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Black Holes, Quantum Gravity and the Curvature of spacetime

  1. Dec 19, 2006 #1
    What is Quantum Gravity and the Curvature of Spacetime and how is it all relevant to one another?
     
  2. jcsd
  3. Dec 19, 2006 #2
    Welcome to the forum.
    As your just getting started here allow me to offer a few tips.
    If your not working on a classroom or homework problem (Top of the main page), go to the appropriate forum for the subject.
    Looks like you've found your way kind of close to the area you want, but still forums work best when you know enough about the area to be able to ask a pointed question.
    For questions like "What is this subject and what does it mean for some other subject" are better handled by starting with a book so you can have enough knowlage to ask a question.
    And once you know enough to ask; remember you can often find where your question has already been asked use the SEARCH Function - find a few relevant threads and go though them, then you can also get a feel how to use the forum from the example of how other questions have been handled. Find and read the sticky threads (on top) and actually read and understand the forum rules.

    How to pick a book to read - search for a question. Try looking for "quantum book" or "relativity book" I'm sure you'll see some recommendations and maybe some web site explanations to read as well.
     
  4. Dec 19, 2006 #3
    Actually how quantum gravity relates to curvature of space-time seems like an interesting question. Is it really impossible to give some overview on the general approach on how to introduce backgound independence into quantum theory?
     
  5. Dec 19, 2006 #4
    Because my main interest was in understanding what is known about black holes, i began reading on the properties of black holes. in the article that i was reading Quantum Gravity is mentioned. now i am reading on Quantum Gravity and how it what occurs when Quantum Gravity Meets the Quantum Theory, my problem now is this equation and what it means in relation to Quantum Gravity and to the properties of a black hole.
    "In general relativity, mass and energy are treated in a purely classical manner, where ‘classical’ means that physical quantities such as the strengths and directions of various fields and the positions and velocities of particles have definite values. These quantities are represented by tensor fields, sets of (real) numbers associated with each spacetime point. For example, the stress, energy, and momentum Tab(x,t) of the electromagnetic field at some point (x,t), are functions of the three components Ei, Ej, Ek, Bi, Bj, Bk of the electric and magnetic fields E and B at that point. These quantities in turn determine, via Einstein's equations, an aspect of the ‘curvature’ of spacetime, a set of numbers Gab(x,t) which is in turn a function of the spacetime metric. The metric gab(x,t) is a set of numbers associated with each point which gives the distance to neighboring points. At the end of the day, a model of the world according to general relativity consists of a spacetime manifold with a metric, the curvature of which is constrained by the stress-energy-momentum of the matter distribution. All physical quantities — the value of the x-component of the electric field at some point, the scalar curvature of spacetime at some point — have definite values, given by real (as opposed to complex or imaginary) numbers. Thus general relativity is a classical theory in the sense given above."
     
  6. Dec 19, 2006 #5

    marcus

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    Oh, I did not see your most recent post. This is a reply to your original post.
    Juan, the first thing to understand is the classical idea of the curvature of space, from back in 1915 before quantum theory entered the picture

    it was Einstein's insight that what we experience as gravity is really geometry, and the Einstein equation of 1915 shows how the distribution of matter determines the shape of space around it-----this is the main equation of Gen Rel

    a famous physicist later put that equation into words: "Matter tells spacetime how to curve. Spacetime tells matter how to move."

    =================

    starting in 1919 the geometrical theory of gravity (Gen Rel) was tested---repeatedly and with increasing precision. It really does predicts what will happen more accurately than non-geometric theories----theories in which space is a rigid rectilinear framework and gravity is explained by force vectors

    ===============
    so after 80 years of testing Gen Rel, we pretty much accept that space is a dynamic, changing, active thing-----its shape changes as matter moves around in it.

    fortunately it doesnt change very much except for very dense massive things, so we dont notice------it is still approximately the foresquare rigid spacetime that Newton imagined, so for practical purposes we still think of it like that.
    ===============

    quantum theory comes in when you try to give this dynamic geometry, interacting with matter, a QUANTUM description-----that means using stuff like wave-functions, and having uncertainty built in.

    it doesnt mean that space has to be divided up into little bits:rofl:

    (sometimes people think space must be made of quanta)

    it means that things that you observe and measure about the geometry of space----like SURFACE AREA, and ANGLE, and VOLUME, and even the dimensionality itself-----are no longer fixed definite things but are instead quantum observables (which can incorporate uncertainty)

    For example, in a quantum model of a region of spacetime, the curvature is allowed to have some uncertainty---and depend on the quantum state of the system.

    that's all I can provide as an introduction. the main thing is to understand the pre-quantum 1915 business first-----when that is assimilated it is easier to think about shifting to a quantum version of it.
     
  7. Dec 19, 2006 #6
    If and when someone can do it I suppose they might, but being able to give a correct way to start would mean you knew were you were going.
    Smolin in his book and Perimeter Institute papers seem to show they have tried several approaches and are still looking very hard.
    Personally I do not think they will succeed in combining the background independence of GR with QM or the Standard Model.
     
  8. Dec 19, 2006 #7
    Thank you, this clears up a lot. But how is it all relevant to a black hole and it's properties?
     
  9. Dec 19, 2006 #8

    marcus

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    Several people are around here who could reply well to that. I will give someone else a chance.
     
  10. Dec 20, 2006 #9
    juan_rod:” What is Quantum Gravity and the Curvature of Spacetime and how is it all relevant to one another?”

    marcus:” a famous physicist later put that equation into words: "Matter tells spacetime how to curve. Spacetime tells matter how to move."

