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Philosophical issues of background (in)dependence in QG (long)

  1. Apr 8, 2004 #1
    I want to ask about the philosophical perspectives of physicists: Why they have these views; How strictly they adhere to them; How are they manifest in approaches to QG; How does this influence the conception of spacetime, pre- and post- QG.

    I am not a physicist. I am a philosophy/logic, maths, and chemistry major. I only dabble a little in theoretical physics for fun. However, I am writing a paper on spacetime in QG for a philosophy class. So please go ahead and shoot holes in my argument. It'll be helpful. Not to mention, hopefully interesting.

    What I'm most concerned about is this notion of background dependence. So in time honoured philosophical tradition, I'm taking it apart and questioning the constitutent parts: What is a background? What does it mean for a theory to be background dependent? Is dependence a matter of degree? Is it at all possible to achieve total background independence? Is background independence equivalent to background free? Now, I probably won't concern myself with all of these questions.

    Also: Why are physicists so concerned about formulating a background independent theory of QG? This is clearly a philosophical doctrine they are adopting. What argument is there in support of this? What argument against it? The question is not only how plausible a background dependent theory of QG is, but also how desirable it is.

    Now, let's see if I can bring up some details: In GR, the Riemannian metric represents a concrete object: the gravitational field or the dynamic spacetime. We can make a local coordinate transformation to a Minkowski metric, but not a global coordinate transformation. This is because in general the Riemannian metric is not identical to the Minkowski metric, and so to make a global transformation would represent changing the concrete object. So the gravitational field equations represent a case where we have two dynamic systems which can be described with respect to eachother. It is in this sense that I conceive of GR being background independent. The dynamics are not described with respect to some system which can not be described by reference to any other system.

    Looking at an article by Witten, from the book "Physics meets philosophy at the Planck Scale", by Callender & Huggett: He provides the Langrangian of a string tracing out a 2D worldsheet embedded in a 4D-spacetime. Specifically, in Minkowski spacetime. The Langrangian explicitly contains the Minkowski metric. Witten then goes on to argue that spacetime emerges from the conformal invariance of the field theory. So we've got two spacetimes going on here. Presumably, as Witten seems to be implying, the phenomenological spacetime is that which emerges from the conformal invariance of the field theory. So it seems that the Minkowski spacetime is playing the role of a background. It's used to describe the dynamics of the string, but it can not be described by reference to some other system.

    Now Witten argues that there's nothing to prevent us from changing the Minkowski metric to a general Riemannian metric. Well, I don't know about this. Firstly, let's suppose that we can - for the sake of argument - choose either a global Minkowski metric or a global general metric. But since this is a background, we can't describe it with reference to some other system. So how do we make the choice between the Minkowski metric and the general metric. After all, they are not globally equivalent, in general. But this presupposes that what we are describing is something of physical meaning. What if we get rid of this assumption? Then we can transform between the Minkowski and the general metrics. We don't have two spacetimes. The phenomenological spacetime, the one which emerges from the field theory, is the real spacetime. The background is just a mathematical tool used for description. But there's another problem: Why this particular method of description? Why a metric? Why a Hausdorff space? Why 4-dimensional? In this case, I don't think we've got the same problem. I think the only thing that needs to be said is: If the particular method of description is accurate, practical, and perhaps elegant, that is also what matters. And I think this statement ties in with the pragmatic naturalism that physicists seem to espouse. If we are not presupposing something of physical meaning, I don't think we've got the same case of background dependence.

    So: How reasonable really is perturbative superstring theory? If we grant that the background tools do not have physical meaning, then perhaps the theory is, in some sense, background independent. Perhaps the desire for a background independent theory comes from other sources.

    What does GR teach us? Let's suppose that we can decompose curved spacetime into gravitational perturbation and flat background spacetime. Rovelli says we shouldn't do this because GR says otherwise, but that's a poor argument. Why does GR tell us otherwise? What is the philosophical impetus of GR? Given that we can only measure objects in a gravitational field, we have no way of describing them in reference to a nondynamic background. And also that if we were to decompose curved spacetime, why should the background spacetime be flat? There is no a priori reason for that to be the case. This is a strong philosophical stance. It's not a physical argument. It's an epistemic argument: Since we can't know about such-and-such we shouldn't postulate that such-and-such exists. Ockham's razor, principle of parsimony. Call it what you want. But it actually doesn't provide any convincing ontological argument. What justifies moving from "We don't know if this true, so we'll leave our description incomplete" to "There's no evidence for this to be true, so we will assume that it doesn't exist"?

    It is a question, I think, of elegance, pragmatism, and minimalism. It makes things easier to work with. Of course, in the case of GR we also have the empirical data. And that's fundamentally important. The central tenet of pragmatism is that we should concern ourselves with the consequences of a hypothesis. Simply: A hypothesis should describe two distinct states of the universe. One where the hypothesis is true, one where the hypothesis is not true. If those states are distinct, then the hypothesis is worth investigating. One way or another, it will provide us with information about the universe. But if those states are indistinguishable, then the hypothesis isn't worth investigating. We can't know whether it is one way or the other, it has no empirical import if it one way or the other. What's the point of investigating it?

    GR and QM have the empirical data to back them up. For GR, this adds to the epistemological attraction created by its background independence. But what about QM? After all, it assumes a nondynamic flat background. What happened to our logical positivist view here? My guess is that the mathematical formalism represents so well the empirical data and dynamics, that we are happy to rationalise this background dependence. But the point is that background dependence is not necessary for a theory to be valuable.

    So why is it so important in QG? Suppose we had some background dependent QG theory. And we had convincing empirical data to verify it. Do we accept the theory, or still move on to developing a background independent theory that correlates with the empirical data? It seems to me that there's a presupposition that space is real.

    Anyway, that's a pretty unstructured post. I hope that some can make sense of it and tell me what I've missed. I just wanted to raise discussion on the philosophical presuppositions in approaches to QG. And of course get an idea of how right or wrong I am regarding the physics, so I can fix things up and hopefully get a better mark for my essay!
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  3. Apr 8, 2004 #2


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    this is already material for an interesting essay
    congrats on getting the idea to do it and getting so far along already
    it seems to me that if you add the organization you mentioned
    and some quotes from Rovelli's book----passages from Chapter 2 to
    show what you are talking about----then you have already something
    that at least I like (hope yr teacher does too!)

    Rovelli's book (Cambridge U.P.) will be coming out in paper this year.
    the Chapter 2 deals with philosophical issues of GR
    what diffeo invariance (DI) means and what background indep.(BI) means
    how Einstein grappled with these issues between 1912 and 1915

    You may have been reading Chapter 2. If so you realize that a lot of the discussion is non-mathematical but uses examples and philosophical reasoning.
    When you say:
    "...Rovelli says we shouldn't do this because GR says otherwise, but that's a poor argument. Why does GR tell us otherwise? What is the philosophical impetus of GR? Given that we can only measure objects in a gravitational field, we have no way of describing them in reference to a nondynamic background. And also that if we were to decompose curved spacetime, why should the background spacetime be flat?..."

    When you say that, it looks as if you are reading the key philosophical arguments in Chapter 2 and challenging them, on philosophical grounds. This is a very good thing to be doing! But you first must see exactly what he says
    (not just have a general impression) and what arguments he makes, or
    borrows from Einstein.

    So I would urge you to quote some philosophical passages from Rovelli in your essay to show your teacher a solid connection with what you are criticizing, and to provide some solid grist for your argument-mill.

    In case you havent already been reading the online draft. It takes about 10 minutes to download but then you can store it on your computer's "desktop"
    as an icon and thereafter get it without having to wait.

    I will try to comment on specifics in what you say later, or to discuss with you what I understand by background indep. which may be different from what you have in mind. Right now I'm just thinking generally about how you
    can make a solid connection in your essay with what you are analysing.

    ------some links if anybody else is reading this----
    Rovelli posted the 30 December 2003 draft of his book "Quantum Gravity", to be published this year by Cambridge University Press.
    The PDF file is at his homepage
    The book is around 350 pages long and takes a few (like ten?) minutes to download and convert.
    To download the 30 December 2003 draft of the book directly:
    Last edited: Apr 8, 2004
  4. Apr 8, 2004 #3


