Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time in Quantum Gravity

  1. Oct 18, 2004 #1

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    want to read together this recent Bojowald paper?
    Time Dependence in Quantum Gravity
    http://arxiv.org/gr-qc/0408094

    Bojo is at Albert Einstein Institute (AEI-Gölm) one of
    the premier places for QG. It looks like not too hard
    and it clarifies things about time in QG. So could be
    useful to assimilate.

    Besides Bojowald the other two authors are
    Pamapreet Singh (IGPG-Penn State) and
    Aureliano Skirzewski (AEI-Gölm).

    Meteor probably posted the link for this when it came out
    but I only just now realized the special value of it.
     
  2. jcsd
  3. Oct 18, 2004 #2

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    OK, I have saved the paper and read the intro and the first section on Marolf's group averaging. I worked through the examples. Do we have any discussion points on this part of the material? Group averaging was also used by Thiemann in his string quantization, and we talked about Marolf's paper then.
     
  4. Oct 18, 2004 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    thanks! I thought already in the introduction there were some things people might want to discuss. I'd like to make it as inclusive as possible---minimal prerequisites.

    You may already be too advanced to be interested in what i have in mind, selfAdjoint :smile:

    Frankly I found the fourth paragraph of the introduction already interesting, where it says "A particularly striking difference between the classical and the quantum theory is the issue of time..."

    this is at the bottom of page 2, which is really the first page of the article because page 1 is just a cover-page containing the abstract and listing the authors.
     
  5. Oct 18, 2004 #4

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Yes, I find it interesting that he brings in relational time, and then (it seems to me regretfully) rejects it because it can't be fitted into the math. What do you think about his next statements, that in the canonical approach where the Hamiltonian is a second class constraint, time is just a gauge degreee of freedom? The implication is that if you fix the gauge, as one does, you get no time.
     
  6. Oct 19, 2004 #5

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    I'm glad to have someone to think about these things with. I think we at a place where intuition can originate or be cultivated.

    Relational time works, as he says. And it is used for calculating the jumps from geometry to geometry at planck scale. I remember how surprised I was when i read Bojo's 2001 paper about no-bigbang-singularity and the followup one by Bojo, Ashtekar, Lewandowski that did the same thing with more detail and rigor.

    the hamiltonian constraint H Psi = 0 was a difference equation that showed the evolution of the universe geometry in little steps, planck step by planck step. And there was no time. They were using the size of the universe as the evolution parameter to correlate other stuff to.
    The size of the universe was their clock.
    At a fundamental level you have to have something real to be your clock and you correlate to that.

    However Time kicks in after about 100 planck steps. Amazingly the approximation to the semiclassical, the differential equation, the familiar time-evolution, is very very good after on the order of 100 jerky geometric jumps. And it is smooth sailing.

    So Time is an abstraction, an approximation, that works if you dont try to parse evolution finer than about 10-40 second, or 10-41 second, that is, finer than about 100 planck time units.

    If you try to be fundamental you do not see a physically meaningful, MEASURABLE, time function----you have to make an arbitary choice of something measurable, like the scale parameter of the universe, and use it to keep track of the other measurable things. You arbitrarily choose something to be your clock. there is no ultimate criterion of steady running!
    this is hard to swallow (or so i found)

    but if you can wait you get a very good approximate time, idealization, not fundamentally physical, but practically approximated by possible-to-construct realistic clocks. It is only at the fundamental scale that you cant have this nice time to which we are so accustomed.

    I am talking too much, sorry.

    Also if you try to see things at a fundamental level you do not see a unitary time-evolution operator, a oneparameter group of nice probabilityconserving operators. you just see the damn constraint equation which says H Psi = 0. it is saying that the physical states are distinguished by being solutions of the H = 0 equation. And Bojowald derives his difference equation from this, showing how the geometry progresses in microscopic jumps.

    So at fundmental level there is no unitary time-evolution, but again if you are patient and can wait 10-40 second then the semiclassical approximation kicks in and things begin to look very normal.

