July 20 9.30
Probability in the Everett picture
Speaker: David Z. Albert
Commentator: David Papineau
Floor speakers (in order of appearance):
Lehner
Ladyman
Wallace
Saunders
Greaves
Loewer
Vaidman
45
Comment by Papineau
1. That was great, you did put all these issues on the table and that’s very helpful and address all the – I just want to make one general point; this’ll take about ten minutes, I hope you’ll bear with me, I won’t waste everybody’s time. Let me first make one specific point about one of your arguments, the fatness argument; I just want to make one little comment on that because it’s relevant to what I’m going to say in a second. I think it’s important that even if we go with Hilary and the fission programme and we have Everettian – I’m going to call them probabilities, but that’s just a word - I mean these things that we orient our actions to. Even if we have them without uncertainty, without any ignorance, and so we can think of them as a measure of caring for future branches, we need to distinguish to kinds of caring. There’s a kind of caring that goes with ordinary wanting, desiring certain outcomes and there’s a kind of caring that goes with expecting certain results. I don’t think you disagree about this. I mean, they’re both kinds of caring in the sense that they inform decisions without any uncertainty or ignorance around. But they’re still different, they have a different direction of fit to the world. The carings that go with wantings are kind of up to you, everybody to their own taste. Whereas the carings that go with expectings are supposed to be somehow responsive to features of the world. So, having made that distinction, your question is: can you rationally expect the fat future more than the thin one; the two branches, even the squared moduli of the amplitudes of the two branches are just the same and you don’t actually care wanting-wise about fatness and thinness, that’s the question, and I don’t know what the answer to that is, I just wanted to clarify these different kinds of caring. I suspect you’re right and that the Deutsch-Wallace proof doesn’t force the Born rule on Everettians, but I’m not going to talk about that. What I want to try and show is that even if the Deutsch-Wallace proof doesn’t do the job it’s advertised to do, even so, Everettians are much better off with probability than orthodox metaphysics.
2. My view, and I don’t know if I’m the only one, has always been that we should accept Everett because of what it says about probability, not despite what it says about probability. I think that the issue here is a decision-theoretic one – I know you don’t think about it like this – I think the central issue is why should we maximise objective expected utility. Equally, why should we bet with the probabilities, subjective probabilities; why should we set our credences equal to the squared amplitudes, why should we conform to the Principal Principle – that’s all variants of the same idea. There’s a chancy roulette wheel in front of us, red is two-to-one on, black is two-to-one against, you’re offered a bet of evens, you should bet on red. Why? Why should you bet on red? I don’t think you realise how much of a mess orthodoxy is in with respect to that question. Some of your remarks suggested that this is something to do with frequencies; we bet the way we do as a rational reaction to the frequencies of outcomes. I just don’t – I mean I’d like to see it spelt -. So, we’re not sure to win this time but if we do it ten times, no, we’re not sure to win .. ten times. So you can go, you know, the infinite long run and frequency theories of probability and – I just don’t think it works. I think that once one looks through all that what one has to realise is that the principle of betting with the probabilities is a primitive principle, the Principal Principle is primitive. There’s no further explanation.
3. I think that means that Everettianism is no worse off than orthodoxy with respect to chancy decisions. Both of them just say it’s a primitive fact that you ought to set your credences to the squared amplitudes and act accordingly. Lev said to me yesterday that that’s an unorthodox view. And I guess it depends on where you come from. I was brought up in Cambridge by Richard Braithwaite and Hugh Mellor and Ian Rankin and I was taught it’s obvious that the Principal Principle is primitive. It’s obvious that you can’t get a further justification. And I take that to be – Anyway, the point is that if you think that then Everettian is no worse off than orthodoxy. Actually, I think, having got this far, that I can show that not only is orthodoxy as badly off as Everett, it’s worse off than Everett. Think about an ordinary person …. I’m going to talk about an ordinary gambler but this is a model for decisions in general. Even after the ordinary gambler has embraced the Principal Principle as a primitive constraint on actions there’s still something funny about the ordinary decision makers. Here they are, they’re maximising expected utility they’ve committed themselves to choosing their actions to maximise objective expected utility, but that’s not what they want; what they want is the money. They don’t want to make the bet that will maximise expected utility over the two possible outcomes, they want actually to win. So what they’re doing is not what they’re after and one wants to know, well, why are you doing this thing given what you’re after is that? Now, maybe that this is a bit of an obscure question; what I’m in fact saying is that we want a justification for the Principal Principle because there’s this gap between what they’re doing and what they’re after, and we haven’t got it. You might feel this is an obscure sort of question but still it is a question and I can bring out that it’s a real question by comparing the ordinary gambler with the dedicated gambler. Imagine a dedicated gambler; this is somebody that doesn’t care about money, he’s one of the world’s … he’s got a lot of money. What he cares about is making good bets. So, I mean gambler’s have a notion of a bet that offers good value and my dedicated gambler is looking out for good value bets. He’s looking for cases where his bets will give him positive expected utility and when he finds such a case he makes a bet. But after that he doesn’t care; he thinks it’s vulgar to be upset if the bet doesn’t win. What satisfies him is that it’s a good bet; he’s found a good bet; he’s made it. Now, this person’s a bit odd maybe but people take pride in all kinds of different things, I can make sense of that. The point isn’t that how odd this person is. But for this person this kind of betting behaviour isn’t chancy. There’s no issue after the person’s made the bet whether it worked out okay. For them, given their aims, all bets are sure-things so to speak.
