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Good introductions to LQG

  1. Mar 6, 2013 #1

    marcus

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    There were questions in a couple of threads about what books/papers/recorded lectures could serve to give a good introduction to LQG. I gathered some excerpts from Leucippus' posts and want to make a fresh start---trying to understand and to stay more focused on the central problem.
    In general terms this is not an unusual situation to be in. At the moment I'm not sure how to answer. What I hope to do is gradually add references that might fill the bill for someone who wants up-to-date, say 2009 or later, introductory material specifically to LQG (and I would include LQC and Spinfoam).

    Some actual LQG researchers (e.g. Hellmann, Vidotto) are PF members and do occasionally post here, so if we are lucky we might get advice from them, or equally well-qualified people. In any event we can make the attempt.
     
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  3. Mar 7, 2013 #2

    marcus

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    Hi Leucippus, as you pointed out, you were quoting a post of mine from a long ways back. I'm a little embarrassed by the naive optimism that comes out later.:redface: That was October 2003.
    It's late here now. I'll see what I can find along those lines tomorrow.
     
    Last edited: Mar 7, 2013
  4. Mar 7, 2013 #3
    This seems as good an opportunity as any to introduce a paper I have been working on, along with a collaborator, which is intended as a bare-bones intro to LQG. Since the paper is not quite complete yet, it hasn't been uploaded to arXiv. However, since people seem to show continued interest and a need for something like this - notwithstanding the several existing introductions, including the excellent one by Dona and Speziale - I've decided to take this project public.

    The draft pdf is attached to this message.

    The paper isn't quite "10 pages" long, but hopefully those seeking to understand LQG might find it useful. The completed version will eventually end up on arXiv.
     

    Attached Files:

  5. Mar 7, 2013 #4

    Demystifier

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    Looks nice! :smile:

    One technical question:
    How do you make those orange (to-do-later) comments in LaTeX? :confused:
     
  6. Mar 7, 2013 #5
    Hopefully it reads nice too :smile:

    Using the latex package "todonotes".
     
  7. Mar 7, 2013 #6

    Demystifier

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    It certainly does.

    Thanks!
     
  8. Mar 7, 2013 #7

    marcus

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    At least one of the authors (see page 23) is a fan of the best in English prose style--early 19th C--typifying lightness, wit, lucidity.
    This monograph, at least at first sight, seems exactly what we were looking for! Happy voyaging with it to whatever is the proper conclusion!
     
  9. Mar 7, 2013 #8

    atyy

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    Until LQG recovers classical general relativity, what is the point of LQG being "minimal" compared to string theory?
     
  10. Mar 7, 2013 #9
    Thanks to Marcus for starting this thread.

    And special thanks to Space Cadet for posting your introductory PDF.

    I can even just print out your table of contents and use that for a nice organizing template.

    Shamefully, I can see where I'm going to need to brush up on General Relativity and QFT. I'm somewhat familiar with the general ideas of both of these fields, but it appears that I'm going to need to have a working knowledge of the mathematics behind them. So I guess learning this prerequisite mathematics is going to keep me pretty busy for a while.

    I almost hate to ask in fear of derailing the thread, but since GR and QFT are both prerequisites can anyone point to books that can help someone get up and running on those subjects relativity quickly? Assume an undergraduate level of entry.

    Also at 63 years old, am I just kidding myself that I could ever catch up?

    I know they say that its never too late, but surely there has to come a time when that saying no longer holds true. I'm pretty sure it's too late for me to consider going out for professional Ice Hockey, for example.

    Can I learn the mathematics of GR and QFT side-by-side in a year in a meaningful way?

    It appears that a solid working knowledge of these two subjects is going to be paramount to getting anywhere in LQG.
     
  11. Mar 7, 2013 #10

    atyy

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    For GR, I liked Matthias Blau's notes http://www.blau.itp.unibe.ch/Lecturenotes.html, and for QFT David Tong's were pretty friendly http://www.damtp.cam.ac.uk/user/tong/qft.html .

    Blau's GR notes are temporarily unavailable, so one could also try Woodhouse's https://people.maths.ox.ac.uk/nwoodh/ or Hamilton's http://casa.colorado.edu/~ajsh/phys5770_10/notes.html .

    To supplement Tong's QFT notes, I found Srednicki's draft version of his book easy-going http://web.physics.ucsb.edu/~mark/qft.html .
     
    Last edited: Mar 7, 2013
  12. Mar 7, 2013 #11
    Thanks atyy,

    I downloaded Woodhouse's lectures on both SR and GR. They book look great. He takes SR into some serious transformations right off the bat. So it won't hurt me to start in on his SR course to reacquaint myself with with vector transformations and lineal algebra. It looks like he takes all that for granted right off the bat in GR.

    I also downloaded Hamliton's book on GR. That's really solid too. That's an actual book, not just lecture notes, and he too starts right off with SR which is a nice way for me to get a grip on entering into the more complex tensors of GR.

    I also downloaded Srednicki's QFT book. Although in the preface of his book he says the following:

    http://users.csonline.net/designer/images/eq.gif [Broken]

    The second one up from the bottom looks familiar.