    Now what i am saying is extremely impressionistic. Mostly comes from
    bojowald papers and the basic ABL gr-qc/0304074 (Asht., Bojo, Lewand.)
    But also this host of follower-research that has been repeating the same thing with variations since 2001. It is what i am used to seeing (impressionistically speaking) from each new paper as it comes along.
    they talk about bounce, and inflation, and vary the assumptions, and
    generalize the conditions and add in this or that, but the basic picture stays the same. bojowald has a lot of bibliography on pages 30-33.

    Now you have pointed out a special nontrivial detail which is the
    Don Marolf paper gr-qc/9508015 which is bojowald's reference [23]
    and which has "group averaging".
    he talks about that on page 3 (midpage) and then again on page 5 (top of page) and he does a sample calculation which can be interpreted as an instance of it. My feeling is that he is not seriously invoking anything. Everything here is kind of rudimentary so he does not have to invoke theorems or powerful technical tools. he is just doing something modest that happens to be a simple case of a celebrated technique. but he might have done it anyway. But that is just my take, and I am far from being the expert here. You are much more knowledgeable about Marolf and "refined algebraic quantization" and solving constraints, or so I think.

    Well that's my unedited view of the matter for the time being. I will leave it un-concise and garulous and hope you can find something useful in it.
     
  7. Oct 19, 2004 #6

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    BTW it turns out Aureliano Skirzewski is from Venezuela.

    he was doing string theory or something at a university of Venezuela and
    got a gig at Trieste for a year or so, and I guess Nicolai spotted him brought him to AEI.

    I wouldnt have guessed from the name Skirzewski that he was from Venezuela, (but the name Aureliano is right out of Marquez great Columbian epic novel 100 years of solitude)

    Looks like Thomas Thiemann is settled back at AEI now.
    I am just guessing this from the list of participants and papers at the Perimeter Institute 19-31 October conference. Junior people at AEI who work with Thiemann (Brunneman, Dittrich) will be reporting in Canada on research that Thiemann is involved in. If I was going to write him email i believe I'd use his AEI address (but of course i could be mistaken)
     
  8. Oct 19, 2004 #7

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    hope some others have looked at the Bojo paper Time in QG and have some thoughts about time in QG they want to share,

    but for now its only selfAdjoint who I know is reading the paper---have to read at least the introduction, y'all it is easy enough for sure---and plenty of PF people could get interested the rest as well.

    I am beginning to think that the view of space and time coming out of QG is right----time is not infinitely divisible. If you look closely enough you dont see time.

    only a bunch of things changing together in a correlated way and you have to pick one as the evolution parameter--and physically measurable things change in a jerky jumpy fashion

    so time just goes away when you look closely. I think this, I dont know it.

    And I think space is not infinitely divisible either. Physically there is no such thing as a "diffeomorphism". When you look close the manifold goes away. the continuum goes away. I think that's basic (but again cant be certain)

    the beauty is how the discrete evolution quantum regime can be calculated and merges into the semiclassical and ultimately the classical----how rapidly the approximation gets good. People are beginning to do QG computer modeling and it is really helpful that the convergence to the semiclassical or classical limit is fast. I will try to find a "Recent Progress" paper discussing this. IIRC Bojowald's gr-qc/0402053
    Certainly Ashtekar discussed it on page 23 of his recent
    http://arxiv.org/gr-qc/0410054 "Gravity and the Quantum" but he just gave a birdseye view.

    ---quote Ashtekar page 23---
    ...The detailed calculations have revealed another surprising feature. The fact that the quantum effects become prominent near the big bang, completely invalidating the classical predictions, is pleasing but not unexpected. However, prior to these calculations, it was not clear how soon after the big-bang one can start trusting semi-classical notions and calculations. It would not have been surprising if we had to wait till the radius of the universe became, say, a few billion times the Planck length. These calculations strongly suggest that a few tens of Planck lengths should suffice. This is fortunate because it is now feasible to develop quantum numerical relativity; with computational resources commonly available, grids with (109)3 points are hopelessly large but one with (100)3 points could be manageable.
    ---end quote---
     