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    hopefully other people here at PF will have comment on your
    beginnings of an essay, and on the idea of BI
    this PF message board seems like a good place to
    sharpen an essay like yours
    especially if you get comment from several different people
    and perspectives
  5. Apr 8, 2004 #4
    Regarding Rovelli... No disrespect intended to him, but his philosophical discussion has always struck me as somewhat naive. For instance, he claims that Descartes held that space was relational, which is false. It seems that Rovelli has run into a confusion. It seems that Descartes did have a relational notion of location. But not space. He held that space and matter were identical. He in fact had a substantival view of space. Different to Newton's substantivalism, but substantivalism all the same.
  6. Apr 8, 2004 #5


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    Hi Stevo,
    the essay gets even better if you quote specific arguments from book and then give counterarguments

    we are not talking authority here but discussion of interesting matters.

    more power to you if you quote something about BI from Chap 2 and then give your own reasoning that it is naive!

    here are some places to look:

    "hole" argument pages 48, 49

    the quote from einstein on page 50

    if you quote and then answer or counterargue these things you are doing good (no matter who's right in the end it is the classic way of scientific discussion)
  7. Apr 8, 2004 #6


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    Stevo if you are game for it, maybe
    the bullseye of your target should be page 53

    there is a one-line quote from einstein

    and then a highly condensed couple of short paragraphs by rovelli
    that say forthrightly what he means by background independence

    "In Newtonian physics, if we take away the dynamical entities, what remains is space and time. In general relativistic physics, if we take away the dynamical entities, nothing remains.

    The space and time of Newton and Minkowski are reinterpreted as a configuration of one of the fields, the gravitational field."
  8. Apr 8, 2004 #7
    Sorry, all I meant to point out was that Rovelli's text isn't what one would really want to be using as a guide, or arguing against, in a philosophy paper. Two reasons: Firstly, because he does run into the occasional misinterpretation, that makes it risky business to use him as support. Secondly, because of those misinterpretations, there's little point in arguing against him. Simply, there's better texts available.

    That being said, it's interesting reading his views on the philosophy of physics in general. These are things I'm interested in discussing. For instance, his claim that we should assume QM and GR to be correct in formulating QG. There's a lot of assumptions regarding the nature, credibility, and applicability of empirical evidence in claiming that. There's a philosophical position there. I'm looking at bringing that position out into the open, discussing what reasons there are for that position, and trying to make clear how that philosophical position influences the conception of spacetime in approaches to QG.

    I'm not too concerned with GR overall... I'm not going to argue about some of the more subtle matters of covariance and physical meaning. I'm just using it as the paradigmatic case of a background independent theory, and a case which presents a strongly verificationist position.
  9. Apr 8, 2004 #8
    The question is, though, why did Einstein formulate his theory in this way? Why did he adopt a verificationist position?

    I agree that that quote of Einstein and Rovelli's remarks put in a succinct way what is quite relevant. But it doesn't really analyse the epistemological impetus of the theory. Which is actually fundamentally important here. Since, the quote and those remarks are making an ontological statement. But the reasons they have for making such a statement are epistemological. I want to analyse those reasons.
  10. Apr 8, 2004 #9


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    its a kind of conservatism (scientific, not political)
    rough paraphrase: dont throw out the basic lessons of past successful theories
    dont look for extreme novelty, that's not how progress has usually been made in the past, try to keep the key features of the different theories that work and put them together, change them just enough so they fit and merge

    extreme novelty is attention-getting but not how scientific theory grows

    just a paraphrase of the "philosophical position" you say is there

    for clear statement in Rovelli's words (instead of paraphrase)
    there is Appendix C "On method and truth" page 305
    especially the first part "The cumulative aspects of scientific knowledge"

    we've probably said everything useful we can about this for the time being :smile: unless other people chime in and add different viewpoints.
    good luck with the essay
  11. Apr 8, 2004 #10
    Yeah, I agree with you. The problem there is that it's a value judgement. QG is going to probe scales for which empirical data of QM and GR have no relevance. What's the problem with arguing that just as QM and GR work very well in their respective domains, that a theory of QG will work very well in its respective domain - and all those domains with their respective theories are mutually exclusive? Since I'm also doing a fair bit of maths, I like things to be neat. I like the appeal of a physical theory which ties things together. But philosophically, I'm not sure it's really necessary. It depends on perspective.

    I haven't gotten that far along in Rovelli's book, so I'll have to read it. I have encountered this view of his in other places. But I would assume he expands on it in the book, which would make it worth reading.
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