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Quantized Gravity (Unification of GR and QM)

  1. Sep 9, 2007 #1
    I am just wondering, when we talk about fundamental forces we refer to the strong force, electromagnetism, the weak force and gravity. But is it not true that gravity is just the curvature of the space time fabric, in which case it is technically not a force. So when we say gravity is a fundamental force, what are we actually talking about?

    If gravity is just the curvature of space-time, then when we talk about gravity as being quantized (gravity at the quantum-mechanical level), are we talking about the fabric of space and time at a quantum level?

    Also, just curious

    Whats the go with inflation, when the universe expanded faster than the speed of light, could anyone explain to me how that is possible?

  2. jcsd
  3. Sep 9, 2007 #2


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    this will just be my take---others may see it differently. I think there are choices in how you view quantizing gravity.
    As a PRACTICAL matter 1915 classic GR works better than any other model of gravity, it just predicts more accurately
    but GR says gravity = geometry

    the gravitational field, represented by the metric g, is the geometry of spacetime and indeed spacetime HAS NO INDEPENDENT EXISTENCE apart from its geometry.

    this is a key nontrivial idea and there are some quotes from Einstein to emphasize it.
    spacetime is nothing a web of geometric relations, there is no absolute pre-ordained fixed stage on which things happen, there is only the gravitational field itself. Other fields are defined on the gravitational field rather than on or at points of spacetime (which have no independent existence).

    I'm not telling you anything new, I think you know this about GR already. I just want to emphasize that GR is a very radical, drastic revision of how things were seen up to 1915.

    but GR has going for it the exquisite precision of its confirmed predictions that are difficult to duplicate using a fixed geometric stage and forces within that fixed geometry.
    So one is led to take GR seriously, and say maybe the world really is that way. Maybe geometry is dynamic and gravity = geometry.

    and if we TAKE GR SERIOUSLY then quantizing GR means to have a quantum state of the geometry of spacetime. One has to have a quantum state of the geometry of the universe, or some big representative chunk of it.

    This means that the TESTING GROUND OF ANY QUANTUM GRAVITY is likely to be observational cosmology. How you tell if a QG is good is you ask how does it explain inflation, how does it explain dark energy, how does it handle the BigBang, does it get rid of the BB and BH singularities, what does it predict about structure formation and the spectrum of fluctuations in the CMB. how does the actual expansion history of the universe (measured e.g. by Type IA supernovae) compare with the predicted history of expansion? Does it predict some variable delay in light signals that have traveled cosmological distances, depending say on energy, and is this observed?

    The more carefully you measure things like GammarayBursts (GRB) and ActiveGalacticNuclei (AGN) flares, and CMB temperature map, and structure map from the Sloan Survey, and standard candles like the supernovae, the closer you get to being able to constrain QG and distinguish between good and bad QG.

    So there is a welldefined QG program and a welldefined QG testing ground. I find it hard see gravity as analogous to the three forces you mentioned. At some point we will have a Lagrangian or an action and there will be terms in it for all these things-----but the terms governing the quantum geometry may be rather different from the terms in which electromagnetism enters and the fine structure constant plays a role. I don't see how one can confidently put all four of these phenomena on the same footing and expect them to all appear the same way in some imagined future Lagrangian.
    Maybe this is simply due to my own limitations.

    You ask about inflation. This is an issue where I think Martin Reuter's QEG approach ("quantum einstein gravity") is ahead of some of the others. He quantizes the metric and shows that GR is renormalizable (which people didnt think was the case) so he brings GR into the orbit of Quantum Field Theory notions. He has a Renormalization Group flow and running coupling constants. the Newton G(k) and cosmological constant Lambda(k) run with the cutoff scale parameter k.
    k has the dimensions of inverse length. so k--> infty corresponds to high energy small distance limit.
    The exciting thing about Reuter's work is that he does the minimum necessary to show that GR is renormalizable, calculates the RG flow trajectory (which has a long classical segment where G and Lambda are just what we measure) and then he gets a lot of stuff for FREE.

    Like 60 e-folds of inflation, with graceful exit, and a physical reheating process, WITHOUT needing any exotic matter like an inflaton or a "slow-roll" potential. he doesnt need any of the fantasy stuff that people usually assume to make inflations scenarios work. Because Lamba runs.
    I put Reuter's renormalization group flow picture as my avatar. He first calculated the RG flow and found the trajectory that Nature seems to follow (to explain known values of G and Lambda) and THEN he found that it explains inflation without needing exotic matter. It came as a BONUS,
    he also got the right number for the entropy of the CMB, again for free.

    So it's impressive. And I would say that this shows that Reuter QEG is some kind of final answer but it raises the bar and it shows WHAT SHOULD BE EXPECTED FROM A QUANTUM THEORY OF GRAVITY.