4. Compare the dedicated gambler with the ordinary gambler. In a sense they’ve both made an arbitrary commitment. The ordinary gambler has committed themselves arbitrarily to setting their credences to match the squared amplitudes, say; they conform to the Principal Principle. The dedicated gambler has committed themselves to desiring good bets. There’s a kind of isomorphism between the two commitments, they’ll both act the same. But there is a difference; there’s a question that arises for the ordinary gambler that doesn’t arise for the dedicated gambler. Why are you acting in this way? Why are you maximising expected utility? That’s not what you want. You want something else. With the dedicated gambler that question has gone away. You can’t ask the dedicated gambler are you maximising, that’s what the dedicated gambler is after ….. there’s no further question about it. No further …… Okay, well I hope you can see where I’m – the analogy’s not perfect but the point is that if we’re knowledgeable Everettians then we’ll be like the dedicated gambler, not the ordinary gambler with respect to the question ‘Why are you behaving this way?’. If you’re a dedicated Everettian you will favour maximising expected utility over the future branches per se, not as a means to some further end. I mean, the whole idea of there being some further end assumes that either you’ll win or you won’t. But our knowledgeable Everettian doesn’t think like that. There’s a branch, two-thirds intensity, where you’ll win and a one-third intensity branch where you won’t. If the winning branch has two-thirds intensity that was a good bet. Once you’ve done the bet, which is good in this sense, there’s no further question of whether the bet worked out well in this particular case. So there’s no room to ask a knowledgeable Everettian, as you can ask the ordinary gambler, the person who thinks of themselves as in an orthodox universe, ‘Why are you maximising expected utility?’. There’s no further aim beyond maximising expected utility for the Everettian. There’s no further result that might or might not happen.
5. So I take the fact that this nasty philosophical question that arises for the ordinary gambler and doesn’t arise for the Everettian to be a very strong point in favour of Everettians. That’s actually what got me to believe Everettian in the first place. I used to worry about this thing, I was brought up to worry about it and I saw that if you were an Everettian the question just went away. Okay, maybe not everyone is bugged by that puzzling philosophical question about maximising expected utility in the way was taught to worry about it so maybe this isn’t the place to make it. But at least I hope that I’ve been able to show that probabilities are a plus for Everett and not a minus.
Albert
6. Very, very briefly, look, on this first terminological issue, I’m inclined to follow Hilary. Hilary’s quite adamant, and I think rightly, that in the context of a fission picture expectation is absolutely the wrong word for this kind of caring. Hilary is pretty clear as I remember, in earlier papers. You want to know what to expect? Expect each of the results. Period, end of story. I think that’s an admirably clear way to put it and it seems to me to dangerously muddy the waters to use the language of expectation about that kind of caring. I think Hilary’s choice of ‘caring’ to describe this – of these amplitudes if I use them in a way I use probabilities in ordinary decision theory are representing the degree to which I’m concerned about what goes on on this or that branch. That seems to me exactly the right way to put it.
7. As to your much larger second point, there’s a lot to say about that, let me just confine myself to one line. and there’ll be much more to say later I know. Which is that it doesn’t seem a very compelling – yeah, probability’s hard and philosophy is hard and philosophy of probability is particularly hard and there are lots of mysteries about it. It’s never been for me a compelling way to argue for something to say, look, we have no idea what it is, why not say it’s this? It is hard, but there are things that we always thought we knew about it, even if they were far from everything, and one of those things was well you’re talking, in cases where probabilistic language is intelligible, you’re talking about cases of one outcome, or something like that. I don’t see any – of course things are going to get a lot easier if you say, oh, what I was really after was never the money, it was just maximising this function or something like that. That seems to be a way of avoiding seeing what’s hard about these problems rather than solving them. But we can talk more about that later, and thank you very much for your comment.
