein and Milgrom have a way -\nbut it\'s incredibly ugly.\n\nSo, MOND should instantly make any decent physicist cringe. Esthetics\nalone would be enough to rule it out, except for one slight problem: it\nseems to fit the data! In some cases it matches the observed rotation of\ngalaxies in an appallingly accurate way, fitting every wiggle in the graph\nof stellar rotation velocity as a function of distance from the center.\n\nSo, even if MOND is wrong, there may need to be some reason why it *acts*\nlike it\'s right! Apparently even some proponents of dark matter agree\nwith this.\n\nBut: take everything I\'m saying here with a grain of salt. I\'m no expert\non this stuff, so if you know any astrophysics you should read the\nliterature and make up your own mind.\n\nHere are two reviews that Smolin especially recommended:\n\n13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics\nas an Alternative to Dark Matter, available as astro-ph/0204521.\n\n14) Anthony Aguirre, Alternatives to dark matter (?), available as\nastro-ph/0310572.\n\nHere\'s McGaugh\'s website with links to many papers on MOND, including\nMilgrom\'s original papers:\n\n15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html\n\nMcGaugh is a strong proponent of MOND - though he didn\'t start out that\nway - so the selection may be biased. Does anyone know an intelligent\ndetailed critique of MOND? If so, I want to see it! We can\'t throw out\nNewton\'s law of gravity (or more precisely, general relativity, which has\nNewtonian gravity as a limiting case for low densities and low velocities)\nunless we have *very* good reasons! So we have to think about things\ncarefully, and weigh the evidence on both sides.\n\nIf I could duplicate myself, I\'d have one copy try to get to the bottom\nof this dark matter / MOND puzzle. But I can\'t...\n\n.... so if you\'re an expert who knows a lot about this, let me\nknow what you think - or better yet, post an article about this to\nsci.physics.research!\n\n-----------------------------------------------------------------------\nPrevious issues of "This Week\'s Finds" and other expository articles on\nmathematics and physics, as well as some of my research papers, can be\nobtained at\n\nhttp://math.ucr.edu/home/baez/\n\nFor a table of contents of all the issues of This Week\'s Finds, try\n\nhttp://math.ucr.edu/home/baez/twf.html\n\nA simple jumping-off point to the old issues is available at\n\nhttp://math.ucr.edu/home/baez/twfshort.html\n\nIf you just want the latest issue, go to\n\nhttp://math.ucr.edu/home/baez/this.week.html\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>Also available at http://math.ucr.edu/home/baez/week206.html

May 10, 2004
This Week's Finds in Mathematical Physics - Week 206
John Baez

I just got back from Marseille, where Carlo Rovelli, Laurent Freidel
and Phillipe Roche held the first really big conference on loop quantum
gravity and spin foams since the 2nd Warsaw workshop run by Jerzy
Lewandowski back in 1997:

1) Non Perturbative Quantum Gravity: Loops and Spin Foams,
3-7 May 2004, CIRM, Luminy, Marseille, France,
http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

It was good to see old friends and talk about quantum gravity near
the "Calanques" - the rugged limestone cliffs lining the Mediterranean
coastline. 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. But most of all, it was good to
see some progress on the tough problem of understanding dynamics in
nonperturbative quantum gravity.

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*?

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? 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. But, the
main lesson of general relativity is that spacetime is *not* a fixed
stage: it's a lively, dynamical entity! There's no good way to separate
the ripples from the lake. This distinction is no more than a convenient
approximation - and a dangerous one at that.

So, we should learn to make do without a background when studying quantum
gravity. But it's tough! 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!

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!

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.

String theorists are pragmatic in a certain sense: they don't mind using
a background, and they don't mind doing what physicists always do:
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. Some estimates guess there are over
10^{100}. Leonard Susskind guesses there are 10^{500}, and argues that
we'll need the anthropic principle to choose the one describing our
world:

2) Leonard Susskind, The Landscape, article and interview on John
Brockman's "EDGE" website,
http://www.edge.org/3rd_culture/susskind03/susskind_index.html

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. 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. So, it's quite possible that our failures
with the former are just a matter of inexperience.

Given all this, I'm delighted to see some real progress on getting 4d
spacetime to emerge from nonperturbative quantum gravity:

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.

This trio of researchers have revitalized an approach called "dynamical
triangulations" where we calculate path integrals in quantum gravity by
summing over different ways of building spacetime out of little 4-simplices.
They showed that if we restrict this sum to spacetimes with a well-behaved
concept of causality, we get good results. This is a bit startling,
because after decades of work, most researchers had despaired of getting
general relativity to emerge at large distances starting from the dynamical
triangulations approach. But, these people hadn't noticed a certain flaw
in the approach... a flaw which Loll and collaborators noticed and fixed!

If you don't know what a path integral is, don't worry: it's pretty
simple. Basically, in quantum physics we can calculate the expected value
of any physical quantity by doing an average over all possible histories
of the system in question, with each history weighted by a complex number
called its "amplitude". For a particle, a history is just a path in
space; to average over all histories is to integrate over all paths -
hence the term "path integral". But in quantum gravity, a history is
nothing other than a SPACETIME.

Mathematically, a "spacetime" is something like a 4-dimensional manifold
equipped with a Lorentzian metric. But it's hard to integrate over all
of these - there are just too darn many. So, sometimes people instead
treat spacetime as made of little discrete building blocks, turning
the path integral into a sum. You can either take this seriously or treat
it as a kind of approximation. Luckily, the calculations work the same
either way!

If you're looking to build spacetime out of some sort of discrete building
block, a handy candidate is the "4-simplex": the 4-dimensional analogue
of a tetrahedron. This shape is rigid once you fix the lengths of its 10
edges, which correspond to the 10 components of the metric tensor in
general relativity.

There are lots of approaches to the path integrals in quantum gravity
that start by chopping spacetime into 4-simplices. The weird special
thing about dynamical triangulations is that here we usually assume
every 4-simplex in spacetime has the same shape. The different spacetimes
arise solely from different ways of sticking the 4-simplices together.

Why such a drastic simplifying assumption? To make calculations quick
and easy! The goal is get models where you can simulate quantum geometry
on your laptop - or at least a supercomputer. The hope is that simplifying
assumptions about physics at the Planck scale will wash out and not make
much difference on large length scales.

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. Given this, it seems we're bound to get general relativity at
large distance scales - perhaps with a nonzero cosmological constant, and
perhaps including various forms of matter.

Unfortunately, in all previous dynamical triangulation models, the path
integral was *NOT* dominated by spacetimes that look like nice 4d manifolds
from afar! Depending on the details, one either got a "crumpled phase"
dominated by spacetimes where almost all the 4-simplices touch each other,
or a "branched polymer phase" dominated by spacetimes where the 4-simplices
form treelike structures. There's a transition between these two phases,
but unfortunately it seems to be a 1st-order phase transition - not the
sort we can get anything useful out of. For a nice review of these
calculations, see:

4) Renate Loll, Discrete approaches to quantum gravity in four dimensions,
available as http://www.arxiv.org/abs/gr-qc/9805049 or as a website at Living Reviews in Relativity,
http://www.livingreviews.org/Articles/Volume1/1998-13loll/

Luckily, all these calculations shared a common flaw!

Computer calculations of path integrals become a lot easier if instead of
assigning a complex "amplitude" to each history, we assign it a positive
real number: a "relative probability". The basic reason is that unlike
positive real numbers, complex numbers can cancel out when you sum them!

When we have relative probabilities, it's the *highly probable* histories
that contribute most to the expected value of any physical quantity. We
can use something called the "Metropolis algorithm" to spot these highly
probable histories and spend most of our time worrying about them.

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!

For this reason, physicists often use a trick called "Wick rotation"
that converts amplitudes to relative probabilities. To do this trick, we
just replace time by imaginary time! In other words, wherever we see the
variable "t" for time in any formula, we replace it by "it". Magically,
this often does the job: our amplitudes turn into relative probabilities!
We then go ahead and calculate stuff. Then we take this stuff and go
back and replace "it" everywhere by "t" to get our final answers.

While the deep inner meaning of this trick is mysterious, it can be
justified in a wide variety of contexts using the "Osterwalder-Schrader
theorem". Here's a pretty general version of this theorem, suitable
for quantum gravity:

5) Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann,
Osterwalder-Schrader reconstruction and diffeomorphism invariance,
preprint available as http://www.arxiv.org/abs/quant-ph/9904094.

People use Wick rotation in all work on dynamical triangulations.
Unfortunately, this is *not* a context where you can justify this trick
by appealing to the Osterwalder-Schrader theorem. The problem is that
there's no good notion of a time coordinate "t" on your typical
spacetime built by sticking together a bunch of 4-simplices!

The new work by Ambjorn, Jurkiewiecz and Loll deals with this by
restricting to spacetimes that *do* have a time coordinate. More
precisely, they fix a 3-dimensional manifold and consider all possible
triangulations of this manifold by regular tetrahedra. These are the
allowed "slices" of spacetime - they represent different possible
geometries of space at a given time. They then consider spacetimes
having slices of this form joined together by 4-simplices in a few
simple ways.

The slicing gives a preferred time parameter "t". On the one hand this
goes against our desire in general relativity to avoid a preferred time
coordinate - but on the other hand, it allows Wick rotation. So, they
can use the Metropolis algorithm to compute things to their hearts'
content and then replace "it" by "t" at the end.

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! Take a look at their graphs
and pictures - a picture is worth a thousand words.

Naturally, what *I'd* like to do is use their work to develop some spin
foam models with better physical behavior than the ones we have so far.
Now that Loll and her collaborators have gotten something that works,
we can try to fiddle around and make it more elegant while making sure it
still works. In particular, I'm hoping we can get well-behaved models
that don't introduce a preferred time coordinate as long as they rule out
"topology change" - that is, slicings where the topology of space changes.
After all, the Osterwalder-Schrader theorem doesn't require a *preferred*
time coordinate, just *any* time coordinate together with good behavior
under change of time coordinate. For this we mainly need to rule out
topology change. Moreover, Loll and her collaborators have argued in 2d
toy models that topology change is one thing that makes models go bad: the
path integral can get dominated by spacetimes where "baby universes" keep
branching off the main one:

6) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative
Lorentzian quantum gravity, causality and topology change, Nucl. Phys.
B536 (1998) 407-434. Also available as http://www.arxiv.org/abs/hep-th/9805108.

Renate Loll and W. Westra, Space-time foam in 2d and the sum over
topologies, Acta Phys. Polon. B34 (2003) 4997-5008. Also available as
http://www.arxiv.org/abs/hep-th/0309012.

By the way, it's also reading about their 3d model:

7) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative 3d
Lorentzian quantum gravity, Phys.Rev. D64 (2001) 044011. Also available
as http://www.arxiv.org/abs/hep-th/0011276.

and for a general review, try this:

8) Renate Loll, A discrete history of the Lorentzian path integral,
Lecture Notes in Physics 631, Springer, Berlin, 2003, pp. 137-171.
Also available as http://www.arxiv.org/abs/hep-th/0212340.

All this is great, but don't get me wrong - there were a lot of *other*
cool talks at the conference besides Loll's. I'll just mention a few.

Laurent Freidel spoke on his work on spin foam models. Especially
exciting is how David Louapre and he have managed to "sum over
topologies" in 3d Riemannian quantum gravity with vanishing cosmological
constant - otherwise known as the Ponzano-Regge model He has to subtract
out a counterterm that would otherwise lead to a bubble divergence, but
then he gets a beautiful theory where the sum over spin foams is Borel
summable:

9) Laurent Freidel and David Louapre, Non-perturbative summation over
3D discrete topologies, Phys.Rev. D68 (2003) 104004. Also available as
http://www.arxiv.org/abs/hep-th/0211026.

Their work on gauge-fixing and the inclusion of spinning point particles
in the Ponzano-Regge model is also very impressive, especially given how
long this model has been studied. It shows we have lots left to learn!

10) Laurent Freidel and David Louapre, Ponzano-Regge model revisited I:
Gauge fixing, observables and interacting spinning particles, available
as http://www.arxiv.org/abs/hep-th/0401076.

The title suggests we're in for more treats to come.

Kirill Krasnov gave a talk entitled simple "ln(3)" - it was all about
the appearance of this constant in the work of Hod, Dreyer, Motl and
Neitzke on black hole entropy and the ringing of black holes. I've
discussed all this at length in "week198", but Krasnov has given an elegant
new proof of Hod's conjecture using Riemann surface theory. One can
even think of this as a "stringy" explanation of the quasinormal modes
of black holes - but much remains mysterious here:

11) Kirill Krasnov, Black hole thermodynamics and Riemann surfaces,
Class. Quant. Grav. 20 (2003) 2235-2250. Also available as http://www.arxiv.org/abs/gr-qc/0302073.

Kirill Krasnov and Sergey N. Solodukhin, Effective stringy description
of Schwarzschild black holes, available as http://www.arxiv.org/abs/hep-th/0403046.

While I'm at it, I can't resist mentioning Krasnov's work on including
point particles in 3d Lorentzian quantum gravity with negative
cosmological constant, since it has close connections with that of
Freidel and Louapre, though the context is a bit different:

12) Kirill Krasnov, \Lambda<0 quantum gravity in 2+1 dimensions I:
quantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002)
3977-3998. Also available as http://www.arxiv.org/abs/hep-th/0112164.

Kirill Krasnov, \Lambda<0 quantum gravity in 2+1 dimensions II:
black hole creation by point particles, Class. Quant. Grav. 19 (2002)
3999-4028. Also available as http://www.arxiv.org/abs/hep-th/0202117.

If I could duplicate myself, I'd have one copy write a book on 3d quantum
gravity that would synthesize all these wonderful results in a nice big
picture. It's not realistic physics; it's just a toy model. But the
math is *so* nice, and so enlightening for real-world physics in some
ways, that it's hard to resist pondering it! TQFTs, Riemann surfaces,
hyperbolic geometry, spinning point particles colliding and creating
black holes - a wonderful stew! Alas, I don't have time to savor it.

There were a lot of other interesting talks - but I don't have time to go
through and describe all of them, either. So, I'll wrap up with something
very different!

Lee Smolin told me some neat stuff about MOND - that's "Modified
Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
the strange behavior of galaxies without invoking dark matter. The basic
problem with galaxies is that the outer parts rotate faster than they
should given how much mass we actually see.

If you have a planet in a circular orbit about the Sun, Newton's laws
say its acceleration is proportional to 1/r^2, where r is its distance to
the Sun. Similarly, if almost all the mass in a galaxy were concentrated
right at the center, a star orbiting in a circle at distance r from the
center would have acceleration proportional to 1/r^2. Of course, not all
the mass is right at the center! So, the acceleration should drop off
more slowly than 1/r^2 as you go further out. And it does. But, the
observed acceleration drops off a lot more slowly than the acceleration
people calculate from the mass they see. It's not a small effect: it's a
HUGE effect!

One solution is to say there's a lot of mass we don't see: "dark matter"
of some sort. If you take this route, which most astronomers do, you're
forced to say that *most* of the mass of galaxies is in the form of dark
matter.

Milgrom's solution is to say that Newton's laws are messed up.

Of course this is a drastic, dangerous step: the last guy who tried this
was named Einstein, and we all know what happened to him. Milgrom's theory
isn't even based on deep reasoning and beautiful math like Einstein's!
Instead, it's just a blatant attempt to fit the experimental data.
And it's not even elegant. In fact, it's downright ugly.

Here's what it says: the usual Newtonian formula for the acceleration
due to gravity is correct as long as the acceleration is bigger than

a = 2 x 10^{-10} m/sec^2

But, for accelerations less than this, you take the geometric mean
of the acceleration Newton would predict and this constant a.

In other words, there's a certain value of acceleration such that above
this value, the Newtonian law of gravity works as usual, while below this
value the law suddenly changes.

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." Not in fundamental
physics, anyway! Sure, water is solid below centigrade and fluid above
this, but that's not a fundamental law - it presumably follows from other
stuff. Not that anyone has derived the melting point of ice from first
principles, mind you. But we think we could if we were better at big
messy calculations.

Furthermore, you can't easily invent a Lagrangian for gravity that makes
it fall off more *slowly* than 1/r^2. It's easy to get it to fall off
*faster* - just give the graviton a mass, for example! But not more
slowly. It turns out you can do it - Bekenstein and Milgrom have a way -
but it's incredibly ugly.

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! In some cases it matches the observed rotation of
galaxies in an appallingly accurate way, fitting every wiggle in the graph
of stellar rotation velocity as a function of distance from the center.

So, even if MOND is wrong, there may need to be some reason why it *acts*
like it's right! Apparently even some proponents of dark matter agree
with this.

But: take everything I'm saying here with a grain of salt. I'm no expert
on this stuff, so if you know any astrophysics you should read the
literature and make up your own mind.

Here are two reviews that Smolin especially recommended:

13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics
as an Alternative to Dark Matter, available as http://www.arxiv.org/abs/astro-ph/0204521.

14) Anthony Aguirre, Alternatives to dark matter (?), available as
http://www.arxiv.org/abs/astro-ph/0310572.

Here's McGaugh's website with links to many papers on MOND, including
Milgrom's original papers:

15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html

McGaugh is a strong proponent of MOND - though he didn't start out that
way - so the selection may be biased. Does anyone know an intelligent
detailed critique of MOND? If so, I want to see it! We can't throw out
Newton's law of gravity (or more precisely, general relativity, which has
Newtonian gravity as a limiting case for low densities and low velocities)
unless we have *very* good reasons! So we have to think about things
carefully, and weigh the evidence on both sides.

If I could duplicate myself, I'd have one copy try to get to the bottom
of this dark matter / MOND puzzle. But I can't...

.... so if you're an expert who knows a lot about this, let me
know what you think - or better yet, post an article about this to
sci.physics.research!

-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at

http://math.ucr.edu/home/baez/

For a table of contents of all the issues of This Week's Finds, try

http://math.ucr.edu/home/baez/twf.html

A simple jumping-off point to the old issues is available at

http://math.ucr.edu/home/baez/twfshort.html

If you just want the latest issue, go to

http://math.ucr.edu/home/baez/this.week.html

Thomas Larsson

May12-04, 06:05 AM

<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>\n\n\nbaez@math.removethis.ucr.andthis.edu (John Baez) wrote in message news:<c7pbsa\\$p9\\$1@glue.ucr.edu>...\n>\n> Given all this, I\'m delighted to see some real progress on getting 4d\n> spacetime to emerge from nonperturbative quantum gravity:\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>\n> This trio of researchers have revitalized an approach called "dynamical\n> triangulations" where we calculate path integrals in quantum gravity by\n> summing over different ways of building spacetime out of little 4-simplices.\n> They showed that if we restrict this sum to spacetimes with a well-behaved\n> concept of causality, we get good results. This is a bit startling,\n> because after decades of work, most researchers had despaired of getting\n> general relativity to emerge at large distances starting from the dynamical\n> triangulations approach. But, these people hadn\'t noticed a certain flaw\n> in the approach... a flaw which Loll and collaborators noticed and fixed!\n\nThis is pretty exciting. It is sort of obvious that you can formally\nput gravity on a lattice, but I always thought that there wasn\'t a\ncontinuum limit. If the numerical evidence in this paper is true, and\nit seems quite strong, then we see a new field open up here, perhaps\nlike when Wilson invented lattice gauge theory in 1974. A lot of\ninteresting things can be done, e.g. to apply standard techniques in\nlattice models, introduce gauge and fermion fields, and try to find\ndifferent continuum formulations. I would not be surprised if this is\nthe next bandwagon and a lot of smart people will jump onto it.\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>baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message news:<c7pbsa$p9$1@glue.ucr.edu>...
>
> Given all this, I'm delighted to see some real progress on getting 4d
> spacetime to emerge from nonperturbative quantum gravity:
>
> 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.
>
> This trio of researchers have revitalized an approach called "dynamical
> triangulations" where we calculate path integrals in quantum gravity by
> summing over different ways of building spacetime out of little 4-simplices.
> They showed that if we restrict this sum to spacetimes with a well-behaved
> concept of causality, we get good results. This is a bit startling,
> because after decades of work, most researchers had despaired of getting
> general relativity to emerge at large distances starting from the dynamical
> triangulations approach. But, these people hadn't noticed a certain flaw
> in the approach... a flaw which Loll and collaborators noticed and fixed!

This is pretty exciting. It is sort of obvious that you can formally
put gravity on a lattice, but I always thought that there wasn't a
continuum limit. If the numerical evidence in this paper is true, and
it seems quite strong, then we see a new field open up here, perhaps
like when Wilson invented lattice gauge theory in 1974. A lot of
interesting things can be done, e.g. to apply standard techniques in
lattice models, introduce gauge and fermion fields, and try to find
different continuum formulations. I would not be surprised if this is
the next bandwagon and a lot of smart people will jump onto it.

alistair

May12-04, 06:05 AM

<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>Modified Newtonian Dynamics\n\nMOND basically says that if you double the distance of a star\nfrom the galactic centre, then you half the force of gravity, instead\nof quartering it as Newton\'s inverse square law would say.\nThis is what a physical theory needs to explain.\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>Modified Newtonian Dynamics

MOND basically says that if you double the distance of a star
from the galactic centre, then you half the force of gravity, instead
of quartering it as Newton's inverse square law would say.
This is what a physical theory needs to explain.

Alf P. Steinbach

May12-04, 03:58 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>* baez@math.removethis.ucr.andthis.edu (John Baez) schriebt:\n>\n> Milgrom\'s solution is to say that Newton\'s laws are messed up.\n>\n> Of course this is a drastic, dangerous step: the last guy who tried this\n> was named Einstein, and we all know what happened to him. Milgrom\'s theory\n> isn\'t even based on deep reasoning and beautiful math like Einstein\'s!\n> Instead, it\'s just a blatant attempt to fit the experimental data.\n> And it\'s not even elegant. In fact, it\'s downright ugly.\n>\n> Here\'s what it says: the usual Newtonian formula for the acceleration\n> due to gravity is correct as long as the acceleration is bigger than\n>\n> a = 2 x 10^{-10} m/sec^2\n>\n> But, for accelerations less than this, you take the geometric mean\n> of the acceleration Newton would predict and this constant a.\n\nAre you sure this is a correct description?\n\nThe geometric mean of this and that is just (this*that)^0.5, which if the\nabove is correct means essentially using the square root of the Newtonian\nvalue, scaled by a constant.\n\nI assume that by "acceleration" what is meant is not the acceleration of\nan object in a given frame of reference, but the acceleration component due\nto gravitational attraction to some other object or collection of objects.\n\nAnd if so I assume further that this implies some distance between \'em, that\nthe other object(s) in question is the total gravitational attraction of the\ngalaxy hosting the object.\n\nAnd if so isn\'t it possible that the effect that is attributed to weak\neffective gravitational attraction above might instead be due to distance?\n\nSo, have anybody calculated the effect of accelerated Hubble expansion on the\napparent law of gravity over the distances involved?\n\nIt seems to provide the necessary non-square-distance-law to modify Newton\'s\nlaw at sufficient distance. The questions I as a layman can see are (1)\nwhether it is of sufficient magnitude for the observed effects, and (2) (when\nthe math is done, and at least for some reasonable cosmological model) whether\nit provides a sharp enough departure from Newton\'s law to appear as a\nMOND-like sharply changed behavior in the effective law of gravity, and (3)\nwhether the particular form, namely apparent square root, is critical, and if\nso whether Hubble law gives that or can approximate it.\n\n--\nA: Because it messes up the order in which people normally read text.\nQ: Why is top-posting such a bad thing?\nA: Top-posting.\nQ: What is the most annoying thing on usenet and in e-mail?\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>* baez@math.removethis.ucr.andthis.edu (John Baez) schriebt:
>
> Milgrom's solution is to say that Newton's laws are messed up.
>
> Of course this is a drastic, dangerous step: the last guy who tried this
> was named Einstein, and we all know what happened to him. Milgrom's theory
> isn't even based on deep reasoning and beautiful math like Einstein's!
> Instead, it's just a blatant attempt to fit the experimental data.
> And it's not even elegant. In fact, it's downright ugly.
>
> Here's what it says: the usual Newtonian formula for the acceleration
> due to gravity is correct as long as the acceleration is bigger than
>
> a = 2 x 10^{-10} m/sec^2
>
> But, for accelerations less than this, you take the geometric mean
> of the acceleration Newton would predict and this constant a.

Are you sure this is a correct description?

The geometric mean of this and that is just (this*that)^0.5, which if the
above is correct means essentially using the square root of the Newtonian
value, scaled by a constant.

I assume that by "acceleration" what is meant is not the acceleration of
an object in a given frame of reference, but the acceleration component due
to gravitational attraction to some other object or collection of objects.

And if so I assume further that this implies some distance between 'em, that
the other object(s) in question is the total gravitational attraction of the
galaxy hosting the object.

And if so isn't it possible that the effect that is attributed to weak
effective gravitational attraction above might instead be due to distance?

So, have anybody calculated the effect of accelerated Hubble expansion on the
apparent law of gravity over the distances involved?

It seems to provide the necessary non-square-distance-law to modify Newton's
law at sufficient distance. The questions I as a layman can see are (1)
whether it is of sufficient magnitude for the observed effects, and (2) (when
the math is done, and at least for some reasonable cosmological model) whether
it provides a sharp enough departure from Newton's law to appear as a
MOND-like sharply changed behavior in the effective law of gravity, and (3)
whether the particular form, namely apparent square root, is critical, and if
so whether Hubble law gives that or can approximate it.

--
A: Because it messes up the order in which people normally read text.
Q: Why is top-posting such a bad thing?
A: Top-posting.
Q: What is the most annoying thing on usenet and in e-mail?

carlip@no-physics-spam.ucdavis.edu

May12-04, 04:00 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>In sci.astro.research John Baez <baez@math.removethis.ucr.andthis.edu> wrote:\n\n> So, even if MOND is wrong, there may need to be some reason why it *acts*\n> like it\'s right! Apparently even some proponents of dark matter agree\n> with this.\n\nTry this:\n\nM. Kaplinghat and M. S. Turner, "How Cold Dark Matter Theory Explains\nMilgrom\'s Law," astro-ph/0107284, Astrophys.J. 569 (2002) L19. Note\nthat this analysis also explains why the ``critical acceleration\'\'\nin MOND does *not* apply at cluster scales. There is some debate over\nthese results, but the paper is certainly worth reading.\n\nSteve Carlip\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>In sci.astro.research John Baez <baez@math.removethis.ucr.andthis.edu> wrote:

> So, even if MOND is wrong, there may need to be some reason why it *acts*
> like it's right! Apparently even some proponents of dark matter agree
> with this.

Try this:

M. Kaplinghat and M. S. Turner, "How Cold Dark Matter Theory Explains
Milgrom's Law," http://www.arxiv.org/abs/astro-ph/0107284, Astrophys.J. 569 (2002) L19. Note
that this analysis also explains why the ``critical acceleration''
in MOND does *not* apply at cluster scales. There is some debate over
these results, but the paper is certainly worth reading.

Steve Carlip

Phillip Helbig---remove CLOTHES to reply

May12-04, 06:20 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>In article <c7pbsa\\$p9\\$1@glue.ucr.edu>,\nbaez@math.removet his.ucr.andthis.edu (John Baez) writes:\n\n\n> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n> the strange behavior of galaxies without invoking dark matter. The basic\n> problem with galaxies is that the outer parts rotate faster than they\n> should given how much mass we actually see.\n\nFor the non-experts, I should point out that "dark matter" has been used\nin several contexts. First, the mass-to-light ratio of the universe is\nless than 1 in solar units. No big deal; that just means that on\naverage stars aren\'t as bright as the sun and doesn\'t necessarily imply\nsome form of "mysterious" dark matter (although it could). Second,\nthere is a lot of non-baryonic matter, which can\'t consist of any known\nparticles. No-one debates this, but we don\'t know what it is---except\nperhaps if MOND is correct. Third, when some folks used to believe\n(some still do) that Omega_matter=1, then one needs a lot of additional\ndark matter to make up the difference between 1 and the 0.3 which is\nmore or less directly inferred.\n\nDark matter, non-baryonic matter etc is often presented as something\nmysterious, but a priori why should most of the universe be composed of\nsomething we are familiar with, being made of baryons dependent on the\nlight of a star? Thus, I don\'t agree with some MOND enthusiasts that\ndark matter is a priori a bad idea, a deus ex machina to save\nappearances etc.\n\nAlso, it is possible that there is dark matter AND some form of MOND\nis correct. Most people will cry "ugly!", "it has to be one or the\nother!" etc. Just a few years ago, such armchair-cosmology arguments\nwere used to "prove" that a universe with a cosmological constant is so\nunnatural it can\'t be correct.\n\nAnother interesting point, noted in McGaugh\'s pages, is that MOND has\nactually made a lot of predictions, which years later were verified by\nobservation, often by folks who didn\'t even know about MOND or\npredictions. Many of the more mainstream cosmological ideas don\'t even\nmake testable predictions, much less have had them verified. In this\nrespect, MOND has been a good guy.\n\n> Instead, it\'s just a blatant attempt to fit the experimental data.\n> And it\'s not even elegant. In fact, it\'s downright ugly.\n\nInitially, perhaps, but since predictions were made, it is NOT just a\nposteriori curve fitting, and CAN be falsified.\n\n> Here are two reviews that Smolin especially recommended:\n>\n> 13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics\n> as an Alternative to Dark Matter, available as astro-ph/0204521.\n\nSanders is also a MOND proponent and has written several papers on it.\n\n> 14) Anthony Aguirre, Alternatives to dark matter (?), available as\n> astro-ph/0310572.\n>\n> Here\'s McGaugh\'s website with links to many papers on MOND, including\n> Milgrom\'s original papers:\n>\n> 15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html\n>\n> McGaugh is a strong proponent of MOND - though he didn\'t start out that\n> way - so the selection may be biased.\n\nTrue to some extent, perhaps...but less biased than a lot of anti-MOND\npropaganda! :-)\n\n> Does anyone know an intelligent\n> detailed critique of MOND? If so, I want to see it!\n\nIndeed!\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>In article <c7pbsa$p9$1@glue.ucr.edu>,
baez@math.removethis.ucr.andthis.edu (John Baez) writes:

> Lee Smolin told me some neat stuff about MOND - that's "Modified
> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
> the strange behavior of galaxies without invoking dark matter. The basic
> problem with galaxies is that the outer parts rotate faster than they
> should given how much mass we actually see.