    You also mention about parts of the universe receding away from each other faster than light.
    this is a standard part of the mainstream cosmology consensus.
    Recession speed is not limited by speed of light. distant things arent in the same Minkowski frame so SR doesnt apply.
    You could ask about that in Cosmology forum next door. There are some links about it.
    One that people often recommend is an article called "Expanding Confusion"
    by Lineweaver and Davis. It deals with misconceptions people have about the expanding universe model.
    this is not special to the presumed inflation episode.
    Basically it involves large scale distances between things that are not tied together (like parts of the same galaxy) and it says that at present all these distances are expanding by about 1 percent every 140 million years.

    the expansion is proportional to size. so if the distance is large enough the expansion has to be at a rate exceeding c.

    at the present time anything we can observe that has a redshift greater than around 2 (which includes a lot of stuff) was receding from us at a rate > c at the time it emitted the light we are now getting from it. this puzzles a lot of people when they hear it for the first time, and for good reason! :smile: but this is classical cosmology and doesnt belong here.
    Last edited: Sep 9, 2007
  4. Sep 9, 2007 #3
    You might be interested to know that there is an alternative theory of gravity, which doesn't involve space-time curvature and yet explains all relativistic gravitational effects pretty well. Moreover, this theory is perfectly compatible with quantum mechanics, unlike GR.



  5. Oct 26, 2007 #4


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    As a funny aside: you can actually think of ALL of these forces as the "curvature of space". In particular, Yang-Mills theory (including the "trivial YM" of E&M) can be described as the curvature of some "internal space", and the "force" that we feel is nothing but the "curvature" of that space. Indeed, there is a close parallel between the electric and magnetic fields, and the Riemann curvature in GR.

    So talking about curvature vs force is not just a gravity thing - "force" and "curvature" are synonyms. The trick is trying to answer: "What's the thing that's curved?"
  6. Oct 27, 2007 #5


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    The distinguishing aspect of gravity is its background independence. There is no evidence it is overlayed [so far a we know] on a more 'fundamental' background. The other 3 fundamental forces, on the other hand, are mapped upon the gravity thing. How do we know this? The short answer is provided by particle physics. The electromagnetic and weak forces combine in high energy environments. The nuclear strong force is next on the list - albeit we have not experimentally verified the energy level at which this occurs. What is nearly certain, theoretically, is that gravity is the last man standing in the maelstrom of high energy physics. It logically follows that gravity is the most fundamental of all properties of nature, and all of the universe is necessarily written upon that surface. The state of the universe before gravity broke free is currently unknown. A universe devoid of time and space is not easily modeled. The 'bounce' hypothesis is a laudable, but inadequate effort. Our universe may well be the result of process in a 'mother' universe, but this is an unsatisfactory explanation. It evades the more fundamental question IMO.
  7. Oct 27, 2007 #6


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    The main problem with the YM/gravity analogy is the following: The fundamental object in gravity is the Riemann Tensor which is a set of pde's involving 2nd derivatives in the connection form.

    By contrast the YM curvature form (a Lie algebra valued 2 form) only involves 1st degree derivatives in the gauge connection form A.

    Subtle difference, but its there all the same.
  8. Oct 27, 2007 #7


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    I think this an illustrative perspective that a geodesic is just another name for force-free trajectory.

    IMO, the concept of force implicity refers to an sort of "default expectation" of change. How is this "default expectation" determined? My personal view of this is that the expectation is a result of the observers processing and retention of information throughout the history and that this default expectation is simply the compilation of experience yielding a "most probable expectation", in which case geometry could be seen as a statistical structure that by construction is self-stabilising since it's selected to the be "most probable expectation", and intertial phenomena are information updates.

    So my personal vision of "what the thing is that is beeing curved is", is that the "curvature" is a deviation from our expectation and intertia is to be identified with intertia of information, which in turn I associate with the state of, and the nature of, the microstructure constituting the observer.

    So in the abstract view I think we are dealing with deviations from dynamically remodelled expectations, and perhaps spacetime is a special type of condensation of expectations.

    I don't know what the best formalism is to express this, but this is my personal current view. I mainly adhere to the approaches of relational information. And I've got a feeling we need a new probabilistic formalism to deal with this. I think Feymanns path ingerals is close, but there is something wrong in there. I got the feeling that there is a deeper generalisation of an action principle, where the action itself can adapt in the sense of minimum action - minimum information divergence, but taken into a dynamical context.

    So, I also have a hard time to imagine gravity on quite equal footing as the other forces.

  9. Oct 28, 2007 #8


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    I like the information theory [IT] approach. It is a powerful tool, IMO. I also really like Fra's idea. I would only argue the need for a background for gravity. Gravity is the background in our universe, IMO.
  10. Oct 28, 2007 #9


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    Hmm, I think you meant to say that the Riemann tensor involves second derivatives of the metric. The Riemann tensor doesn't have second derivatives of the connection. In fact, using the MacDowell-Mansouri approach, gravity can be described as a YM theory. And, this way, it can be unified with the other forces as a big YM theory.
  11. Oct 29, 2007 #10


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    Err yes, sorry mind fart.
  12. Oct 29, 2007 #11
    nothing can exceed the speed of light WITHIN space - objects that are moving away from us faster than the speed of light aren't moving through space, but the space that is between us is "stretching" - there is no limit on how fast space itself can move or expand, only on how fast things can move THROUGH space.
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