    Last edited: Oct 19, 2004
  9. Oct 28, 2004 #8
    hi guys, I just wanted to say that relational time not just works, is the "only" way to construct a consistent, realistic physical theory! You may want to take a look to these papers (I am sure Marcus will like them :))

    gr-qc/0302064
    Consistent discrete gravity solution of the problem of time: a model
    Authors: Rodolfo Gambini, Rafael A. Porto and Jorge Pullin
    *
    quant-ph/0209044
    Title: A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories
    Authors: Rodolfo Gambini, Rafael A. Porto
    New J.Phys. 5 (2003) 105
    *
    quant-ph/0205027
    Title: Relational Description of the Measurement Process in Quantum Field Theory
    Authors: Rodolfo Gambini, Rafael A. Porto
    New J.Phys. 4 (2002) 58
    *
    quant-ph/0105146
    Title: Relational Reality in Relativistic Quantum Mechanics
    Authors: Rodolfo Gambini, Rafael A. Porto
    Phys.Lett. A294 (2002) 129-133
    *
    gr-qc/0101057
    Relational time in generally covariant quantum systems: four models
    Authors: Rodolfo Gambini, Rafael A. Porto
    Phys.Rev. D63 (2001) 105014
    *
     
  10. Oct 28, 2004 #9

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Edgar, thanks for posting these articles.
    I am not entirely clear about minor differences between
    Gambini/Pullin approach to quantum gravity and, say, that of
    Ashtekar. Whatever the differences of approach, I see a move in the direction of relational time which is more or less inclusive of everybody. Please correct me if I have the wrong impression.

    On another matter, did you happen to see these articles?

    Gambini Porto Pullin
    Realistic clocks, universal decoherence and the black hole information paradox
    http://arxiv.org/abs/hep-th/0406260

    Gambini Porto Pullin
    No black hole information puzzle in a relational universe
    http://arxiv.org/hep-th/0405183

    I was intrigued by their limit (derived by thought-experiment)
    on the possible lifetime and precision of real clocks. Time, even macroscopically, has no meaning apart from measuring it. Operationally one cannot speak of time unless one has a real clock. If one tries to make a clock more and more long-lived and more and more precise then one is compelled to make it so massive that it collapses forming a black hole. Then if one tries to use black holes as one's clocks, this turns out to be the best possible sort of clock but unfortunately they evaporate. And so there is a theoretical limit on how good it can get. I thought this was nice.
    If you read them how did they seem to you?
     
  11. Oct 29, 2004 #10

    Chronos

    User Avatar
    Science Advisor
    Gold Member
    2015 Award

    Ouch. The Hamiltonian is a second class restraint? That pretty much blows me right out of the water. To follow that up with the concept of time as a gauge field is truly painful. I had a hard enough time understanding the whole spacetime concept as it was. I admit, I ate pizza back when I thought I understood the concept. And I played hearts on weekends, but I never played with the cards face down while eating pizza. God may not play dice, but surely eats pizza and plays cards on Sundays.
     
  12. Oct 29, 2004 #11

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    What I didn't see in any of those Pullin-Porto papers titles was the word quantum. It looks like they are doing all their work in classical theory.

    BTW Marcus, back a few posts, on the 19th, you wondered if you were talking too much. Absolutely not! I missed that post before and just now went back to read it, and it cleared a lot of things up for me, because I haven't really been following relational time, or really the cosmology angle of LQG at all. Thank you.

    I wonder if we can parcel out the study here. You have a clear view of relational time in LQG cosmology, and Edgar1813 can tell us some detail about the Pullin-Porto approach, and I'll reread the part on group averaging in Bojo's paper and bring something or other from Marolf to the party. And what happens then, happens. How about it?
     