Lehner
8. I’ll save the big questions for later. Just a small question about your fat and skinny example. Is the fatness and skinniness supposed to be some physical property or supervene over some physical property?
Albert
9. Yeah, sure.
Lehner
10. So why isn’t that just part of the payoff?
Albert
11. It’s not, because I’ve said explicitly that this guy’s preferences are such that if you give him a choice between two deterministic evolutions, one in which he’s fat and one in which he’s thin, he’s indifferent between them.
Lehner
12. Look, I would personally rather be thin, right. So I think to me it doesn’t matter that the world is deterministic and I’m insecure? about the future or
Albert
13. No, no, I think you’re misunderstanding what I’m saying. There’s a simple test, okay, for what kind of role this is playing in his decision theory. Whether it’s playing the role of a weight, as it were (unfortunate comment), or the role of a preference. Here’s how to distinguish between them. If you offer the guy – you forget about branching – you say to the guy, you have a choice: if I press button A you’re gonna be fat, for sure, and if I press button B you’re gonna be thin, okay. If the guy is indifferent between those, which I’m positing he is, then his calculations are not coming out the way they are because of a preference to be fat or thin. They’re coming out the way they are because this fatness and thinness is playing the role of what Hilary calls the caring measure, rather than playing the role of a preference. So I’m positing that he’s indifferent between those; the claim that he’s indifferent has a perfectly definite measurable cash value and I’m telling you what that is.
[new question]
Ladyman
14. ……a question about the explanatory requirement of Everett ….. Why isn’t the claimed explanation that the Everettian approach gives of the frequencies we actually observe just a kind of standard one, that we say, look, so why do we get – a random shuffle of cards gives a very discernable pattern of suits or numbers because there are many more deals like that, than there are where everything comes out…………so why do we observe that the frequencies of a repeated series of Stern-Gerlach experiments are those predicted by the Born rule, well, because there are just many more branches the relative frequency … the Born rule …
Albert
15. Right. This was a conception that I mentioned at the very beginning of the talk. I just, I don’t understand how an account of the kind you just described can make sense without there being some element of either stochasticity or ignorance in the world, okay. And it’s both of those that are being resolutely denied when we start off with something like, say, the fission picture. That is, in the case of the cards, typically, it’s going to be a case of our ignorance of the exact initial conditions and we find that it turns out to be an empirically successful hypothesis to put a uniform probability over which of those might obtain and so on and so forth. In the case where you’re not ignorant of the initial conditions, as I say, and maybe this is what you’re doing in the back of your mind, there’s a strong semi-conscious temptation to say to yourself something like: well, I guess what I do, what the real me does is pick at random among these branches or something like that. But it’s important to see that the minute you catch yourself thinking like that you’ve got to pull back, because you’re going down – your either kidding yourself about what you’re doing, about whether you’re genuinely adhering to the Everett picture, or, if you do go down that road, you’re going to end up like Barry and me, in this single-minds picture, and you don’t want to go there.
[new question]
Wallace
16. Two quick points. One very quick point about the motivation for these semantic type arguments. They go something like this. Yes, absolutely, as you’ve said at various points, we know quite a lot about probability, uncertainty. We know quite a lot about the rules of epistemic confirmation an so on. That stuff we know in natural language and the danger is that how to phrase that in metaphysical language depends on how that language maps on. So we get one story as to how it works in a single universe and a different story about how it works in branching universes. So to assume that the correct metaphysical level story is the single universe story and then criticise Everett for breeching that on the grounds that we need a single universe story to be correct is to beg the question.
Albert
17. But let me just ask you a question here because I’m really not sure I understand the situation very well. I want to know more about what these arguments aim to accomplish. You guys are very forthright when you make these arguments, about saying: you want to know what the metaphysics is? It’s the fission metaphysics. Period, end of story, okay. Now, as far as I can tell, but I may be misunderstanding my own reasoning here; as far as I can tell, once that’s granted all the worries I have about this stay in place. All the worries I have about this come from the fundamental metaphysics of the fission picture. So that, if somebody’s telling me about some manoeuvre they’re making that’s going to leave all that in place my immediate reaction is, gee, this manoeuvre isn’t going to be interesting vis a vis solving these problems. Do you think I’m missing something when I say this?
Wallace
18. I think you are. I think what you’re missing is that it does leave the metaphysics in place but it doesn’t leave the correct epistemology and confirmation theory in place that maps onto that metaphysical story.
Albert
19. Okay, we should talk about that more.
Saunders
20. As co-author here, perhaps David and I disagree about this. I don’t think it leaves the fission picture in place at all.