For the non-experts, I should point out that "dark matter" has been used
in several contexts. First, the mass-to-light ratio of the universe is
less than 1 in solar units. No big deal; that just means that on
average stars aren't as bright as the sun and doesn't necessarily imply
some form of "mysterious" dark matter (although it could). Second,
there is a lot of non-baryonic matter, which can't consist of any known
particles. No-one debates this, but we don't know what it is---except
perhaps if MOND is correct. Third, when some folks used to believe
(some still do) that \Omega_matter=1, then one needs a lot of additional
dark matter to make up the difference between 1 and the .3 which is
more or less directly inferred.

Dark matter, non-baryonic matter etc is often presented as something
mysterious, but a priori why should most of the universe be composed of
something we are familiar with, being made of baryons dependent on the
light of a star? Thus, I don't agree with some MOND enthusiasts that
dark matter is a priori a bad idea, a deus ex machina to save
appearances etc.

Also, it is possible that there is dark matter AND some form of MOND
is correct. Most people will cry "ugly!", "it has to be one or the
other!" etc. Just a few years ago, such armchair-cosmology arguments
were used to "prove" that a universe with a cosmological constant is so
unnatural it can't be correct.

Another interesting point, noted in McGaugh's pages, is that MOND has
actually made a lot of predictions, which years later were verified by
observation, often by folks who didn't even know about MOND or
predictions. Many of the more mainstream cosmological ideas don't even
make testable predictions, much less have had them verified. In this
respect, MOND has been a good guy.

> Instead, it's just a blatant attempt to fit the experimental data.
> And it's not even elegant. In fact, it's downright ugly.

Initially, perhaps, but since predictions were made, it is NOT just a
posteriori curve fitting, and CAN be falsified.

> Here are two reviews that Smolin especially recommended:
>
> 13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics
> as an Alternative to Dark Matter, available as http://www.arxiv.org/abs/astro-ph/0204521.

Sanders is also a MOND proponent and has written several papers on it.

> 14) Anthony Aguirre, Alternatives to dark matter (?), available as
> http://www.arxiv.org/abs/astro-ph/0310572.
>
> Here's McGaugh's website with links to many papers on MOND, including
> Milgrom's original papers:
>
> 15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html
>
> McGaugh is a strong proponent of MOND - though he didn't start out that
> way - so the selection may be biased.

True to some extent, perhaps...but less biased than a lot of anti-MOND
propaganda! :-)

> Does anyone know an intelligent
> detailed critique of MOND? If so, I want to see it!

Indeed!

ebunn@lfa221051.richmond.edu

May13-04, 11:15 AM

<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>\nIn article <861c1b21.0405111214.8a3e2d1@posting.google.com>,\ nalistair <alistair@goforit64.fsnet.co.uk> wrote:\n>Modified Newtonian Dynamics\n>\n>MOND basically says that if you double the distance of a star\n>from the galactic centre, then you half the force of gravity, instead\n>of quartering it as Newton\'s inverse square law would say.\n>This is what a physical theory needs to explain.\n\nThis is not accurate. John Baez\'s description of MOND is much\ncloser to what the theory actually says.\n\nJohn\'s description was essentially this: if you define a_N to be\nthe Newtonian acceleration\n\na_N = F / m\n\nthen the actual acceleration of an object is\n\na = a_N if a_N > a_0\na = sqrt(a_N a_0) if a < a_0\n\nHere a_0 is some fundamental constant.\n\nHe pointed out, quite correctly, that it\'s ugly for a fundamental\nlaw to be split into cases like that. Last time I checked,\nthe MOND people weren\'t dogmatic about this exact form. They\nconsidered smooth functional relationships between a and a_N.\nI think that as long as the relationship approaches the above behavior\nin the limits,\n\na -> a_N when a_N >> a_0\na -> sqrt(a_N a_0) when a_N << a_0\n\nthe MOND people are satisfied. So I guess something like\n\na = sqrt(a_N (a_N + a_0))\n\nmight do the trick.\n\nPersonally, I can\'t get past my theorist\'s objections to MOND. It\ndoesn\'t play well at all with general relativity, and I just don\'t\nbelieve that general relativity is completely on the wrong track. But\nof course the issue should be settled observationally, not based on\ntheoretical prejudice (however well-justified!).\n\n-Ted\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\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>In article <861c1b21.0405111214.8a3e2d1@posting.google.com>,
alistair <alistair@goforit64.fsnet.co.uk> wrote:
>Modified Newtonian Dynamics
>
>MOND basically says that if you double the distance of a star
>from the galactic centre, then you half the force of gravity, instead
>of quartering it as Newton's inverse square law would say.
>This is what a physical theory needs to explain.

This is not accurate. John Baez's description of MOND is much
closer to what the theory actually says.

John's description was essentially this: if you define a_N to be
the Newtonian acceleration

a_N = F / m

then the actual acceleration of an object is

a = a_N[/itex] if a_N > a_0a = \sqrt(a_N a_0) if a < a_0

Here a_0 is some fundamental constant.

He pointed out, quite correctly, that it's ugly for a fundamental
law to be split into cases like that. Last time I checked,
the MOND people weren't dogmatic about this exact form. They
considered smooth functional relationships between a and a_N.
I think that as long as the relationship approaches the above behavior
in the limits,

a -> a_N when a_N >> a_0a -> \sqrt(a_N a_0) when [itex]a_N << a_0

the MOND people are satisfied. So I guess something like

a = \sqrt(a_N (a_N + a_0))

might do the trick.

Personally, I can't get past my theorist's objections to MOND. It
doesn't play well at all with general relativity, and I just don't
believe that general relativity is completely on the wrong track. But
of course the issue should be settled observationally, not based on
theoretical prejudice (however well-justified!).

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

Melroy

May13-04, 11:15 AM

<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>> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n> the strange behavior of galaxies without invoking dark matter. The basic\n> problem with galaxies is that the outer parts rotate faster than they\n> should given how much mass we actually see.\n\nFrom\nhttp://www.astro.ucla.edu/~wright/density.html#MOND\nit seems MOND fails on the scale of galaxy clusters.\nalso I don\'t know if MOND can explain an accelerating universe,\npredict correct elemental abundances, provide a good fit to CMB anisotropy\nspectrum.\n\nanyhow I think the fantastic fit of WMAP and SDSS,2DF to the standard\nLambda+CDM\nis more or less a nail in the coffin for all alternative models.\nNevertheless the standard model requires BOTH non-baryonic\ndark matter and dark energy\nfor which there is no laboratory evidence. So I guess as good scientists\nit makes sense to think of alternatives and try to test them experimentally :-)\n\nanyhow I have a question to experts on gravitation & cosmology on this forum.\nwhat do you think about Conformal gravity which is cited in the paper by Aguirre\n(mentioned by John above?) As far as I know unlike MOND this cannot be ruled\nout at cluster scales. It also provides a natural explanation for an\naccelerating universe. I however don\'t know if Conformal gravity is consistent\nwith predictions of GR at solar-system and binary pulsar distance scales.\nThanks\n\n[Moderator\'s note: Excessively quoted text truncated by moderator. Please\nquote with care. See http://www-stud.uni-essen.de/~sb0264/HowToPost.html\n-usc]\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>> Lee Smolin told me some neat stuff about MOND - that's "Modified
> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
> the strange behavior of galaxies without invoking dark matter. The basic
> problem with galaxies is that the outer parts rotate faster than they
> should given how much mass we actually see.

From
http://www.astro.ucla.edu/~wright/density.html#MOND
it seems MOND fails on the scale of galaxy clusters.
also I don't know if MOND can explain an accelerating universe,
predict correct elemental abundances, provide a good fit to CMB anisotropy
spectrum.

anyhow I think the fantastic fit of WMAP and SDSS,2DF to the standard
\Lambda+CDM
is more or less a nail in the coffin for all alternative models.
Nevertheless the standard model requires BOTH non-baryonic
dark matter and dark energy
for which there is no laboratory evidence. So I guess as good scientists
it makes sense to think of alternatives and try to test them experimentally :-)

anyhow I have a question to experts on gravitation & cosmology on this forum.
what do you think about Conformal gravity which is cited in the paper by Aguirre
(mentioned by John above?) As far as I know unlike MOND this cannot be ruled
out at cluster scales. It also provides a natural explanation for an
accelerating universe. I however don't know if Conformal gravity is consistent
with predictions of GR at solar-system and binary pulsar distance scales.
Thanks

[Moderator's note: Excessively quoted text truncated by moderator. Please
quote with care. See http://www-stud.uni-essen.de/~sb0264/HowToPost.html
-usc]

Torquemada

May14-04, 05:10 AM

<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>I checked out this article: http://www.astro.umd.edu/~ssm/mond/astronow.html\nand there\'s an example of a graph of rotation velocity vs. radius showing\none of the wiggles JB mentions, with the note "even the kink observed in the\ngas distribution is reflected in the rotation".\n\nForgive me for being a little sceptical but the Newtonian prediction has\nexactly the same kink. In fact, the MOND curve is just the Newtonian curve\nscaled up. Just about any reasonably well behaved modification of the\nNewtonian formula that has a scaling effect that brings the Newtonian curve\nroughly in alignment with measured results is going to have that kink. So\nwhile it may be impressive that MOND predicts this overall scaling\ncorrectly, I\'m not in the least bit impressed with it managing to match this\nwiggle. Are there examples where MOND predicts a wiggle that simply isn\'t\npresent in the Newtonian case. That\'d be impressive.\n\nOr am I misinterpreting the graph?\n--\nTorque\n\n"John Baez" <baez@math.removethis.ucr.andthis.edu> wrote in message\nnews:c7pbsa\\$p9\\$1@glue.ucr.edu...\n>\n >\n> Also available at http://math.ucr.edu/home/baez/week206.html\n>\n> May 10, 2004\n> This Week\'s Finds in Mathematical Physics - Week 206\n> John Baez\n>\n> I just got back from Marseille, where Carlo Rovelli, Laurent Freidel\n> and Phillipe Roche held the first really big conference on loop quantum\n> gravity and spin foams since the 2nd Warsaw workshop run by Jerzy\n> Lewandowski back in 1997:\n>\n> 1) Non Perturbative Quantum Gravity: Loops and Spin Foams,\n> 3-7 May 2004, CIRM, Luminy, Marseille, France,\n> http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/\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. 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. But most of all, it was good to\n> see some progress on the tough problem of understanding dynamics in\n> nonperturbative quantum gravity.\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>\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? 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. But, the\n> main lesson of general relativity is that spacetime is *not* a fixed\n> stage: it\'s a lively, dynamical entity! There\'s no good way to separate\n> the ripples from the lake. This distinction is no more than a convenient\n> approximation - and a dangerous one at that.\n>\n> So, we should learn to make do without a background when studying quantum\n> gravity. But it\'s tough! There are knotty conceptual issues like the\n> "problem of time": how do we describe time evolution without using a fixed\n> background to measure the passage of time? There are also practical\n> problems: in most attempts to describe spacetime from the ground up in\n> a quantum way, all hell breaks loose!\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>\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>\n> String theorists are pragmatic in a certain sense: they don\'t mind using\n> a background, and they don\'t mind doing what physicists always do:\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. Some estimates guess there are over\n> 10^{100}. Leonard Susskind guesses there are 10^{500}, and argues that\n> we\'ll need the anthropic principle to choose the one describing our\n> world:\n>\n> 2) Leonard Susskind, The Landscape, article and interview on John\n> Brockman\'s "EDGE" website,\n> http://www.edge.org/3rd_culture/susskind03/susskind_index.html\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. And let\'s face\n> it: we haven\'t spent nearly as much time thinking about background-free\n> or nonperturbative physics as we\'ve spent on background-dependent\n> or perturbative physics. So, it\'s quite possible that our failures\n> with the former are just a matter of inexperience.\n>\n> Given all this, I\'m delighted to see some real progress on getting 4d\n> spacetime to emerge from nonperturbative quantum gravity:\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>\n> This trio of researchers have revitalized an approach called "dynamical\n> triangulations" where we calculate path integrals in quantum gravity by\n> summing over different ways of building spacetime out of little\n4-simplices.\n> They showed that if we restrict this sum to spacetimes with a well-behaved\n> concept of causality, we get good results. This is a bit startling,\n> because after decades of work, most researchers had despaired of getting\n> general relativity to emerge at large distances starting from the\ndynamical\n> triangulations approach. But, these people hadn\'t noticed a certain flaw\n> in the approach... a flaw which Loll and collaborators noticed and fixed!\n>\n> If you don\'t know what a path integral is, don\'t worry: it\'s pretty\n> simple. Basically, in quantum physics we can calculate the expected value\n> of any physical quantity by doing an average over all possible histories\n> of the system in question, with each history weighted by a complex number\n> called its "amplitude". For a particle, a history is just a path in\n> space; to average over all histories is to integrate over all paths -\n> hence the term "path integral". But in quantum gravity, a history is\n> nothing other than a SPACETIME.\n>\n> Mathematically, a "spacetime" is something like a 4-dimensional manifold\n> equipped with a Lorentzian metric. But it\'s hard to integrate over all\n> of these - there are just too darn many. So, sometimes people instead\n> treat spacetime as made of little discrete building blocks, turning\n> the path integral into a sum. You can either take this seriously or treat\n> it as a kind of approximation. Luckily, the calculations work the same\n> either way!\n>\n> If you\'re looking to build spacetime out of some sort of discrete building\n> block, a handy candidate is the "4-simplex": the 4-dimensional analogue\n> of a tetrahedron. This shape is rigid once you fix the lengths of its 10\n> edges, which correspond to the 10 components of the metric tensor in\n> general relativity.\n>\n> There are lots of approaches to the path integrals in quantum gravity\n> that start by chopping spacetime into 4-simplices. The weird special\n> thing about dynamical triangulations is that here we usually assume\n> every 4-simplex in spacetime has the same shape. The different spacetimes\n> arise solely from different ways of sticking the 4-simplices together.\n>\n> Why such a drastic simplifying assumption? To make calculations quick\n> and easy! The goal is get models where you can simulate quantum geometry\n> on your laptop - or at least a supercomputer. The hope is that\nsimplifying\n> assumptions about physics at the Planck scale will wash out and not make\n> much difference on large length scales.\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. Given this, it seems we\'re bound to get general relativity at\n> large distance scales - perhaps with a nonzero cosmological constant, and\n> perhaps including various forms of matter.\n>\n> Unfortunately, in all previous dynamical triangulation models, the path\n> integral was *NOT* dominated by spacetimes that look like nice 4d\nmanifolds\n> from afar! Depending on the details, one either got a "crumpled phase"\n> dominated by spacetimes where almost all the 4-simplices touch each other,\n> or a "branched polymer phase" dominated by spacetimes where the\n4-simplices\n> form treelike structures. There\'s a transition between these two phases,\n> but unfortunately it seems to be a 1st-order phase transition - not the\n> sort we can get anything useful out of. For a nice review of these\n> calculations, see:\n>\n> 4) Renate Loll, Discrete approaches to quantum gravity in four dimensions,\n> available as gr-qc/9805049 or as a website at Living Reviews in\nRelativity,\n> http://www.livingreviews.org/Articles/Volume1/1998-13loll/\n>\n> Luckily, all these calculations shared a common flaw!\n>\n> Computer calculations of path integrals become a lot easier if instead of\n> assigning a complex "amplitude" to each history, we assign it a positive\n> real number: a "relative probability". The basic reason is that unlike\n> positive real numbers, complex numbers can cancel out when you sum them!\n>\n> When we have relative probabilities, it\'s the *highly probable* histories\n> that contribute most to the expected value of any physical quantity. We\n> can use something called the "Metropolis algorithm" to spot these highly\n> probable histories and spend most of our time worrying about them.\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>\n> For this reason, physicists often use a trick called "Wick rotation"\n> that converts amplitudes to relative probabilities. To do this trick, we\n> just replace time by imaginary time! In other words, wherever we see the\n> variable "t" for time in any formula, we replace it by "it". Magically,\n> this often does the job: our amplitudes turn into relative probabilities!\n> We then go ahead and calculate stuff. Then we take this stuff and go\n> back and replace "it" everywhere by "t" to get our final answers.\n>\n> While the deep inner meaning of this trick is mysterious, it can be\n> justified in a wide variety of contexts using the "Osterwalder-Schrader\n> theorem". Here\'s a pretty general version of this theorem, suitable\n> for quantum gravity:\n>\n> 5) Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann,\n> Osterwalder-Schrader reconstruction and diffeomorphism invariance,\n> preprint available as quant-ph/9904094.\n>\n> People use Wick rotation in all work on dynamical triangulations.\n> Unfortunately, this is *not* a context where you can justify this trick\n> by appealing to the Osterwalder-Schrader theorem. The problem is that\n> there\'s no good notion of a time coordinate "t" on your typical\n> spacetime built by sticking together a bunch of 4-simplices!\n>\n> The new work by Ambjorn, Jurkiewiecz and Loll deals with this by\n> restricting to spacetimes that *do* have a time coordinate. More\n> precisely, they fix a 3-dimensional manifold and consider all possible\n> triangulations of this manifold by regular tetrahedra. These are the\n> allowed "slices" of spacetime - they represent different possible\n> geometries of space at a given time. They then consider spacetimes\n> having slices of this form joined together by 4-simplices in a few\n> simple ways.\n>\n> The slicing gives a preferred time parameter "t". On the one hand this\n> goes against our desire in general relativity to avoid a preferred time\n> coordinate - but on the other hand, it allows Wick rotation. So, they\n> can use the Metropolis algorithm to compute things to their hearts\'\n> content and then replace "it" by "t" at the end.\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! Take a look at their graphs\n> and pictures - a picture is worth a thousand words.\n>\n> Naturally, what *I\'d* like to do is use their work to develop some spin\n> foam models with better physical behavior than the ones we have so far.\n> Now that Loll and her collaborators have gotten something that works,\n> we can try to fiddle around and make it more elegant while making sure it\n> still works. In particular, I\'m hoping we can get well-behaved models\n> that don\'t introduce a preferred time coordinate as long as they rule out\n> "topology change" - that is, slicings where the topology of space changes.\n> After all, the Osterwalder-Schrader theorem doesn\'t require a *preferred*\n> time coordinate, just *any* time coordinate together with good behavior\n> under change of time coordinate. For this we mainly need to rule out\n> topology change. Moreover, Loll and her collaborators have argued in 2d\n> toy models that topology change is one thing that makes models go bad: the\n> path integral can get dominated by spacetimes where "baby universes" keep\n> branching off the main one:\n>\n> 6) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative\n> Lorentzian quantum gravity, causality and topology change, Nucl. Phys.\n> B536 (1998) 407-434. Also available as hep-th/9805108.\n>\n> Renate Loll and W. Westra, Space-time foam in 2d and the sum over\n> topologies, Acta Phys. Polon. B34 (2003) 4997-5008. Also available as\n> hep-th/0309012.\n>\n> By the way, it\'s also reading about their 3d model:\n>\n> 7) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative 3d\n> Lorentzian quantum gravity, Phys.Rev. D64 (2001) 044011. Also available\n> as hep-th/0011276.\n>\n> and for a general review, try this:\n>\n> 8) Renate Loll, A discrete history of the Lorentzian path integral,\n> Lecture Notes in Physics 631, Springer, Berlin, 2003, pp. 137-171.\n> Also available as hep-th/0212340.\n>\n> All this is great, but don\'t get me wrong - there were a lot of *other*\n> cool talks at the conference besides Loll\'s. I\'ll just mention a few.\n>\n> Laurent Freidel spoke on his work on spin foam models. Especially\n> exciting is how David Louapre and he have managed to "sum over\n> topologies" in 3d Riemannian quantum gravity with vanishing cosmological\n> constant - otherwise known as the Ponzano-Regge model He has to subtract\n> out a counterterm that would otherwise lead to a bubble divergence, but\n> then he gets a beautiful theory where the sum over spin foams is Borel\n> summable:\n>\n> 9) Laurent Freidel and David Louapre, Non-perturbative summation over\n> 3D discrete topologies, Phys.Rev. D68 (2003) 104004. Also available as\n> hep-th/0211026.\n>\n> Their work on gauge-fixing and the inclusion of spinning point particles\n> in the Ponzano-Regge model is also very impressive, especially given how\n> long this model has been studied. It shows we have lots left to learn!\n>\n> 10) Laurent Freidel and David Louapre, Ponzano-Regge model revisited I:\n> Gauge fixing, observables and interacting spinning particles, available\n> as hep-th/0401076.\n>\n> The title suggests we\'re in for more treats to come.\n>\n> Kirill Krasnov gave a talk entitled simple "ln(3)" - it was all about\n> the appearance of this constant in the work of Hod, Dreyer, Motl and\n> Neitzke on black hole entropy and the ringing of black holes. I\'ve\n> discussed all this at length in "week198", but Krasnov has given an\nelegant\n> new proof of Hod\'s conjecture using Riemann surface theory. One can\n> even think of this as a "stringy" explanation of the quasinormal modes\n> of black holes - but much remains mysterious here:\n>\n> 11) Kirill Krasnov, Black hole thermodynamics and Riemann surfaces,\n> Class. Quant. Grav. 20 (2003) 2235-2250. Also available as gr-qc/0302073.\n>\n> Kirill Krasnov and Sergey N. Solodukhin, Effective stringy description\n> of Schwarzschild black holes, available as hep-th/0403046.\n>\n> While I\'m at it, I can\'t resist mentioning Krasnov\'s work on including\n> point particles in 3d Lorentzian quantum gravity with negative\n> cosmological constant, since it has close connections with that of\n> Freidel and Louapre, though the context is a bit different:\n>\n> 12) Kirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions I:\n> quantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002)\n> 3977-3998. Also available as hep-th/0112164.\n>\n> Kirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions II:\n> black hole creation by point particles, Class. Quant. Grav. 19 (2002)\n> 3999-4028. Also available as hep-th/0202117.\n>\n> If I could duplicate myself, I\'d have one copy write a book on 3d quantum\n> gravity that would synthesize all these wonderful results in a nice big\n> picture. It\'s not realistic physics; it\'s just a toy model. But the\n> math is *so* nice, and so enlightening for real-world physics in some\n> ways, that it\'s hard to resist pondering it! TQFTs, Riemann surfaces,\n> hyperbolic geometry, spinning point particles colliding and creating\n> black holes - a wonderful stew! Alas, I don\'t have time to savor it.\n>\n> There were a lot of other interesting talks - but I don\'t have time to go\n> through and describe all of them, either. So, I\'ll wrap up with something\n> very different!\n>\n> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n> the strange behavior of galaxies without invoking dark matter. The basic\n> problem with galaxies is that the outer parts rotate faster than they\n> should given how much mass we actually see.\n>\n> If you have a planet in a circular orbit about the Sun, Newton\'s laws\n> say its acceleration is proportional to 1/r^2, where r is its distance to\n> the Sun. Similarly, if almost all the mass in a galaxy were concentrated\n> right at the center, a star orbiting in a circle at distance r from the\n> center would have acceleration proportional to 1/r^2. Of course, not all\n> the mass is right at the center! So, the acceleration should drop off\n> more slowly than 1/r^2 as you go further out. And it does. But, the\n> observed acceleration drops off a lot more slowly than the acceleration\n> people calculate from the mass they see. It\'s not a small effect: it\'s a\n> HUGE effect!\n>\n> One solution is to say there\'s a lot of mass we don\'t see: "dark matter"\n> of some sort. If you take this route, which most astronomers do, you\'re\n> forced to say that *most* of the mass of galaxies is in the form of dark\n> matter.\n>\n> Milgrom\'s solution is to say that Newton\'s laws are messed up.\n>\n> Of course this is a drastic, dangerous step: the last guy who tried this\n> was named Einstein, and we all know what happened to him. Milgrom\'s\ntheory\n> isn\'t even based on deep reasoning and beautiful math like Einstein\'s!\n> Instead, it\'s just a blatant attempt to fit the experimental data.\n> And it\'s not even elegant. In fact, it\'s downright ugly.\n>\n> Here\'s what it says: the usual Newtonian formula for the acceleration\n> due to gravity is correct as long as the acceleration is bigger than\n>\n> a = 2 x 10^{-10} m/sec^2\n>\n> But, for accelerations less than this, you take the geometric mean\n> of the acceleration Newton would predict and this constant a.\n>\n> In other words, there\'s a certain value of acceleration such that above\n> this value, the Newtonian law of gravity works as usual, while below this\n> value the law suddenly changes.\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." Not in fundamental\n> physics, anyway! Sure, water is solid below 0 centigrade and fluid above\n> this, but that\'s not a fundamental law - it presumably follows from other\n> stuff. Not that anyone has derived the melting point of ice from first\n> principles, mind you. But we think we could if we were better at big\n> messy calculations.\n>\n> Furthermore, you can\'t easily invent a Lagrangian for gravity that makes\n> it fall off more *slowly* than 1/r^2. It\'s easy to get it to fall off\n> *faster* - just give the graviton a mass, for example! But not more\n> slowly. It turns out you can do it - Bekenstein and Milgrom have a way -\n> but it\'s incredibly ugly.\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! In some cases it matches the observed rotation of\n> galaxies in an appallingly accurate way, fitting every wiggle in the graph\n> of stellar rotation velocity as a function of distance from the center.\n>\n> So, even if MOND is wrong, there may need to be some reason why it *acts*\n> like it\'s right! Apparently even some proponents of dark matter agree\n> with this.\n>\n> But: take everything I\'m saying here with a grain of salt. I\'m no expert\n> on this stuff, so if you know any astrophysics you should read the\n> literature and make up your own mind.\n>\n> Here are two reviews that Smolin especially recommended:\n>\n> 13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics\n> as an Alternative to Dark Matter, available as astro-ph/0204521.\n>\n> 14) Anthony Aguirre, Alternatives to dark matter (?), available as\n> astro-ph/0310572.\n>\n> Here\'s McGaugh\'s website with links to many papers on MOND, including\n> Milgrom\'s original papers:\n>\n> 15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html\n>\n> McGaugh is a strong proponent of MOND - though he didn\'t start out that\n> way - so the selection may be biased. Does anyone know an intelligent\n> detailed critique of MOND? If so, I want to see it! We can\'t throw out\n> Newton\'s law of gravity (or more precisely, general relativity, which has\n> Newtonian gravity as a limiting case for low densities and low velocities)\n> unless we have *very* good reasons! So we have to think about things\n> carefully, and weigh the evidence on both sides.\n>\n> If I could duplicate myself, I\'d have one copy try to get to the bottom\n> of this dark matter / MOND puzzle. But I can\'t...\n>\n> ... so if you\'re an expert who knows a lot about this, let me\n> know what you think - or better yet, post an article about this to\n> sci.physics.research!\n>\n> -----------------------------------------------------------------------\n> Previous issues of "This Week\'s Finds" and other expository articles on\n> mathematics and physics, as well as some of my research papers, can be\n> obtained at\n>\n> http://math.ucr.edu/home/baez/\n>\n> For a table of contents of all the issues of This Week\'s Finds, try\n>\n> http://math.ucr.edu/home/baez/twf.html\n>\n> A simple jumping-off point to the old issues is available at\n>\n> http://math.ucr.edu/home/baez/twfshort.html\n>\n> If you just want the latest issue, go to\n>\n> http://math.ucr.edu/home/baez/this.week.html\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>I checked out this article: http://www.astro.umd.edu/~ssm/mond/astronow.html
and there's an example of a graph of rotation velocity vs. radius showing
one of the wiggles JB mentions, with the note "even the kink observed in the
gas distribution is reflected in the rotation".

