Transcript discussion Hartle

July 20 17.00
Quantum cosmology
Speaker: James B. Hartle
Floor speakers (in order of appearance):
Saunders
Kent
Vaidman
Timpson
Pooley
Barbour
Wallace

76

[questions only]

Saunders
1. A comment on FAPP..

Hartle
2. I shouldn’t have done it; I was tempted and I fell.

Saunders
3. I think branching within a regime where one does have a well-defined unitarily evolving state is also FAPP you see. I think merely calling it FAPP is neither here nor there. But the question I have is really….

Hartle
4. I thought of introducing myself in another way, as a person for whom FAPP is not a dirty word.

Saunders
5. You’re talking to another one.

Hartle
6. Basically all of physics is FAPP anyway.

Saunders
7. The framework of history space..[noise]….one I happen to find most favourable where I do have inter alia?.......quantum?..state, but the criterion as to whether to count these histories as real autonomous entities is to do with robustness, to do with higher-order ontology, to do with all of those things that David talked about in his introductory talk. Mere consistency doesn’t seem to be enough and I take that to be very much the point of Adrian Kent’s work with Fay Dowker in the mid-nineties, so I suppose the question that I would push is: are you not in that same ballpark? Whereby one could, as it were, modify the history space, more or less arbitrarily, whilst retaining the consistency condition so there just isn’t going to be a natural criterion for singling out one such history space rather than another, even whilst keeping the whilst keeping the initial and final condition the same. So that would be the worry, from an Everettian point of view one would wonder whether this is at all………..not meaning that it’s not meaningful or whatever but meaning that one wouldn’t have the same sort of rationality………….histories as being there.

Hartle
8. Well, as I mentioned, I’m not sure of the answer to this question. I should have said that - David’s language from his talk - what I’m talking about is: we’re given the wave function of the universe and we have to define some set of structure which we’re going to calculate. I’ve defined a particular set of structure for quantum gravity which involves spacetimes, histories of them, four-dimensional diomorphism?.........Now your question is - by robustness, for example, would you allow that the classical histories were robust?

Saunders
9. Within a quasi-classical domain?

Hartle
10. Yeah.

Saunders
11. Indeed. And let’s ask Adrian. The question is whether the sort of apology?,that Adrian was able to establish in the case of consistency alone is also going to be operating in this…

Hartle
12. I think so. But it seems to me it operates in all the formulations as far as I know.

Saunders
13. No, I don’t think so.

Hartle
14. What is the pathology exactly? Adrian showed, for example, that if you go up to a certain point and you can all sorts of operators that branch the history

Saunders
15. That’s right. Are you saying you can do that in a quasi-classical domain?

Hartle
16. Not in a quasi-classical domain. What a quasi-classical domain means first of all is something in which the spacetime is classical, that’s seldom mentioned, right.

Saunders
17. Quite. I’m just saying that the pathology that Adrian was, as it were, demonstrating may afflict this framework………does not afflict the quasiclassical domain, which is the basis within Everett for postulating a plurality of independent autonomous worlds.

Hartle
18. The particular formulation which I gave is a little more resistant to this because it was a sum-over-histories formulation in which I picked a particular set of variables, so I didn’t allow any arbitrary set of operators really in continuing the histories. So, that would be a restriction, but I wouldn’t advocate that as some great salvation. So I think we’ll have to explore this; I was under the impression that we can define what we mean by a quasi-classical domain. Roughly speaking, a quasi-classical domain is, first of all, when you emerge from a quantum-gravitational fog that you have a classical spacetime. That’s an important subject and, by the way, we’re finding in the calculation that it isn’t always true. Once you have classical spacetime you have symmetries, once you have symmetries then you have conservation laws, once you have conservation laws then you can consider densities of approximately conserved quantities. Those quantities, because they’re approximately conserved, can hold up in the face of noise the typical mechanisms of decoherence…..that is they can persist in active orbits.

19. I keep approaching David trying to have this conversation and failing, so I’ll just do it in the talk. It’s a much stronger notion than I think you advocated in your talk. Because, for example, we would regard it as essential that we have a closed system of equations to describe the classical evolution. Where does that come from? It comes from local equilibrium, which is a standard statistical-mechanical ……which also has to be demonstrated a property …coarse-grained. So you have a picture of boxes, little tiny volumes, not too big, or they won’t approach local equilibrium in the dynamical timescales, and not too small because then you’ll loose decoherence, they will recohere. So we’re interested in the maximal refinement in some sense. So, that’s our picture of the quasi-classical domain, something that has classical spaeetime where we get symmetries, conservation laws, approximately conserved quantities, local equilibrium, giving rise to closed classical equations of motion. But I imagine there must be many other different sets. Let Adrian answer this question.

Kent
20. I think I agree with your intuition, you’re right of course, ….-group approach is restricted in some sense but it’s still got an awful lot…….[very faint]…..

Hartle
21. But Simon are you saying that your ……doesn’t have this problem?

Saunders
22. No.

[new question]

Vaidman
23. Two remarks. First, this worry that branching is not something at an exact time it’s just when we have a ……….situation or it corresponds to …..experiments in our room?.and discrete photon and …..detectors.

Hartle
24. You have an approximation in which it occurs at one time.