    What am I missing here?
     
    Last edited by a moderator: May 6, 2017
  13. Mar 7, 2013 #12

    atyy

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    Missing?

    BTW, I'm a biology major who studied physics for fun. I started learning about LQG and string theory a few years ago when my physics friends all started talking about Smolin's TTWP, and I didn't understand any of their conversations. My knowledge is very superficial, just enough to understand physics bar talk.
     
  14. Mar 7, 2013 #13
    I majored in physics and chemistry when I was in college and none of those equations on his list look familiar to me. So I'm wondering what courses I missed.

    I have no clue what these equations are. Here are my best guesses, and trust me, these are really lame guesses:

    http://users.csonline.net/designer/images/eq1.gif [Broken]

    Equation #1 appears to be describing the derivative of sigma with respect to omega, but I have no clue what the sigma or omega represent. This derivative appears to be equal to the magnitude squared of some function that appears to depend upon to angles.

    My guess would be that this has something to do with electromagnetic fields. But clearly I'm guessing and I don't recall ever seeing this particular relationship using this specific notation.

    In what course would I have learned this equation?

    http://users.csonline.net/designer/images/eq2.gif [Broken]
    http://users.csonline.net/designer/images/eq3.gif [Broken]

    Equations 2 and 3 both appear to be state equations representing the state of some systems. But again. I don't recognize these specific equations.

    http://users.csonline.net/designer/images/eq4.gif [Broken]

    Equation #4 appears to be a solution to Schrodinger's wave equation. But I have no clue what it is the wave function of. Again, just guessing I would imagine it's a wave function of something simply like a hydrogen atom.

    http://users.csonline.net/designer/images/eq5.gif [Broken]

    Equation #5 I have no clue. I would guess that the dotted q might represent the derivative of a dynamic charge? And that's a really wild guess just to take a stab at it.

    http://users.csonline.net/designer/images/eq6.gif [Broken]

    Equation #6, again I'm clueless. I would guess that it might have something do to with a magnetic field. But again, that's just an intuitive hunch. I don't recognize the equation.

    On second guess I'm thinking it could also be a Lorentz transformation equation?

    You can tell I'm really guessing on these.


    http://users.csonline.net/designer/images/eq7.gif [Broken]

    Finally something I recognize. At least I hope so. It appears to be relating Energy with momentum and mass. A Special Relativity relationship. I know I've worked with that equation before, but even so I can recall the precise details, but if I got back into it and worked with it again, I'm sure it would come flooding back.

    http://users.csonline.net/designer/images/eq8.gif [Broken]

    Equation #8 appears to be making a statement about an electric field, so this appears to be associated with Maxwell's equations. I've worked with Maxwell's equations before too, so I could potentially regain that fairly quickly.

    But for the most part this is all Greek to me.


    I don't know. Maybe I should just stick with the barroom chatter. I might be too far behind in the math to do any serious work with this stuff.
     
    Last edited by a moderator: May 6, 2017
  15. Mar 7, 2013 #14

    atyy

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    1. scattering cross section
    2. raising operator (see harmonic oscillator)
    3. Clebsch-Gordon coeficients (see angular momentum)
    4. time-evolution of observable (see Heisenberg picture)
    5. definition of Hamiltonian in terms of Lagrangian
    6. Lorentz transformation
    7.
    8. electric field in terms of the vector and scalar potential
     
  16. Mar 7, 2013 #15

    atyy

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    There's a great quantum mechanics course by Balakrishnan on Youtube.

    The operator treatment of the harmonic oscillator is in lecture 12

    The Clebsch-Gordon coefficients are in lecture 17

    The vector potential is in lecture 16
     
    Last edited by a moderator: Sep 25, 2014
  17. Mar 7, 2013 #16
    I might be too far behind the train at this point.

    Maybe I should just give up and go fishing.
     
  18. Mar 7, 2013 #17
    Oh, that's cool.

    I watch those!

    I enjoy watching lectures. :)
     
    Last edited by a moderator: Sep 25, 2014
  19. Mar 7, 2013 #18

    atyy

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    Is the weather good for fishing?

    LQG (in its original form) is based on the Hamiltonian or canonical formulation of general relativity. This has its roots in classical mechanics, and there's quantum version of it (which is why you'll always hear about the Hamiltonian operator in Balakrishnan's lectures). Anyway, that means a knowledge of classical Hamiltonian mechanics is very useful. It is essentially a reformulation of Newton's equations for systems in which energy is conserved. Tong has a description in the last part of http://www.damtp.cam.ac.uk/user/tong/dynamics.html

    GR, as discovered by Einstein, is more in a form that is like Newton's second law. The first Hamiltonian formulation of GR was the ADM formulation http://en.wikipedia.org/wiki/ADM_formalism. Later Ashtekar found another Hamiltonian formulation http://en.wikipedia.org/wiki/Ashtekar_variables. LQG started from the Ashtekar variables.

    If you want LQG bar talk, I recommend Wuthrich's thesis http://philosophyfaculty.ucsd.edu/faculty/wuthrich/pub/WuthrichChristianPhD2006Final.pdf [Broken].