  13. Oct 29, 2004 #12
    Hey,

    Yes Marcus I'm aware of those papers too. With respect to the differences between consistent discrete quantum gravity (Gambini-Pullin approach) and LQG I would say that the main difference is the disappearance of the space-time constraints (Internal constraints, like Gauss law, is expected to survive as well as the loop transformation.) which allows a cleaner quantization and a consistent relational description, where all observables including time are turned into quantum operators. You may want to take a look at this paper:

    Dirac-like approach for consistent discretizations of classical constrained theories. http://xxx.lanl.gov/abs/gr-qc/0405131

    for an introduction in the classical realm. With respect to the word "quantum", selfadjoint might want to take a closer look to the papers I think include all the ingredients including quantization:

    A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence
    http://xxx.lanl.gov/abs/gr-qc/0402118

    and

    Consistent discrete gravity solution of the problem of time: a model
    http://xxx.lanl.gov/abs/gr-qc/0302064

    Some of the papers Marcus mentioned are also worth reading.

    The idea of decoherence seems to be related to treating time as a quantum physical object and its fundamental character, as Marcus pointed out, is associated to fundamental limits nature puts in how to build up an accurated clock.
    What seems to happen is that intrinsic Heisenberg uncertainties limits the mass of the clock from below and black hole collapse limits it from above. Combining the two there is a fundamental inequality that turns out to be an equality for black holes promoting them as the best available clocks in nature!
    All this observation are quantum in nature as well as the modified non-unitary evolution that seems to be implied by the non existence of ideal time.
    All this implies that nature has an intrinsic non-unitary behavior in "real time" that, although small is big enough to rule out the black hole information puzzle and turned into not a paradox at all!
    Instead of looking for a modification of gravity what it's been said here is: "Look QM is intrinsically non-unitary once time is taken to be a quantum real observable, why should we bother about the BH puzzle in the first place since the BH will loose coherence anyway at the same speed as Hawking radiate."

    Best
     
  14. Oct 29, 2004 #13

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    The way I see it, Gambini and Pullin are a quantum gravity team of comparatively long standing. Porto is a junior member who has appeared sometimes more recently.

    The question to ask might be how to describe Gambini group's approach (or approaches) to Quantum Gravity? And what do they mean by "discrete" quantum gravity?

    For what it's worth, here are the most recent 4 papers from this group:

    1. Rodolfo Gambini, Jorge Pullin Consistent discretization and loop quantum geometry
    gr-qc/0409057

    2. R. Gambini, S. Jay Olson, J. Pullin Unified model of loop quantum gravity and matter
    gr-qc/0409045

    3. Rodolfo Gambini, Rafael Porto, Jorge Pullin Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance
    gr-qc/0408050

    4. Rodolfo Gambini, Jorge Pullin Consistent discretizations and quantum gravity
    gr-qc/0408025

    I have sometimes seen Gambini's approach desribed as the "Southern School" of LQG, to distinguish it from the versions developed by Ashtekar and Rovelli. If there are two schools, then the two cite each other a lot. Gambini et al will cite Ashtekar, Thiemann etc. and they in turn cite Gambini. Distinct, at least on the surface, but somehow not conflicting.

    Some Gambini papers I've looked at dont resemble LQG at all, to my limited perception at least! I'm afraid I dont know enough sort it out. They go to the same conferences. the same family. Like brothers: the same but different.

    ============
    Notice that I am saying "Gambini et al." instead of, as you said, "Pullin Porto" papers.
    It may seem pointless and ridiculous of me to try to get clear on who's-who details like this, but lets take time to sort things out. I will use the arxiv counts to form an idea of the Gambini bunch.

    Gambini has 64 papers, many with Pullin, a few with Porto, and lots with other people as well.
    Pullin has 25 papers, most are with Gambini. Indeed, aside from his MoG newsletter and 5 others, all are with Gambini
    Porto has 11 papers, all with Gambini. The 7 most recent are also with Pullin. So far, anything that is Pullin-Porto has also been Gambini-Pullin-Porto.
    ============
    Just to get a sample of their interests, by glancing at titles, here are the 11 papers you get on arxiv for Rafael Porto:

