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Perche i nostri discorsi-Galileo quoted by Rovelli

  1. Oct 9, 2003 #1

    marcus

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    Perche i nostri discorsi---Galileo quoted by Rovelli

    "Dialogo sopra i massimi sistemi del mondo", one of Galileo's dialogs about science, contains this quote:

    "Perche i nostri discorsi hanno a essere sopra un mondo sensibile, e non sopra un mondo di carta."

    http://www.swif.uniba.it/lei/scuola/filosofi/filosofi3h1.htm

    Because our discourses have to be about the real world and not about a world of paper.

    Hey there, old Galileo! You made it into arxiv, on page 5 of:

    http://arxiv.org/hep-th/0310077

    thanks to ranyart for the link. Great modern dialog in the tradition of controversial dialogs on science issues going back to Galileo (if not earlier:wink: )
     
  2. jcsd
  3. Oct 10, 2003 #2
    You know, that quote (from Galileo) was one of the logical errors that I found in Sal's argument (in the link that ranyart provided on this thread.
     
  4. Oct 10, 2003 #3

    marcus

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    Please continue:smile:

    what other logical errors besides the quote from Galileo?
     
  5. Oct 10, 2003 #4
    I've found this paper to be fun, and is interesting that the author, founder of LQG, has assigned the paper of Simplicius to the stringer
    A pair of questions about the paper:
    a)What are those infinite fields that cause problems in string theory?
    b)What heck can this mean?: LQG has difficulties in recovering the low energy limit
     
  6. Oct 10, 2003 #5

    marcus

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    ?
    has assigned the part of Simplicius to....
    has assigned the role of Simplicius to...

    greatest debunker of all time (of the Aristotelian system to make way for modern empirical science, and of the Ptolemaic system to make way for the heliocentric model, and his preferred explosive seems to have been serious comic dialogs. Latin flavor in what is going on in quantum gravity, cant quite decide what it is
     
  7. Oct 10, 2003 #6
    I'm sorry, my english is quite elementary
    I meant role, of course
     
  8. Oct 10, 2003 #7

    marcus

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    and I was pedantic of course
    besides which, to be just, it is certainly not elementary!
    BTW have you noticed most people currently at the
    front in loop quantum gravity research speak
    as their first language something other than English.
    Today I was reading two papers by some people at
    University of Cordoba in Argentina. the people contributing
    most tend to have first-languages like French, Spanish, German,
    Hindi, Polish, Italian (ah! Italian). I wonder if the skew is
    just an illusion and if it means anything
     
  9. Oct 11, 2003 #8

    selfAdjoint

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    Mentat still hasn't told us why he thinks the quote from Galilleo was illogical...

    Rovelli's vision of how to move forward beyond present day physics boils down to this. Couple the standard model to the set of quantized QG loops so there will be interactions with eigenvalues of length and eigenvalues of momentum, etc. Combined states. Work on the theory non-perturbatively in that way. No infinity problems because no "classical points" - same advantage stringy physics gives, but with perhaps a more basic underpinning. The point for me is, if you could do this you could calculate numbers for the accelerators. The advantage over normal analysis would be non-perturbative calculations without infinities. The advantage over lattice would be, well it's proposed as real physics, no continuum limit required.

    I was thinking of posting this up in the mkaku quantum revolution forum, but I felt it would be kind of an insult to kaku, who is so big with string theory.
     
  10. Oct 11, 2003 #9
    Very sorry. I ran out of time yesterday, and couldn't respond here (partially due to the Chat that I had to leave early ).

    The quote from Galileo is illogical because, if the world were all like we experience, then we would have no need of science (all of our original assumptions would be correct). Also, it was most inappropriate that this be brought up when deciding about the next step after QM and GR (both of which challenge "common experience" at every turn).

    I'm saving my actual notes on the discussion (which I typed as I was reading) for the thread that I'm hoping ranyart will start soon.
     
