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Why quantize gravity?

  1. Oct 14, 2013 #1
    What rational says that gravity at the Planck scale needs to be quantized? I often read just the rather vague statement that it is because when all Planck constants become relevant we need an unification of quantum theory and gravity at this scale.

    But why does that unifcation have to mean quantization of gravity?

    Of course, there is the Einstein field equation. If the stress-energy tensor is the expectation value of some quantum state, but spacetime and the metric are classical entities, then this will lead to difficulties when we measure the quantum states of matter (see Wald's GR book p.382).

    But on the other hand, since probing distances shorter than the Planck length is already forbidden by classical GR (creations of black holes in ultra-high energy scattering, all singularities are hidden via the censorship theorem for black holes and inflation for the big bang), might there not some conspiracy by Nature that sweeps these inconsistencies under the rug?

    In Zee new GR book (p.766) I even read there is a "classificalization of gravity" program, which claims "..it maybe that when quantum gravity enters into Planck distance scales, quantum physics will inturn be replaced by classical physics somehow."

    So my question again: why do we need to quantize gravity?

    thank you!
     
  2. jcsd
  3. Oct 14, 2013 #2

    jedishrfu

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    From a math standpoint, quantizing gravity means it'll use the same mathematical structure as QM. There is a problem when factoring GR gravity into the mix where things can't be renormalized which result in infinities and so the search for how to quantize gravity so it can work with QM.

    See wikipedia:

    http://en.wikipedia.org/wiki/Quantum_gravity

    Conceptually to me, its basically the question of whether nature is smooth at all scales of investigation or does it becomes pixilated at plank lengths. QM implies the pixilated approach but this is just speculative thinking on my part (and others).
     
  4. Oct 14, 2013 #3

    mathman

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    The basic problem is that General Relativity and Quantum theory are in conflict where they both have apply. Quantum gravity is an attempt as resolving this problem.
     
  5. Oct 14, 2013 #4

    marcus

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    I like the way you put the question. It's an interesting one. But we don't know with certainty that we HAVE to quantize geometry. The question is really what is the rationale for thinking it is a good idea to try to quantize geometry. Why do some people think it is a good idea to try to find a quantum theory of how geometry behaves (in response to measurement or interaction with other systems).

    Like you say, there might be some as-yet-unimagined CONSPIRACY that harmonizes the LHS and RHS of the Einstein GR equation. Or one can speculate that there is some deeper theory more fundamental than EITHER QM or GR!

    It is only some people who are motivated to try to develop a quantum theory of geometry. You seem to be asking to understand their motivation. I'm not expert but I watch QG and what I think is this:
    These are people who think that it is a good bet to take both QM and GR core ideas seriously and try to develop the tools for general covariant quantum field theory. So far QFT is only special relativistic. Maybe there should be a general relativistic QFT.

    Obviously I don't mean QFT on a prior fixed "curved spacetime" because that is not how nature works. The geometry responds to what matter does.

    Rovelli has pointed to some historical precedents supporting the idea that it might be a good bet to do this (instead of trying to guess or make up a completely new more basic theory underlying both, or imagining a conspiracy). When Newton put the parabolas of Galileo and the ellipses of Kepler together into a combined theory of motion he didn't need any new observational data. It is a conservative idea: to take seriously and be guided by two established successful theories which appear disjoint. There is no guarantee but sometimes this works.
     
  6. Oct 14, 2013 #5
    If two theories work quite perfectly, as it is the case for GTR and QT, perhaps is it just a clear indication: we don't yet have really understood the (mathematical) logic connecting them (no conspiracy, just our collective low intellectual level!). The nature unifies these two faces permanently in front of our eyes. Gravitation acts everywhere at any time, inclusively when the curvature appears to be very tiny as it is the fact in interstellar vacuum. This doesn't empeach the propagation of EM waves which (as we also know) are "carrying" a quantized energy. Why do we see a frontier where there is none? Dirac's equations are the first historical example where covariance (inherited from the GTR considerations) works perfectly in a QT context. I think that the fictive "dichotomy" between matter, wave and geometry is obscurcing our vision and our understanding. We want a mathematical unification for objects which we presuppose are of different nature (particles and geometry for example); but are they really of different nature?
     
  7. Oct 14, 2013 #6

    marcus

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    I thought the Dirac equation was special relativistic, not relativistic in the full sense.
    I think that is part of the motivation: why should QT be stuck half way?

    And the electron obeying Dirac equation is not influencing the geometry around it (which is typically flat Mink'ski space). But we know that all matter is interacting with the surrounding geometry.

    So I think the picture strikes some people intuitively as incomplete.

    But maybe it does not seem so to YOU. That's perfectly fine, there is plenty of room for differing opinion. I think the original thread question was about trying to understand the rationale or motivation of those people who think QG is a good bet, a good research direction to pursue. We are not talking about certainties, because we don't know what new mathematical tools and ideas may appear, or how things will turn out in the end.
     
  8. Oct 14, 2013 #7

    marcus

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    Maybe we need to stop thinking of differential manifolds as real. We don't know that spacetime IS a smooth manifold. What we have are discrete measurements (of angles, distances, momenta...) and a manifold is a convenient device to keep track of and interrelate this large finite number of measurements.

    Personally I suspect that at a small enough scale some geometric measurements do not commute.
    If you try to measure the six edgelengths framing a small enough tetrahedron you could keep on measuring one after the other and keep getting new answers :smile:

    It wouldn't let you permanently pin down its shape, I suspect. The order you measure in would matter---whether you measured one first, before the other five, or last.

    And I imagine that probably in the long run the REGGE model of geometry where space geometry is described by a bunch of tetrahedra, and spacetime by a bunch of pentatopes (the 4d analog of a tet) is probably more basic. Because corresponding more closely to the idea of a large finite number of discrete measurements.

    A poster named Nugatory had this to say recently. I liked it so much I want to quote it. He is explaining that you shouldn't think of space or geometry as a material/substance/fabric etc. It is a bunch of geometric relationships.

     
    Last edited: Oct 14, 2013
  9. Oct 14, 2013 #8

    Haelfix

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    It doesn't, and in fact I would say the current belief is that you can't quantize gravity in a straightforward way, at least as conceptualized by 20th century physics methods. As far as we can see, the canonical quantization and path integral methods and programs have essentially been failures, and the underlying objects probably do not exist mathematically.

    Now, what is of course manifestly inconsistent is choosing to do nothing, and keeping geometry exactly classical. This is of course forbidden by Walds thought experiment, as well as many others. Therefore either gravity needs to be quantized (eg by putting hats over the Ricci tensor and assorted metric field) in some way, or the equations must be replaced by more convoluted objects in some way (think of trying to ask how to quantize fluid mechanics)

    The classicalization program you refer too is a neat idea by Dvali and coworkers, that exploits what is known as the UV/IR correspondence in a clever way. It relies on some tricks that are controversial at this time, but despite its name, is still highly quantum mechanical.
     
  10. Oct 15, 2013 #9
    I agree with Haelfix. I think the current consensus among most Physicist is that GR is an emergent theory, and quantizing it is just quantizing an effective field theory. Not to mention that all attempts to do so have generally been almost a complete failure. So why quantize gravity? I think the mundane answer is because nobody knew what else to do.
     
  11. Oct 15, 2013 #10

    Chronos

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    The feeling that QM is THE theory of reality, and GR is emergent is strong. One problem is no one has even figured out exactly where any conflict arises. The current consensus is the Planck scale.
     
  12. Oct 15, 2013 #11

    mathman

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    I thought that the interior of a black hole and the beginning of the big bang are examples of conflict.
     
  13. Oct 15, 2013 #12

    marcus

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    I think that's right, and there is also a scattering amplitude regime for nearly headon collisions where the energy is not high enough for the colliding particles to form a black hole but still high enough that geometry is being affected and ordinary QFT does not apply. I'm told we don't have predictive theoretical coverage of that "No-Man's Land" region of parameter space between QFT and GR.

    I was talking about that, and also other motivations for studying quantum geometry in a Cosmo forum thread:
     
  14. Oct 15, 2013 #13
    How does the "running of the constants" at higher energies fit into this picture of QFT in curved spacetimes? How much "running" do we see at LHC energies? Do we need to get into the realm of curving spacetime to see this running effect? Thanks.
     
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