    1. Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance

    2. Realistic clocks, universal decoherence and the black hole information paradox

    3. No black hole information puzzle in a relational universe

    4. Dirac-like approach for consistent discretizations of classical constrained theories

    5. A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence

    6. Loss of coherence from discrete quantum gravity

    7. Consistent discrete gravity solution of the problem of time: a model

    8. A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories

    9. Relational Description of the Measurement Process in Quantum Field Theory

    10. Relational Reality in Relativistic Quantum Mechanics

    11. Relational time in generally covariant quantum systems: four models


    for more detail, see
    http://arxiv.org/find/grp_physics/1/au:+Porto_R/0/1/0/all/0/1

    for a full list of Gambini preprints (which include these 11) see
    http://arxiv.org/find/grp_physics/1/au:+Gambini_R/0/1/0/all/0/1


    =====

    Does a clear pattern emerge from this small sample? Not for me anyway!
    But there it is, in case you want to draw your own conclusions. The titles certainly do not all say "discrete QG" on them---nevertheless suspect that is what Gambini and co-workers would call the main focus of their effort.
    or maybe they would call it a version of LQG.

    Nonunitary probably knows, and could explain.
     
    Last edited: Oct 29, 2004
  15. Oct 29, 2004 #14

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Edgar, I just now saw your post. I like your summary of this argument!
    I have bolded the punchline, for emphasis. this is a fine logical argumentation. But I want to be cautious. I was listening to a talk by Ashtekar on "Black Hole Evaporation" that he gave 20 September. In his treatment, if someone can wait a very long time, the final state is pure.
    There is ultimately no decoherence. It is as if Ashtekar is unaware of
    the Gambini et al argument. So I am trying to keep these two conflicting possibilities in mind---not to let one win out over the other, and hope that ultimately something will resolve the contradiction.

    Edgar, did you happen to listen to the audio of Ashtekar's talk?
    http://www.phys.psu.edu/events/index.html?event_id=934;event_type_ids=0;span=2004-08-20.2004-12-25
     
    Last edited: Oct 29, 2004
  16. Oct 30, 2004 #15
    Hey,

    Just a remark, Gambini and Pullin have each more than 110 papers. They have contributed to classical GR as much as QG.
    Gambini indeed was amongst the first to introduce loop space in gauge theories in the early 80's and he has done important contributions to lattice YM theories as well. Pullin also made seminal contributions to black hole collisions, gravitational waves and numerical GR. Rodolfo has been recently awarded the TWAS (third world academy of science) prize in the ICTP Trieste for his work and leadership in his native country: Uruguay.

    http://www.ictp.trieste.it/~twas/publ/TWAS_12Dec03_Uru.html

    Jorge also received the Edward Bouchet award of the American Physical Society.

    http://www.aps.org/praw/bouchet/01winner.cfm

    As far as I know they have been working together since 1990 and published more than 50 papers in collaboration.
    Rafael A. Porto was ('is') Rodolfo's student and they have been working together since 2000. He is now at Carnegie Mellon U. getting a phd and working as well in gravitational radiation and effective field theories.
    As you can see from their papers their main motivation it's been trying to construct a consistent, purely quantum relational description of covariant theories and the understanding of its physical implications, from a philosophical view to experimental observation. They have made contributions to the interpretation of relativistic QM and QFT as well building upon relational ideas and also proposed a potential physical distinction between the covariant-realistic approach they developed and the non-covariant instrumentalist one. Incidentally their first paper was the first in showing
    that relational time could be consistently applied in several models considered crucial tests.

    GPP have been working together as a team since 2002 and they have shown that, remarkably, the Gambini-Pullin quantization approach seems to allow for the introduction, for the first time, of a consistent purely quantum description therefore solving the so called 'problem of time', one of the long-standing fundamental problems of quantum gravity. The potential empirical evidences are now in the form of a fundamental decoherence effect which renders the BH paradox unobservable and might be tested in a near future in macroscopical quantum superpositions like Bose-Einstein condensates. Furthermore, the theory has already been successfully used to treat a variety of systems, including cosmological models, Yang-Mills theories, BF-theory and general relativity on the lattice. The formal structure has been since emerging.

    I believe there is by now compelling evidence that these ideas seem to be in the right track. However, as a friend of mine used to repeat: "Prediction is very difficult, especially if it's about the future." I think it was Bohr although he claims it was a famous beisbol player :)

    best.
     