    BTW, string theory is the best candidate for a working theory of quantum gravity at the moment. In AdS/CFT there is a non-perturbative and background independent candidate formulation for quantum gravity in AdS spaces. It probably doesn't model our universe, but because it is (non-rigourously) the only working theory of quantum gravity in some universe, it is something anyone interested in quantum gravity should know. Furthermore string theory has calculated the black hole entropy, whereas there is no such calculation in LQG (that is undisputed). That does not mean that you as a non-professional sohuld not study LQG first, but it's something to bear in mind.
     
    Last edited by a moderator: May 6, 2017
  20. Mar 7, 2013 #19
    Not really. I'm more of the gardening type anyway. And it is getting close to gardening season here. So that's really what I should be doing with my time.


    In the spirit of bar room chatter let me pass some stuff by you.

    I heard that someone had discovered a relationship between the surface area of the event horizon of a black hole and the entropy contained by the black hole. I have no clue how that was done mathematically. Was that indeed done using string theory?

    In any case, I found that result to be quite intriguing because I have some "theories" (or speculative uneducated guesses) concerning black holes, that I'd like to pass by some knowledgeable physicists.

    Let's suppose a person falls into a black hole. There are two perspectives. One is the perspective of an outside observer watching the unfortunate victim falling into the hole. The other perspective is the person who is falling into the hole.

    But what do they see?

    Well, the observer outside the black hold sees the victim falling toward the black hole, but never really reaching the event horizon. Is that correct? The person will appear to be falling more and more slowly until they basically freeze forever at the horizon. So the person outside the black hole never actually see anyone fall into the black hole.

    On the other hand, what does the person who's falling into the black hole see?

    Well looking back out toward the universe the falling observer would see the universe behaving more and more rapidly. Right? Because for them time is slowing down. This means that they will see the universe "speeding up".

    If they observe the universe carefully enough they would notice that super novas are popping off at a phenomenal rate as they fall toward the black hole. Time will slow down for them to the point where it's basically almost at a stand still by the time they reach the event horizon.

    If that's true, then when they look out at the universe they must see the universe racing off into its future. They will see stars blowing up in galaxies at a phenomenal rate. The galaxies will even be going dark as their stars die off, and the galaxies will all be racing away from each other at an increasing speed. By the time the victim actually reaches the event horizon the universe will basically be "over". All of time will have passed for the external universe.

    In fact, wouldn't the event horizon itself represent infinitely slow time passing for the victim who's falling into the black hole?

    Will there be any time left for them to actually "pass through" the event horizon?

    And if they did such a thing, wouldn't that actually represent negative time for them?

    Wouldn't time stop at the event horizon where the acceleration due to gravity requires a speed greater than that of light to escape?

    If so, does it even make sense to speak about the "inside" of a black hole?

    Maybe the event horizon is all there is to a black hole and they have no interior at all. It just doesn't exist.

    Have another beer, this is just barroom chat remember? :smile:

    If you have objections to my ideas above, that's cool, I'll be glad to hear them. But for now, let's assume that the event horizon is the black hole. It has no singularity within. In fact it has no "within" at all.

    The event horizon is the black hole, and this explains why the entire entropy of the black hole is contained on the event horizon (because that's all there is to it).

    When I heard about LQG and defining a fabric of spacetime based on some sort of "spin networks" (whatever that is), I started to wonder if it might be possible that the fabric of spacetime itself is something real, and when compressed to a certain point it is actually forced into a spherical shape. And when it's in that shape it warps the fabric around it and it stays in that shape like a knot or kink in the fabric of spacetime.

    So that's what I have on my mind. Maybe black holes have no inside at all. Maybe they are just spherical bubbles of the fabric of spacetime. And if you fall "onto" one, what actually happens is that you instantly become part of that sphere thus increasing its surface area. And there is no actual "hole" at all. It's just a warped bubble of spacetime that basically has no interior at all.

    Trying to figure out what's going on in the "center" of a black hole may be a totally erroneous idea.

    So that's why I'm interested in learning how to describe a black hole in terms of a spacetime fabric. But chances are that's never going to happen because I'm too far behind the learning curve to realistically catch up.

    So maybe I'll just stick with gardening, and let the pros figure out the black holes. :cool:

    By the way, thanks for all the cool links. This is far better than me trying to find this information on my own. I'll definitely be looking into this stuff. How far I'll get with it is yet to be discovered.
     
  21. Mar 8, 2013 #20

    atyy

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    Hawking derived the black hole entropy in semi-classical gravity.

    In string theory, there is a derivation from full quantum gravity of the entropy for a class of black holes called "extremal". There is, as far as I know, no comparable derivation in LQG.

    There are several different attempts to calculate the entropy in LQG

    LQG seems to have a calculation of the black hole entropy, but not from the full quantum theory, but a semiclassical one, somewhat like Hawkings. http://arxiv.org/abs/1204.5122

    There are also attempts reviewed by http://arxiv.org/abs/1201.6102 , but I don't think any succeed fully.

    String theory also has not calculated the black hole entropy for non-extremal black holes.
     
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