Albert
21. Oh, okay, but you say it does!
Saunders
22. No,…..[hubbub]
Albert
23. Well, one of you…the paper says it does. It says, look – it’s important for the reader to understand, and I’ll read the quote, that we’re not looking for deep metaphysics from our semantics we’re looking for serviceability.
Saunders
24. And in particular the fission picture is metaphysics. And we’re not looking to find truth about that
Albert
25. Oh, I see, so the way you regard it is that on metaphysical questions you’re being agnostic; is that it?
Saunders
26. Not quite.
Wallace
27. I think there’s a slight misunderstanding about what counts as semantics and what counts as metaphysics
[hubbub]
Saunders
28. Take the single universe, now take four-dimensionalism; we have a complete physics, suppose its General Relativity, we’ve known this theory, we know the kind of picture of the universe it represents – 4-dimensionalism. Philosophers for a century, but especially in the last thirty or forty years, debate how ordinary language usage should map on to that physics. There was never any question of the physics, the question was how to extend ordinary language beyond ordinary usage. That question is a metaphysical one it is not a physical one.
Albert
29. Okay, good, now I see what David meant a second ago, good. The question is if someone’s coming to you in my position where the worry is, look, what’s left fixed by all these debates is already where the problem is then he’s not going to be impressed by these arguments. Now, David thinks that that’s not the case, that part of what’s in play here, part of what’s in flux here, are questions of epistemic strategy and so on and so forth. And, good, that’s worth talking about.
[new question]
Greaves
30. My question is about…whether or not …theory of rationality is relevant to….. You said that you agree that, yes, this narrow sense of the physical modelling of a system where it shouldn’t be relevant and isn’t in the sorts of ……[Albert saying ‘right,right,right’]…….You also agree that it should be relevant when what we’re talking about is confirmation theory. But you think, no, what we’re really talking about is this third thing, explanation, and it shouldn’t be relevant to that. So I’d just like to make a comment about that.
31. There’s always been this sort of minimal explanation you can get from an Everett interpretation where you just say, look, I had a theory which entailed that there would exist all these branches and there would exist all these observers and in particular there would exist an observer with precisely the record of sequence of actions [?] that you have in fact got…..[noise]…..and what you found out was that, indeed, there is……[noise]…….and the reply that one usually gives to the question is: here’s what more I want, a minimal explanation doesn’t give me a reason for having increased my degree of belief in the theory or regarding the theory as confirmed as a result of what I’ve seen. So the more that we want is precisely confirmation-theoretic and then we’re back to the second thing.
Albert
32. But no, that doesn’t seem the right way to put it. The right way to put it seems to be: what I want explained is why these frequencies as opposed to others are the ones that emerge; are the ones that I saw.
Greaves
33. Because that’s the branch that you’re on.
Albert
34. Good, but that’s not – Here’s a way to explain everything: everything happens with certainty. Let’s go home. You know, science is over. That’s not a good explanation. What we want is an explanation of why these particular frequencies emerged. I didn’t put that question in a way that involves observers or rationality or degrees of belief or anything like that. That’s what I want explained.
[new question]
Loewer
35. A question to David Papineau. I just didn’t understand how it is that you’re getting around the problem of providing some understanding of rationality?.........many-worlds……I mean, the question could arise that? somebody could be trained to minimise expected utility. Or to maximise on Monday, minimise on Tuesday, you could have all sorts of desires..
Papineau
36. I wasn’t trying to do that at all. I still take the principle that you should maximise expected utility to be primitive and not justified in terms of anything else. Both for the Everettian and for the orthodox metaphysician. My complaint was: the orthodox metaphysician, that was putting the primitive commitment in the wrong place. You are committing yourself to doing something that was detached from what outcome you hoped to achieve. Whereas for the Everettian you’re putting the primitive commitment in the right place. I wasn’t justifying the commitment at all.
Loewer
37. Why would anyone have such a primitive commitment?
Papineau
38. You tell me why you’ve got it as an orthodox – why are you maximising….
Loewer
39. ..as a step to explain – expected utility with? .a high chance of luck…….tell a story about chance….Okay, now, are there stories about chance……………..yeah, there are stories
Papineau
40. You kind of neo-Lewisians have “things that you can see dimly but well enough”. Now you can justify acting on the probabilities…….[laughter]……..I was presupposing in my argument that that wasn’t going to work. There’s a further issue about whether this Lewisian finite-frequentism business can give a justification of acting with the probabilities. I don’t believe it for a moment.