  17. Oct 30, 2004 #16

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    I have been reading (but not really deeply) a couple of the papers you kindly gave links to. I have a question that is probably easy to answer but which is bothering me. The authors discuss the importance of their n, the counter of the steps in their consistent discretization. They say they couldn't develop their relational time in the discretization approach without n serving as an ordering parameter, and they point out that n has some of the mathematical properties (orthogonal to physical observables, etc.) that time has in classical theory. So my question is, have they perhaps smuggled time into their theory in the disguise on this n?

    This is not intended to be a knock at their work, or at the implications of relational time. It's just a request for clarification.
     
  18. Oct 30, 2004 #17

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    Hi selfAdjoint, by coincidence I also have been reading (probably) a similar couple of papers, and wondering what, if anything, I could say.
    To be specific, this morning I've been reading
    http://arxiv.org/gr-qc/0408025
    Consistent discretizations and quantum gravity
    http://arxiv.org/gr-qc/0409057
    Consistent discretizations and loop quantum geometry

    I see that in his most recent review paper ("Gravity and the Quantum") Ashtekar cites the first of these papers. the second was probably too new at time of writing for him to have included.
    I hope that you and Edgar can make some progress with these questions. I would like to participate, but I have a rehearsal this morning.

    My understanding about the discrete steps being a kind of time probably parallels what you are saying. In cosmology, Bojowald chose a size index as the "clock", something that increases in discrete steps, and correlated the other observables to that. he does not use the word "relational" but he does pick some real process (in this case the expansion of the universe) as a clock and he does the analysis with discrete timesteps. In planck-scale cosmology (as Bojowald does it, and maybe other areas as well) there is no external criterion for saying that the discrete steps are "equal".

    the idea of a steady uniform time quickly emerges as an approximation.
    but the more fundamental planck-scale analysis seems to call for
    some real process advancing in discrete steps to which one can correlate the rest.

    this is a bit hasty, I wanted to contribute at least something to this conversation before having to get ready to leave for the morning.
     
    Last edited: Oct 30, 2004
  19. Oct 30, 2004 #18
    Hey,

    The meaning of time by itself is a rather subtle issue it would take lot time to discuss. What I can say is that think of $n$ as coordinates in GR since actually they are just a discrete counterpart. In classical GR, as Einstein pointed out, coordinates are just labels and physics is built upon what he called coincidences (you can read about the hole argument in Rovelli's papers as well). The relationship between coordinates and observers is somehow subtle (Rovelli has a set of wonderful papers about this issues you might want to take a look:

    1) QUANTUM REFERENCE SYSTEMS.

    2) WHAT IS OBSERVABLE IN CLASSICAL AND QUANTUM GRAVITY?

    By Carlo Rovelli Class.Quant.Grav.8:297-332,1991)