Forgive me for being a little sceptical but the Newtonian prediction has
exactly the same kink. In fact, the MOND curve is just the Newtonian curve
scaled up. Just about any reasonably well behaved modification of the
Newtonian formula that has a scaling effect that brings the Newtonian curve
roughly in alignment with measured results is going to have that kink. So
while it may be impressive that MOND predicts this overall scaling
correctly, I'm not in the least bit impressed with it managing to match this
wiggle. Are there examples where MOND predicts a wiggle that simply isn't
present in the Newtonian case. That'd be impressive.

Or am I misinterpreting the graph?
--
Torque

"John Baez" <baez@math.removethis.ucr.andthis.edu> wrote in message
news:c7pbsa$p9$1@glue.ucr.edu...
>
>
> Also available at http://math.ucr.edu/home/baez/week206.html
>
> May 10, 2004
> This Week's Finds in Mathematical Physics - Week 206
> John Baez
>
> I just got back from Marseille, where Carlo Rovelli, Laurent Freidel
> and Phillipe Roche held the first really big conference on loop quantum
> gravity and spin foams since the 2nd Warsaw workshop run by Jerzy
> Lewandowski back in 1997:
>
> 1) Non Perturbative Quantum Gravity: Loops and Spin Foams,
> 3-7 May 2004, CIRM, Luminy, Marseille, France,
> http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/
>
> It was good to see old friends and talk about quantum gravity near
> the "Calanques" - the rugged limestone cliffs lining the Mediterranean
> coastline. 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. But most of all, it was good to
> see some progress on the tough problem of understanding dynamics in
> nonperturbative quantum gravity.
>
> 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*?
>
> 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? 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. But, the
> main lesson of general relativity is that spacetime is *not* a fixed
> stage: it's a lively, dynamical entity! There's no good way to separate
> the ripples from the lake. This distinction is no more than a convenient
> approximation - and a dangerous one at that.
>
> So, we should learn to make do without a background when studying quantum
> gravity. But it's tough! 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!
>
> 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!
>
> 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.
>
> String theorists are pragmatic in a certain sense: they don't mind using
> a background, and they don't mind doing what physicists always do:
> 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. Some estimates guess there are over
> 10^{100}. Leonard Susskind guesses there are 10^{500}, and argues that
> we'll need the anthropic principle to choose the one describing our
> world:
>
> 2) Leonard Susskind, The Landscape, article and interview on John
> Brockman's "EDGE" website,
> http://www.edge.org/3rd_culture/susskind03/susskind_index.html
>
> 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. 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. So, it's quite possible that our failures
> with the former are just a matter of inexperience.
>
> Given all this, I'm delighted to see some real progress on getting 4d
> spacetime to emerge from nonperturbative quantum gravity:
>
> 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.
>
> This trio of researchers have revitalized an approach called "dynamical
> triangulations" where we calculate path integrals in quantum gravity by
> summing over different ways of building spacetime out of little
4-simplices.
> They showed that if we restrict this sum to spacetimes with a well-behaved
> concept of causality, we get good results. This is a bit startling,
> because after decades of work, most researchers had despaired of getting
> general relativity to emerge at large distances starting from the
dynamical
> triangulations approach. But, these people hadn't noticed a certain flaw
> in the approach... a flaw which Loll and collaborators noticed and fixed!
>
> If you don't know what a path integral is, don't worry: it's pretty
> simple. Basically, in quantum physics we can calculate the expected value
> of any physical quantity by doing an average over all possible histories
> of the system in question, with each history weighted by a complex number
> called its "amplitude". For a particle, a history is just a path in
> space; to average over all histories is to integrate over all paths -
> hence the term "path integral". But in quantum gravity, a history is
> nothing other than a SPACETIME.
>
> Mathematically, a "spacetime" is something like a 4-dimensional manifold
> equipped with a Lorentzian metric. But it's hard to integrate over all
> of these - there are just too darn many. So, sometimes people instead
> treat spacetime as made of little discrete building blocks, turning
> the path integral into a sum. You can either take this seriously or treat
> it as a kind of approximation. Luckily, the calculations work the same
> either way!
>
> If you're looking to build spacetime out of some sort of discrete building
> block, a handy candidate is the "4-simplex": the 4-dimensional analogue
> of a tetrahedron. This shape is rigid once you fix the lengths of its 10
> edges, which correspond to the 10 components of the metric tensor in
> general relativity.
>
> There are lots of approaches to the path integrals in quantum gravity
> that start by chopping spacetime into 4-simplices. The weird special
> thing about dynamical triangulations is that here we usually assume
> every 4-simplex in spacetime has the same shape. The different spacetimes
> arise solely from different ways of sticking the 4-simplices together.
>
> Why such a drastic simplifying assumption? To make calculations quick
> and easy! The goal is get models where you can simulate quantum geometry
> on your laptop - or at least a supercomputer. The hope is that
simplifying
> assumptions about physics at the Planck scale will wash out and not make
> much difference on large length scales.
>
> 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. Given this, it seems we're bound to get general relativity at
> large distance scales - perhaps with a nonzero cosmological constant, and
> perhaps including various forms of matter.
>
> Unfortunately, in all previous dynamical triangulation models, the path
> integral was *NOT* dominated by spacetimes that look like nice 4d
manifolds
> from afar! Depending on the details, one either got a "crumpled phase"
> dominated by spacetimes where almost all the 4-simplices touch each other,
> or a "branched polymer phase" dominated by spacetimes where the
4-simplices
> form treelike structures. There's a transition between these two phases,
> but unfortunately it seems to be a 1st-order phase transition - not the
> sort we can get anything useful out of. For a nice review of these
> calculations, see:
>
> 4) Renate Loll, Discrete approaches to quantum gravity in four dimensions,
> available as http://www.arxiv.org/abs/gr-qc/9805049 or as a website at Living Reviews in
Relativity,
> http://www.livingreviews.org/Articles/Volume1/1998-13loll/
>
> Luckily, all these calculations shared a common flaw!
>
> Computer calculations of path integrals become a lot easier if instead of
> assigning a complex "amplitude" to each history, we assign it a positive
> real number: a "relative probability". The basic reason is that unlike
> positive real numbers, complex numbers can cancel out when you sum them!
>
> When we have relative probabilities, it's the *highly probable* histories
> that contribute most to the expected value of any physical quantity. We
> can use something called the "Metropolis algorithm" to spot these highly
> probable histories and spend most of our time worrying about them.
>
> 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!
>
> For this reason, physicists often use a trick called "Wick rotation"
> that converts amplitudes to relative probabilities. To do this trick, we
> just replace time by imaginary time! In other words, wherever we see the
> variable "t" for time in any formula, we replace it by "it". Magically,
> this often does the job: our amplitudes turn into relative probabilities!
> We then go ahead and calculate stuff. Then we take this stuff and go
> back and replace "it" everywhere by "t" to get our final answers.
>
> While the deep inner meaning of this trick is mysterious, it can be
> justified in a wide variety of contexts using the "Osterwalder-Schrader
> theorem". Here's a pretty general version of this theorem, suitable
> for quantum gravity:
>
> 5) Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann,
> Osterwalder-Schrader reconstruction and diffeomorphism invariance,
> preprint available as http://www.arxiv.org/abs/quant-ph/9904094.
>
> People use Wick rotation in all work on dynamical triangulations.
> Unfortunately, this is *not* a context where you can justify this trick
> by appealing to the Osterwalder-Schrader theorem. The problem is that
> there's no good notion of a time coordinate "t" on your typical
> spacetime built by sticking together a bunch of 4-simplices!
>
> The new work by Ambjorn, Jurkiewiecz and Loll deals with this by
> restricting to spacetimes that *do* have a time coordinate. More
> precisely, they fix a 3-dimensional manifold and consider all possible
> triangulations of this manifold by regular tetrahedra. These are the
> allowed "slices" of spacetime - they represent different possible
> geometries of space at a given time. They then consider spacetimes
> having slices of this form joined together by 4-simplices in a few
> simple ways.
>
> The slicing gives a preferred time parameter "t". On the one hand this
> goes against our desire in general relativity to avoid a preferred time
> coordinate - but on the other hand, it allows Wick rotation. So, they
> can use the Metropolis algorithm to compute things to their hearts'
> content and then replace "it" by "t" at the end.
>
> 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! Take a look at their graphs
> and pictures - a picture is worth a thousand words.
>
> Naturally, what *I'd* like to do is use their work to develop some spin
> foam models with better physical behavior than the ones we have so far.
> Now that Loll and her collaborators have gotten something that works,
> we can try to fiddle around and make it more elegant while making sure it
> still works. In particular, I'm hoping we can get well-behaved models
> that don't introduce a preferred time coordinate as long as they rule out
> "topology change" - that is, slicings where the topology of space changes.
> After all, the Osterwalder-Schrader theorem doesn't require a *preferred*
> time coordinate, just *any* time coordinate together with good behavior
> under change of time coordinate. For this we mainly need to rule out
> topology change. Moreover, Loll and her collaborators have argued in 2d
> toy models that topology change is one thing that makes models go bad: the
> path integral can get dominated by spacetimes where "baby universes" keep
> branching off the main one:
>
> 6) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative
> Lorentzian quantum gravity, causality and topology change, Nucl. Phys.
> B536 (1998) 407-434. Also available as http://www.arxiv.org/abs/hep-th/9805108.
>
> Renate Loll and W. Westra, Space-time foam in 2d and the sum over
> topologies, Acta Phys. Polon. B34 (2003) 4997-5008. Also available as
> http://www.arxiv.org/abs/hep-th/0309012.
>
> By the way, it's also reading about their 3d model:
>
> 7) Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative 3d
> Lorentzian quantum gravity, Phys.Rev. D64 (2001) 044011. Also available
> as http://www.arxiv.org/abs/hep-th/0011276.
>
> and for a general review, try this:
>
> 8) Renate Loll, A discrete history of the Lorentzian path integral,
> Lecture Notes in Physics 631, Springer, Berlin, 2003, pp. 137-171.
> Also available as http://www.arxiv.org/abs/hep-th/0212340.
>
> All this is great, but don't get me wrong - there were a lot of *other*
> cool talks at the conference besides Loll's. I'll just mention a few.
>
> Laurent Freidel spoke on his work on spin foam models. Especially
> exciting is how David Louapre and he have managed to "sum over
> topologies" in 3d Riemannian quantum gravity with vanishing cosmological
> constant - otherwise known as the Ponzano-Regge model He has to subtract
> out a counterterm that would otherwise lead to a bubble divergence, but
> then he gets a beautiful theory where the sum over spin foams is Borel
> summable:
>
> 9) Laurent Freidel and David Louapre, Non-perturbative summation over
> 3D discrete topologies, Phys.Rev. D68 (2003) 104004. Also available as
> http://www.arxiv.org/abs/hep-th/0211026.
>
> Their work on gauge-fixing and the inclusion of spinning point particles
> in the Ponzano-Regge model is also very impressive, especially given how
> long this model has been studied. It shows we have lots left to learn!
>
> 10) Laurent Freidel and David Louapre, Ponzano-Regge model revisited I:
> Gauge fixing, observables and interacting spinning particles, available
> as http://www.arxiv.org/abs/hep-th/0401076.
>
> The title suggests we're in for more treats to come.
>
> Kirill Krasnov gave a talk entitled simple "ln(3)" - it was all about
> the appearance of this constant in the work of Hod, Dreyer, Motl and
> Neitzke on black hole entropy and the ringing of black holes. I've
> discussed all this at length in "week198", but Krasnov has given an
elegant
> new proof of Hod's conjecture using Riemann surface theory. One can
> even think of this as a "stringy" explanation of the quasinormal modes
> of black holes - but much remains mysterious here:
>
> 11) Kirill Krasnov, Black hole thermodynamics and Riemann surfaces,
> Class. Quant. Grav. 20 (2003) 2235-2250. Also available as http://www.arxiv.org/abs/gr-qc/0302073.
>
> Kirill Krasnov and Sergey N. Solodukhin, Effective stringy description
> of Schwarzschild black holes, available as http://www.arxiv.org/abs/hep-th/0403046.
>
> While I'm at it, I can't resist mentioning Krasnov's work on including
> point particles in 3d Lorentzian quantum gravity with negative
> cosmological constant, since it has close connections with that of
> Freidel and Louapre, though the context is a bit different:
>
> 12) Kirill Krasnov, \Lambda<0 quantum gravity in 2+1 dimensions I:
> quantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002)
> 3977-3998. Also available as http://www.arxiv.org/abs/hep-th/0112164.
>
> Kirill Krasnov, \Lambda<0 quantum gravity in 2+1 dimensions II:
> black hole creation by point particles, Class. Quant. Grav. 19 (2002)
> 3999-4028. Also available as http://www.arxiv.org/abs/hep-th/0202117.
>
> If I could duplicate myself, I'd have one copy write a book on 3d quantum
> gravity that would synthesize all these wonderful results in a nice big
> picture. It's not realistic physics; it's just a toy model. But the
> math is *so* nice, and so enlightening for real-world physics in some
> ways, that it's hard to resist pondering it! TQFTs, Riemann surfaces,
> hyperbolic geometry, spinning point particles colliding and creating
> black holes - a wonderful stew! Alas, I don't have time to savor it.
>
> There were a lot of other interesting talks - but I don't have time to go
> through and describe all of them, either. So, I'll wrap up with something
> very different!
>
> Lee Smolin told me some neat stuff about MOND - that's "Modified
> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
> the strange behavior of galaxies without invoking dark matter. The basic
> problem with galaxies is that the outer parts rotate faster than they
> should given how much mass we actually see.
>
> If you have a planet in a circular orbit about the Sun, Newton's laws
> say its acceleration is proportional to 1/r^2, where r is its distance to
> the Sun. Similarly, if almost all the mass in a galaxy were concentrated
> right at the center, a star orbiting in a circle at distance r from the
> center would have acceleration proportional to 1/r^2. Of course, not all
> the mass is right at the center! So, the acceleration should drop off
> more slowly than 1/r^2 as you go further out. And it does. But, the
> observed acceleration drops off a lot more slowly than the acceleration
> people calculate from the mass they see. It's not a small effect: it's a
> HUGE effect!
>
> One solution is to say there's a lot of mass we don't see: "dark matter"
> of some sort. If you take this route, which most astronomers do, you're
> forced to say that *most* of the mass of galaxies is in the form of dark
> matter.
>
> Milgrom's solution is to say that Newton's laws are messed up.
>
> Of course this is a drastic, dangerous step: the last guy who tried this
> was named Einstein, and we all know what happened to him. Milgrom's
theory
> isn't even based on deep reasoning and beautiful math like Einstein's!
> Instead, it's just a blatant attempt to fit the experimental data.
> And it's not even elegant. In fact, it's downright ugly.
>
> Here's what it says: the usual Newtonian formula for the acceleration
> due to gravity is correct as long as the acceleration is bigger than
>
> a = 2 x 10^{-10} m/sec^2
>
> But, for accelerations less than this, you take the geometric mean
> of the acceleration Newton would predict and this constant a.
>
> In other words, there's a certain value of acceleration such that above
> this value, the Newtonian law of gravity works as usual, while below this
> value the law suddenly changes.
>
> 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." Not in fundamental
> physics, anyway! Sure, water is solid below centigrade and fluid above
> this, but that's not a fundamental law - it presumably follows from other
> stuff. Not that anyone has derived the melting point of ice from first
> principles, mind you. But we think we could if we were better at big
> messy calculations.
>
> Furthermore, you can't easily invent a Lagrangian for gravity that makes
> it fall off more *slowly* than 1/r^2. It's easy to get it to fall off
> *faster* - just give the graviton a mass, for example! But not more
> slowly. It turns out you can do it - Bekenstein and Milgrom have a way -
> but it's incredibly ugly.
>
> 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! In some cases it matches the observed rotation of
> galaxies in an appallingly accurate way, fitting every wiggle in the graph
> of stellar rotation velocity as a function of distance from the center.
>
> So, even if MOND is wrong, there may need to be some reason why it *acts*
> like it's right! Apparently even some proponents of dark matter agree
> with this.
>
> But: take everything I'm saying here with a grain of salt. I'm no expert
> on this stuff, so if you know any astrophysics you should read the
> literature and make up your own mind.
>
> Here are two reviews that Smolin especially recommended:
>
> 13) Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics
> as an Alternative to Dark Matter, available as http://www.arxiv.org/abs/astro-ph/0204521.
>
> 14) Anthony Aguirre, Alternatives to dark matter (?), available as
> http://www.arxiv.org/abs/astro-ph/0310572.
>
> Here's McGaugh's website with links to many papers on MOND, including
> Milgrom's original papers:
>
> 15) The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html
>
> McGaugh is a strong proponent of MOND - though he didn't start out that
> way - so the selection may be biased. Does anyone know an intelligent
> detailed critique of MOND? If so, I want to see it! We can't throw out
> Newton's law of gravity (or more precisely, general relativity, which has
> Newtonian gravity as a limiting case for low densities and low velocities)
> unless we have *very* good reasons! So we have to think about things
> carefully, and weigh the evidence on both sides.
>
> If I could duplicate myself, I'd have one copy try to get to the bottom
> of this dark matter / MOND puzzle. But I can't...
>
> ... so if you're an expert who knows a lot about this, let me
> know what you think - or better yet, post an article about this to
> sci.physics.research!
>
> -----------------------------------------------------------------------
> Previous issues of "This Week's Finds" and other expository articles on
> mathematics and physics, as well as some of my research papers, can be
> obtained at
>
> http://math.ucr.edu/home/baez/
>
> For a table of contents of all the issues of This Week's Finds, try
>
> http://math.ucr.edu/home/baez/twf.html
>
> A simple jumping-off point to the old issues is available at
>
> http://math.ucr.edu/home/baez/twfshort.html
>
> If you just want the latest issue, go to
>
> http://math.ucr.edu/home/baez/this.week.html

=?ISO-8859-1?Q?Morris_Carr=E9?=

May14-04, 05:13 AM

<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>ebunn@lfa221051.richmond.edu wrote:\n\n> then the actual acceleration of an object is\n>\n> a = a_N if a_N > a_0\n> a = sqrt(a_N a_0) if a < a_0\n>\n> Here a_0 is some fundamental constant.\n\nAm I dreaming, or isn\'t there something "planckscalish" to the idea ?\n\nMakes one wonder why this isn\'t tried by doctoring perhaps not acceleration,\nbut any dimension appropriate to a similar treatment by simplest form of\ndeviation to the general law, below the Planck scale appropriate for the\ndimension. Or is it the case that the existence/legitimacy of MOND reads as\nthe symptom that the community has already tried every obvious avenue of what\nI just proposed, so that it is now exploring variants with a relaxed\nunderstanding of the "effective planck scale" ? Or that the MOND proponents\nactually think of their a_0 as a genuine member of the admitted family of\nplanck scales ?\n\nTIA for clarifications,\n\nMorris Carr=E9\n--\npy>>> assert "BUSH" <> filter(lambda W : W not in "ILLITERATE","********"=\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>ebunn@lfa221051.richmond.edu wrote:

> then the actual acceleration of an object is
>
> a = a_N if a_N > a_0
> a = \sqrt(a_N a_0) if a < a_0
>
> Here a_0 is some fundamental constant.

Am I dreaming, or isn't there something "planckscalish" to the idea ?

Makes one wonder why this isn't tried by doctoring perhaps not acceleration,
but any dimension appropriate to a similar treatment by simplest form of
deviation to the general law, below the Planck scale appropriate for the
dimension. Or is it the case that the existence/legitimacy of MOND reads as
the symptom that the community has already tried every obvious avenue of what
I just proposed, so that it is now exploring variants with a relaxed
understanding of the "effective planck scale" ? Or that the MOND proponents
actually think of their a_0 as a genuine member of the admitted family of
planck scales ?

TIA for clarifications,

Morris Carr=E9
--
py>>> assert "BUSH" <> filter(\lambda W : W not in "ILLITERATE","********"=
)

John Baez

May15-04, 03:45 AM

<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>In article <24a23f36.0405112105.6569f265@posting.google.com>, \nThomas Larsson <thomas_larsson_01@hotmail.com> wrote:\n\n>baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message\n>news:<c7pbsa\\$p9\\$1@glue.ucr.edu>...\n \n>> Given all this, I\'m delighted to see some real progress on getting 4d\n>> spacetime to emerge from nonperturbative quantum gravity:\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\n>This is pretty exciting.\n\nI\'m glad you think so! I sure do!\n\n>It is sort of obvious that you can formally\n>put gravity on a lattice, but I always thought that there wasn\'t a\n>continuum limit.\n\nRight - this is what everyone thought, except for a few people\nwho argued that Euclidean quantum gravity calculations were\nirrelevant to the real Lorentzian world unless one did them in\na way where Wick rotation was justified. See below for my\ndiscussion of this with Jacques Distler back in 2001. My\nattempt to get around this was to develop discretized models\nof Lorentzian quantum gravity that completely avoid Euclidean\ntechniques; this hasn\'t succeeded yet. Loll\'s approach was to\ndevelop discretized models of Lorentzian quantum gravity where\nWick rotation is justified, and then do calculations in the\nEuclidean realm and analytically continue back. This seems to\nbe working.\n\n>If the numerical evidence in this paper is true, and\n>it seems quite strong, then we see a new field open up here, perhaps\n>like when Wilson invented lattice gauge theory in 1974. A lot of\n>interesting things can be done, e.g. to apply standard techniques in\n>lattice models, introduce gauge and fermion fields, and try to find\n>different continuum formulations. I would not be surprised if this is\n>the next bandwagon and a lot of smart people will jump onto it.\n\nSmart or not, I\'m hoping to work on it with Dan Christensen,\nand Fotini Markopoulou told me she was planning to work on it\nwith a grad student of hers.\n\nAs you\'ll see from the discussion below, Distler agreed with me\nthat old-school Euclidean quantum gravity was "phoney-baloney" -\nbut he didn\'t expect doing things right to save quantum gravity in\n4 dimensions. Now Loll & Co.\'s work seems to be showing otherwise...\nbut it\'s still too early to be sure: there are a lot of things to\ncheck!\n\n.................................... ......................................\n\nFrom: baez@galaxy.ucr.edu (John Baez)\nNewsgroups: sci.physics.research\nSubject: The discrete charm of quantum gravity\nDate: Mon, 2 Jul 2001 21:02:39 +0000 (UTC)\nMessage-ID: <9hqnhf\\$6lk\\$1@glue.ucr.edu>\n\nIn article <p05100301b761dbc8a381@golem.ph.utexas.edu>,\nJacq ues Distler <distler@golem.ph.utexas.edu> wrote:\n\n>Mind you, there are a zillion ways to define a lattice-regularized\n>theory of quantum "gravity" (Regge calculus, dynamic triangulations,\n>LQG, MQG, . . .). People like Ambjorn, Hamber, Gross and others have\n>spent years doing Monte Carlo simulations in various of these lattice\n>approaches. The upshot is the NONE of these approaches have YET been\n>seen to have a "continuum" (large-volume spacetime) limit. They ALWAYS\n>turn out to be in some horrible crumpled phase where the dominant\n>spactimes have Planckian curvatures and Planckian sizes.\n\nThat\'s true as far as it goes, but it\'s worth noting a crucial catch.\n\nALL the Monte Carlo simulations you mention were studying theories\nof "Euclidean quantum gravity", where we take the Einstein-Hilbert\naction S for Riemannian metrics and do a discretized version of\nthe path integral involving exp(-S). The people doing these calculations\nALWAYS crossed their fingers and hoped, for no very good reason, that\ntheir results would be relevant to what we\'re really terested in:\nLorentzian quantum gravity, where we take the action S for *Lorentzian*\nmetrics and do a path integral involving *exp(iS)*. They NEVER justified\nthis assumption.\n\nOf course in ordinary quantum field theory on flat spacetime, we can\njustify the switch from exp(-S) to exp(iS) via Wick rotation, which\nis naively the substitution t -> it. However, for the calculations\nin question here there is no good way to justify this trick... and\nthere are good reasons to doubt it will work:\n\n1) there is no god-given time parameter t here, so we don\'t\nknow how to do the replacement t -> it.\n\n2) in theories which allow topology change in the Euclidean context,\nWick rotation is especially problematic, since the spacetime isn\'t\neven of the form R x S.\n\nThus many workers in quantum gravity have long doubted the relevance\nof the Monte Carlo calculations you mention.\n\nBut here\'s the really cool part:\n\nRecently, Ambjorn has switched tactics and begun to do calculations\nwith Renate Loll in models where you *can* rigorously justify Wick\nrotation. If you take these models and do things the bad old way -\nnot making sure to do the stuff needed to justify the process of\nWick rotation - you get the bad old results: for example, fractal\nspacetimes. But if you do things the right way, you get good results -\nnice spacetimes that have the dimensions they\'re supposed to!\n\nAmbjorn, Loll and others have both analytical and numerical results\nin 2d models of this sort. They are also tackling 4d models, which\nare too complicated to study analytically, but are well-suited to numerical\ncalculation. This work should eventually hook up with spin foam models\nof 4d quantum gravity in an interesting way, since the Barrett-Crane spin\nfoam model provides a well-defined *Lorentzian* discretized path integral\nfor general relativity.\n\nOf course, it\'s not clear that things will work even when we do things\nright. But there\'s really no excuse for doing the wrong calculation and\nthen blaming quantum gravity for the bad results!\n\nHere are 2 places to read more:\n\nDiscrete Lorentzian Quantum Gravity\nRenate Loll\nNucl. Phys. Proc. Suppl. 94 (2001) 96-107\nhttp://xxx.lanl.gov/abs/hep-th/0011194\n\nAbstract:\n\nJust as for non-abelian gauge theories at strong coupling, discrete lattice\nmethods are a natural tool in the study of non-perturbative quantum gravity.\nThey have to reflect the fact that the geometric degrees of freedom are\ndynamical, and that therefore also the lattice theory must be formulated\nin a background-independent way. After summarizing the status quo of\ndiscrete covariant lattice models for four-dimensional quantum gravity,\nI describe a new class of discrete gravity models whose starting point\nis a path integral over Lorentzian (rather than Euclidean) space-time\ngeometries. A number of interesting and unexpected results that have\nbeen obtained for these dynamically triangulated models in two and three\ndimensions make discrete Lorentzian gravity a promising candidate for a\nnon-trivial theory of quantum gravity.\n\n\nEuclidean and Lorentzian Quantum Gravity - Lessons from Two Dimensions\nJ. Ambjorn, J.L. Nielsen, J. Rolf, R. Loll\nChaos Solitons Fractals 10 (1999) 177-195\nhttp://xxx.lanl.gov/abs/hep-th/9806241\n\nAbstract:\n\nNo theory of four-dimensional quantum gravity exists as yet. In this\nsituation the two-dimensional theory, which can be analyzed by conventional\nfield-theoretical methods, can serve as a toy model for studying some\naspects of quantum gravity. It represents one of the rare settings in a\nquantum-gravitational context where one can calculate quantities truly\nindependent of any background geometry. We review recent progress in our\nunderstanding of 2d quantum gravity, and in particular the relation\nbetween the Euclidean and Lorentzian sectors of the quantum theory.\nWe show that conventional 2d Euclidean quantum gravity can be obtained from\nLorentzian quantum gravity by an analytic continuation only if we allow\nfor spatial topology changes in the latter. Once this is done, one\nobtains a theory of quantum gravity where space-time is fractal: the\nintrinsic Hausdorff dimension of usual 2d Euclidean quantum gravity is\nfour, and not two. However, certain aspects of quantum space-time remain\ntwo-dimensional, exemplified by the fact that its so-called spectral\ndimension is equal to two.\n\n.......................................... .................................\n\nFrom: Jacques Distler <distler@golem.ph.utexas.edu>\nNewsgroups: sci.physics.research\nSubject: Re: The discrete charm of quantum gravity\nDate: Wed, 04 Jul 2001 07:01:13 GMT\nOrganization: Physics Department, University of Texas at Austin\nMessage-ID: <Zaz07.14184\\$WT.3025922@typhoon.austin.rr.com>\n Originator: baez@math-cl-n05.math.ucr.edu (John Baez)\n\nIn article\n<Pine.SOL.4.10.10107022247260.3017-100000@physsun3.rutgers.edu>,\nLubos Motl <motl@physics.rutgers.edu> wrote:\n\n>John Baez wrote:\n\n>> Thus many workers in quantum gravity have long doubted the relevance\n>> of the Monte Carlo calculations you mention.\n>>\n>> Of course, it\'s not clear that things will work even when we do things\n>> right. But there\'s really no excuse for doing the wrong calculation and\n>> then blaming quantum gravity for the bad results!\n\n>This logic is very far from what I consider a rational approach. It is a\n>well-known fact that the path integral is more well-defined in the\n>Euclidean context. For example, there exists a rigorous definition of the\n>functional measure in the case of exp(-S) - while mathematicians have\n>proved that there is no measure on the functional spaces (defined in the\n>mathematically rigorous way) associated with exp(iS) in the Feynman\n>integral.\n>\n>The integrals with exp(-S) are more convergent. They behave better. The\n>questions of topology are clearer - therefore also string theorists like\n>to use Euclidean worldsheets to compute the amplitudes - although they can\n>show the equivalence of those amplitudes to the amplitudes computed from a\n>Minkowski light-cone gauge Hamiltonian. In every reasonable theory that\n>people have seen, the Wick rotation is a legitimate tool.\n\nEuclidean worldsheets and Euclidean target spaces are a totally\ndifferent matter. John is talking about Euclidean target spaces.\n\nFor a general (d-1,1)- manifold, there is no reasonable notion of\nWick-rotation. Indeed, in 2+1 dimensional gravity (formulated as a\nChern-Simons gauge theory), the Euclidean and Minkowskian theories are\ntotally different; they are not related by Wick rotation.\n\nMore to the point (as I alluded to in my post), the Euclidean path\nintegral for the Einstein-Hilbert action -- in the semiclassical\napproximation -- contains known pathologies (the Euclidean action is\nunbounded from below). So in no sense is exp(-S) better behaved than\nexp(iS) for (semiclassical) gravity.\n\nFor these and other reasons, it is NOT unreasonable to say that gravity\nmust be understood in the Minkowskian signature and that you can\'t use\nsome phoney-baloney Wick rotation to Euclidean signature study it.\n\nNone of this detracts from your basic intuition that, whatever tricks\nmay serve to define a continuum limit of a theory of lattice gravity in\n2 or 3 dimensions will not generalize to 4 dimensions.\n\nIt was, actually, surprising that lattice gravity in 3 dimensions did\nnot (heretofore) appear to have a continuum limit even though we knew\nperfectly well that there *was* a continuum theory of 3D quantum gravity.\n\nAmbjorn and collaborators have repaired this apparent breakdown of the\nlattice approach in 3D. But I do not believe that their results have\nmuch promise of producing a "miracle" in 4D.\n\nJacques\n\n--\nPGP public key: http://golem.ph.utexas.edu/~distler/distler.asc\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>In article <24a23f36.0405112105.6569f265@posting.google.com>,
Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:

>baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message
>news:<c7pbsa$p9$1@glue.ucr.edu>...