Albert
41. But if that’s what you’re doing, isn’t the rhetorical structure here, like I was saying, to get a lot of mileage – it’s some kind of mystery-mongering. Look, we don’t know what it is, it could be anything, it could be a hippopotamus, you know, let’s say it’s that.
Papineau
42. If you’re presenting an argument here it had better be something other than that the Everettian view of these matters is unfamiliar. Of course it’s different – what I’m happy to call probabilities isn’t a matter of a measure of some outcomes, chances of success, in the competition to become real. It’s a different kind of thing. So it’s different from what you think of, but is it incoherent? Unfamiliarity isn’t incoherence. You’ve got to do something to show it’s incoherent.
Albert
43. Well, I have tried to do something..
Papineau
44. Sure, sure
Vaidman
45. Just a brief reply to your complaints. First you said it’s avoidable. I don’t think it’s avoidable. Just to make it vivid, I put a sleeping pill in……in every quantum experiment the branching will happen much faster than your conciousness.. thinking?
Albert
46. Yeah, but there won’t be a period when you’re saying to yourself I wonder what’s going on.
Vaidman
47. But, again, conceptually in fact all your thinking? ..will be…
Albert
48. Well, okay, I don’t understand why that’s relevant but go ahead
Vaidman
49. …you say it’s too late. It’s too late to get ….chance…uncertainty….I don’t claim so, I think there’s no probability, no uncertainty, what there is is a kind of effective probability justification for this caring measure…That you have an ignorance probability you can define, and I don’t want to prove it, I just take the postulate, Born postulate, and define it, but I have to find some…
Albert
50. Okay, this is something I want to know more about. This hooks up with what David was talking about a few minutes ago. The view of this that I guess I understand best is the one that Hilary seems to have which is adamant about justifying the caring measure having nothing to do with epistemic issues at all. This is a case of decision theory in the face of certainty; your job is to choose which branches – which branchings, excuse me, not branches – which branchings you prefer and there are supposed to be arguments to the effect that you’d be crazy, given basic preferences for more money and on and so forth, not to choose certain branchings over other branchings. And notions of ignorance on here view have nothing at all to do with it. Now, a number of people seem to think that if I deprive myself of this talk of ignorance, or if I deprive many-worlders of their talk of ignorance, I’m going to be depriving them of very important resources with which they can do a lot, even though the basic metaphysics remains the same. I guess I’m not understanding yet how that works. But I’m eager to.
Saturday, September 15, 2007
Transcript discussion Greaves and Myrvold
July 20
11.30
Everett and evidence
Speakers: Hilary Greaves and Wayne Myrvold
Commentator: Barry Loewer
Floor speakers (in order of appearance):
Vaidman
Hartle
Maudlin
Barbour
Albert
Rae
Brown
Bacciagaluppi
55
Comment by Loewer
1. I think that Hilary and Wayne’s paper is really interesting and clever and I see it as really very interesting line of response to thought I just can’t make sense of confirmation if I thought the universe was branching, as Wayne said. And I want to first bring out some things about the branching situation and then I thought ………...and I’d like to put something else on the table that we might find relevant to the discussion. First it’s this; in thinking about this what’s the difference……a gamble where there’s a chance situation, the different is you’ve got an actual outcome and something else which is possible. In the bramble case, the branching case, both things are actual. The question is, can that difference make any difference to confirmation ……..no. And somebody who’s sceptical about this …..this is worth pushing, was to see whether or not this metaphysical difference can end up making a difference to confirmation. I want to suggest a couple of places where it might. I also wanted to bring this out; I think this is clear in the paper but to see, at least as I understand it, how confirmation would go for them. So here’s just a familiar Bayes theorem [reference to board] but with something a little unfamiliar about it, is let’s say we’re testing – P is Everettian quantum mechanics, K is some other theory, maybe it’s a quantum-mechanical theory, maybe it’s a non-quantum-mechanical theory, but it’s a chance theory, it doesn’t have branching in it. Well this is what Bayes’ theory will look like, a credence of T given some evidence is going to have these credences in it, it’s also going to have subjective weights in it, these are the numbers that they get out of the Savage representation theorem. So these are the numbers that are associated with the outputs. So they will get a subjective weight of E on T and where does that come from? Well, if we’re testing Everettian quantum mechanics then that comes from Everettian quantum mechanics……..I want my preferences, I want these numbers to come from quantum mechanics. So at this point you get this….making use of the Principal Principle. Wayne said he wasn’t going to say much about it but I’m going to say quite a bit about it in a little while.