    either we fix a gauge and attach to it some "physical meaning" through the study of the solution and its geometrical properties or we introduce the idea of gauge invariant correlations between what Rovelli calls "partial observables", namely those objects with ontological meaning as clocks and rods. In the latter coordinates are just used as a device to construct relational observers in pretty much the same fashion that one use any parameter to describe the world line of a particle given the same physics for x(x^0).
    At the classical level both procedures give the same "physics" and that is perhaps why people doesnt really bother much with the difference. The introducction of $n$ and the lost of constraints may resemble the gauge fixing process at the classical level although it is not quite the same since we still have all degrees of freedom in the theory and one doesnt add further constraints.
    At the quantum level the story detour completely. One can still fix a gauge and define a classical time which will be kept classical througout the evolution with a sort of Schrodinger like equation. The constraints now are second class and are impossed as strong relationships. This approach lacks the fundamental ingredient that time itself is a physical observable subject to quantum fluctuations and in principle in equal foot to all other physical variables. in other word, the classical choice might not represent a realistic clock or rods (Think in a rotating coordinate system, the "edge" of the axis will exceed the speed of light!)
    On the contrary, in the relational spirit one quantize the whole space and then introduce the correlations between quantum partial observables choosing one, of several of them as the clock. The quantization itself lies in formal grounds, namely build up a set of n-Hilbert spaces, a canonical algebra of well defined selfadjoint operators and a unitary mapp between this n-equivalent Hilbert spaces.
    One could have done this in the continuum theory as well using the coordinates as auxiliar elements to construct the
    physical measurable objects like the correlations and using the unitary mapp given by the Schroedinger equation in coordinate time $t$.
    In that sense $n$ doesnt play a different role that the time coordinate in GR. Furthermore, the decoherence effect obtained from the relational approach could be also derived from the continuum description in a similar fashion if we would succeed in building a consistent theory (I havent looked at it but I imagine it can be also obtained from bojowald's approach).
    There are subtelties I wont discuss here but it could be done in principle. The idea of discrete quantum gravity departs from usual QG since the phase space has more degrees of freedom due the lack of constraints, it recovers GR though since the symmetries are still encoded in the solutions. It provides us with a consistent quantization and a relational evolution with all variables, included time, turned into the quantum realm.
    The meaning of $n$ is like discussing the meaning of the metric in GR or the coordinates of space time itself. Somehow physics has been built upon objects that do not seem to have a direct observable character but whose symmetries or general properties allow a cleaner treatment.
    As in any physical theory there is an underlying ontological meaning for certain objects that it is put into the theory by us. That is why this is a human construction, and as Einstein used to say: "I cant add my brain into the theory". There is always something "outside" the theory although inside the universe, and depending the type of question asked nature will answer relationally. Different question will give different, perhaps even non comparable answers.
    You can think of the universe as a block sequence of snapshots in $n$ where internal correlations are measured. For a perfect clock we can correlate this god-time with what we call time and have the ilusion of "evolution" and a well defined local theory. In general probabilites would be associated to the whole story of the universe and the formalism, although still applicable in non Schroedinger-like regimes, would be rather different to what we experience today.
    Most of the papers of GPP and GP have discussed on these issues, I hope I have made it clearer.

    best
     
  20. Oct 30, 2004 #19

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Thank you for that clear explanation. With that and reading the "Consistent Discretations and Loop Quantum Gravity", I think I understand the approach better. In the latter case we have a time in the classical theory, and they discretize it out, resulting in a hamiltonian system without constraints (because would would have been a constraint turns out to constrain the system at different n's and thus vanishes identically). Then they are free to choose any one of the observables after quantization to play the role of time using conditional probability.
     
  21. Oct 30, 2004 #20

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    thanks Edgar, it does make it clearer.
    If I remember correctly the concept of "partial observable" was discussed in Rovelli's textbook Quantum Gravity, in chapter 3 but also in some sections near the end of chapter 2. I will see if I can find page references for some discussion.

    IIRC a partial observable is PARTIAL because to make a full meaningful observation involves measuring the correlation between it and something
    else.

    a partial observable is like saying "Three O'clock!"
    or "25 meters North from my nose!"

    It does not mean anying unless associated with something else, an event, a motion, a prediction.

    At some point rovelli points out that one can observe a P.O. ("in a vacuum" so to speak) but one cannot predict it will have some value as long as there is nothing on which to base the prediction.

    Anyway there is the idea of incompleteness about it. Some other measurement must be made simultaneously or inconnection with it, to give the whole thing meaning. the real thing of interest is the correlation of other measurements with the P.O.

    rovelli also warns, in chapter 3, that he sometimes calls a partial observable by the alternative name relativistic observable. and
    also if the context is understood he simply says "observable".

    To me this simpler usage makes sense----I do not expect quantum observables to have some absolute meaning apart from correlations between different ones----so I do not need to hear the qualifier "partial".

    Well then, in this context, the measurement of time, by looking at some clock or by observing the expansion of the universe or whatever----looking in my glass to see how much beer is left----this is just another observation, which I can correlate with other observations. there is no One Absolute Clock and there is not any more a Perfect Steady Time, just there are a lot of observables all on the same footing.

    I see that i am just repeating what Edgar and selfAdjoint already said or understood. this comes from attending choral rehearsal all day. this is very interesting but I will go have a nap.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted