- #1
Stevo
- 114
- 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 each other. 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!
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 each other. 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!
unless other people chime in and add different viewpoints.