2. So the Principal Principle …[skipped and aside clarifying background of PP] …I have two kinds of worries really. One is whether or not really conditionalisation is appropriate for them, in a branching situation, and there my worries are very familiar ones…talk about them in discussion period…..and then the status of this, the analogue to the Principal Principle. So, what about conditionalisation here? Well there’re two thoughts that people have about this, about experiments and getting information from experiments; they are old ones and I appear to be something of a troglodyte to be saying we’ve got to stick with them, but they’re really part of a law of experimentation. One is, if someone proposes an experiment and they think they know the outcome before they do the experiment then the experiment isn’t going to provide them with any information about the theory. They know the outcome beforehand. The experiment isn’t going to provide them with any information about what the experiment’s about. So an experiment which just has a particular outcome isn’t going to provide them with information. So it’s no experiment at all. So before doing the experiment, if you know what the outcome is going to be, it isn’t going to tell you anything about it. In the many-worlds case you know beforehand that you’re going to get all the outcomes, so it’s not going to tell you anything. After the experiment, there’ll be fission, there’ll be branching; think about the guys on the different branches. Well, they now, of course, will have particular evidence, particular outcomes. So you might think they should conditionalise on them but of course on the assumption that many-worlds is true it’ll follow that there’re all these other guys (there may not be guys there) with all the other outcomes. That’s their total evidence; they should conditionalise on that. But then of course they won’t get the right result either. So here’s a kind of, you know, two old principle of Baysian inference or statistical inference. One is, if an experiment doesn’t have alternatively possible outcomes, but you know for sure what the outcome is going to be, it’s not really and experiment. The other one is that you should conditionalise on the total evidence that you have, given that the theory is – on the many-worlds theory the total evidence is all the branches with all the various outcomes. So these leave me a little bit worried about conditionalisation in this context. But I don’t think these are very decisive these little objections because the reply is going to be that, well, this is a new kind of situation, a situation we haven’t thought of before, and these old rules just don’t apply, or don’t apply like that.
3. What I want to do now is look at the way the Principal Principle works and I think actually the best way for me to do it is to look at the list …[ref. to projection of page of the paper]… here’s what they’ve done on this page. What they’ve done is they’ve taken the branch weight case and the chance case and they’ve played out a complete analogy between the two. So that, as far as confirmation is concerned, chances and objective branch weights and credences and subjective weights are completely on a par, that’s the idea of the list. What I wanted to do, and I didn’t think about doing this until the discussion earlier, is to put another column on there which is a view about chance but a particular view about chance, David Lewis’s view. Probably most people here are familiar with it. I’m going to say very quickly what it is. Lewis makes a connection between what actually happens in the world and what the chances are, let me call them the L-chances. That’s tighter than the kind of chances that Wayne was talking about. It’s tighter in this way: what the chances are is that built into the laws, and the laws are given by the theory which best summarises all the facts about the world, all the fundamental facts about the world. So Lewis has an idea of there being a theory of the world which best combines simplicity and informativeness. That’s what’s meant by best summary. And one way to be very informative while staying simple is to introduce a notion of probability, a probabilistic notion. Then you have to say something about how that notion, of how those probability claims, inform about the world and the idea is that a principle connecting them to the world will tell you how it’s informing about the world. The Principal Principle is a way of making that connection. So the Lewis account has the Principal Principle, understood this way (this isn’t quite the way Lewis understood it), built right into it. Okay, so imagine that it’s in the list there.
4. If you put it in the list there too, I want to point out, this’ll be the whole of my comments really, is to point out some differences (they have all similarities) between what’s said under the Lewis account and also one difference under the chance account and the branch weight account. As far as the Lewis account is concerned, it agrees with everything that is said under chances. So Lewis chances satisfy the first thing, the theory assigns chances to possible worlds; the second, about updating; the third, there are possible worlds in which anomalous statistics occur. The next one is that a frequentist analysis of chance is untenable. That’s right for Lewis, the simple frequentist analysis is not Lewis’s, but Lewis’s is closer to an actual frequentist account because what the Lewis chances are can on the whole history, the actual facts of the world. So wereas the sort of primitivist propensities account of chance makes chances something over and above the ordinary facts of the world, Lewis’s account makes them supervenient on the categorical facts in the world. Similarly, on the branch weight case the amplitudes, which are gonna be identified with the objective weights, those are over and above the branching strucure, that is, the categorical structure. Now, you might think of the branch weights as themselves additional categorical structure, I’ll come to that in just a second. So you go through the list you see this and here is what seems to me to be some interesting differences that we might want to focus on.
5. In the case of propensity chances, and Lewis, but not in the case of the branches, the chances are built into the laws. The laws are the explanatory structure in the world. Some people don’t find the Lewis laws the appropriate thing to do explaining, that’s a different argument, but the Lewis account is sort of in the ball park here as an account that builds the chances and the laws in together. Whereas in the branch case that’s not so and I’m thinking, I’m wondering, if this gets at David Albert’s worry that we’re not really getting explanations from the branches of why it is that we obtain various frequencies on the various branches; why we don’t get explanations for the weights, objective weights. Next two lesser points. One is that the Lewis account as I explained it, but I think not in a way that’s very persualsive, it talkes a long story, I think the Lewis account provides an understanding, a kind of rationale, for why the principal connecting these Lewis chances and the facts of the actual world, the degrees of belief about the facts of the actual world, are connected with each other. As has been emphasised by Wayne and Hilary, and David Papineau earlier, this is just accepted as a primitive principle withing the branching account and within the chancy account. I think Lewis’s account is better off there. [noise]..was struck by the fact that Lewis’s account simply doesn’t apply to the many-worlds account, to the many-worlds ontology, because you have all of these frequencies, all of the branches, which have all of the frequencies. If you’re going to give a simple informative account of all that what it would be is the Schrodinger equation. Nothing that corresponds to probabilities would even show up there. Of course some people might respond to that by saying so much the worse for Lewis’s account. I’m mentioning it here because I think Lewis’s account is in better shape but also I’m looking for – and other people can come to some decision about these questions using the fundamental question: can you find some fundamental differences in these two kinds of cases, one where you have one actual thing happening and the others remain merely possible, and the those where you have all the outcomes being actual; some fundamental difference which makes for a difference with respect to confirmation. I’ve suggested two kinds, one having to do with these worries about conditionalisation the other having to do with this worry about making a connection between the Principal Principle and the various views about chances or weight.
Vaidman
6. …. [verbatim is difficult here, much interference – I summarise the question] … In the one world view of quantum mechanics with the Born rule if we want to get information we perform an experiment and look at the frequencies in our world. In the many-worlds view we perform an experiment and look at the frequencies in our world. Where is the difference?
7. Myrvold – Right; that’s our point. [pause, laughter] It’s not obvious that there isn’t a relevant difference there and actually I do think you have to – okay, you look at the records and the statistics perform to the Born rule – on the ordinary account by which that is confirmatory is the sort of thing we gave here, you have certain degrees of belief about chances, you update by conditionalisation and you think, okay, quantum mechanics is getting the chances right. That’s how the statistics become confirmatory for quantum mechanics, as evidence that quantum mechanics is getting the chances right. There isn’t any obvious sense in which we can talk about probability or chance in Everttian quantum mechanics; we can’t in any obvious sense take these statistics as evidence that quantum mechanics is getting the probabilities right so we have to say something a little bit more before we get to say, yes, there really isn’t a difference, the statistics confirms Everettian quantum mechanics with Born rule branch weights in exactly the same way as it confirms [non-]Everettian quantum mechanics with Born rule chances.
Vaidman
8. ………is there any other alternative in many-worlds to confirmation?
Myrvold
9. The worry is that confirmation just falls apart in that context. David [Albert] spent most of his talk trying to press that worry so think if you weren’t conviced by that I can’t do it in the next few minutes.
[next question]
Hartle
10. This is a general question which might be addressed to you all. This afternoon I’m going to give a talk in which I’m going to describe, let’s say for the sake of simplicity, how to take a particular theory of the wavefunction of the universe and calculate let’s say the microwave background ……I’m going to do that probabilistically by squaring a certain amplitude and if the probability is relatively high and I don’t see that particular high prediction I throw the theory away and look at another wavefunction of the universe. If there’s a high probability for what we observe I’m going to say that’s good and I’m going to go on to the next conditional probability that’s high and try to check that out experimentally. Now, what are you going to say? Are you going to say …….that’s a pretty…point of view and we can back you up with a theory of preferences….and that sort of work, or are you going to say that’s completely incoherent and we shouldn’t draw any conclusions?
Myrvold
11. I’m going to do neither. I’m going to say, yes, that’s exactly what you should do – if I have a theory that here’s a probability for what we observe and what we actually observe gets low probability then, yes, that’s evidence against the theory. So the ordinary way of thinking about it, yeah, we’re completely endorsing and that is the ordinary way of proceeding. What we’re adding to that is saying : even if you think of yourself as living in an Everettian branching universe and so there’s one kind of background on some branches and another kind on other ones, what you can do is, by the theory that calculates a high branch weight for what I observe then that theory is confirmed by what I observe, if the theory calculates a low branch weight for what I observe then you throw the theory away exactly as you would if you were taking amplitudes squared as probabilities.