    “it means that things that you observe and measure about the geometry of space----like SURFACE AREA, and ANGLE, and VOLUME, and even the dimensionality itself-----are no longer fixed definite things but are instead quantum observables (which can incorporate uncertainty)

    For example, in a quantum model of a region of spacetime, the curvature is allowed to have some uncertainty---and depend on the quantum state of the system.

    that's all I can provide as an introduction. the main thing is to understand the pre-quantum 1915 business first-----when that is assimilated it is easier to think about shifting to a quantum version of it.”

    It seems that nature like follow to something very exceptional. In addition to
    Marcus suggestion and in accordance with him look also the elliptical geometry in S7 E.Cartan “sphere” which admits an absolute parallelism.

    juan_rod:” But how is it all relevant to a black hole and it's properties?”

    I have no idea.
     
  11. Dec 20, 2006 #10
    Hence my problem... thanks a lot everyone.
     
  12. Dec 20, 2006 #11

    marcus

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    Wait, Juan and Anonym, I will try to reply. I thought some other people would like to reply, but they didn't.

    You ask what BH has to do with classic 1915 Gen Rel and also with QG.

    I think maybe you know the answer or part of the answer.

    everything that has been observed about BH so far is simply consistent with classic Gen Rel and has nothing to do with QG

    I think you will agree. If not, please say how I am mistaken. Astronomers have no observation of BH hawking radiation or BH evaporating. So there is no empirical data about relation of QG to BH!

    By contrast there is a large amount of empirical data about stuff observed falling into BH and the minimal stable orbit radius----and the redshift of X ray from iron very close to hole----and so on. Wonderful empirical data. Stars have been observed orbiting the central BH in our galaxy and so on. All that is wonderful but perfectly classical.

    So your question about what is relevance of QG to BH has a peculiar status. Unless we get some new observation, the question concerns something about which there is no empirical data, but is a rather more speculative question, purely about theory.
     
    Last edited: Dec 20, 2006
  13. Dec 20, 2006 #12
    Well you seem more advanced than I thought your OP indicated.
    I’d recommend considering what you already know about the fundamentals behind the two ideas: “Quantum Gravity” “Curvature of Spacetime” and how they are relevant to each other, before you worry about how they may be relevant to a Black Hole.

    “Quantum Gravity” - Fundamentally based a quantum approach, utilizing QM (its derivatives or equivalents) and uses the Standard Model including the idea of particle exchange of gravitons (yet to be discovered) to account for gravity.

    “Curvature of Spacetime” – Fundamentally linked to GR and accounting gravity by curves or warping in a 4D Dimensions (some claim 5) with our view of 3 dimensions and time along with gravity being the result. Note the lack of need or use of particle exchange.

    Most see these two ideas, as completely incompatible. I agree with the view (but not all do) that they cannot be combined. As in, at least one must be shown as wrong (but they both work so well) some day! Hence my opinion that Smolin will not succeed in combining the background independence of GR with QM or the Standard Model.

    Got to hand to those with the persistence to keep trying to combine them, IMO they are working on the core of your question.
     
  14. Dec 20, 2006 #13

    marcus

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    Parampreet Singh in Ashtekar's group at Penn State has proposed a new phenomenon to look for in Gammaray Bursts (GRB) that would have a QG signature. I heard this in a recorded Penn State seminar talk

    :smile:

    you see, I have to stretch very hard to reach some contact with empirical observation. He says that some instances of gravitational collapse would release a GRB with a distinctive lightcurve. I don't remember, the lightcurve would have some peculiar feature that astronomers could be told to look for.

    In QG, gravitational collapse is different because gravity actually turns repulsive at near-Planck density. Some extreme cases might look different.

    My apologies----I do not know if this work of Singh has even been published.
    ==================

    I will try to think of some more cases. If one has no observational check then there is no certitude of talking about something real---it could all be just weaving words about the artifacts of theory.
     
  15. Dec 20, 2006 #14
    From my basic understanding of QG and QM, i know that quantum leaps from within electrons in the matter surrounding and in front of a BH make it seem as if time curves and or slows down. i also understand that space-time curvature helps both find and identify a BH.

    if any of my assertions are wrong please share some insight.
     
  16. Dec 22, 2006 #15
    Marcus:” Wait, Juan and Anonym”
    “everything that has been observed about BH so far is simply consistent with classic Gen Rel”

    Sorry, when I was a student, I attended the seminar given by Y.Zeldovich at Moskow Stecklov Institute. The issue was not a particular problem or particular solution of some problem. Y.Zeldovich presented analysis whether the Einstein GR contains essential singularity. If I understood him correctly, the answer was no.
    However, I agree to wait
     
  17. Dec 22, 2006 #16
    Of course, what happens to RT at this singularity?
     
  18. Dec 23, 2006 #17
    With regards to this question I am interested to see what the members here think of integrating quantum theory with the priniciple of general covariance. Is it at all possible or would it indicate a fundamental flaw in at least one of the theories?
     
  19. Dec 24, 2006 #18
    DocN:” what happens to RT at this singularity?”

    I beg your pardon for my ignorance, what RT stands for?
     
  20. Dec 24, 2006 #19

    marcus

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    I think he means "renormalization theory" or something like that

    [EDIT: correction, I see from DocN next post that he may have meant "relativity theory"]

    Anonym, I was interested by what you said here:
    I agree that classical Einstein GR with a positive cosmological constant Lambda can have a bounce that begins the expansion phase. It does not absolutely need to have a cosmological singularity there. But I am not sure that I understand what you are reporting from Zeldovich.

    I was glad to hear that you were attending seminars at the Steklov. This is to be congratulated as a kind of good fortune. Very famous institute. I hope your present location is also stimulating and has plenty of ideas.
     
    Last edited: Dec 25, 2006
  21. Dec 25, 2006 #20
    doestn't relativity theory "collapse" at the singularity just like all physics laws?
    Doc
     
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