>> Given all this, I'm delighted to see some real progress on getting 4d
>> spacetime to emerge from nonperturbative quantum gravity:
>>
>> 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.

>This is pretty exciting.

I'm glad you think so! I sure do!

>It is sort of obvious that you can formally
>put gravity on a lattice, but I always thought that there wasn't a
>continuum limit.

Right - this is what everyone thought, except for a few people
who argued that Euclidean quantum gravity calculations were
irrelevant to the real Lorentzian world unless one did them in
a way where Wick rotation was justified. See below for my
discussion of this with Jacques Distler back in 2001. My
attempt to get around this was to develop discretized models
of Lorentzian quantum gravity that completely avoid Euclidean
techniques; this hasn't succeeded yet. Loll's approach was to
develop discretized models of Lorentzian quantum gravity where
Wick rotation is justified, and then do calculations in the
Euclidean realm and analytically continue back. This seems to
be working.

>If the numerical evidence in this paper is true, and
>it seems quite strong, then we see a new field open up here, perhaps
>like when Wilson invented lattice gauge theory in 1974. A lot of
>interesting things can be done, e.g. to apply standard techniques in
>lattice models, introduce gauge and fermion fields, and try to find
>different continuum formulations. I would not be surprised if this is
>the next bandwagon and a lot of smart people will jump onto it.

Smart or not, I'm hoping to work on it with Dan Christensen,
and Fotini Markopoulou told me she was planning to work on it
with a grad student of hers.

As you'll see from the discussion below, Distler agreed with me
that old-school Euclidean quantum gravity was "phoney-baloney" -
but he didn't expect doing things right to save quantum gravity in
4 dimensions. Now Loll & Co.'s work seems to be showing otherwise...
but it's still too early to be sure: there are a lot of things to
check!

.................................................. ........................

From: baez@galaxy.ucr.edu (John Baez)
Newsgroups: sci.physics.research
Subject: The discrete charm of quantum gravity
Date: Mon, 2 Jul 2001 21:02:39 +0000 (UTC)
Message-ID: <9hqnhf$6lk$1@glue.ucr.edu>

In article <p05100301b761dbc8a381@golem.ph.utexas.edu>,
Jacques Distler <distler@golem.ph.utexas.edu> wrote:

>Mind you, there are a zillion ways to define a lattice-regularized
>theory of quantum "gravity" (Regge calculus, dynamic triangulations,
>LQG, MQG, . . .). People like Ambjorn, Hamber, Gross and others have
>spent years doing Monte Carlo simulations in various of these lattice
>approaches. The upshot is the NONE of these approaches have YET been
>seen to have a "continuum" (large-volume spacetime) limit. They ALWAYS
>turn out to be in some horrible crumpled phase where the dominant
>spactimes have Planckian curvatures and Planckian sizes.

That's true as far as it goes, but it's worth noting a crucial catch.

ALL the Monte Carlo simulations you mention were studying theories
of "Euclidean quantum gravity", where we take the Einstein-Hilbert
action S for Riemannian metrics and do a discretized version of
the path integral involving \exp(-S). The people doing these calculations
ALWAYS crossed their fingers and hoped, for no very good reason, that
their results would be relevant to what we're really terested in:
Lorentzian quantum gravity, where we take the action S for *Lorentzian*
metrics and do a path integral involving *\exp(iS)*. They NEVER justified
this assumption.

Of course in ordinary quantum field theory on flat spacetime, we can
justify the switch from \exp(-S) to \exp(iS) via Wick rotation, which
is naively the substitution t -> it. However, for the calculations
in question here there is no good way to justify this trick... and
there are good reasons to doubt it will work:

1) there is no god-given time parameter t here, so we don't
know how to do the replacement t -> it.

2) in theories which allow topology change in the Euclidean context,
Wick rotation is especially problematic, since the spacetime isn't
even of the form R x S.

Thus many workers in quantum gravity have long doubted the relevance
of the Monte Carlo calculations you mention.

But here's the really cool part:

Recently, Ambjorn has switched tactics and begun to do calculations
with Renate Loll in models where you *can* rigorously justify Wick
rotation. If you take these models and do things the bad old way -
not making sure to do the stuff needed to justify the process of
Wick rotation - you get the bad old results: for example, fractal
spacetimes. But if you do things the right way, you get good results -
nice spacetimes that have the dimensions they're supposed to!

Ambjorn, Loll and others have both analytical and numerical results
in 2d models of this sort. They are also tackling 4d models, which
are too complicated to study analytically, but are well-suited to numerical
calculation. This work should eventually hook up with spin foam models
of 4d quantum gravity in an interesting way, since the Barrett-Crane spin
foam model provides a well-defined *Lorentzian* discretized path integral
for general relativity.

Of course, it's not clear that things will work even when we do things
right. But there's really no excuse for doing the wrong calculation and
then blaming quantum gravity for the bad results!

Here are 2 places to read more:

Discrete Lorentzian Quantum Gravity
Renate Loll
Nucl. Phys. Proc. Suppl. 94 (2001) 96-107
http://xxx.lanl.gov/abs/http://www.arxiv.org/abs/hep-th/0011194

Abstract:

Just as for non-abelian gauge theories at strong coupling, discrete lattice
methods are a natural tool in the study of non-perturbative quantum gravity.
They have to reflect the fact that the geometric degrees of freedom are
dynamical, and that therefore also the lattice theory must be formulated
in a background-independent way. After summarizing the status quo of
discrete covariant lattice models for four-dimensional quantum gravity,
I describe a new class of discrete gravity models whose starting point
is a path integral over Lorentzian (rather than Euclidean) space-time
geometries. A number of interesting and unexpected results that have
been obtained for these dynamically triangulated models in two and three
dimensions make discrete Lorentzian gravity a promising candidate for a
non-trivial theory of quantum gravity.

Euclidean and Lorentzian Quantum Gravity - Lessons from Two Dimensions
J. Ambjorn, J.L. Nielsen, J. Rolf, R. Loll
Chaos Solitons Fractals 10 (1999) 177-195
http://xxx.lanl.gov/abs/http://www.arxiv.org/abs/hep-th/9806241

Abstract:

No theory of four-dimensional quantum gravity exists as yet. In this
situation the two-dimensional theory, which can be analyzed by conventional
field-theoretical methods, can serve as a toy model for studying some
aspects of quantum gravity. It represents one of the rare settings in a
quantum-gravitational context where one can calculate quantities truly
independent of any background geometry. We review recent progress in our
understanding of 2d quantum gravity, and in particular the relation
between the Euclidean and Lorentzian sectors of the quantum theory.
We show that conventional 2d Euclidean quantum gravity can be obtained from
Lorentzian quantum gravity by an analytic continuation only if we allow
for spatial topology changes in the latter. Once this is done, one
obtains a theory of quantum gravity where space-time is fractal: 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.

.................................................. .........................

From: Jacques Distler <distler@golem.ph.utexas.edu>
Newsgroups: sci.physics.research
Subject: Re: The discrete charm of quantum gravity
Date: Wed, 04 Jul 2001 07:01:13 GMT
Organization: Physics Department, University of Texas at Austin
Message-ID: <Zaz07.14184$WT.3025922@typhoon.austin.rr.com>
Originator: baez@math-cl-n05.math.ucr.edu (John Baez)

In article
<Pine.SOL.4.10.10107022247260.3017-100000@physsun3.rutgers.edu>,
Lubos Motl <motl@physics.rutgers.edu> wrote:

>John Baez wrote:

>> Thus many workers in quantum gravity have long doubted the relevance
>> of the Monte Carlo calculations you mention.
>>
>> Of course, it's not clear that things will work even when we do things
>> right. But there's really no excuse for doing the wrong calculation and
>> then blaming quantum gravity for the bad results!

>This logic is very far from what I consider a rational approach. It is a
>well-known fact that the path integral is more well-defined in the
>Euclidean context. For example, there exists a rigorous definition of the
>functional measure in the case of \exp(-S) - while mathematicians have
>proved that there is no measure on the functional spaces (defined in the
>mathematically rigorous way) associated with \exp(iS) in the Feynman
>integral.
>
>The integrals with \exp(-S) are more convergent. They behave better. The
>questions of topology are clearer - therefore also string theorists like
>to use Euclidean worldsheets to compute the amplitudes - although they can
>show the equivalence of those amplitudes to the amplitudes computed from a
>Minkowski light-cone gauge Hamiltonian. In every reasonable theory that
>people have seen, the Wick rotation is a legitimate tool.

Euclidean worldsheets and Euclidean target spaces are a totally
different matter. John is talking about Euclidean target spaces.

For a general (d-1,1)- manifold, there is no reasonable notion of
Wick-rotation. Indeed, in 2+1 dimensional gravity (formulated as a
Chern-Simons gauge theory), the Euclidean and Minkowskian theories are
totally different; they are not related by Wick rotation.

More to the point (as I alluded to in my post), the Euclidean path
integral for the Einstein-Hilbert action -- in the semiclassical
approximation -- contains known pathologies (the Euclidean action is
unbounded from below). So in no sense is \exp(-S) better behaved than
\exp(iS) for (semiclassical) gravity.

For these and other reasons, it is NOT unreasonable to say that gravity
must be understood in the Minkowskian signature and that you can't use
some phoney-baloney Wick rotation to Euclidean signature study it.

None of this detracts from your basic intuition that, whatever tricks
may serve to define a continuum limit of a theory of lattice gravity in
2 or 3 dimensions will not generalize to 4 dimensions.

It was, actually, surprising that lattice gravity in 3 dimensions did
not (heretofore) appear to have a continuum limit even though we knew
perfectly well that there *was* a continuum theory of 3D quantum gravity.

Ambjorn and collaborators have repaired this apparent breakdown of the
lattice approach in 3D. But I do not believe that their results have
much promise of producing a "miracle" in 4D.

Jacques

--
PGP public key: http://golem.ph.utexas.edu/~distler/distler.asc

alistair

May15-04, 03:45 AM

<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>ebunn@lfa221051.richmond.edu wrote in message news:<c801h8\\$46f\\$1@lfa222122.richmond.edu>...\ n> In article <861c1b21.0405111214.8a3e2d1@posting.google.com>,\ n> alistair <alistair@goforit64.fsnet.co.uk> wrote:\n> >Modified Newtonian Dynamics\n> >\n> >MOND basically says that if you double the distance of a star\n> >from the galactic centre, then you half the force of gravity, instead\n> >of quartering it as Newton\'s inverse square law would say.\n> >This is what a physical theory needs to explain.\n>\n> This is not accurate.\n\nIt\'s not totally accurate.\n\nBut it gives the right impression of what\nis happening to the gravitational force which\ndark matter or modified GR or anything else must explain.\n\nv = (rg)^1/2\nfor constant v as r doubles g must halve.\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>ebunn@lfa221051.richmond.edu wrote in message news:<c801h8$46f$1@lfa222122.richmond.edu>...
> In article <861c1b21.0405111214.8a3e2d1@posting.google.com>,
> alistair <alistair@goforit64.fsnet.co.uk> wrote:
> >Modified Newtonian Dynamics
> >
> >MOND basically says that if you double the distance of a star
> >from the galactic centre, then you half the force of gravity, instead
> >of quartering it as Newton's inverse square law would say.
> >This is what a physical theory needs to explain.
>
> This is not accurate.

It's not totally accurate.

But it gives the right impression of what
is happening to the gravitational force which
dark matter or modified GR or anything else must explain.

v = (rg)^1/2
for constant v as r doubles g must halve.

Tobias Fritz

May17-04, 07:17 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>\n>\n> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n> the strange behavior of galaxies without invoking dark matter. The basic\n> problem with galaxies is that the outer parts rotate faster than they\n> should given how much mass we actually see.\n>\n> If you have a planet in a circular orbit about the Sun, Newton\'s laws\n> say its acceleration is proportional to 1/r^2, where r is its distance to\n> the Sun. Similarly, if almost all the mass in a galaxy were concentrated\n> right at the center, a star orbiting in a circle at distance r from the\n> center would have acceleration proportional to 1/r^2. Of course, not all\n> the mass is right at the center! So, the acceleration should drop off\n> more slowly than 1/r^2 as you go further out. And it does. But, the\n> observed acceleration drops off a lot more slowly than the acceleration\n> people calculate from the mass they see. It\'s not a small effect: it\'s a\n> HUGE effect!\n>\n> One solution is to say there\'s a lot of mass we don\'t see: "dark matter"\n> of some sort. If you take this route, which most astronomers do, you\'re\n> forced to say that *most* of the mass of galaxies is in the form of dark\n> matter.\n>\n> Milgrom\'s solution is to say that Newton\'s laws are messed up.\n>\n> Of course this is a drastic, dangerous step: the last guy who tried this\n> was named Einstein, and we all know what happened to him. Milgrom\'s\n> theory isn\'t even based on deep reasoning and beautiful math like\n> Einstein\'s! Instead, it\'s just a blatant attempt to fit the experimental\n> data.\n> And it\'s not even elegant. In fact, it\'s downright ugly.\n>\n> Here\'s what it says: the usual Newtonian formula for the acceleration\n> due to gravity is correct as long as the acceleration is bigger than\n>\n> a = 2 x 10^{-10} m/sec^2\n>\n> But, for accelerations less than this, you take the geometric mean\n> of the acceleration Newton would predict and this constant a.\n>\n> In other words, there\'s a certain value of acceleration such that above\n> this value, the Newtonian law of gravity works as usual, while below this\n> value the law suddenly changes.\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." Not in fundamental\n> physics, anyway! Sure, water is solid below 0 centigrade and fluid above\n> this, but that\'s not a fundamental law - it presumably follows from other\n> stuff. Not that anyone has derived the melting point of ice from first\n> principles, mind you. But we think we could if we were better at big\n> messy calculations.\n>\n> Furthermore, you can\'t easily invent a Lagrangian for gravity that makes\n> it fall off more *slowly* than 1/r^2. It\'s easy to get it to fall off\n> *faster* - just give the graviton a mass, for example! But not more\n> slowly. It turns out you can do it - Bekenstein and Milgrom have a way -\n> but it\'s incredibly ugly.\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! In some cases it matches the observed rotation of\n> galaxies in an appallingly accurate way, fitting every wiggle in the graph\n> of stellar rotation velocity as a function of distance from the center.\n>\n> So, even if MOND is wrong, there may need to be some reason why it *acts*\n> like it\'s right! Apparently even some proponents of dark matter agree\n> with this.\n>\n\nDoesn\'t it seem unresonable to discard a theory as successful as GR?\nOr is it somehow possible to fit MOND into the framework of GR, like by\nmodifying the field equations, perhaps by including torsion?\n\nEverybody is talking about "dark matter" or alternative theories, when it is\nnot even really clear what the predictions of GR are: recently I heard a\ntalk about the "averaging problem" in GR; basically, the message was that\nwe do not know if it is valid to take an average energy-momentum-tensor,\nput it into the field equations and see the result as an average metric. By\ngoogling, I found the following paper:\n\nhttp://arxiv.org/abs/gr-qc/9703016\n\nwhich also has some references.\n\nWhat do the experts think?\n--\nhang my head drown my fear\ntill you all just disappear\n\nreverse my forename for mail! - saibot\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>Lee Smolin told me some neat stuff about MOND - that's "Modified
> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
> the strange behavior of galaxies without invoking dark matter. The basic
> problem with galaxies is that the outer parts rotate faster than they
> should given how much mass we actually see.
>
> If you have a planet in a circular orbit about the Sun, Newton's laws
> say its acceleration is proportional to 1/r^2, where r is its distance to
> the Sun. Similarly, if almost all the mass in a galaxy were concentrated
> right at the center, a star orbiting in a circle at distance r from the
> center would have acceleration proportional to 1/r^2. Of course, not all
> the mass is right at the center! So, the acceleration should drop off
> more slowly than 1/r^2 as you go further out. And it does. But, the
> observed acceleration drops off a lot more slowly than the acceleration
> people calculate from the mass they see. It's not a small effect: it's a
> HUGE effect!
>
> One solution is to say there's a lot of mass we don't see: "dark matter"
> of some sort. If you take this route, which most astronomers do, you're
> forced to say that *most* of the mass of galaxies is in the form of dark
> matter.
>
> Milgrom's solution is to say that Newton's laws are messed up.
>
> Of course this is a drastic, dangerous step: the last guy who tried this
> was named Einstein, and we all know what happened to him. Milgrom's
> theory isn't even based on deep reasoning and beautiful math like
> Einstein's! Instead, it's just a blatant attempt to fit the experimental
> data.
> And it's not even elegant. In fact, it's downright ugly.
>
> Here's what it says: the usual Newtonian formula for the acceleration
> due to gravity is correct as long as the acceleration is bigger than
>
> a = 2 x 10^{-10} m/sec^2
>
> But, for accelerations less than this, you take the geometric mean
> of the acceleration Newton would predict and this constant a.
>
> In other words, there's a certain value of acceleration such that above
> this value, the Newtonian law of gravity works as usual, while below this
> value the law suddenly changes.
>
> 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." Not in fundamental
> physics, anyway! Sure, water is solid below centigrade and fluid above
> this, but that's not a fundamental law - it presumably follows from other
> stuff. Not that anyone has derived the melting point of ice from first
> principles, mind you. But we think we could if we were better at big
> messy calculations.
>
> Furthermore, you can't easily invent a Lagrangian for gravity that makes
> it fall off more *slowly* than 1/r^2. It's easy to get it to fall off
> *faster* - just give the graviton a mass, for example! But not more
> slowly. It turns out you can do it - Bekenstein and Milgrom have a way -
> but it's incredibly ugly.
>
> 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! In some cases it matches the observed rotation of
> galaxies in an appallingly accurate way, fitting every wiggle in the graph
> of stellar rotation velocity as a function of distance from the center.
>
> So, even if MOND is wrong, there may need to be some reason why it *acts*
> like it's right! Apparently even some proponents of dark matter agree
> with this.
>

Doesn't it seem unresonable to discard a theory as successful as GR?
Or is it somehow possible to fit MOND into the framework of GR, like by
modifying the field equations, perhaps by including torsion?

Everybody is talking about "dark matter" or alternative theories, when it is
not even really clear what the predictions of GR are: recently I heard a
talk about the "averaging problem" in GR; basically, the message was that
we do not know if it is valid to take an average energy-momentum-tensor,
put it into the field equations and see the result as an average metric. By
googling, I found the following paper:

http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/9703016

which also has some references.

What do the experts think?
--
hang my head drown my fear
till you all just disappear

reverse my forename for mail! - saibot

Christine Dantas

May17-04, 07:23 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>ebunn@lfa221051.richmond.edu wrote in message news:<c801h8\\$46f\\$1@lfa222122.richmond.edu>...\ n\n> Personally, I can\'t get past my theorist\'s objections to MOND. It\n> doesn\'t play well at all with general relativity, and I just don\'t\n> believe that general relativity is completely on the wrong track.\n\nHello all,\n\nConcerning MOND x GR, the recent paper by Bekenstein seems to be\na relevant contribution to this issue (see below).\n\nRegards,\nChristine Dantas\nINPE/Brazil\n\n\n====================================== ===================================\nastro-ph/0403694\nRelativistic gravitation theory for the MOND paradigm\nJacob D. Bekenstein\n\nThe modified newtonian dynamics (MOND) paradigm of Milgrom can boast\nof a number of successful predictions regarding galactic dynamics;\nthese are made without the assumption that dark matter plays a\nsignificant role. MOND requires gravitation to depart from Newtonian\ntheory in the extragalactic regime where dynamical accelerations are\nsmall. So far relativistic gravitation theories proposed to underpin\nMOND have either clashed with the post-Newtonian tests of general\nrelativity, or failed to provide significant gravitational lensing, or\nviolated hallowed principles by exhibiting superluminal scalar waves\nor an a priori vector field. We develop a relativistic MOND inspired\ntheory which resolves these problems. In it gravitation is mediated by\nmetric, a scalar field and a 4-vector field, all three dynamical. For\na simple choice of its free function, the theory has a Newtonian limit\nfor nonrelativistic dynamics with significant acceleration, but a MOND\nlimit when accelerations are small. We calculate the beta and gamma\nPPN coefficients showing them to agree with solar system\nmeasurements. The gravitational light deflection by nonrelativistic\nsystems is governed by the same potential responsible for dynamics of\nparticles. Consequently, the new theory predicts gravitational lensing\nby extragalactic structures that cannot be distinguished from that\npredicted within the dark matter paradigm by general\nrelativity. Cosmological models based on the theory are quite similar\nto those based on general relativity; they predict slow evolution of\nthe scalar field. For a range of initial conditions, this last result\nmakes it easy to rule out superluminal propagation of metric, scalar\nand vector waves.\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>ebunn@lfa221051.richmond.edu wrote in message news:<c801h8$46f$1@lfa222122.richmond.edu>...

> Personally, I can't get past my theorist's objections to MOND. It
> doesn't play well at all with general relativity, and I just don't
> believe that general relativity is completely on the wrong track.

Hello all,

Concerning MOND x GR, the recent paper by Bekenstein seems to be
a relevant contribution to this issue (see below).

Regards,
Christine Dantas
INPE/Brazil

================================================== =======================
http://www.arxiv.org/abs/astro-ph/0403694
Relativistic gravitation theory for the MOND paradigm
Jacob D. Bekenstein

The modified newtonian dynamics (MOND) paradigm of Milgrom can boast
of a number of successful predictions regarding galactic dynamics;
these are made without the assumption that dark matter plays a
significant role. MOND requires gravitation to depart from Newtonian
theory in the extragalactic regime where dynamical accelerations are
small. So far relativistic gravitation theories proposed to underpin
MOND have either clashed with the post-Newtonian tests of general
relativity, or failed to provide significant gravitational lensing, or
violated hallowed principles by exhibiting superluminal scalar waves
or an a priori vector field. We develop a relativistic MOND inspired
theory which resolves these problems. In it gravitation is mediated by
metric, a scalar field and a 4-vector field, all three dynamical. For
a simple choice of its free function, the theory has a Newtonian limit
for nonrelativistic dynamics with significant acceleration, but a MOND
limit when accelerations are small. We calculate the \beta and \gamma
PPN coefficients showing them to agree with solar system
measurements. The gravitational light deflection by nonrelativistic
systems is governed by the same potential responsible for dynamics of
particles. Consequently, the new theory predicts gravitational lensing
by extragalactic structures that cannot be distinguished from that
predicted within the dark matter paradigm by general
relativity. Cosmological models based on the theory are quite similar
to those based on general relativity; they predict slow evolution of
the scalar field. For a range of initial conditions, this last result
makes it easy to rule out superluminal propagation of metric, scalar
and vector waves.
================================================== =======================

John Baez

May17-04, 08:37 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>In article <72Ooc.2431\\$1z6.1942@newssvr16.news.prodigy.com> ,\nTorquemada <torquemada1@nospam.sigfpe.com> wrote:\n\n>I checked out this article: http://www.astro.umd.edu/~ssm/mond/astronow.html\n>and there\'s an example of a graph of rotation velocity vs. radius showing\n>one of the wiggles JB mentions, with the note "even the kink observed in the\n>gas distribution is reflected in the rotation".\n>\n>Forgive me for being a little sceptical [....]\n\nWe should all be VERY skeptical as far as both MOND and dark matter\nare concerned! I\'m not trying to get people to accept MOND, just to\ntalk about this stuff.\n\n>[...] but the Newtonian prediction has\n>exactly the same kink. In fact, the MOND curve is just the Newtonian curve\n>scaled up. Just about any reasonably well behaved modification of the\n>Newtonian formula that has a scaling effect that brings the Newtonian curve\n>roughly in alignment with measured results is going to have that kink.\n\nI guess you\'re right, but aren\'t you basically buying MOND if you\nposit a "reasonably well behaved modification of the Newtonian formula\nthat has a scaling effect that brings the Newtonian curve roughly in\nalignment with measured results"?\n\nAfter all, the real point of MOND is not the specific formula for\nthe gravitational force which I wrote down in "week206". I may not\nhave explained this well, but as Ted Bunn notes, all sorts of roughly\nsimilar formulas would also fit the data about equally well. The\nproblem is, all these formulas require us to accept that gravity doesn\'t\nwork as expected at large distances! - or more precisely, at low\naccelerations. Accepting any one would require us to toss general\nrelativity out the window. And all of them force us to dream up\ntheories of forces that die off more slowly than 1/r^2 - a difficult\ntask.\n\nOr are you suggesting that dark matter could also explain these galaxy\nrotation curves? For that, I guess the dark matter distribution would\nhave to closely mimic the visible matter distribution - see for example\nthe plot for the galaxy NGC 1580 in Figure 3 on page 39 here:\n\nhttp://xxx.lanl.gov/abs/astro-ph/0204521\n\nDo proponents of dark matter claim this is how it works? I thought\notherwise. (But mind you, I\'m no expert, so I could be ignoring all\nsorts of important stuff.)\n\nI thank Ethan Vishniac and Steve Carlip for telling me about some\nthings to read... but I haven\'t read \'em yet!\n\n\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>In article <72Ooc.2431$1z6.1942@newssvr16.news.prodigy.com>,
Torquemada <torquemada1@nospam.sigfpe.com> wrote:

>I checked out this article: http://www.astro.umd.edu/~ssm/mond/astronow.html
>and there's an example of a graph of rotation velocity vs. radius showing
>one of the wiggles JB mentions, with the note "even the kink observed in the
>gas distribution is reflected in the rotation".
>
>Forgive me for being a little sceptical [....]

We should all be VERY skeptical as far as both MOND and dark matter
are concerned! I'm not trying to get people to accept MOND, just to
talk about this stuff.

>[...] but the Newtonian prediction has
>exactly the same kink. In fact, the MOND curve is just the Newtonian curve
>scaled up. Just about any reasonably well behaved modification of the
>Newtonian formula that has a scaling effect that brings the Newtonian curve
>roughly in alignment with measured results is going to have that kink.

I guess you're right, but aren't you basically buying MOND if you
posit a "reasonably well behaved modification of the Newtonian formula
that has a scaling effect that brings the Newtonian curve roughly in
alignment with measured results"?

After all, the real point of MOND is not the specific formula for
the gravitational force which I wrote down in "week206". I may not
have explained this well, but as Ted Bunn notes, all sorts of roughly
similar formulas would also fit the data about equally well. The
problem is, all these formulas require us to accept that gravity doesn't
work as expected at large distances! - or more precisely, at low
accelerations. Accepting any one would require us to toss general
relativity out the window. And all of them force us to dream up
theories of forces that die off more slowly than 1/r^2 - a difficult
task.

Or are you suggesting that dark matter could also explain these galaxy
rotation curves? For that, I guess the dark matter distribution would
have to closely mimic the visible matter distribution - see for example
the plot for the galaxy NGC 1580 in Figure 3 on page 39 here:

http://xxx.lanl.gov/abs/http://www.arxiv.org/abs/astro-ph/0204521

Do proponents of dark matter claim this is how it works? I thought
otherwise. (But mind you, I'm no expert, so I could be ignoring all
sorts of important stuff.)

I thank Ethan Vishniac and Steve Carlip for telling me about some
things to read... but I haven't read 'em yet!

John Baez

May17-04, 08:46 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>In article <40A483D1.7030304@users.ch>, Morris Carré\n<ruses@users.ch> wrote:\n\n>ebunn@lfa221051.richmond.edu wrote about Modified Newtonian Dynamics:\n\n>> then the actual acceleration of an object is\n>>\n>> a = a_N if a_N > a_0\n>> a = sqrt(a_N a_0) if a < a_0\n>>\n>> Here a_0 is some fundamental constant.\n\n>Am I dreaming, or isn\'t there something "planckscalish" to the idea ?\n\nSort of:\n\nThe reason why Smolin was interested in MOND is that this constant\n\na_0 = 2 x 10^{-10} m/sec^2\n\nis supposedly about equal the acceleration of the expansion of\nthe universe due to the cosmological constant, for objects that are...\none Hubble away? Or something like that... I\'m too lazy to check,\nI could be horribly far off, and Smolin shouldn\'t be blamed if I\'m\nmisremembering and saying something really stupid!\n\nDoes someone have the energy to check?\n\n[Moderator\'s note: The order of magnitude is about right, anyway. -TB]\n\nAnyway, Smolin was wondering if the MOND acceleration scale was somehow\nrelated to the cosmological constant - he said he\'s spent lots of nights\nlying in bed staring at the ceiling trying to figure something out about\nthis, so far with no success.\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>In article <40A483D1.7030304@users.ch>, Morris Carré
<ruses@users.ch> wrote:

>ebunn@lfa221051.richmond.edu wrote about Modified Newtonian Dynamics:

>> then the actual acceleration of an object is
>>
>> a = a_N if a_N > a_0>> a = \sqrt(a_N a_0) if a < a_0
>>
>> Here a_0 is some fundamental constant.

>Am I dreaming, or isn't there something "planckscalish" to the idea ?

Sort of:

The reason why Smolin was interested in MOND is that this constant

a_0 = 2 x 10^{-10} m/sec^2

is supposedly about equal the acceleration of the expansion of
the universe due to the cosmological constant, for objects that are...
one Hubble away? Or something like that... I'm too lazy to check,
I could be horribly far off, and Smolin shouldn't be blamed if I'm
misremembering and saying something really stupid!

Does someone have the energy to check?

[Moderator's note: The order of magnitude is about right, anyway. -TB]

Anyway, Smolin was wondering if the MOND acceleration scale was somehow
related to the cosmological constant - he said he's spent lots of nights
lying in bed staring at the ceiling trying to figure something out about
this, so far with no success.

Lubos Motl

May17-04, 09:00 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>On Sat, 15 May 2004, John Baez wrote:\n\n> > Someone: This [a paper on discretization of gravity] is pretty exciting.\n> http://www.arxiv.org/abs/hep-th/0404156\n>\n> I\'m glad you think so! I sure do!\n\nWell, I am sure that you would be even more happy if I agreed, too. But I\ndon\'t. There is just no evidence that the resulting physics is physics of\ngravity, and there is evidence against the conjecture that it will be\nlocally Lorentz-invariant. Below, I will argue that this unjustified\nexcitement about these models returns again and again, and that these\nmodels never lead anywhere.\n\nIt is not too difficult to construct a discrete & "background-independent"\nsystem that will have the tendency to organize the elementary building\nblocks into a structure that approaches flat space - or another type of\nspace, for that matter. For example, crystals are an example (from\ncondensed matter physics) where the underlying laws (at low temperatures)\ntend to organize the atoms into a regular structure. The nontrivial\nproperty of GR is a combination of two requirements - that physics is\nlocally Lorentz-invariant (i.e. approximated by special relativity for a\nfreely falling observer), and that physics is general covariant.\n\nThere is no evidence for the Lorentz invariance in any of these discrete\nmodels, and therefore it is likely that the Einstein-Hilbert action does\nnot approximate the low energy limit of the theory.\n\n> >It is sort of obvious that you can formally\n> >put gravity on a lattice, but I always thought that there wasn\'t a\n> >continuum limit.\n>\n> Right - this is what everyone thought, except for a few people\n> who argued that Euclidean quantum gravity calculations were\n> irrelevant to the real Lorentzian world unless one did them in\n> a way where Wick rotation was justified.\n\nThe Euclidean path integral is always better behaved than the Minkowski\npath integral - it can be rigorously defined in terms of the Lebesgue\nmeasure, for example - and the Minkowski path integral in a working theory\nand a simple enough background can be defined as the Wick rotation applied\nto the Euclidean path integral.\n\n> Of course in ordinary quantum field theory on flat spacetime, we can\n> justify the switch from exp(-S) to exp(iS) via Wick rotation, which\n> is naively the substitution t -> it. However, for the calculations\n> in question here there is no good way to justify this trick...\n\nThe reason why can\'t one justify the Wick rotation is that the theory does\nnot admit states that are described as perturbations of the Minkowski (or\nanother well-defined) vacuum. If a theory predicts the Minkowski vacuum,\nit is always possible to continue the graviton scattering amplitudes\nanalytically, for example, and use the Euclidean path-integral techniques.\n\n> and there are good reasons to doubt it will work:\n>\n> 1) there is no god-given time parameter t here, so we don\'t\n> know how to do the replacement t -> it.\n\nThat\'s exactly what I am saying. If there is no God-given time parameter\n"t" in this setup, it means that the setup does not allow the existence of\nthe Minkowski background because the Minkowski vacuum *has* a God-given\ntime coordinate "t" which is unique up to Poincare transformations.\n\n> 2) in theories which allow topology change in the Euclidean context,\n> Wick rotation is especially problematic, since the spacetime isn\'t\n> even of the form R x S.\n\nSure. But you can\'t ever find new physics just by repeating negative\nstatements that things can be difficult, and therefore no failures should\ndiscourage us. New physical insights can only be obtained if one consider\nsomething that is simple enough, something that is doable and controllable\n- and if one actually solves it. The Minkowski (or another maximally\nsymmetric) vacuum is something that should exist in a theory that reduces\nto GR at low energies. All these non-trivial-topology difficulties are\nabsent for excitations of these backgrounds, and the Wick rotation\ntechniques must work, for some appropriate choices of the contours etc.,\nif the theory is consistent.\n\n> Nucl. Phys. Proc. Suppl. 94 (2001) 96-107\n> http://xxx.lanl.gov/abs/hep-th/0011194\n\nNote that such articles are proposed again and again, and they never lead\nanywhere. This one was written almost four years ago, which is a pretty\nlong time, and in 2001 you had described it with the same enthusiasm as\nthe recent one - although it has only affected 10 papers by Loll, Smolin,\nand Markopoulou (10 self-citations, so to say). I wonder whether there is\nsome dogma that such things must be tried forever, despite increasingly\nobvious failures. How many more failures are necessary to rule out the\nconjecture that a consistent and complete theory of 4D quantum gravity is\nobtained by discretization of the low-energy equations? It just seems to\nme that the motivation that drives this type of research is something\ndifferent than the scientific desire to understand something that no one\ncan know in advance - namely the answer to the question how the Universe\nreally works.\n\n> Jacques Distler: Euclidean worldsheets and Euclidean target spaces are\n> a totally different matter. John is talking about Euclidean target\n> spaces.\n\nThey are related. For example, you can\'t embed a Minkowski worldsheet to a\nEuclidean target space.\n\n> JD: For a general (d-1,1)- manifold, there is no reasonable notion of\n> Wick-rotation. Indeed, in 2+1 dimensional gravity (formulated as a\n> Chern-Simons gauge theory), the Euclidean and Minkowskian theories are\n> totally different; they are not related by Wick rotation.\n\nAs I said, you can find contexts where everything is confusing and\ndifficult and where you can hide any inconsistency behind a huge cloud of\nmist, but fortunately you can also make a better choice and find contexts\nwhere the questions *can* be studied, and if one studies them, the results\nshow that those proposals don\'t work.\n\n3D gravity is a very different animal than 4D gravity. It has no dynamical\ndegrees of freedom, and it is topological in nature. Topology for\nMinkowski and Euclidean signatures are very different; on the other hand,\nthe analytical form of the scattering amplitude on Minkowski and Euclidean\nflat background are related by analytical continuation.\n\n> For these and other reasons, it is NOT unreasonable to say that gravity\n> must be understood in the Minkowskian signature and that you can\'t use\n> some phoney-baloney Wick rotation to Euclidean signature study it.\n\nDo you still think, Jacques, that the gravitational scattering amplitudes\ncannot be continued to the Euclidean space, for example?\n\n> Ambjorn and collaborators have repaired this apparent breakdown of the\n> lattice approach in 3D. But I do not believe that their results have\n> much promise of producing a "miracle" in 4D.\n\nRight. It has been a couple of years without any success to say that even\nthose proposals by Loll et al. were most likely dead ends.\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>On Sat, 15 May 2004, John Baez wrote:

> > Someone: This [a paper on discretization of gravity] is pretty exciting.
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0404156
>
> I'm glad you think so! I sure do!

Well, I am sure that you would be even more happy if I agreed, too. But I
don't. There is just no evidence that the resulting physics is physics of
gravity, and there is evidence against the conjecture that it will be
locally Lorentz-invariant. Below, I will argue that this unjustified
excitement about these models returns again and again, and that these
models never lead anywhere.

It is not too difficult to construct a discrete & "background-independent"
system that will have the tendency to organize the elementary building
blocks into a structure that approaches flat space - or another type of
space, for that matter. For example, crystals are an example (from
condensed matter physics) where the underlying laws (at low temperatures)
tend to organize the atoms into a regular structure. The nontrivial
property of GR is a combination of two requirements - that physics is
locally Lorentz-invariant (i.e. approximated by special relativity for a
freely falling observer), and that physics is general covariant.

There is no evidence for the Lorentz invariance in any of these discrete
models, and therefore it is likely that the Einstein-Hilbert action does
not approximate the low energy limit of the theory.

> >It is sort of obvious that you can formally
> >put gravity on a lattice, but I always thought that there wasn't a
> >continuum limit.
>
> Right - this is what everyone thought, except for a few people
> who argued that Euclidean quantum gravity calculations were
> irrelevant to the real Lorentzian world unless one did them in
> a way where Wick rotation was justified.

The Euclidean path integral is always better behaved than the Minkowski
path integral - it can be rigorously defined in terms of the Lebesgue
measure, for example - and the Minkowski path integral in a working theory
and a simple enough background can be defined as the Wick rotation applied
to the Euclidean path integral.

> Of course in ordinary quantum field theory on flat spacetime, we can
> justify the switch from \exp(-S) to \exp(iS) via Wick rotation, which
> is naively the substitution t -> it. However, for the calculations
> in question here there is no good way to justify this trick...

The reason why can't one justify the Wick rotation is that the theory does
not admit states that are described as perturbations of the Minkowski (or
another well-defined) vacuum. If a theory predicts the Minkowski vacuum,
it is always possible to continue the graviton scattering amplitudes
analytically, for example, and use the Euclidean path-integral techniques.

> and there are good reasons to doubt it will work:
>
> 1) there is no god-given time parameter t here, so we don't
> know how to do the replacement t -> it.

That's exactly what I am saying. If there is no God-given time parameter
"t" in this setup, it means that the setup does not allow the existence of
the Minkowski background because the Minkowski vacuum *has* a God-given
time coordinate "t" which is unique up to Poincare transformations.

> 2) in theories which allow topology change in the Euclidean context,
> Wick rotation is especially problematic, since the spacetime isn't
> even of the form R x S.

Sure. But you can't ever find new physics just by repeating negative
statements that things can be difficult, and therefore no failures should
discourage us. New physical insights can only be obtained if one consider
something that is simple enough, something that is doable and controllable
- and if one actually solves it. The Minkowski (or another maximally
symmetric) vacuum is something that should exist in a theory that reduces
to GR at low energies. All these non-trivial-topology difficulties are
absent for excitations of these backgrounds, and the Wick rotation
techniques must work, for some appropriate choices of the contours etc.,
if the theory is consistent.

> Nucl. Phys. Proc. Suppl. 94 (2001) 96-107
> http://xxx.lanl.gov/abs/http://www.arxiv.org/abs/hep-th/0011194

Note that such articles are proposed again and again, and they never lead
anywhere. This one was written almost four years ago, which is a pretty
long time, and in 2001 you had described it with the same enthusiasm as
the recent one - although it has only affected 10 papers by Loll, Smolin,
and Markopoulou (10 self-citations, so to say). I wonder whether there is
some dogma that such things must be tried forever, despite increasingly
obvious failures. How many more failures are necessary to rule out the
conjecture that a consistent and complete theory of 4D quantum gravity is
obtained by discretization of the low-energy equations? It just seems to
me that the motivation that drives this type of research is something
different than the scientific desire to understand something that no one
can know in advance - namely the answer to the question how the Universe
really works.

> Jacques Distler: Euclidean worldsheets and Euclidean target spaces are
> a totally different matter. John is talking about Euclidean target
> spaces.

They are related. For example, you can't embed a Minkowski worldsheet to a
Euclidean target space.

> JD: For a general (d-1,1)- manifold, there is no reasonable notion of
> Wick-rotation. Indeed, in 2+1 dimensional gravity (formulated as a
> Chern-Simons gauge theory), the Euclidean and Minkowskian theories are
> totally different; they are not related by Wick rotation.

As I said, you can find contexts where everything is confusing and
difficult and where you can hide any inconsistency behind a huge cloud of
mist, but fortunately you can also make a better choice and find contexts
where the questions *can* be studied, and if one studies them, the results
show that those proposals don't work.

3D gravity is a very different animal than 4D gravity. It has no dynamical
degrees of freedom, and it is topological in nature. Topology for
Minkowski and Euclidean signatures are very different; on the other hand,
the analytical form of the scattering amplitude on Minkowski and Euclidean
flat background are related by analytical continuation.

> For these and other reasons, it is NOT unreasonable to say that gravity
> must be understood in the Minkowskian signature and that you can't use
> some phoney-baloney Wick rotation to Euclidean signature study it.

Do you still think, Jacques, that the gravitational scattering amplitudes
cannot be continued to the Euclidean space, for example?

> Ambjorn and collaborators have repaired this apparent breakdown of the
> lattice approach in 3D. But I do not believe that their results have
> much promise of producing a "miracle" in 4D.

Right. It has been a couple of years without any success to say that even
those proposals by Loll et al. were most likely dead ends.
__{_______________________________________________ _____________________________}
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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Thomas Larsson

May18-04, 04:44 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>baez@galaxy.ucr.edu (John Baez) wrote in message news:<c82uao\\$i34\\$1@glue.ucr.edu>...\n> In article <24a23f36.0405112105.6569f265@posting.google.com>, \n> Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:\n>\n> >baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message\n> >news:<c7pbsa\\$p9\\$1@glue.ucr.edu>...\n>\n> >> Given all this, I\'m delighted to see some real progress on getting 4d\n> >> spacetime to emerge from nonperturbative quantum gravity:\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>\n> >This is pretty exciting.\n>\n> I\'m glad you think so! I sure do!\n>\nMaybe I was overreacting. It was becoming boring to be\nnegative all the time, so when I realized that somebody\nhad made tangible progress towards some kind of quantum\ngravity, I got carried away.\n\nAnyway, I would like to discuss to what extent AJL really\nhave succeed in constructing a model of QG in 4D. As I\nsee it, there are three things that could go wrong: that\nthe model isn\'t quantum, that it isn\'t gravity, or that\nthe measure is wrong.\n\n1. Is the AJL model really quantum? Some time ago, Urs\nSchreiber argued that LQG, or at least the LQG string,\nfails to be a true quantum theory, and I tend to agree.\nHowever, the AJL model can be viewed as a statistical\nlattice model, and if such a model has a good continuum\nlimit, it is AFAIK always described by some kind of QFT.\nWhat else could it be?\n\n2. It the AJL model really gravity. The action is a rather\nstraightforward discretization of the Einstein action with\na cosmological term:\n\n\\int R => sum over (d-2)-simplices\n\n\\int det g = volume => sum over d-simplices.\n\nWhat is perhaps somewhat unusual is that all edges have\nthe same length, which is different from Regge calculus.\nNevertheless, I don\'t think that this really matters, but\none could check if the results look different if you\nallow for variable edge lengths.\n\n3. Is the measure right? Here is the place where AJL differ\nsignificantly from previous simulations. AFAIU, the crux is\nthat AJL insist on a strict form of causality: they exclude\nspacetimes where the metric is singular, even at isolated\npoints. This may seem like an innoscent restriction, but it\nrules out things like topology change and baby universes,\nwhich require that the metric be singular somewhere.\n\nIt is not obvious to me whether one should insist on such a\nstrong form of causality or not, but this assumption leads\nat least to better results, e.g. a reasonably smooth 4D\nspacetime. Thus, I believe that it is a fair chance that\nAJL have indeed succeeded in quantizing gravity. They do so\nnot by assuming a lot of experimentally unconfirmed new\nphysics, but rather by strictly implementing the\ntime-honored principles of old physics, especially\ncausality. That is cool.\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>baez@galaxy.ucr.edu (John Baez) wrote in message news:<c82uao$i34$1@glue.ucr.edu>...
> In article <24a23f36.0405112105.6569f265@posting.google.com>,
> Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:
>
> >baez@math.removethis.ucr.andthis.edu (John Baez) wrote in message
> >news:<c7pbsa$p9$1@glue.ucr.edu>...
>
> >> Given all this, I'm delighted to see some real progress on getting 4d
> >> spacetime to emerge from nonperturbative quantum gravity:
> >>
> >> 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.
>
> >This is pretty exciting.
>
> I'm glad you think so! I sure do!
>
Maybe I was overreacting. It was becoming boring to be
negative all the time, so when I realized that somebody
had made tangible progress towards some kind of quantum
gravity, I got carried away.

Anyway, I would like to discuss to what extent AJL really
have succeed in constructing a model of QG in 4D. As I
see it, there are three things that could go wrong: that
the model isn't quantum, that it isn't gravity, or that
the measure is wrong.

1. Is the AJL model really quantum? Some time ago, Urs
Schreiber argued that LQG, or at least the LQG string,
fails to be a true quantum theory, and I tend to agree.
However, the AJL model can be viewed as a statistical
lattice model, and if such a model has a good continuum
limit, it is AFAIK always described by some kind of QFT.
What else could it be?

2. It the AJL model really gravity. The action is a rather
straightforward discretization of the Einstein action with
a cosmological term:

\int R => sum over (d-2)-simplices

\int det g = volume => sum over d-simplices.

What is perhaps somewhat unusual is that all edges have
the same length, which is different from Regge calculus.
Nevertheless, I don't think that this really matters, but
one could check if the results look different if you
allow for variable edge lengths.

3. Is the measure right? Here is the place where AJL differ
significantly from previous simulations. AFAIU, the crux is
that AJL insist on a strict form of causality: they exclude
spacetimes where the metric is singular, even at isolated
points. This may seem like an innoscent restriction, but it
rules out things like topology change and baby universes,
which require that the metric be singular somewhere.

It is not obvious to me whether one should insist on such a
strong form of causality or not, but this assumption leads
at least to better results, e.g. a reasonably smooth 4D
spacetime. Thus, I believe that it is a fair chance that
AJL have indeed succeeded in quantizing gravity. They do so
not by assuming a lot of experimentally unconfirmed new
physics, but rather by strictly implementing the
time-honored principles of old physics, especially
causality. That is cool.

John Baez

May18-04, 04:45 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>In article <c83uek\\$q62\\$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu> wrote:\n\n>The reason why Smolin was interested in MOND is that this constant\n>\n>a_0 = 2 x 10^{-10} m/sec^2\n>\n>is supposedly about equal the acceleration of the expansion of\n>the universe due to the cosmological constant, for objects that are...\n>one Hubble away?\n\n>Does someone have the energy to check?\n\n>[Moderator\'s note: The order of magnitude is about right, anyway. -TB]\n\nOkay, thanks. That\'s good enough: it\'s just one of those rough\nnumerical coincidences that makes you - or in this case, Smolin -\nlie in bed staring at the ceiling wondering if there could be\nsomething funny going on involving gravity and this particular\nacceleration scale.\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>In article <c83uek$q62$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu> wrote:

>The reason why Smolin was interested in MOND is that this constant
>
>a_0 = 2 x 10^{-10} m/sec^2
>
>is supposedly about equal the acceleration of the expansion of
>the universe due to the cosmological constant, for objects that are...
>one Hubble away?

>Does someone have the energy to check?

>[Moderator's note: The order of magnitude is about right, anyway. -TB]

Okay, thanks. That's good enough: it's just one of those rough
numerical coincidences that makes you - or in this case, Smolin -
lie in bed staring at the ceiling wondering if there could be
something funny going on involving gravity and this particular
acceleration scale.

Arun Gupta

May20-04, 12:50 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>baez@galaxy.ucr.edu (John Baez) wrote in message news:<c8drpf\\$gqp\\$1@glue.ucr.edu>...\n> In article <c83uek\\$q62\\$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu> wrote:\n>\n> >The reason why Smolin was interested in MOND is that this constant\n> >\n> >a_0 = 2 x 10^{-10} m/sec^2\n> >\n> >is supposedly about equal the acceleration of the expansion of\n> >the universe due to the cosmological constant, for objects that are...\n> >one Hubble away?\n>\n> >Does someone have the energy to check?\n>\n> >[Moderator\'s note: The order of magnitude is about right, anyway. -TB]\n>\n> Okay, thanks. That\'s good enough: it\'s just one of those rough\n> numerical coincidences that makes you - or in this case, Smolin -\n> lie in bed staring at the ceiling wondering if there could be\n> something funny going on involving gravity and this particular\n> acceleration scale.\n\nIf I put an object one Hubble away, then from a Newtonian point of view,\nto keep at rest w.r.t. me, I have to put a little rocket motor on it, firing\naway from me. So, Hubble expansion would make Newtonian gravity\nseem weaker, but MOND makes it seem stronger. So why should there\nbe any connection between a_0 and Hubble?\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>baez@galaxy.ucr.edu (John Baez) wrote in message news:<c8drpf$gqp$1@glue.ucr.edu>...
> In article <c83uek$q62$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu> wrote:
>
> >The reason why Smolin was interested in MOND is that this constant
> >
> >a_0 = 2 x 10^{-10} m/sec^2
> >
> >is supposedly about equal the acceleration of the expansion of
> >the universe due to the cosmological constant, for objects that are...
> >one Hubble away?
>
> >Does someone have the energy to check?
>
> >[Moderator's note: The order of magnitude is about right, anyway. -TB]
>
> Okay, thanks. That's good enough: it's just one of those rough
> numerical coincidences that makes you - or in this case, Smolin -
> lie in bed staring at the ceiling wondering if there could be
> something funny going on involving gravity and this particular
> acceleration scale.

If I put an object one Hubble away, then from a Newtonian point of view,
to keep at rest w.r.t. me, I have to put a little rocket motor on it, firing
away from me. So, Hubble expansion would make Newtonian gravity
seem weaker, but MOND makes it seem stronger. So why should there
be any connection between a_0 and Hubble?

John Baez

May20-04, 04:48 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>In article <2ggpluF2hi83U1@uni-berlin.de>,\nTobias Fritz <tobias@mad.scientist.com> wrote:\n\n>> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n>> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n>> the strange behavior of galaxies without invoking dark matter. The basic\n>> problem with galaxies is that the outer parts rotate faster than they\n>> should given how much mass we actually see.\n\n>Doesn\'t it seem unreasonable to discard a theory as successful as GR?\n\nOf course! I don\'t think anyone wants to discard GR because of the\ndark matter problems. But, it does make sense to have some people\nplay around with other ideas.\n\nExcept for a few partisans, nobody will take MOND seriously until\nit\'s extended to a full-fledged theory that matches the successes of\nGR and isn\'t horribly ugly - or until it makes some prediction that\'s\nalmost impossible to match using conventional means (e.g. fine-tuned\ndark matter).\n\nBut, it\'s still good to look at the rotation curves in the paper I\nreferred to, and wonder what\'s really going on!\n\n>Or is it somehow possible to fit MOND into the framework of GR, like by\n>modifying the field equations, perhaps by including torsion?\n\nPeople are trying very hard to fit MOND into GR in all possible ways,\nand also to design dark matter that mimics the predictions of MOND.\nBekenstein\'s new paper:\n\nJacob D. Bekenstein\nRelativistic gravitation theory for the MOND paradigm\nhttp://www.arXiv.org/abs/astro-ph/0403694\n\nseems like the best attempt so far to make MOND into a respectable\ntheory. It\'s still not elegant.\n\n>Everybody is talking about "dark matter" or alternative theories, when it is\n>not even really clear what the predictions of GR are: recently I heard a\n>talk about the "averaging problem" in GR; basically, the message was that\n>we do not know if it is valid to take an average energy-momentum-tensor,\n>put it into the field equations and see the result as an average metric.\n\nIt\'s a nonlinear equation, so of course this is only approximately right\nat best. The question is: is the approximation good enough for practical\npurposes?\n\nUnless there\'s strong evidence that the approximation is *not* good enough,\nI think it\'s a bit over-sensational to say "it\'s not even really clear what\nthe predictions of GR are". In every application of fundamental theories\nof physics to real-world problems, people make approximations. Trying to\nrigorously justify these approximations leads to difficult and interesting\nproblems in mathematical physics. But, we rarely claim that it\'s not clear\nwhat the theory actually predicts until we have made everything rigorous!\nSo, claiming this here might fool nonexperts into thinking there\'s a big\nproblem with general relativity, when it\'s actually just "life as usual".\n\n>By googling, I found the following paper:\n>\n>http://arxiv.org/abs/gr-qc/9703016\n>\n>which also has some references.\n>\n>What do the experts think?\n\nI think someone, e.g. the author of this paper, should do some\nback-of-the-envelope calculations to guess how much error is introduced\ninto astrophysical or cosmological calculations by means of this\naveraging approximation. If it\'s a lot, this is a subject of real\nimportance in astronomy. If it\'s a little, this subject will mainly\nbe interesting to mathematical physicists.\n\nI can\'t imagine this "averaging problem" is big enough to explain the\neffects that made people resort to dark matter and MOND, for example!\n\nIt might be relevant to understanding the details of hypernovae,\nthough: you\'ve got a lot of dense matter moving around at relativistic\nspeeds, maybe turbulent, getting ready to collapse into a black hole...\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>In article <2ggpluF2hi83U1@uni-berlin.de>,
Tobias Fritz <tobias@mad.scientist.com> wrote:

>> Lee Smolin told me some neat stuff about MOND - that's "Modified
>> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
>> the strange behavior of galaxies without invoking dark matter. The basic
>> problem with galaxies is that the outer parts rotate faster than they
>> should given how much mass we actually see.

>Doesn't it seem unreasonable to discard a theory as successful as GR?

Of course! I don't think anyone wants to discard GR because of the
dark matter problems. But, it does make sense to have some people
play around with other ideas.

Except for a few partisans, nobody will take MOND seriously until
it's extended to a full-fledged theory that matches the successes of
GR and isn't horribly ugly - or until it makes some prediction that's
almost impossible to match using conventional means (e.g. fine-tuned
dark matter).

But, it's still good to look at the rotation curves in the paper I
referred to, and wonder what's really going on!

>Or is it somehow possible to fit MOND into the framework of GR, like by
>modifying the field equations, perhaps by including torsion?

People are trying very hard to fit MOND into GR in all possible ways,
and also to design dark matter that mimics the predictions of MOND.
Bekenstein's new paper:

Jacob D. Bekenstein
Relativistic gravitation theory for the MOND paradigm
http://www.arXiv.org/abs/http://www.arxiv.org/abs/astro-ph/0403694

seems like the best attempt so far to make MOND into a respectable
theory. It's still not elegant.

>Everybody is talking about "dark matter" or alternative theories, when it is
>not even really clear what the predictions of GR are: recently I heard a
>talk about the "averaging problem" in GR; basically, the message was that
>we do not know if it is valid to take an average energy-momentum-tensor,
>put it into the field equations and see the result as an average metric.

It's a nonlinear equation, so of course this is only approximately right
at best. The question is: is the approximation good enough for practical
purposes?

Unless there's strong evidence that the approximation is *not* good enough,
I think it's a bit over-sensational to say "it's not even really clear what
the predictions of GR are". In every application of fundamental theories
of physics to real-world problems, people make approximations. Trying to
rigorously justify these approximations leads to difficult and interesting
problems in mathematical physics. But, we rarely claim that it's not clear
what the theory actually predicts until we have made everything rigorous!
So, claiming this here might fool nonexperts into thinking there's a big
problem with general relativity, when it's actually just "life as usual".

>By googling, I found the following paper:
>
>http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/9703016
>
>which also has some references.
>
>What do the experts think?

I think someone, e.g. the author of this paper, should do some
back-of-the-envelope calculations to guess how much error is introduced
into astrophysical or cosmological calculations by means of this
averaging approximation. If it's a lot, this is a subject of real
importance in astronomy. If it's a little, this subject will mainly
be interesting to mathematical physicists.

I can't imagine this "averaging problem" is big enough to explain the
effects that made people resort to dark matter and MOND, for example!

It might be relevant to understanding the details of hypernovae,
though: you've got a lot of dense matter moving around at relativistic
speeds, maybe turbulent, getting ready to collapse into a black hole...

Phillip Helbig---remove CLOTHES to reply

May21-04, 03:46 AM

<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>\nIn article <c8j2hp\\$15l\\$1@glue.ucr.edu>, baez@galaxy.ucr.edu (John Baez)\nwrites:\n\n> In article <2ggpluF2hi83U1@uni-berlin.de>,\n> Tobias Fritz <tobias@mad.scientist.com> wrote:\n>\n> >> Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> >> Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying to explain\n> >> the strange behavior of galaxies without invoking dark matter. The basic\n> >> problem with galaxies is that the outer parts rotate faster than they\n> >> should given how much mass we actually see.\n>\n> >Doesn\'t it seem unreasonable to discard a theory as successful as GR?\n>\n> Of course! I don\'t think anyone wants to discard GR because of the\n> dark matter problems. But, it does make sense to have some people\n> play around with other ideas.\n>\n> Except for a few partisans, nobody will take MOND seriously until\n> it\'s extended to a full-fledged theory that matches the successes of\n> GR and isn\'t horribly ugly - or until it makes some prediction that\'s\n> almost impossible to match using conventional means (e.g. fine-tuned\n> dark matter).\n>\n> But, it\'s still good to look at the rotation curves in the paper I\n> referred to, and wonder what\'s really going on!\n\nPerhaps MOND is now at the stage of the Old Quantum Theory. There were\nlots of reasons not to accept it as the final theory, and some things\nabout it are in some sense just plain wrong. Nevertheless, it was\nsomehow on the right track, and led to full quantum mechanics later on.\n\n> >Or is it somehow possible to fit MOND into the framework of GR, like by\n> >modifying the field equations, perhaps by including torsion?\n>\n> People are trying very hard to fit MOND into GR in all possible ways,\n> and also to design dark matter that mimics the predictions of MOND.\n> Bekenstein\'s new paper:\n>\n> Jacob D. Bekenstein\n> Relativistic gravitation theory for the MOND paradigm\n> http://www.arXiv.org/abs/astro-ph/0403694\n>\n> seems like the best attempt so far to make MOND into a respectable\n> theory. It\'s still not elegant.\n>\n> >Everybody is talking about "dark matter" or alternative theories, when it is\n> >not even really clear what the predictions of GR are: recently I heard a\n> >talk about the "averaging problem" in GR; basically, the message was that\n> >we do not know if it is valid to take an average energy-momentum-tensor,\n> >put it into the field equations and see the result as an average metric.\n>\n> It\'s a nonlinear equation, so of course this is only approximately right\n> at best. The question is: is the approximation good enough for practical\n> purposes?\n>\n> Unless there\'s strong evidence that the approximation is *not* good enough,\n> I think it\'s a bit over-sensational to say "it\'s not even really clear what\n> the predictions of GR are". In every application of fundamental theories\n> of physics to real-world problems, people make approximations. Trying to\n> rigorously justify these approximations leads to difficult and interesting\n> problems in mathematical physics. But, we rarely claim that it\'s not clear\n> what the theory actually predicts until we have made everything rigorous!\n> So, claiming this here might fool nonexperts into thinking there\'s a big\n> problem with general relativity, when it\'s actually just "life as usual".\n>\n> >By googling, I found the following paper:\n> >\n> >http://arxiv.org/abs/gr-qc/9703016\n> >\n> >which also has some references.\n> >\n> >What do the experts think?\n>\n> I think someone, e.g. the author of this paper, should do some\n> back-of-the-envelope calculations to guess how much error is introduced\n> into astrophysical or cosmological calculations by means of this\n> averaging approximation. If it\'s a lot, this is a subject of real\n> importance in astronomy. If it\'s a little, this subject will mainly\n> be interesting to mathematical physicists.\n>\n> I can\'t imagine this "averaging problem" is big enough to explain the\n> effects that made people resort to dark matter and MOND, for example!\n\nHasn\'t there been some progress here since 1997? I seem to recall that\nsome of the usual suspects---Ehlers, G.F.R. Ellis, Buchert---had made\nsome progress in the averaging problem in the last few years. It might\nbe worth a search of the archives for these three names to see if they\nhave published anything on this.\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>In article <c8j2hp$15l$1@glue.ucr.edu>, baez@galaxy.ucr.edu (John Baez)
writes:

> In article <2ggpluF2hi83U1@uni-berlin.de>,
> Tobias Fritz <tobias@mad.scientist.com> wrote:
>
> >> Lee Smolin told me some neat stuff about MOND - that's "Modified
> >> Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
> >> the strange behavior of galaxies without invoking dark matter. The basic
> >> problem with galaxies is that the outer parts rotate faster than they
> >> should given how much mass we actually see.
>
> >Doesn't it seem unreasonable to discard a theory as successful as GR?
>
> Of course! I don't think anyone wants to discard GR because of the
> dark matter problems. But, it does make sense to have some people
> play around with other ideas.
>
> Except for a few partisans, nobody will take MOND seriously until
> it's extended to a full-fledged theory that matches the successes of
> GR and isn't horribly ugly - or until it makes some prediction that's
> almost impossible to match using conventional means (e.g. fine-tuned
> dark matter).
>
> But, it's still good to look at the rotation curves in the paper I
> referred to, and wonder what's really going on!

Perhaps MOND is now at the stage of the Old Quantum Theory. There were
lots of reasons not to accept it as the final theory, and some things
about it are in some sense just plain wrong. Nevertheless, it was
somehow on the right track, and led to full quantum mechanics later on.

> >Or is it somehow possible to fit MOND into the framework of GR, like by
> >modifying the field equations, perhaps by including torsion?
>
> People are trying very hard to fit MOND into GR in all possible ways,
> and also to design dark matter that mimics the predictions of MOND.
> Bekenstein's new paper:
>
> Jacob D. Bekenstein
> Relativistic gravitation theory for the MOND paradigm
> http://www.arXiv.org/abs/http://www.arxiv.org/abs/astro-ph/0403694
>
> seems like the best attempt so far to make MOND into a respectable
> theory. It's still not elegant.
>
> >Everybody is talking about "dark matter" or alternative theories, when it is
> >not even really clear what the predictions of GR are: recently I heard a
> >talk about the "averaging problem" in GR; basically, the message was that
> >we do not know if it is valid to take an average energy-momentum-tensor,
> >put it into the field equations and see the result as an average metric.
>
> It's a nonlinear equation, so of course this is only approximately right
> at best. The question is: is the approximation good enough for practical
> purposes?
>
> Unless there's strong evidence that the approximation is *not* good enough,
> I think it's a bit over-sensational to say "it's not even really clear what
> the predictions of GR are". In every application of fundamental theories
> of physics to real-world problems, people make approximations. Trying to
> rigorously justify these approximations leads to difficult and interesting
> problems in mathematical physics. But, we rarely claim that it's not clear
> what the theory actually predicts until we have made everything rigorous!
> So, claiming this here might fool nonexperts into thinking there's a big
> problem with general relativity, when it's actually just "life as usual".
>
> >By googling, I found the following paper:
> >
> >http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/9703016
> >
> >which also has some references.
> >
> >What do the experts think?
>
> I think someone, e.g. the author of this paper, should do some
> back-of-the-envelope calculations to guess how much error is introduced
> into astrophysical or cosmological calculations by means of this
> averaging approximation. If it's a lot, this is a subject of real
> importance in astronomy. If it's a little, this subject will mainly
> be interesting to mathematical physicists.
>
> I can't imagine this "averaging problem" is big enough to explain the
> effects that made people resort to dark matter and MOND, for example!

Hasn't there been some progress here since 1997? I seem to recall that
some of the usual suspects---Ehlers, G.F.R. Ellis, Buchert---had made
some progress in the averaging problem in the last few years. It might
be worth a search of the archives for these three names to see if they
have published anything on this.

alistair

May22-04, 05:49 AM

<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>Can MOND make any useful predictions about electromagnetic phenomena?\nIt\'s a modification of Newton\'s laws and they can be used in gravity\nand electromagnetism.\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>Can MOND make any useful predictions about electromagnetic phenomena?
It's a modification of Newton's laws and they can be used in gravity
and electromagnetism.

Charlie Stromeyer Jr.

May24-04, 05:31 AM

<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>\n\n> ... so if you\'re an expert who knows a lot about this, let me\n> know what you think - or better yet, post an article about this to\n> sci.physics.research!\n\nI\'ve never read anything about MOND other than what you have written\nabove, but I have taken separate astronomy courses from two professors\nwho I thought were great teachers, Rosanne DiStefano and Eric\nChaisson.\n\nDiStefano was the first person to teach me that there is no\nsignificant difference between dark matter and dark energy other than\npressure. I haven\'t looked closely at this issue for about two years\nbut AFAIK this is still the conventional view.\n\nAnyways, there is brand new and reasonably good evidence for dark\nenergy [1]. Additionally, recent experiments done only with electrons\nhave found parity violation in electroweak interactions, thus\nproviding further and somewhat non-trivial evidence for the SM [2].\n\n\n[1] http://www.washingtonpost.com/wp-dyn/articles/A37604-2004May18.html\n\n[2] http://sciencenow.sciencemag.org/cgi/content/full/2004/426/2\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>... so if you're an expert who knows a lot about this, let me
> know what you think - or better yet, post an article about this to
> sci.physics.research!

I've never read anything about MOND other than what you have written
above, but I have taken separate astronomy courses from two professors
who I thought were great teachers, Rosanne DiStefano and Eric
Chaisson.

DiStefano was the first person to teach me that there is no
significant difference between dark matter and dark energy other than
pressure. I haven't looked closely at this issue for about two years
but AFAIK this is still the conventional view.

Anyways, there is brand new and reasonably good evidence for dark
energy [1]. Additionally, recent experiments done only with electrons
have found parity violation in electroweak interactions, thus
providing further and somewhat non-trivial evidence for the SM [2].

[1] http://www.washingtonpost.com/wp-dyn/articles/A37604-2004May18.html

[2] http://sciencenow.sciencemag.org/cgi/content/full/2004/426/2

Nicolaas Vroom

May24-04, 12:51 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>"Tobias Fritz" <tobias@mad.scientist.com> schreef in bericht\nnews:2ggpluF2hi83U1@uni-berlin.de...\n>\n> >\n> > Lee Smolin told me some neat stuff about MOND - that\'s "Modified\n> > Newtonian Dynamics", which is Mordehai Milgrom\'s way of trying\n> > to explain the strange behavior of galaxies without invoking\n> > dark matter. The basic problem with galaxies\n> > is that the outer parts rotate faster than they\n> > should given how much mass we actually see.\n> >\n> > If you have a planet in a circular orbit about the Sun,\n> > Newton\'s laws say its acceleration is proportional to 1/r^2,\n> > where r is its distance to the Sun. Similarly, if almost all the\n> > mass in a galaxy were concentrated right at the center, a star orbiting\n> > in a circle at distance r from the center would have acceleration\n> > proportional to 1/r^2. Of course, not all the mass is right at the\ncenter!\n> > So, the acceleration should drop off more slowly than 1/r^2\n> > as you go further out. And it does.\n> > But, the observed acceleration drops off a lot more slowly than\n> > the acceleration people calculate from the mass they see.\n> > It\'s not a small effect: it\'s a HUGE effect!\n> >\n> > One solution is to say there\'s a lot of mass we don\'t see: "dark matter"\n> > of some sort. If you take this route, which most astronomers do,\n> > you\'re forced to say that *most* of the mass of galaxies is in\n> > the form of dark matter.\n> >\n\nThat is one solution but may be there is a slightly different point of view.\nFirst of all a galaxy consists of a bulge and a disc.\nTo simulate the bulge (a sphere) using Newton\'s Law is easy\nand what you get is a rotation curve with lineair increases\nwith distance.\nTo simulate the disc is a slightly different endavour.\nWhen the disc only consists of some sun sized test stars\n(like the planets around the sun)\nthen the rotation curve will follow the curve: sqroot(M*G/r)\n\nHowever that picture is too simple.\nFirst of all there are not some sun sized visible stars in the disc\nbut many and when you take those into acount the rotation curve\nbecomes more flat.\nSecondly the number of visible stars to make the rotation flatter\nis not large, specific along the rim the density becomes small\nThird even outside the visible rim of the galaxy it is easy possible\nthat that there are sun sized stars (or slightly smaller) which\nare overall invisible because the density is so low.\nThis becomes the more of a problem the further away the galaxy is.\n\nMy point is that before you can introduce dark matter\nfirst you must make a 3D picture of ALL the visible matter included\nand calulate the rotation curve based on that.\nThe question is if this calulated curve matches which what is\nobserved.\nIf it matches there is no reason to introduce dark matter.\nIf it does not match you could introduce dark matter in this 3D\npicture such that it matches.\nBut my guess is that no HUGE amounts are required\nnor that *most* of the mass is in the form of dark matter\n\nHowever you have to be carefull where you envision\nthis dark matter.\nIt can not be in the close neighbourhood of our Sun,\nbecause it will effect the trajectories of our planets,\nnor it can be close to any Star in the disc,\nbecause why should out Sun be special.\nAlso in a sphere around the visible rim of the galaxy\n(like the oort cloud outside the kuiper belt around our Sun)\nis tricky because it will only effect the rim.\n\nIn short a 3D picture of a Galaxy, with dark matter included,\nis complicated.\n\nNicolaas Vroom\nhttp://users.pandora.be/nicvroom/\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>"Tobias Fritz" <tobias@mad.scientist.com> schreef in bericht
news:2ggpluF2hi83U1@uni-berlin.de...
>
> >
> > Lee Smolin told me some neat stuff about MOND - that's "Modified
> > Newtonian Dynamics", which is Mordehai Milgrom's way of trying
> > to explain the strange behavior of galaxies without invoking
> > dark matter. The basic problem with galaxies
> > is that the outer parts rotate faster than they
> > should given how much mass we actually see.
> >
> > If you have a planet in a circular orbit about the Sun,
> > Newton's laws say its acceleration is proportional to 1/r^2,
> > where r is its distance to the Sun. Similarly, if almost all the
> > mass in a galaxy were concentrated right at the center, a star orbiting
> > in a circle at distance r from the center would have acceleration
> > proportional to 1/r^2. Of course, not all the mass is right at the
center!
> > So, the acceleration should drop off more slowly than 1/r^2
> > as you go further out. And it does.
> > But, the observed acceleration drops off a lot more slowly than
> > the acceleration people calculate from the mass they see.
> > It's not a small effect: it's a HUGE effect!
> >
> > One solution is to say there's a lot of mass we don't see: "dark matter"
> > of some sort. If you take this route, which most astronomers do,
> > you're forced to say that *most* of the mass of galaxies is in
> > the form of dark matter.
> >

That is one solution but may be there is a slightly different point of view.
First of all a galaxy consists of a bulge and a disc.
To simulate the bulge (a sphere) using Newton's Law is easy
and what you get is a rotation curve with lineair increases
with distance.
To simulate the disc is a slightly different endavour.
When the disc only consists of some sun sized test stars
(like the planets around the sun)
then the rotation curve will follow the curve: sqroot(M*G/r)

However that picture is too simple.
First of all there are not some sun sized visible stars in the disc
but many and when you take those into acount the rotation curve
becomes more flat.
Secondly the number of visible stars to make the rotation flatter
is not large, specific along the rim the density becomes small
Third even outside the visible rim of the galaxy it is easy possible
that that there are sun sized stars (or slightly smaller) which
are overall invisible because the density is so low.
This becomes the more of a problem the further away the galaxy is.

My point is that before you can introduce dark matter
first you must make a 3D picture of ALL the visible matter included
and calulate the rotation curve based on that.
The question is if this calulated curve matches which what is
observed.
If it matches there is no reason to introduce dark matter.
If it does not match you could introduce dark matter in this 3D
picture such that it matches.
But my guess is that no HUGE amounts are required
nor that *most* of the mass is in the form of dark matter

However you have to be carefull where you envision
this dark matter.
It can not be in the close neighbourhood of our Sun,
because it will effect the trajectories of our planets,
nor it can be close to any Star in the disc,
because why should out Sun be special.
Also in a sphere around the visible rim of the galaxy
(like the oort cloud outside the kuiper belt around our Sun)
is tricky because it will only effect the rim.

In short a 3D picture of a Galaxy, with dark matter included,
is complicated.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

Gordon D. Pusch

May25-04, 02:30 AM

<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>alistair@goforit64.fsnet.co.uk (alistair) writes:\n\n> Can MOND make any useful predictions about electromagnetic phenomena?\n\nNo. In fact, one of the major arguments against MOND is its total\ninability to make any useful prediction of any type whatsoever\nabout the "gravitational lensing" effect produced by galaxies,\nsince light-bending is a general relativistic effect, and MOND\nis incompatible with General Relativity, combined with the fact\nthat the gravitational lensing produced by most non-dwarf galaxies\nas computed using General Relativity is entirely consistent with\nestimates of the masses of "Dark Matter" they must contain based\non their rotation curves and non-MOND Newtonian stellar dynamics.\n\n\n> It\'s a modification of Newton\'s laws and they can be used in gravity\n> and electromagnetism.\n\nActually, Newton\'s Laws _CAN\'T_ be used to handle electromagnetism,\nwhich is one of the reasons why Einstein invented Special Relativity.\nMoreover, Newton\'s Laws have also been shown to be inadaquate to handle\ngravity except in the simultaneous limit of weak fields and slow motion;\nfor particles moving at a significant fraction of the speed of light,\nor near bodies whose escape velocity is a significant fraction of the\nspeed of light, Newton\'s Laws fail miserably.\n\n\n-- Gordon D. Pusch\n\nperl -e \'\\$_ = "gdpusch\\@NO.xnet.SPAM.com\\n"; s/NO\\.//; s/SPAM\\.//; print;\'\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>alistair@goforit64.fsnet.co.uk (alistair) writes:

> Can MOND make any useful predictions about electromagnetic phenomena?

No. In fact, one of the major arguments against MOND is its total
inability to make any useful prediction of any type whatsoever
about the "gravitational lensing" effect produced by galaxies,
since light-bending is a general relativistic effect, and MOND
is incompatible with General Relativity, combined with the fact
that the gravitational lensing produced by most non-dwarf galaxies
as computed using General Relativity is entirely consistent with
estimates of the masses of "Dark Matter" they must contain based
on their rotation curves and non-MOND Newtonian stellar dynamics.

> It's a modification of Newton's laws and they can be used in gravity
> and electromagnetism.

Actually, Newton's Laws _CAN'T_ be used to handle electromagnetism,
which is one of the reasons why Einstein invented Special Relativity.
Moreover, Newton's Laws have also been shown to be inadaquate to handle
gravity except in the simultaneous limit of weak fields and slow motion;
for particles moving at a significant fraction of the speed of light,
or near bodies whose escape velocity is a significant fraction of the
speed of light, Newton's Laws fail miserably.

-- Gordon D. Pusch

perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'

Charlie Stromeyer Jr.

May25-04, 02:32 AM

<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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:\n\n> >> On Sat, 15 May 2004, John Baez wrote:\n>\n> > > Someone: This [a paper on discretization of gravity] is pretty exciting.\n> > http://www.arxiv.org/abs/hep-th/0404156\n> >\n> > I\'m glad you think so! I sure do!\n>\n> Well, I am sure that you would be even more happy if I agreed, too. But I\n> don\'t. There is just no evidence that the resulting physics is physics of\n> gravity, and there is evidence against the conjecture that it will be\n> locally Lorentz-invariant. Below, I will argue that this unjustified\n> excitement about these models returns again and again, and that these\n> models never lead anywhere.\n\nSo do I win a prize win I agree with Lubos for the 100th time ?\nI hope so because I must be close !\n\nHere are three other reasons to be skeptical of discretized approaches\nto gravity:\n\n\n1) How are such approaches to be made compatible with vector\nsupersymmetry (or vsusy) which is a topological type of symmetry that\nappears in both gravity and topological gauge theories [1].\n\n2) How are such approaches to be made compatible with Bell- like\ncorrelations, non-locality and non-causality which are each present in\nthe experiment described in this brief four page paper [2].\n\n3) To paraphrase a sentence that Stephen Hawking once wrote, to not\nbelieve in the beauty and unity of the dualities of M-theory is like\nbelieving that evolution did not occur because instead God placed by\nhand all the fossils in the Earth just to play a joke on the\npaleontologists :-)\n\n\n[1] http://arxiv.org/abs/hep-th/0111273\n\nhttp://arxiv.org/abs/hep-th/0010053\n\n[2] http://arxiv.org/abs/quant-ph/0102109\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>Lubos Motl <motl@feynman.harvard.edu> wrote in message news:

> >> On Sat, 15 May 2004, John Baez wrote:
>
> > > Someone: This [a paper on discretization of gravity] is pretty exciting.
> > http://www.arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0404156
> >
> > I'm glad you think so! I sure do!
>
> Well, I am sure that you would be even more happy if I agreed, too. But I
> don't. There is just no evidence that the resulting physics is physics of
> gravity, and there is evidence against the conjecture that it will be
> locally Lorentz-invariant. Below, I will argue that this unjustified
> excitement about these models returns again and again, and that these
> models never lead anywhere.

So do I win a prize win I agree with Lubos for the 100th time ?
I hope so because I must be close !

Here are three other reasons to be skeptical of discretized approaches
to gravity:

1) How are such approaches to be made compatible with vector
supersymmetry (or vsusy) which is a topological type of symmetry that
appears in both gravity and topological gauge theories [1].

2) How are such approaches to be made compatible with Bell- like
correlations, non-locality and non-causality which are each present in
the experiment described in this brief four page paper [2].

3) To paraphrase a sentence that Stephen Hawking once wrote, to not
believe in the beauty and unity of the dualities of M-theory is like
believing that evolution did not occur because instead God placed by
hand all the fossils in the Earth just to play a joke on the
paleontologists :-)

[1] http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0111273

http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0010053

[2] http://arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0102109

alistair

May25-04, 09:26 AM

<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>\n\nIt\'s interesting that MOND splits Newtonian gravity into two cases\nand the Modified version of Newtonain dynamics seems to happen in\ngalaxies and clusters of galaxies with magnetic fields.What is the\nphysical reason that MOND could be right?\nIf we assume that there is another force interacting with the stars in\na galaxy –\nwhich modifies the Newtonian force law, what generates this force?\n\nOne answer to this question could be this:\nsuppose some charged particles flow over the plane of a spiral galaxy\nand parallel to the plane, from intergalactic space. They encounter\nthe magnetic field lines of the galaxy and a force acts on them\nobeying the equation force = qvB.\nAssuming q v and B stay roughly constant as the charged particles\ncross the galaxy,and\nsince in normal Newtonian dynamics acceleration = Force / mass of\ncharged particle,\nthe charged particles experience a constant acceleration as they move\n(we will assume the particles are separated widely enough to make\ntheir coulomb attractions and repulsions insignificant).\nNegative charges will experience a push in the opposite direction to\npositive charges-\nthe negative and positive charges will move closer together.\nHow much do they move?\nUsing s= ut + (a t ^ 2) / 2 , s = sideways distance moved,\nand setting u, the initial and sideways speed of the charges as they\njust reach edge of the spiral galaxy disc ( we are assuming that this\nlocation is an approximation that will yield useful results) to zero:\n\ns = (a t ^ 2) / 2\n\nsince the normal Newtonian acceleration on the charges is constant,\ns is proportional to t ^ 2.\n\nA charge moving towards the centre of the galaxy takes half the time\nto move\nto a position 0.75 the distance from the centre to the edge of the\ndisc, as it does to move to 0.5 that distance from the centre to the\nedge.\n\nSo if it moves to 0.75 the distance the value of s is (1/2) ^2 i.e\n1 / 4 of what it would be for a movement of a particle to halfway\nacross the galactic plane.So the force exerted on a star would be a\nforce exerted by 1/4\nthe number of particles because the negative and positive charged\nparticles\nwill not have moved so much sideways and so will not be so densely\npacked at 0.75 units distance as they would be at 0.5 units distance\nfrom the galactic centre.\nThe gravitational force depends on 1/ r^2 so at 0.75 units it would be\n( 0.75 / 0.5 ) ^ 2 2.25 times weaker than at 0.5 units distance from\nthe galactic centre.\n\n\nSo if at 0.5 units distance a star experiences a force due to gravity\nof X newtons\nand a force due to the charged particles of Y Newtons, the force on\nthe star\nis X + Y Newtons towards the galactic centre.\n\nat 0.75 units distance, the star would experience a force of:\n\n1 / 2.25 X + 0.25 Y\nThis will apply only for charged particles moving through a\nhomogeneous region\nof the galactic magnetic field and it is assumed that the electric\nforces between charges are negligible.The idea outlined above may need\nmodifying but\nhopefully it gives some insight into a physical mechanism for MOND.\nIt attempts to show that Newton\'s laws are still valid and that MOND\nis right just because it considers only the gravitational force and\nnot other forces that could act upon stars.\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>It's interesting that MOND splits Newtonian gravity into two cases
and the Modified version of Newtonain dynamics seems to happen in
galaxies and clusters of galaxies with magnetic fields.What is the
physical reason that MOND could be right?
If we assume that there is another force interacting with the stars in
a galaxy –
which modifies the Newtonian force law, what generates this force?

One answer to this question could be this:
suppose some charged particles flow over the plane of a spiral galaxy
and parallel to the plane, from intergalactic space. They encounter
the magnetic field lines of the galaxy and a force acts on them
obeying the equation force = qvB.
Assuming q v and B stay roughly constant as the charged particles
cross the galaxy,and
since in normal Newtonian dynamics acceleration = Force / mass of
charged particle,
the charged particles experience a constant acceleration as they move
(we will assume the particles are separated widely enough to make
their coulomb attractions and repulsions insignificant).
Negative charges will experience a push in the opposite direction to
positive charges-
the negative and positive charges will move closer together.
How much do they move?
Using s= ut + (a t ^ 2) / 2 , s = sideways distance moved,
and setting u, the initial and sideways speed of the charges as they
just reach edge of the spiral galaxy disc ( we are assuming that this
location is an approximation that will yield useful results) to zero:

s = (a t ^ 2) / 2

since the normal Newtonian acceleration on the charges is constant,
s is proportional to t ^ 2.

A charge moving towards the centre of the galaxy takes half the time
to move
to a position .75 the distance from the centre to the edge of the
disc, as it does to move to .5 that distance from the centre to the
edge.

So if it moves to .75 the distance the value of s is (1/2) ^2 i.e
1 / 4 of what it would be for a movement of a particle to halfway
across the galactic plane.So the force exerted on a star would be a
force exerted by 1/4
the number of particles because the negative and positive charged
particles
will not have moved so much sideways and so will not be so densely
packed at .75 units distance as they would be at .5 units distance
from the galactic centre.
The gravitational force depends on 1/ r^2 so at .75 units it would be
( .75 / .5 ) ^ 2 2.25 times weaker than at .5 units distance from
the galactic centre.

So if at .5 units distance a star experiences a force due to gravity
of X newtons
and a force due to the charged particles of Y Newtons, the force on
the star
is X + Y Newtons towards the galactic centre.

at .75 units distance, the star would experience a force of:

1 / 2.25 X + .25 Y
This will apply only for charged particles moving through a
homogeneous region
of the galactic magnetic field and it is assumed that the electric
forces between charges are negligible.The idea outlined above may need
modifying but
hopefully it gives some insight into a physical mechanism for MOND.
It attempts to show that Newton's laws are still valid and that MOND
is right just because it considers only the gravitational force and
not other forces that could act upon stars.

Thomas Larsson

May29-04, 12:51 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>Charlie Stromeyer Jr. <cstromey@hotmail.com> skrev i\ndiskussionsgruppsmeddelandet:61773ed7.040524082 2.1c7108de@posting.google.com...\n\n> So do I win a prize win I agree with Lubos for the 100th time ?\n> I hope so because I must be close !\n\nDear Zirkus,\n\nMotl has of course completely missed the main point. Distler\'s\nobjection from 3 years ago was that he didn\'t believe in a good\ncontinuum limit in 4D; a "miracle" as he puts it. This may have\nbeen good point at that time; I thought so myself, although I\nwould have been much less pessimistic if I had known that\nAmbjorn and Loll had already succeeded in 2 and 3D.\n\nThe new thing is that AJL have presented rather compelling\nnumerical evidence for a good continuum limit in 4D, thus making\nDistler\'s objection obsolete. It is the fact that AJL have\napparently succeeded in quantizing gravity numerically that\npeople are so excited about.\n\n>\n> Here are three other reasons to be skeptical of discretized approaches\n> to gravity:\n>\n>\n> 1) How are such approaches to be made compatible with vector\n> supersymmetry (or vsusy) which is a topological type of symmetry that\n> appears in both gravity and topological gauge theories [1].\n\nThe term vector susy is a misnomer, since the superalgebras\nappearing in those papers can hardly qualify as susies. Physical\nfields obey the spin-statistics theorem, so susy generators must\nbe spinors rather than vectors. Instead, what these authors do\nis to treat the diffeomorphism constraint in the BV formalism,\nwhich is the Lagrangian counterpart of the BRST method in\nHamiltonian quantization. This is a neat way to treat a gauge\nsymmetry, at least in the absense of anomalies: one identifies\nphysical states with cohomology classes of a nilpotent BRST\noperator. A superalgebra structure arises naturally since the\nBRST operator is fermionic, but this has nothing to do with\nsupersymmetry.\n\nIn the AJL model, the gauge is already fixed;they formulate the\naction in terms of diff-invariant edge lengths rather than the\nmetric, there is a privileged time direction, etc. Since their\nmodel only contains gauge-invariant quantities, there are no\ndiffeomorphism constraints left, and thus no need for ghosts.\n\n>\n> 2) How are such approaches to be made compatible with Bell- like\n> correlations, non-locality and non-causality which are each present in\n> the experiment described in this brief four page paper [2].\n\nCausality seems to be the whole point with the AJL approach -\nlack of causality, i.e. singular metrics, is explicitly thrown\nout. Whereas things like the EPR paradox are constantly\nconfusing, it does not imply a violation of neither causality\nnor special relativity. One should ponder what Bert Schroer\nwrites in http://arxiv.org/abs/hep-th/0405105, p 3:\n\n"In fact nowadays it is generally excepted among experts that\namong all physical principles which underlie standard QFT,\nEinstein causality for local observables is the most sturdy\nproperty from a conceptual point of view; no matter how many\nwords have been spoken and how many papers had been written on\ncut-offs, regularizations and other ad hoc modifications, nobody\nhas any idea (beyond a wishful incantation) what such\nmanipulations really mean in terms of operators in a Hilbert\nspace. Hence it comes as no surprise that most attempts of\nintroducing deviations from micro-causality actually amount to\nviolating macro-causality in the wake; but macro-causality is\nthe absolute borderline between physics and the realm of\npoltergeists."\n\nAnother reason to believe in strict causality comes from the\nquantum analogue of tensor calculus. The objects that build up\nprojective representations of the diffeomorphism algebra live on\nthe observer\'s trajectory, and are thus automatically causally\nrelated. This can be traced back to the apparent paradox that\nenergy is both a scalar (a number that is bounded from below by\nthe mass) and a vector (the zeroth component of\nenergy-momentum), which is a version of the problem of time.\nThat people haven\'t cared enough about causality may very well\nbe the reason why there hasn\'t been any real progress in quantum\ngravity; the work of AJL and collaborators may be an exception.\n\n>\n> 3) To paraphrase a sentence that Stephen Hawking once wrote, to not\n> believe in the beauty and unity of the dualities of M-theory is like\n> believing that evolution did not occur because instead God placed by\n> hand all the fossils in the Earth just to play a joke on the\n> paleontologists :-)\n\nBeauty lies in the eyes of the beholder. The AJL model is\nadmittedly not very beautiful, but one does not expect that of a\ngauge-fixed and discretized model. A gauge-fixed version of\nlattice gauge theory is not terribly beautiful either, but we\nnevertheless believe that it is a valid quantization of gauge\ntheories.\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>Charlie Stromeyer Jr. <cstromey@hotmail.com> skrev i
diskussionsgruppsmeddelandet:61773ed7.0405240822.1 c7108de@posting.google.com...

> So do I win a prize win I agree with Lubos for the 100th time ?
> I hope so because I must be close !

Dear Zirkus,

Motl has of course completely missed the main point. Distler's
objection from 3 years ago was that he didn't believe in a good
continuum limit in 4D; a "miracle" as he puts it. This may have
been good point at that time; I thought so myself, although I
would have been much less pessimistic if I had known that
Ambjorn and Loll had already succeeded in 2 and 3D.

The new thing is that AJL have presented rather compelling
numerical evidence for a good continuum limit in 4D, thus making
Distler's objection obsolete. It is the fact that AJL have
apparently succeeded in quantizing gravity numerically that
people are so excited about.

>
> Here are three other reasons to be skeptical of discretized approaches
> to gravity:
>
>
> 1) How are such approaches to be made compatible with vector
> supersymmetry (or vsusy) which is a topological type of symmetry that
> appears in both gravity and topological gauge theories [1].

The term vector susy is a misnomer, since the superalgebras
appearing in those papers can hardly qualify as susies. Physical
fields obey the spin-statistics theorem, so susy generators must
be spinors rather than vectors. Instead, what these authors do
is to treat the diffeomorphism constraint in the BV formalism,
which is the Lagrangian counterpart of the BRST method in
Hamiltonian quantization. This is a neat way to treat a gauge
symmetry, at least in the absense of anomalies: one identifies
physical states with cohomology classes of a nilpotent BRST
operator. A superalgebra structure arises naturally since the
BRST operator is fermionic, but this has nothing to do with
supersymmetry.

In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts.

>
> 2) How are such approaches to be made compatible with Bell- like
> correlations, non-locality and non-causality which are each present in
> the experiment described in this brief four page paper [2].

Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out. Whereas things like the EPR paradox are constantly
confusing, it does not imply a violation of neither causality
nor special relativity. One should ponder what Bert Schroer
writes in http://arxiv.org/abs/http://www.arxiv.org/abs/hep-th/0405105, p 3:

"In fact nowadays it is generally excepted among experts that
among all physical principles which underlie standard QFT,
Einstein causality for local observables is the most sturdy
property from a conceptual point of view; no matter how many
words have been spoken and how many papers had been written on
cut-offs, regularizations and other ad hoc modifications, nobody
has any idea (beyond a wishful incantation) what such
manipulations really mean in terms of operators in a Hilbert
space. Hence it comes as no surprise that most attempts of
introducing deviations from micro-causality actually amount to
violating macro-causality in the wake; but macro-causality is
the absolute borderline between physics and the realm of
poltergeists."

Another reason to believe in strict causality comes from the
quantum analogue of tensor calculus. The objects that build up
projective representations of the diffeomorphism algebra live on
the observer's trajectory, and are thus automatically causally
related. This can be traced back to the apparent paradox that
energy is both a scalar (a number that is bounded from below by
the mass) and a vector (the zeroth component of
energy-momentum), which is a version of the problem of time.
That people haven't cared enough about causality may very well
be the reason why there hasn't been any real progress in quantum
gravity; the work of AJL and collaborators may be an exception.

>
> 3) To paraphrase a sentence that Stephen Hawking once wrote, to not
> believe in the beauty and unity of the dualities of M-theory is like
> believing that evolution did not occur because instead God placed by
> hand all the fossils in the Earth just to play a joke on the
> paleontologists :-)

Beauty lies in the eyes of the beholder. The AJL model is
admittedly not very beautiful, but one does not expect that of a
gauge-fixed and discretized model. A gauge-fixed version of
lattice gauge theory is not terribly beautiful either, but we
nevertheless believe that it is a valid quantization of gauge
theories.

Lubos Motl

May31-04, 07:26 AM

<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>\nDear John,\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\ncalculations - 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, unlike the case of classical GR (and\nsome interpretations of LQG); two different geometries can lead to\nidentical physics (by T-duality or mirror symmetry); K3 manifolds with one\ntheory can be equivalent to tori with another (heterotic) theory;\ncharges get continuously transmuted to momenta and vice versa; black holes\nbecome elementary particles (vibrating strings) and vice versa; timelike\nsingularities 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 just reproduces Einstein, with a typically Einsteinian hope that\nquantum physics won\'t modify anything; 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.\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 ingredience - 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; some people\nbelieve that these problems can be attacked directly and they try to do\nso.\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 while mathematical physics always prefers rigor (it\nprefers to be picky).\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 we could have thought centuries\nago) - but it does not change the fact that if string theory teaches us\nabout something, we should listen.\n\nHowever, it is not clear to me whether string theory is trying to teach us\nthat we should work with a huge landscape where the chances to predict\nsomething new are small. Landscape is not like dualities; with dualities,\neverything fits together and we can check hundreds of explicit\nquantitative formulae - and they agree. The landscape is still just a\nvague and qualitative statement based on a philosophical prejudice. I am\nafraid that it will always be.\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. String theory is a well-defined and unique\ntheory and what we have learned is reliable - at least the\nnon-cosmological questions - and any better language in the future must\nconfirm it! Be sure that if another framework would show that the gauge\ngroup of type I string theory must be SO(3200) instead of SO(32), the\nwhole structure would certainly break down. There is no way to undo these\ninsights!\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 with a Planckian energy density (even if the\ncosmological constant is cancelled) - which is not quite what we want.\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\na simple approach - 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 would have been very incorrect\nif they decided in advance that low energy nuclear physics must be simple\nto calculate, and then they tried to force Nature to behave according to\nthis assumption. Such an approach would be very unlikely to lead to the\ncorrect theory.\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 all\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 if it is the unique theory.\n\nString theory is, we think, the unique theory of that type, and this is\nthe only real reason why we focus on it (as opposed to something else one\ncould a priori imagine). It is not because it would simplify some of our\ncalculations; indeed, string theory is complex enough and it requires a\nlot of advanced maths. Also, it has many scenarios how the real Universe\ncan occur in it. Because the scenario within string theory is *not*\nunique, we must admit that we don\'t know which one is correct.\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" the 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). Generically, there is no reason to think\nthat a generic UV theory should flow to GR that admits small ripples\naround a flat space, for example. There is also no reason to think that a\ntheory that is non-relativistic (Lorentz breaking) at the Planck scale\nwill suddenly or automatically flow to a Lorentz invariant theory at long\ndistances.\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. This can be done 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 right path\nintegral should sum over everything. It is not surprising that if we\nrestrict a path integral to contain the configurations that look almost\nexactly like an elephant (equivalently, the action is re-defined to be\ni.infinity for non-elephant configurations), we will get a path integral\ndominated by an elephant. But in that case, we cannot claim that we have\nderived an elephant from a deeper theory! ;-) Simply speaking, I have no\nidea what you can be excited about because the reason of this success (?)\nseems pretty manifest, and the 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. The only nice thing that such a calculation could\ngive is the proportionality factor - but unforunately it does not come out\ncorrectly.\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 exceed 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\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 even after it is\nproved inconsistent. Pure GR has real UV problems, and any faithful\ndescription of it will confirm their existence. One can try to hide these\nproblems - for example by erasing all terms from the path integral that\nare identified as those responsible for the problems - but one cannot get\na 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. What do you think?\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</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,

> 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
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, unlike the case of classical GR (and
some 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 just reproduces Einstein, with a typically Einsteinian hope that
quantum physics won't modify anything; 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.

> 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 ingredience - 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; some people
believe that these problems can be attacked directly and they try to do
so.

> 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 while mathematical physics always prefers rigor (it
prefers to be picky).

> 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 we could have thought centuries
ago) - but it does not change the fact that if string theory teaches us
about something, we should listen.

However, it is not clear to me 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.

> 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. 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. 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 with a Planckian energy density (even if the
cosmological constant is cancelled) - which is not quite what we want.

> 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
a simple approach - 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 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.

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 all
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 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 we 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 maths. 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.

> 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" the 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). 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. 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.

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. This can be done 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 right path
integral should sum over everything. It is not surprising that if we
restrict a path integral to contain 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. The only nice thing that such a calculation could
give is the proportionality factor - but unforunately it does not come out
correctly.

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 exceed 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.

> 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 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. What do you think?

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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

alistair

May31-04, 07:26 AM

<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>\n\nCan MOND make any useful predictions about electromagnetic phenomena?\nIt\'s a modification of Newton\'s laws and they can be used in gravity\nand electromagnetism\n\nThe effect of MOND is supposed to be important when acceleration is\nless than\n10 ^- 10 m / s ^ 2.\nIf this is true then if I place a postive electric charge at a\ndistance from a negative electric charge, such that the acceleration\npredicted by\nk q1 q2/ r ^ 2 on each charge should be 10 ^ - 11 m / s ^ 2,then\naccording to MOND an experimental measurement of the acceleration\nwould show that the prediction of k q1 q2 / r ^ 2 was wrong!\nHas anyone ever performed a test of this kind on MOND?\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>Can MOND make any useful predictions about electromagnetic phenomena?
It's a modification of Newton's laws and they can be used in gravity
and electromagnetism

The effect of MOND is supposed to be important when acceleration is
less than
10 ^- 10 m / s ^ 2.
If this is true then if I place a postive electric charge at a
distance from a negative electric charge, such that the acceleration
predicted by
k q1 q2/ r ^ 2 on each charge should be 10 ^ - 11 m / s ^ 2,then
according to MOND an experimental measurement of the acceleration
would show that the prediction of k q1 q2 / r ^ 2 was wrong!
Has anyone ever performed a test of this kind on MOND?

Urs Schreiber

May31-04, 09:12 AM

<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>\n"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0405302130050.1070 7-100000@feynman.harvard.edu...\n\n> > There\'s no good way to separate the ripples from the lake.\n>\n> That\'s right, and string theory allows us to prove - at least\n> perturbatively, or also in effective field description of nonperturbative\n> physics - that physics of (a coherent state of) ripples is exactly\n> *equivalent* to a modified lake.\n[...]\n> What is more important, however, is that *physics* of string theory does\n> not treat the background as something that is separated from its\n> excitations - and we can easily prove it.\n\nFor those who (like me until recently) haven\'t seen the original literature\non this result I\'d like to mention some important papers:\n\nThis issue has been mostly studied by Ashoke Sen in a long series of papers\nin the 90s:\n\nAshoke Sen,\n\nOn the background independence of string field theory\nNucl. Phys. B 345 (1990) 551\n\nOn the background independence of string field theory (II). Analysis of the\non-shell S-matrix elements\nNucl. Phys. B347 (1990) 270\n\nOn the background independence of string field theory (III). Explicit field\nredefinitions\nNucl. Phys. B391 (1993) 550\nhep-th/9201041\n\nand is briefly reviewed in section 2.4 of\n\nAshoke Sen & Barton Zwiebach\nA proof of local background independence of classical closed string field\ntheory\nhep-th/9307088\n\nOne key idea in these developments is that presented in the short paper\n\nAshoke Sen\nEquations of motion in non-polynomial closed string field theory and\nconformal invariance of two dimensional field theories\nPhys. Lett. B 241 (1990) 350-356\n\nwhich discusses that to every solution Phi of the classical equations of\nmotion of string theory there is a deformed BRST operator\n\n\\tilde Q = Q + [Phi , .]\n\nwhich is the BRST operator of the worldsheet theory which describes string\npropagation in the new background described by Phi.\n\nIn particular this implies that when writing down the action of string field\ntheory, which is of the form\n\nS = < Phi , Q Phi> + Sum_n a_n < Phi , Phi , .... Phi>\n\nfor Phi a string field, Q the BRST operator for a given background and <...>\nthe correlators of the accociated CFT, it _does not matter_ which CFT (=\nbackground) one uses. By simply splitting\n\nPhi = Phi_0 + Psi\n\nwith Phi_0 a classical solution of the above action, one rewrites the above\naction equivalently in the form\n\nS = S_0 + < Psi , \\tilde Q Psi>_0 + Sum_n a_n < Psi , Psi , .... Psi>_0\n\nwhere now all object are evaluated with respect to the shifted background.\n\nSo in this sense the action of string field theory is background\nindependent, even though it is convenient to express it with respect to\n_any_ given background for practical calculations.\n\nBut it can even be made explicitly background independent: It turns out,\nroughly, that the action of the BRST operator itself (which one may think of\nas a high-brow version of the usual kinetic operator for some field in a\ngiven background) can be mimicked by anticommutation with a certain string\nfield Phi_bf, so that\n\n\\tilde Q = 0 + [ Phi_bf, . ]\n\nand that this Phi_bf extremizes the above action with the kinetic term\nremoved.\n\nThis construction goes back to an impressive paper by Hata\n\nH. Hata\nPregeometrical String Field Theory: Creation of Space-Time and Motion\n(1986)\nhttp://ccdb3fs.kek.jp/cgi-bin/img_index?8606274\n\nthat Lubos kindly has made me aware of a while ago.\n\nIt is philosophically rather satisfying that in this formulation the\nequations of motion of string field backgrounds take the concise form\n\nA * A = 0\n\n(where A is a string field and * the star product which describes the\nsplitting/joining interaction of two strings).\n\nThe idea in this paper was later refined (though in a slightly different\ncontext) in\n\nG. Horowitz and J. Lykken and R. Rohm and A. Strominger:\nPurely Cubic Action for String Field Theory\nPhys. Rev. Lett. 57(3) (1986) 283 .\n\nThe crucial technique used there was the use of a simple relation between\n(ghost-)graded string field star commutators and actions of operators on the\nstrings state space.\n\nNamely let w(z) be some current chiral field of unit weight on the\nworldsheet, let W_L be its integral over the left half of the unit circle in\nthe complex plane and let W be the full integral, then we have the identity\n\n[ W_L(I) , Phi ] = W(Phi)\n\nwhere I is the identity string field [.,.] is the graded star product\ncommutator and W(Phi) is the action of W on the state Phi.\n\nUsing this formula it is immediate that the BRST operator Q comes from the\n"background" string field Q_L(I)\n\nQ = [ Q_L(I), . ] .\n\nand that this field is actually a solution of the purely cubic SFT action\n\nS_cube ~ < Phi , Phi , Phi>\n\nwhich (when the correlator is evaluated in the functional fashion described\non p.285 of the above paper) manifestly background independent.\n\nMaybe it should be emphasized that "background independence" here is more\nthan just "independence of a given background _metric_". These actions are\nalso independent of any "background choice of field content"! It is rarely\nmentioned in the context of non-perturbative approaches to quantum gravity\nother than string theory, that all these alternative theories require a\nby-hand choice of field content, even if no background metric is needed. For\ninstance Lee Smolin says that LQG can be performed with large classes of\nadditional fields. From the point of view of background independence this\nshould count as a bug, not as a feature, as has been emphasized by Jacques\nDistler very nicely here:\n\nhttp://golem.ph.utexas.edu/string/archives/000330.html#c000877 .\n\nIn string theory the low-energy field content is not fixed by hand but has a\ndynamics of its own. The problem to actually solve this dynamics is\ncurrently associated with the buzzword "landscape". I think that it is\nimportant to note that the problem string theorists have with understanding\nthe space of classical solutions of the background equations of motion is a\nproblem that is currently absent from other approaches only because they\ncannot even pose the question which, when asked, is hard to answer (for\npractical reasons, not for reasons of principle)!\n\nAnyway, the study of background independent formulations of string field\ntheory can of course also be extended to superstrings. As far as I am aware\nit was Josef Kluson who first noticed in\n\nJ. Kluson\n\nSome remarks about Berkovits\' Superstring Field Theory\nhep-th/0105319\n\nProposal for Background Independent Berkovits\' Superstring Field Theory\nhep-th/0106107\n\nhow the idea by Strominger, Horowitz et al. nicely carries over to\nsuperstring field theory (NSFT, to be precise) and how there, too, one can\nwrite the SFT action in a form that is manifestly independent of any\nbackground.\n\n(J. Kluson also has a nice paper where the relation between certain finite\nSFT background shifts and (so called "marginal") deformation of the\nassociated worldsheet CFT is made explicit:\n\nJ. Kluson\nExact Solutions in SFT and Marginal Deformation in BCFT\nhep-th/0303199)\n\nThis has been generalized to full RNS-SFT (which also deals with the Ramond\nsector) in\n\nM. Sakaguchi\nPregeometrical Formulation of Berkovits\' open RNS Superstring Field Theories\nhep-th/0112135.\n\nAnd it is possible to solve these SFT EOMs non-perturbatively, as for\ninstance shown for the open superstring in\n\nA. Kling, O. Lechtenfeld, A. Popov, S. Uhlmann\nOn Nonperturbative Solutions of Superstring Field Theory\nhep-th/0209186 .\n\nI happen to all these references at hand currently because I was recently\nbeginning to try to understand how deformations of worldsheet SCFTs (in\nparticular as described in hep-th/0401175) come from solutions of string\nfield theory. More details, discussion and hyperlinks of this topic can be\nfound at the\n\nString Coffee Table\n\nhttp://golem.ph.utexas.edu/string/archives/000356.html\nhttp://golem.ph.utexas.edu/string/archives/000366.html\n\nas well as on\n\nsci.physics.strings\n\nhttp://groups.google.de/groups?selm=Pine.LNX.4.31.0404291403370.13988-100000%40feynman.harvard.edu .\n\n(There is a lot more literature on background independent SFT, in particular\nby Barton Zwiebach et al. The above list is just what I can currently\nreasonably make some comments on. More pointers to the literature were given\nby Sabbir Rahman last year at\n\nhttp://groups.google.de/groups?selm=4487dad1.0311161025.4e05c156%40posting .google.com )\n\n> Today, you can almost certainly get 4 out of 10 or 11 because people now\n> claim to have the compactification and the stabilization of all moduli\n> under full control.\n\nAre all moduli under control? In\n\nhttp://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001036\n\nS. Sethi says that " there are no examples of compactifications with all\nmoduli stabilized at large volume ". (?)\n\n> The usual algorithm to extract these histories is to follow the standard\n> perturbation rules where the path integral is dominated by the stationary\n> points of the action, regardless of the signature you work with, and then\n> computing the effects around these stationary points as Taylor expansion\n> in a small parameter. This can be tried for gravity, even without any\n> discretization, and it leads to a non-renormalizable theory. A correctly\n> done discretization is just a different way to reorganize these\n> divergences and problems, but if it is done correctly, it should not\n> change the conclusions about the 2-loop effective action, for example.\n[...]\n> Pure GR has real UV problems, and any\n> faithful description of it will confirm their existence. One can try to\n> hide these problems - for example by erasing all terms from the path\n> integral that are identified as those responsible for the problems - but\n> one cannot get a working & consistent theory based on these tricks.\n>\n> Once again, pure GR simply has these UV problems, and they show that there\n> is new physics at short distances that regulates them.\n\nThis is a point that has been brought up before and to which I have never\nseen an answer to by people working on discretized path integrals of LQG:\n\n"What happens to the 2-loop divergence in LQG?"\n\nI remember that this was asked by Hermann Nicolai at the "Strings meet\nLoops"\nsyomposium\n\nhttp://www.aei-potsdam.mpg.de/events/stringloop.html ,\n\nsee the seventh transparancy of\n\nhttp://www.aei-potsdam.mpg.de/events/StringmLoops/Nicolai.pdf\n\nand that A. Ashtekar said that this is an interesting open question.\nActually I think that if the claim of hep-th/0401172 is correct that LQG\nuses a relaxed notion of quantization which is completely different from\npath integral quantization, this is not all that surprising - but maybe a\nlittle disturbing.\n\n\n> Yang-Mills on some sort of lattice - e.g. using deconstruction - to define\n\nCould you suggest some introductory literature to deconstruction?\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>"Lubos Motl" <motl@feynman.harvard.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0405302130050.10707-100000@feynman.harvard.edu...

> > 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.
[...]
> 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.

For those who (like me until recently) haven't seen the original literature
on this result I'd like to mention some important papers:

This issue has been mostly studied by Ashoke Sen in a long series of papers
in the 90s:

Ashoke Sen,

On the background independence of string field theory
Nucl. Phys. B 345 (1990) 551

On the background independence of string field theory (II). Analysis of the
on-shell S-matrix elements
Nucl. Phys. B347 (1990) 270

On the background independence of string field theory (III). Explicit field
redefinitions
Nucl. Phys. B391 (1993) 550
http://www.arxiv.org/abs/hep-th/9201041

and is briefly reviewed in section 2.4 of

Ashoke Sen & Barton Zwiebach
A proof of local background independence of classical closed string field
theory
http://www.arxiv.org/abs/hep-th/9307088

One key idea in these developments is that presented in the short paper

Ashoke Sen
Equations of motion in non-polynomial closed string field theory and
conformal invariance of two dimensional field theories
Phys. Lett. B 241 (1990) 350-356

which discusses that to every solution \Phi of the classical equations of
motion of string theory there is a deformed BRST operator

\tilde Q = Q + [\Phi , .[/itex]]

which is the BRST operator of the worldsheet theory which describes string
propagation in the new background described by \Phi.

In particular this implies that when writing down the action of string field
theory, which is of the form

S = < \Phi , Q \Phi> + Sum_n a_n < \Phi , \Phi , .... \Phi>

for \Phi a string field, Q the BRST operator for a given background and <...>
the correlators of the accociated CFT, it _does not matter_ which CFT (=
background) one uses. By simply splitting

\Phi = \Phi_0 + \Psi

with \Phi_0 a classical solution of the above action, one rewrites the above
action equivalently in the form

S = S_0 + < \Psi , \tilde Q \Psi>_0 + Sum_n a_n < \Psi , \Psi , ..[itex].. \Psi>_0

where now all object are evaluated with respect to the shifted background.

So in this sense the action of string field theory is background
independent, even though it is convenient to express it with respect to
_any_ given background for practical calculations.

But it can even be made explicitly background independent: It turns out,
roughly, that the action of the BRST operator itself (which one may think of
as a high-brow version of the usual kinetic operator for some field in a
given background) can be mimicked by anticommutation with a certain string
field \Phi_bf, so that

\tilde Q =+ [ \Phi_bf, . ]

and that this \Phi_bf extremizes the above action with the kinetic term
removed.

This construction goes back to an impressive paper by Hata

H. Hata
Pregeometrical String Field Theory: Creation of Space-Time and Motion
(1986)
http://ccdb3fs.kek.jp/cgi-bin/img_index?8606274

that Lubos kindly has made me aware of a while ago.

It is philosophically rather satisfying that in this formulation the
equations of motion of string field backgrounds take the concise form

A * A =

(where A is a string field and * the star product which describes the
splitting/joining interaction of two strings).

The idea in this paper was later refined (though in a slightly different
context) in

G. Horowitz and J. Lykken and R. Rohm and A. Strominger:
Purely Cubic Action for String Field Theory
Phys. Rev. Lett. 57(3) (1986) 283 .

The crucial technique used there was the use of a simple relation between
(ghost-)graded string field star commutators and actions of operators on the
strings state space.

Namely let w(z) be some current chiral field of unit weight on the
worldsheet, let W_L be its integral over the left half of the unit circle in
the complex plane and let W be the full integral, then we have the identity

[ W_L(I) , \Phi ] = W(\Phi)

where I is the identity string field [.,.] is the graded star product
commutator and W(\Phi) is the action of W on the state \Phi.

Using this formula it is immediate that the BRST operator Q comes from the
"background" string field Q_L(I)Q = [ Q_L(I), . ] .

and that this field is actually a solution of the purely cubic SFT action

S_{cube} ~ < \Phi , \Phi , \Phi>

which (when the correlator is evaluated in the functional fashion described
on p.285 of the above paper) manifestly background independent.

Maybe it should be emphasized that "background independence" here is more
than just "independence of a given background _metric_". These actions are
also independent of any "background choice of field content"! It is rarely
mentioned in the context of non-perturbative approaches to quantum gravity
other than string theory, that all these alternative theories require a
by-hand choice of field content, even if no background metric is needed. For
instance Lee Smolin says that LQG can be performed with large classes of
additional fields. From the point of view of background independence this
should count as a bug, not as a feature, as has been emphasized by Jacques
Distler very nicely here:

http://golem.ph.utexas.edu/string/archives/000330.html#c000877 .

In string theory the low-energy field content is not fixed by hand but has a
dynamics of its own. The problem to actually solve this dynamics is
currently associated with the buzzword "landscape". I think that it is
important to note that the problem string theorists have with understanding
the space of classical solutions of the background equations of motion is a
problem that is currently absent from other approaches only because they
cannot even pose the question which, when asked, is hard to answer (for
practical reasons, not for reasons of principle)!

Anyway, the study of background independent formulations of string field
theory can of course also be extended to superstrings. As far as I am aware
it was Josef Kluson who first noticed in

J. Kluson

Some remarks about Berkovits' Superstring Field Theory
http://www.arxiv.org/abs/hep-th/0105319

Proposal for Background Independent Berkovits' Superstring Field Theory
http://www.arxiv.org/abs/hep-th/0106107

how the idea by Strominger, Horowitz et al. nicely carries over to
superstring field theory (NSFT, to be precise) and how there, too, one can
write the SFT action in a form that is manifestly independent of any
background.

(J. Kluson also has a nice paper where the relation between certain finite
SFT background shifts and (so called "marginal") deformation of the
associated worldsheet CFT is made explicit:

J. Kluson
Exact Solutions in SFT and Marginal Deformation in BCFT
http://www.arxiv.org/abs/hep-th/0303199)

This has been generalized to full RNS-SFT (which also deals with the Ramond
sector) in

M. Sakaguchi
Pregeometrical Formulation of Berkovits' open RNS Superstring Field Theories
http://www.arxiv.org/abs/hep-th/0112135.

And it is possible to solve these SFT EOMs non-perturbatively, as for
instance shown for the open superstring in

A. Kling, O. Lechtenfeld, A. Popov, S. Uhlmann
On Nonperturbative Solutions of Superstring Field Theory
http://www.arxiv.org/abs/hep-th/0209186 .

I happen to all these references at hand currently because I was recently
beginning to try to understand how deformations of worldsheet SCFTs (in
particular as described in http://www.arxiv.org/abs/hep-th/0401175) come from solutions of string
field theory. More details, discussion and hyperlinks of this topic can be
found at the

String Coffee Table

http://golem.ph.utexas.edu/string/archives/000356.html
http://golem.ph.utexas.edu/string/archives/000366.html

as well as on

sci.physics.strings

http://groups.google.de/groups?selm=Pine.LNX.4.31.0404291403370.13988-100000%40feynman.harvard.edu .

(There is a lot more literature on background independent SFT, in particular
by Barton Zwiebach et al. The above list is just what I can currently
reasonably make some comments on. More pointers to the literature were given
by Sabbir Rahman last year at

http://groups.google.de/groups?selm=4487dad1.0311161025.4e05c156%40posting .google.com )

> 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.

Are all moduli under control? In

http://golem.ph.utexas.edu/~distler/blog/archives/000359.html#c001036

S. Sethi says that " there are no examples of compactifications with all
moduli stabilized at large volume ". (?)

> 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.
[...]
> 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.

This is a point that has been brought up before and to which I have never
seen an answer to by people working on discretized path integrals of LQG:

"What happens to the 2-loop divergence in LQG?"

I remember that this was asked by Hermann Nicolai at the "Strings meet
Loops"
syomposium

http://www.aei-potsdam.mpg.de/events/stringloop.html ,

see the seventh transparancy of

http://www.aei-potsdam.mpg.de/events/StringmLoops/Nicolai.pdf

and that A. Ashtekar said that this is an interesting open question.
Actually I think that if the claim of http://www.arxiv.org/abs/hep-th/0401172 is correct that LQG
uses a relaxed notion of quantization which is completely different from
path integral quantization, this is not all that surprising - but maybe a
little disturbing.

> Yang-Mills on some sort of lattice - e.g. using deconstruction - to define

Could you suggest some introductory literature to deconstruction?

John Baez

Jun6-04, 05:26 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>In article <61773ed7.0405240822.1c7108de@posting.google.com>, \nCharlie Stromeyer Jr. <cstromey@hotmail.com> wrote:\n\n>Here are three other reasons to be skeptical of discretized approaches\n>to gravity:\n>\n>1) How are such approaches to be made compatible with vector\n>supersymmetry (or vsusy) which is a topological type of symmetry that\n>appears in both gravity and topological gauge theories [1].\n\nThis "vector supersymmetry" is a mathematical feature of certain\nfield theories - not something that anyone has observed experimentally.\n\nNobody has yet constructed a background-free quantum theory that has\ngeneral relativity as its limit at large distance scales. The Ambjorn-\nJurkiewicz-Loll model is the closest anyone has come. If they succeed,\nthis will be of interest regardless of whether their model displays\nmathematical features that appear in certain other theories!\n\n>2) How are such approaches to be made compatible with Bell-like\n>correlations, non-locality and non-causality which are each present in\n>the experiment described in this brief four page paper [2].\n\nAs a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically\nhas Bell-like "entanglement" and all that jazz.\n\n>3) To paraphrase a sentence that Stephen Hawking once wrote, to not\n>believe in the beauty and unity of the dualities of M-theory is like\n>believing that evolution did not occur because instead God placed by\n>hand all the fossils in the Earth just to play a joke on the\n>paleontologists :-)\n\nWe resort to theological arguments in physics only when better arguments\nare lacking. If a scintilla of experimental evidence for M-theory is\never found, people will instantly stop making arguments of the sort\nyou mention here.\n\nPlease understand what I\'m saying:\n\nI\'m not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll\nmodel is "right". M-theory makes too few definite predictions to be wrong.\nThe AJL model does not include matter, so it cannot be right. But the\nAJL model is *interesting*, because it represents the best attempt so far\nto find a background-free quantum theory that reduces to general relativity\nin the large-scale limit!\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>In article <61773ed7.0405240822.1c7108de@posting.google.com>,
Charlie Stromeyer Jr. <cstromey@hotmail.com> wrote:

>Here are three other reasons to be skeptical of discretized approaches
>to gravity:
>
>1) How are such approaches to be made compatible with vector
>supersymmetry (or vsusy) which is a topological type of symmetry that
>appears in both gravity and topological gauge theories [1].

This "vector supersymmetry" is a mathematical feature of certain
field theories - not something that anyone has observed experimentally.

Nobody has yet constructed a background-free quantum theory that has
general relativity as its limit at large distance scales. The Ambjorn-
Jurkiewicz-Loll model is the closest anyone has come. If they succeed,
this will be of interest regardless of whether their model displays
mathematical features that appear in certain other theories!

>2) How are such approaches to be made compatible with Bell-like
>correlations, non-locality and non-causality which are each present in
>the experiment described in this brief four page paper [2].

As a quantum theory, the Ambjorn-Jurkiewicz-Loll model automatically
has Bell-like "entanglement" and all that jazz.

>3) To paraphrase a sentence that Stephen Hawking once wrote, to not
>believe in the beauty and unity of the dualities of M-theory is like
>believing that evolution did not occur because instead God placed by
>hand all the fossils in the Earth just to play a joke on the
>paleontologists :-)

We resort to theological arguments in physics only when better arguments
are lacking. If a scintilla of experimental evidence for M-theory is
ever found, people will instantly stop making arguments of the sort
you mention here.

Please understand what I'm saying:

I'm not saying that M-theory is "wrong" or that the Ambjorn-Jurkiewicz-Loll
model is "right". M-theory makes too few definite predictions to be wrong.
The AJL model does not include matter, so it cannot be right. But the
AJL model is *interesting*, because it represents the best attempt so far
to find a background-free quantum theory that reduces to general relativity
in the large-scale limit!

John Baez

Jun6-04, 05:27 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>In article <24a23f36.0405170344.69e74067@posting.google.com>, \nThomas Larsson <thomas_larsson_01@hotmail.com> wrote:\n\n>1. Is the AJL model really quantum?\n\nYes! It has a Hilbert space of states, observables described\nas noncommuting self-adjoint operators on this Hilbert space,\nand discrete time evolution described by unitary operators on\nthis Hilbert space.\n\n>Some time ago, Urs\n>Schreiber argued that LQG, or at least the LQG string,\n>fails to be a true quantum theory, and I tend to agree.\n\nI disagree, but it\'s not really relevant here: we\'re not\ntalking about those other theories.\n\n>However, the AJL model can be viewed as a statistical\n>lattice model, and if such a model has a good continuum\n>limit, it is AFAIK always described by some kind of QFT.\n>What else could it be?\n\nRight!\n\n>2. It the AJL model really gravity. The action is a rather\n>straightforward discretization of the Einstein action with\n>a cosmological term:\n>\n> \\int R => sum over (d-2)-simplices\n>\n> \\int det g = volume => sum over d-simplices.\n>\n>What is perhaps somewhat unusual is that all edges have\n>the same length, which is different from Regge calculus.\n>Nevertheless, I don\'t think that this really matters, but\n>one could check if the results look different if you\n>allow for variable edge lengths.\n\nRight! But, the test of whether the model "is really\ngravity" is to carefully examine its behavior in the limit\nof large distance scales (i.e. lots of 4-simplices). One\ncan\'t easily guess this from looking at the action.\nNonperturbative effects are too important! So, in the\nabsence of good analytical techniques, one really needs\nto run computer simulations - as AJL are doing.\n\n>3. Is the measure right? Here is the place where AJL differ\n>significantly from previous simulations. AFAIU, the crux is\n>that AJL insist on a strict form of causality: they exclude\n>spacetimes where the metric is singular, even at isolated\n>points. This may seem like an innoscent restriction, but it\n>rules out things like topology change and baby universes,\n>which require that the metric be singular somewhere.\n>\n>It is not obvious to me whether one should insist on such a\n>strong form of causality or not, but this assumption leads\n>at least to better results, e.g. a reasonably smooth 4D\n>spacetime. Thus, I believe that it is a fair chance that\n>AJL have indeed succeeded in quantizing gravity.\n\nThe issue of the "right measure" is very tricky, so tricky\nin fact that I again think the most efficient way to begin\ntackling it is to run computer simulations and see if the\nAJL model acts like general relativity at large length scales.\n\n>They do so not by assuming a lot of experimentally unconfirmed\n>new physics, but rather by strictly implementing the\n>time-honored principles of old physics, especially\n>causality. That is cool.\n\nYes! Very cool!\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>In article <24a23f36.0405170344.69e74067@posting.google.com>,
Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:

>1. Is the AJL model really quantum?

Yes! It has a Hilbert space of states, observables described
as noncommuting self-adjoint operators on this Hilbert space,
and discrete time evolution described by unitary operators on
this Hilbert space.

>Some time ago, Urs
>Schreiber argued that LQG, or at least the LQG string,
>fails to be a true quantum theory, and I tend to agree.

I disagree, but it's not really relevant here: we're not
talking about those other theories.

>However, the AJL model can be viewed as a statistical
>lattice model, and if such a model has a good continuum
>limit, it is AFAIK always described by some kind of QFT.
>What else could it be?

Right!

>2. It the AJL model really gravity. The action is a rather
>straightforward discretization of the Einstein action with
>a cosmological term:
>
> \int R => sum over (d-2)-simplices
>
> \int det g = volume => sum over d-simplices.
>
>What is perhaps somewhat unusual is that all edges have
>the same length, which is different from Regge calculus.
>Nevertheless, I don't think that this really matters, but
>one could check if the results look different if you
>allow for variable edge lengths.

Right! But, the test of whether the model "is really
gravity" is to carefully examine its behavior in the limit
of large distance scales (i.e. lots of 4-simplices). One
can't easily guess this from looking at the action.
Nonperturbative effects are too important! So, in the
absence of good analytical techniques, one really needs
to run computer simulations - as AJL are doing.

>3. Is the measure right? Here is the place where AJL differ
>significantly from previous simulations. AFAIU, the crux is
>that AJL insist on a strict form of causality: they exclude
>spacetimes where the metric is singular, even at isolated
>points. This may seem like an innoscent restriction, but it
>rules out things like topology change and baby universes,
>which require that the metric be singular somewhere.
>
>It is not obvious to me whether one should insist on such a
>strong form of causality or not, but this assumption leads
>at least to better results, e.g. a reasonably smooth 4D
>spacetime. Thus, I believe that it is a fair chance that
>AJL have indeed succeeded in quantizing gravity.

The issue of the "right measure" is very tricky, so tricky
in fact that I again think the most efficient way to begin
tackling it is to run computer simulations and see if the
AJL model acts like general relativity at large length scales.

>They do so not by assuming a lot of experimentally unconfirmed
>new physics, but rather by strictly implementing the
>time-honored principles of old physics, especially
>causality. That is cool.

Yes! Very cool!

ksh95

Jun9-04, 12:08 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>\nLubos Motl <motl@feynman.harvard.edu> wrote in message\n> It is not too difficult to construct a discrete & "background-independent"\n> system that will have the tendency to organize the elementary building\n> blocks into a structure that approaches flat space - or another type of\n> space, for that matter. For example, crystals are an example (from\n> condensed matter physics) where the underlying laws (at low temperatures)\n> tend to organize the atoms into a regular structure.\n\nThis may not be the best example. Even condensed matter (were the\nunderlying laws are WELL understood) is unable to rigorously show that\nordered lattices are necessarily emergent from short distance atomic\nphysics. The free energy landscape is rugged and vast. In principal it\nmay be possible to find global extrema, but in practice......no way.\n\n\nI\'m not claiming that condensed matter is relevant to quantum gravity,\nI\'m just saying that it\'s hard to get long distance physics from short\ndistance physics.\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>Lubos Motl <motl@feynman.harvard.edu> wrote in message
> It is not too difficult to construct a discrete & "background-independent"
> system that will have the tendency to organize the elementary building
> blocks into a structure that approaches flat space - or another type of
> space, for that matter. For example, crystals are an example (from
> condensed matter physics) where the underlying laws (at low temperatures)
> tend to organize the atoms into a regular structure.

This may not be the best example. Even condensed matter (were the
underlying laws are WELL understood) is unable to rigorously show that
ordered lattices are necessarily emergent from short distance atomic
physics. The free energy landscape is rugged and vast. In principal it
may be possible to find global extrema, but in practice......no way.

I'm not claiming that condensed matter is relevant to quantum gravity,
I'm just saying that it's hard to get long distance physics from short
distance physics.

Omina Kui

Jun10-04, 07:47 AM

<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>\n\nbaez@galaxy.ucr.edu (John Baez) wrote in message news:<c9tn1n\\$jn4\\$1@glue.ucr.edu>...\n> In article <24a23f36.0405170344.69e74067@posting.google.com>, \n> Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:\n>\n> >1. Is the AJL model really quantum?\n>\n> Yes! It has a Hilbert space of states, observables described\n> as noncommuting self-adjoint operators on this Hilbert space,\n> and discrete time evolution described by unitary operators on\n> this Hilbert space.\n\nIs that really sufficient to make a theory (or a model) truly Quantum?\n\nConsider a weakly stationary stochastic process. It has the Hilbert\nspace of states, discrete time unitary evolution, and the according\ntime-series could even be interpreted as a result of a Lüders\nmeasurements on the stochastic process. But that doesn\'t make the\ntheory of stochastic processes Quantum. Or does it?\n\n(I am not following this group on a regular basis, but this thread got\nmy attention and hence made this contribution.)\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>baez@galaxy.ucr.edu (John Baez) wrote in message news:<c9tn1n$jn4$1@glue.ucr.edu>...
> In article <24a23f36.0405170344.69e74067@posting.google.com>,
> Thomas Larsson <thomas_larsson_01@hotmail.com> wrote:
>
> >1. Is the AJL model really quantum?
>
> Yes! It has a Hilbert space of states, observables described
> as noncommuting self-adjoint operators on this Hilbert space,
> and discrete time evolution described by unitary operators on
> this Hilbert space.

Is that really sufficient to make a theory (or a model) truly Quantum?

Consider a weakly stationary stochastic process. It has the Hilbert
space of states, discrete time unitary evolution, and the according
time-series could even be interpreted as a result of a Lüders
measurements on the stochastic process. But that doesn't make the
theory of stochastic processes Quantum. Or does it?

(I am not following this group on a regular basis, but this thread got
my attention and hence made this contribution.)

coast99

Jun14-04, 04:11 PM

I think one should be very careful when using galaxy rotation curves to test
MOND or any other gravitation theory. We do not know enough about the structure
of galaxies, e.g. the importance of magnetic fields.

Tests in the solar system (Gravity probe B ) are the preferred experiments and so far
they all favor general relativity.

John Baez

Aug13-04, 07:16 AM

<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>\n>Lubos Motl <motl@feynman.harvard.edu> wrote:\n\n> It is not too difficult to construct a discrete & "background-independent"\n> system that will have the tendency to organize the elementary building\n> blocks into a structure that approaches flat space - or another type of\n> space, for that matter. For example, crystals are an example (from\n> condensed matter physics) where the underlying laws (at low temperatures)\n> tend to organize the atoms into a regular structure.\n\nHere the underlying laws are neither discrete nor background-independent.\nPresumably one can show that under certain conditions the least-energy\nsolution of Schrodinger\'s equation for a bunch of protons and electrons\nis a crystal of solid hydrogen. ("Presumably", because nobody has shown\nit but it\'s got to be true.) But, Schrodinger\'s equation is neither\ndiscrete nor background-independent. It\'s formulated using continuous\nspacetime - and more importantly, it\'s formulated in terms of a fixed\nbackground on this spacetime.\n\nIt\'s easy to discretize Schrodinger\'s equation, say by putting it on a\nlattice... but it\'s still background-dependent. When it comes to\nquantizing gravity, there are no strong arguments for discreteness,\nbut there are pretty good arguments that the theory should be background-\nfree. So, background-independence is more important and also harder\nthan discreteness.\n\nAnyway, if you think it\'s not too difficult to construct a discrete\nand background-independent system that will have the tendency to\norganize the elementary building blocks into a structure that\napproaches flat space, you should give a real example!\n\nI can come up with examples where spacetime is just *forced* to be\nflat, but that\'s not really interesting for quantum gravity.\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>>Lubos Motl <motl@feynman.harvard.edu> wrote:

> It is not too difficult to construct a discrete & "background-independent"
> system that will have the tendency to organize the elementary building
> blocks into a structure that approaches flat space - or another type of
> space, for that matter. For example, crystals are an example (from
> condensed matter physics) where the underlying laws (at low temperatures)
> tend to organize the atoms into a regular structure.

Here the underlying laws are neither discrete nor background-independent.
Presumably one can show that under certain conditions the least-energy
solution of Schrodinger's equation for a bunch of protons and electrons
is a crystal of solid hydrogen. ("Presumably", because nobody has shown
it but it's got to be true.) But, Schrodinger's equation is neither
discrete nor background-independent. It's formulated using continuous
spacetime - and more importantly, it's formulated in terms of a fixed
background on this spacetime.

It's easy to discretize Schrodinger's equation, say by putting it on a
lattice... but it's still background-dependent. When it comes to
quantizing gravity, there are no strong arguments for discreteness,
but there are pretty good arguments that the theory should be background-
free. So, background-independence is more important and also harder
than discreteness.

Anyway, if you think it's not too difficult to construct a discrete
and background-independent system that will have the tendency to
organize the elementary building blocks into a structure that
approaches flat space, you should give a real example!

I can come up with examples where spacetime is just *forced* to be
flat, but that's not really interesting for quantum gravity.

Lubos Motl

Aug19-04, 05:51 AM

<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>\n\nOn 13 Aug 2004, John Baez wrote:\n\n> Here the underlying laws are neither discrete nor background-independent.\n\nIt depends on what you mean by "discrete" and "background-independent",\nand my feeling is that your interpretation of these words is very naive.\nCould you try to define these words that you use so often and happily?\nQuantum mechanics is always "continuous" to some extent - at least the\nwave functions are continuous. On the other hand, it is always discrete to\nanother extent - all separable Hilbert spaces (and Hilbert spaces\ndescribing realistic physics must be separable at the end) have a\ndiscrete, countable basis.\n\nYou might try to say that a "discrete" Hilbert space must have a complete\nset of operators with rational eigenvalues for all eigenstates - but this\ncondition will fail for LQG. You might try to give another definition, but\nyou will always fail, I think. It is a completely fundamental property of\nquantum mechanics - a property that the LQG practitioners clearly don\'t\nappreciate - that some operators can have discrete spectrum while others\nhave a continuous spectrum.\n\nThe only thing I can imagine that you may mean by "discrete" is that there\nis no reasonable continuous basis of the Hilbert space or a sector of it.\nIf this is what you mean, then you apparently think that it is a virtue of\na theory if it has no continuous spectrum anywhere; I think that it is a\nhuge handicap of such a theory - both from the aesthetic viewpoint as well\nas the experimental one.\n\nThe same thing applies to the phrase "background-independent". Newton\'s\ngravitational laws can be written as a background-independent set of\nequations. Does it mean that we should call Newton\'s laws "quantum\ngravity" once we quantize them much like the Coulomb forces was quantized\nby Schrodinger? I don\'t think so.\n\nQuantum gravity is something that contains, at least in the appropriate\nlimit, general relativity, and general relativity is not just something\nthat is "background-independent". General relativity is, first of all, a\ntheory of gravity that respects the rules of special relativity. This is\nwhy it was looked for by Einstein, and this is the only moral advantage of\nGR over Newton\'s laws.\n\nIf a theory cannot be shown to reduce locally (as well as in other limits)\nto special relativity, then it\'s certainly *not* as advanced as general\nrelativity. A theory with no obvious "space" in it may look attractive to\nyou - a mathematician - but it is certainly and completely uninteresting\nfor physics if it cannot reproduce the continuous space whose local\nphysics also respects Lorentz invariance. Having no obvious default\nspacetime to start with may be an aesthetic advantage of a *formulation*,\nbut predicting no space at the end is a much more serious, huge disaster\nof a physical *theory*.\n\nNewton\'s laws are equally background-independent as the laws that you\npropose, but because - unlike your laws - they can reproduce physics of\nthe real world, they are clearly superior over loop quantum gravity, and\nno big sounding words can change anything about it.\n\n> It\'s easy to discretize Schrodinger\'s equation, say by putting it on a\n> lattice... but it\'s still background-dependent.\n\nWhile it is easy to discretize space, it is not that easy to discretize\ntime while retaining the equivalent of a Hamiltonian.\n\n> When it comes to\n> quantizing gravity, there are no strong arguments for discreteness,\n> but there are pretty good arguments that the theory should be background-\n> free. So, background-independence is more important and also harder\n> than discreteness.\n\nNo, it\'s not. Background independence, in the sense that you advocate, is\ncompletely trivial, useless and uninteresting requirement that even the\nNewton\'s laws satisfy if they are written appropriately. It remains\ntrivial and worthless until you show that physics of continuous\nLorentz-invariant spacetime can emerge (among other solutions, if you\nwish). If you want to disagree, you should write what is "more"\nbackground-independent about these laws of yours as compared to Newton\'s\nlaws.\n\n> Anyway, if you think it\'s not too difficult to construct a discrete\n> and background-independent system that will have the tendency to\n> organize the elementary building blocks into a structure that\n> approaches flat space, you should give a real example!\n\nI explained above that every separable space in quantum mechanics is\nequally discrete, because the Hilbert space has a countable basis, and\nvirtually every law of old-fashioned physics can be written in a\nbackground-independent fashion, so be sure that the Schrodinger equation\nfor 10^26 electrons describing a diamond is an example. If you want to\nclaim that it is less discrete or less background-independent, be more\nspecific. My feeling is that my example might be less stupid and less\nnaive, but it is equally discrete and equally background-independent.\n\nBest\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</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>On 13 Aug 2004, John Baez wrote:

> Here the underlying laws are neither discrete nor background-independent.

It depends on what you mean by "discrete" and "background-independent",
and my feeling is that your interpretation of these words is very naive.
Could you try to define these words that you use so often and happily?
Quantum mechanics is always "continuous" to some extent - at least the
wave functions are continuous. On the other hand, it is always discrete to
another extent - all separable Hilbert spaces (and Hilbert spaces
describing realistic physics must be separable at the end) have a
discrete, countable basis.

You might try to say that a "discrete" Hilbert space must have a complete
set of operators with rational eigenvalues for all eigenstates - but this
condition will fail for LQG. You might try to give another definition, but
you will always fail, I think. It is a completely fundamental property of
quantum mechanics - a property that the LQG practitioners clearly don't
appreciate - that some operators can have discrete spectrum while others
have a continuous spectrum.

The only thing I can imagine that you may mean by "discrete" is that there
is no reasonable continuous basis of the Hilbert space or a sector of it.
If this is what you mean, then you apparently think that it is a virtue of
a theory if it has no continuous spectrum anywhere; I think that it is a
huge handicap of such a theory - both from the aesthetic viewpoint as well
as the experimental one.

The same thing applies to the phrase "background-independent". Newton's
gravitational laws can be written as a background-independent set of
equations. Does it mean that we should call Newton's laws "quantum
gravity" once we quantize them much like the Coulomb forces was quantized
by Schrodinger? I don't think so.

Quantum gravity is something that contains, at least in the appropriate
limit, general relativity, and general relativity is not just something
that is "background-independent". General relativity is, first of all, a
theory of gravity that respects the rules of special relativity. This is
why it was looked for by Einstein, and this is the only moral advantage of
GR over Newton's laws.

If a theory cannot be shown to reduce locally (as well as in other limits)
to special relativity, then it's certainly *not* as advanced as general
relativity. A theory with no obvious "space" in it may look attractive to
you - a mathematician - but it is certainly and completely uninteresting
for physics if it cannot reproduce the continuous space whose local
physics also respects Lorentz invariance. Having no obvious default
spacetime to start with may be an aesthetic advantage of a *formulation*,
but predicting no space at the end is a much more serious, huge disaster
of a physical *theory*.

Newton's laws are equally background-independent as the laws that you
propose, but because - unlike your laws - they can reproduce physics of
the real world, they are clearly superior over loop quantum gravity, and
no big sounding words can change anything about it.

> It's easy to discretize Schrodinger's equation, say by putting it on a
> lattice... but it's still background-dependent.

While it is easy to discretize space, it is not that easy to discretize
time while retaining the equivalent of a Hamiltonian.

> When it comes to
> quantizing gravity, there are no strong arguments for discreteness,
> but there are pretty good arguments that the theory should be background-
> free. So, background-independence is more important and also harder
> than discreteness.

No, it's not. Background independence, in the sense that you advocate, is
completely trivial, useless and uninteresting requirement that even the
Newton's laws satisfy if they are written appropriately. It remains
trivial and worthless until you show that physics of continuous
Lorentz-invariant spacetime can emerge (among other solutions, if you
wish). If you want to disagree, you should write what is "more"
background-independent about these laws of yours as compared to Newton's
laws.

> Anyway, if you think it's not too difficult to construct a discrete
> and background-independent system that will have the tendency to
> organize the elementary building blocks into a structure that
> approaches flat space, you should give a real example!

I explained above that every separable space in quantum mechanics is
equally discrete, because the Hilbert space has a countable basis, and
virtually every law of old-fashioned physics can be written in a
background-independent fashion, so be sure that the Schrodinger equation
for 10^26 electrons describing a diamond is an example. If you want to
claim that it is less discrete or less background-independent, be more
specific. My feeling is that my example might be less stupid and less
naive, but it is equally discrete and equally background-independent.

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)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

John Baez

Aug24-04, 05:41 AM

<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>Lubos Motl <motl@feynman.harvard.edu> wrote:\n\n>On 13 Aug 2004, John Baez wrote:\n\n>> Here the underlying laws are neither discrete nor background-independent.\n\n>It depends on what you mean by "discrete" and "background-independent",\n>and my feeling is that your interpretation of these words is very naive.\n>Could you try to define these words that you use so often and happily?\n\nI could - but notice what just happened. First you claimed that\nthe laws governing a crystal were discrete and background-independent.\nI disagreed. Then you claimed that background-independence is a\n"completely trivial, useless and uninteresting requirement", while\n"every separable space in quantum mechanics is equally discrete".\n\nI conclude that you\'re defending your original statement by saying\nthat it was vacuously true. That\'s fine, but it makes your claim\ninsufficiently interesting to pursue further.\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>Lubos Motl <motl@feynman.harvard.edu> wrote:

>On 13 Aug 2004, John Baez wrote:

>> Here the underlying laws are neither discrete nor background-independent.

>It depends on what you mean by "discrete" and "background-independent",
>and my feeling is that your interpretation of these words is very naive.
>Could you try to define these words that you use so often and happily?

I could - but notice what just happened. First you claimed that
the laws governing a crystal were discrete and background-independent.
I disagreed. Then you claimed that background-independence is a
"completely trivial, useless and uninteresting requirement", while
"every separable space in quantum mechanics is equally discrete".

I conclude that you're defending your original statement by saying
that it was vacuously true. That's fine, but it makes your claim
insufficiently interesting to pursue further.