Vaidman
25. So here it works, it’s just when you go to singularities…

Hartle
26. No, no, not singularities. Anything to do with spacetime geometry will not be at one moment of time because there are no diffeomorphism-invariant splits, if you like, at one moment of time, because there’s no well-defined notion of time that is diffeomorphism-invariant.

Vaiman
27. …I ask again for clarification what’s…probabilities out?..of?

Hartle
28. Ah, good. Well we’ve had a morning of discussion so as I already anticipated in this morning’s discussion, I just square the amplitude and that’s the probability. Provided it’s decoherent of course, and if, for example, the probability is high, or let’s suppose the wave function of the universe did not predict classical spacetime with high probability with certain coarse-graining…….that, and go to work on another one. So that’s my operational definition of what the probability means. But I await clarification from deeper thinkers on the subject.

[new question]

Timpson
29. A question about the generalised quantum theory. How much of the Hilbert space structure is it using? For example, are the fine-grained histories represented by sets of projectors?

Hartle
30. It depends on which level you’re talking about. You can have generalised quantum-mechanical theories - for example, Guido described two-time sort of - that doesn’t have states on spacelike surfaces also…one state, it does have two at the level it’s describing but that makes use of the Hilbert space structure that we would regard as a generalisation of quantum mechanics. It…….exactly the sense of the word?..we’re dealing with. One wave function…….exactly a Hilbert space. I’d say that the problem is a little ambiguous exactly what……..I think we’re talking about two Hilbert spaces, one in which the wave function is defined and the other in which alternatives which satisfy the so-called constraint. So, for example, let’s take spin foams. There you would have two Hilbert spaces, a big one, which is called, um, “the big Hilbert space”, and the subset of that in which the only states in it satisfy the constraints. And if you construct the histories from those spin-foam histories in the latter and - so the state would be …..I’m getting it the wrong way round. The spin-foam would be constructed in the bigger one and the states would be constructed in the small one. So it’s a little complicated, right, it has to do with whether the Hilbert space - The real point is, it’s a pity Chris Isham isn’t here, because the question is how rigourously you can define a pattern. If you knew that then we’d know whether there’s a connection with Hilbert space. And he promised me he was going to use topos theory to define these path integrals rigorously.

[new question]

Pooley
31. My question’s about the status of it as a four-dimensional theory. It’s really a question to ask you to say a bit more about what you’re summing between. So I can see that you may be able to talk about these sums over histories without there being a corresponding formalism of an evolving state, but still these sums over histories look like they’re giving you transition amplitudes between three-dimensional things. So although they’re sums over four-dimensional things the basic probabilistic quantities you’re getting out seem to - in one sense the fundamental quantum things you’re talking about look like three-dimensional things so…..

Hartle
32. Alright, it’s a perfectly reasonable question and so, I mean, I was very schematic in the structure. So basically we take the super-space..[noise]..three-geometries, we consider hypersurfaces where there’s a natual de Witt metric on that and we consider spacelike hypersurfaces, at least in the models, in those and we calculate the transition amplitudes, if you like, between those and then we adjoin the initial state by means of the de Witt inner product. Because if the state satisfies the constraints and the alternative is diffeomorphism-invariant ..independent of where you place the surface in superspace and the same on the final edge with some suitable definition what the final states…collection of things which define the final state. So, they really are histories in the middle because they’re paths in super-space that we’re summing over but between two surfaces in super-space, but it doesn’t make any difference where we - it’s not like there’s one particularly preferred time which is observable, it doesn’t make any difference we put the surfaces, as long as they’re outside the region that’s constrained by the coarse-graining.

[new question]

Barbour
33. In the spirit of trying to get, with David Deutsch, some conjectures about what the multiverse could be like, I know you prefer to close dynamical systems, would you mean by that that they’re spatially closed because it seems to me ……..it does imply something like spatial closure, which has a lot of attractions for actually having a well-defined definite theory.

Hartle
34. By ‘closed system’ I meant a much more modest discussion, that there’s nothing - we have all the variables inside the system, there’s nothing outside it.

Barbour
35. But if it’s spatially infinite your in a bit of…

Hartle
36. Well, we have a certain amount of trouble defining what ….by the wave function. But, you know, we can take compactifications, for example, on a torus and then study the thing as the length of the torus gets bigger and bigger and of course there’s observational evidence on how big such a torus could be today from the CMB. I brand that a technical problem and I hope I’m right.

[new question]

Wallace
37. As you say…..variables ………definite configurations…I find it quite surprising these turn out to be decoherent histories……this is partly David’s point I guess, most….theories you find that that configuration space basis isn’t all that decoherent………..so why is it do you think that your particular model it does turn out that definite field configuration or…definite field configuration histories turn out to be…

Hartle
38. They’re the fine-grained histories. The coarse-grainings are typically coarse-grainings of the histories, so, values of fields, say in spacetime regions, for certain ranges of the values that you….It’s like you could measure the electric field in this room.

Wallace
39. I’m kind of worried matter fields don’t tend to work that way. They only seem to be approximately localised in configuration?.space. There seems to be this rather obvious………

Hartle
40. ……local in space. So, in each one of the contributing geometries you have a notion of field defined at a point on that geometry. When we consider coarse-grainings of those fields it’s complicated…get diffeomorphism-invariant………whole geometries and yet we do it every day in some sense. So, if you’re question’s about ..it’s tricky?..to do that, then I agree.