  11. Oct 11, 2003 #10
    I apologize again for that. If it were up to me, I would be on much more than my currently alotted hour per day, but it's not up to me.
     
  12. Oct 11, 2003 #11

    marcus

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    this is a welcome condensed view that gets at the essence IMO. There are two short papers that bear on this:

    Relation between polymer and Fock excitations
    Ashtekar/Lewandowski
    http://arxiv.org/gr-qc/0107043

    Polymer and Fock representations for a Scalar field
    Ashtekar/Lewandowski/Sahlmann
    http://arxiv.org/gr-qc/0211012

    "To bridge the gap between background independent, non-perturbative quantum gravity and low-energy physics...Minkowskian Fock states are located, analyzed and used in the background independent framework..."

    The papers impress me as well written and as confronting basic questions:

    "Can the background independent, non-perturbative theory reproduce the familiar low-energy physics on, say, suitable coarse-graining? and, Can one pin-point where and why perturbation theory fails?"

    The coupling you mention seems to depend in a crucial way on connecting polymer and Fock representations as is done in these two papers. As well as "numbers for the accelerators" one can expect numbers for observational astronomy---hardly needs mention since it goes without saying
     
  13. Oct 11, 2003 #12
    Liminocentric Structures

    Liminocentric structures

    If U(1)=5d, how is it we could have turned things around?

    The limits of energy and matter distinctions, had to be recognized, and how they could flow from one into another?

    Here photon interactions, from the source, and back to gravitational influence(thinking of the spacetime fabric and how mass effects)?

    Supersymmetry, and the gravity field recognized as a repesentative of interactive forms in matter considerations?

    How I came to arrive at U(1)=5d(Kaluza and Klein were instrumental in leading the discussion from spacetime considerationsto [Boson Productions off the Brane]):


    Holography and Dimensional Relevance

    Heisenberg's Physics and Philospohies

    Re:Holography and Dimensional Relevance



    I am open here to corrections. I apologize if I am breaking the continuity of the thread.:)

    Sol
     
    Last edited by a moderator: Oct 11, 2003
  14. Oct 11, 2003 #13

    selfAdjoint

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    Marcus, Thanks for the two links. I scanned the first one, and noticed many old friends, like CYL and its dual. The polymerized Fock states lie in CYL*, which lies in full Fock space, but the Fock space product does not leave CYL* invariant. Bummer! Maybe an indication of why they went after the algebraic approach?

    I really need to get behind the terminology to se how they do Maxwell theory (first paper) and Klein-Gordan (second one) on the "polymer" realization of their quantum simplexes.
     
  15. Oct 12, 2003 #14

    marcus

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    selfAdjoint, I would be interested to know if you found
    the comparison in the dialog between modernday Simplicio and Salviati to be untrue or unfair at any point---particularly, if it is possible to point to a specific line on some page.
     
  16. Oct 15, 2003 #15

    marcus

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    the intuitive gist of Loop Gravity

    Probably what we need most now is an intuitive sketch of what makes Loop Gravity different from your typical field theory----how is the backgroundlessness implemented?

    Things are coming to a head. Rovelli's new book "Quantum Gravity" is major and has IMO material for a bunch of PhD dissertations just expanding on details. It also contains the "Dialog" as a final chapter. You can connect the points made about loop gravity in the Dialog to chapters and sections in the main part of the book. Also Smolin's April 2003 paper lays out what has been accomplished and what remains to do and what the prospects are for getting loop gravity tested---it is a thorough review and comparison: "How far are we from a quantum theory of gravity?"

    Plus we have good accounts of loop cosmology by Bojowald
    like the recent paper "Quantum Gravity and the Big Bang", and in some of Ashtekar's papers. It appears progress in cosmology has been dramatic of late. New researchers have been getting into LQG at the level of cosmology.

    Plus there is this month's Berlin symposium "Strings meets Loops" which will probably generate a series of overview talks
    aimed at wider audience----e.g. another cosmology overview by Bojowald, another full theory overview by Ashtekar, a spin foam overview by Rovelli, and so on.

    So there is more and more accessible information than there was a year ago, about loop gravity. It looks to me as if new research possibilities are coming into focus. For example, these days I keep seeing papers about the "low energy limit" or "semi-classical limit", another place where newcomers are getting in (like those Argentine people this month---Kozameh, Gleiser, Parisi)

    It seems to me to be a good time to try to say what loop gravity is about, in the simplest possible way. I am apt to make several false starts on this. If someone else has been thinking about it and wants to try, go ahead
     
  17. Oct 15, 2003 #16

    selfAdjoint

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    I dug further back into the references from the papers you cited and am reading hep-ph/0005233, by Thiemann, which is the first of a series of papers he wrote with various coauthors on the implementation of a "coherent states" form of QFT on the spin-edged simplex lattice of LQG. He asserts that the coherent state approach is equivalent to the usual approach and more suitable to the purpose. I will try to read up and bring some news on this demarche.
     
  18. Oct 15, 2003 #17

    marcus

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    Great! I very much look forward to hearing what you find.
     
  19. Oct 16, 2003 #18

    selfAdjoint

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    First, the Coherent State Transform.

    In 1994 Brian C. Hall (at UCSD) generalized an old (1962) result of Segal and Bargmann by defining a transform from the Hilbert Space of square integrable fucntions under the Haar measure for a compact group to the space of holomorphic functions on the complexified version of the group, supplied with a measure he defined to make the functions "act nice". This was all pure functional analysis, but it caused breakthroughs in a wide range of fields. So now if you google on Coherent State Transform you will find results on its applications to geodesy, to wavelets, to algebraic varieties, and also to this paper by Ashtekar,Lewandowski, Marolf, Mourao, and Thiemann, gr-qc/9412014 which generalizes the Hall transform and applies it to defining gauge theory on a GR spacetime.

    It is this generalized Coherent State Transform which is at the heart of Thiemann's attempt to define quantum theory on the network of LQG.
     
  20. Oct 16, 2003 #19

    marcus

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    You've got my complete attention. I will look up the reference and check back to see what follows
     
  21. Oct 17, 2003 #20

    selfAdjoint

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    The Hall Coherent State Transform.

    This is the straight Hall transform, as described in the ALMMT paper gr-qc/9412014.
    You have a compact group H and the set of square integrable functions from G to the reals, R, I will denote this set by L and a typical element in it by f. A typical element of G will be denoted g.

    The group can be complexified resulting in the group GC with typical element gC. Hall has defined a measure on GC using heat kernel methods. I won't go into details on that unless requested to; the meanure is denoted ν. Now the complexified group has irreps into complex vector spaces, and these irreps fall into isomorphism equivalence classes, so in talking about irreps it will be sufficient to consider one representative in each class. The generic irrep in this sense is denoted π. It maps into the complex vector space Vπ. Then define a normalizing constant σ, depending on ν and π by 1/dim Vπ times the integral over GCdν(gC DET(π(gC-1))2.

    Now define a prototype holomorphic function ρ from GC to the complex numbers by
    &pho;(gC) = Sum over π (dime Vπ/SQRT(σ)) Trace(π(gC -1)).

    So at each element of the complexification you project with the current irrep for the inverse of that element, resulting in a matrix, and you take the trace of that matrix, which is of course a complex number. The factor in &sigma guarantees that the sum doesn't blow up, so the function ρ is holomorphic. We're almost there.

    Now we define Hall's transform from the square integrable functions on G to the holomorphic functions on GC. For each f the value of the transformed function will be obtained by integrating over G with the Harr measure. At each element of g we will have the value f(g), a real number, and we will also have the complex partner of g, gC, and the complexification allows the element g-1gC to be well determined. The integrand is then f(g)ρ(g-1gC). Notice the interplay of group inverses.

    This is the transform as Hall did it. The authors , with an assist from John Baez, now generalize this transform for their purposes, which I will get to in the next post on this thread.
     
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