[new question]
Maudlin
12. I don’t understand anything……actually a particular problem which maybe goes back to something David Wallace said……..So, there’s this very fundamental puzzle on the Everett picture which is easy to state but which just gets lost………which goes: as far as decision theory goes, this is decision theory under certainty, and that’s easy. It’s not a problematic thing; under certainty you have various options, each option has an outcome, you have a preference order …..that’s fine, you take the one you……..All this stuff about having an outcome space, normally I have an outcome space when? When I’m uncertain about something. Outcome spaces are the very positive………one of which I think is going to occur…[interference]……..You go back to David Papineau’s question, if you want money why do you bet to maximise expected utility? Answer: because I ………what’s going to give me money, right. There’s no puzzle about why I’m doing something other than going for what I want because I don’t know what’s going to give me what I want. ….under certainty I know what’s going to give me what I want. Now, here’s a situation………..let me just spell it out. There’s a kind of Schrodingerian ….device….I’m going to prepare an x-spin-up electron, I’m going to measure the spin near x-spin but not quite on. I’ve got two boxes, if it comes out one way one box will be filled with deadly gas, if it comes out the other way the other box will be filled with deadly gas. I’ ve got Kitty, I love Kitty, I grew up with Kitty. I have two choices in front of me. I can put Kitty in box One or I can put Kitty in box Two. From an Everett point of view it looks like I know what’s going to happen in each case; there’s no uncertainty. I put Kitty in box One, I end up with two equal-caring? .branches, one with dead Kitty, the other with Kitty surviving. If I put Kitty in the other box I’ll also? .have two branches with equal-caring?.....Now, here’s my real fundamental puzzle, and I put this in a way to David in Budapest and he gave me an he repeated, nobody else understood it, he repeated……….And I said, look, what are the………..? Just ignore the amplitudes? And he said I don’t know what you mean by ignore the amplitudes, all I’ve got is the amplitudes. So here’s what I think?. The branches decohere, what we’re told is all that matters is the structure and the structure doesn’t change if I pump up and down the relative amplitudes of the wave?. The structure doesn’t change and you’ve told me that as an Everettian all I care about is structure. So the difference between putting Kitty in…..by putting Kitty in box A or putting Kitty in box B, the only difference is the relative amplitudes of the branches and that doesn’t make any difference to the relevant structure of the branches so as far as I’m and Everettian I don’t care whether dead Kitty ends up on a high amplitude branch or a relatively low amplitude branch. And I don’t understand; Hilary can come along and say maybe I have a further, unexplained, primitive desire that I care about high-amplitude Kitty more than low-amplitude Kitty….but that seems to be smack in direct conflict with David’s talk which said what I care about is structure, and the structure’s the same. So I’d just like somebody to answer that question.
Greaves
13. Well we were fighting about who was going to answer it so we’ll probably both answer it, but let me jump in first. First a brief comment about the last thing you said and then I want to jump back to…..So, as for this stuff about structure, it’s true that adjusting relative amplitudes doesn’t affect the in-branch structure of either of the branches but it does affect the structure of the overall state and you said yourself in the earlier part of the question what you care about is this holistic thing, the state as a whole and you think that the thing you know is going to result with certainty. So I can’t see any conflict between saying on the one hand what I care about is structure and on the hand I care about amplitudes. So that’s a brief comment about the last bit. Let me go back to the thing that I think is more important. This line comes up a lot when people apply decision theory in the way that all of us have been to the Everettian case this line that, look, the decision theory for making decisions under conditions of certainty is trivial. I think this is just a mistake. Let me look at it this way. In cases of uncertainty we could if we wanted write down a trivial decision theory. It would say, your preferences over gambles have to be transitive that’s all there is to it. We can also write down a non-trivial decision theory, that’s what Savage did. Simlarly, in the Everettian case we could if we wanted write down a trivial decision theory which said that your preferences over these ‘brambles’ as Barry calls them, have to be transitive, I take it that’s the way you want to think, or you could do what we’ve been proposing which is to write down a non-trivial decision theory for preferences over brambles. So, the objection can’t be the decision theory for the branching is trivial. We have both a trivial and a non-trivial one and our argument has been the non-trivial one is just as defensible in the branching case as the non-trivial one is in the non-branching case. So, that’s my reply.
Myrvold
14. Okay, I just want to endorse that and maybe give an example. I don’t think it’s true, or it’s not obvious to me that decision-making under conditions of certainty – there’s nothing you can say about that. And here’s my example. I like everybody in this room. I have a choice, choice One makes it certain that half the people in the room are going to get a cup-cake and choice Two makes it certain that everyone in the room is going to get a cup-cake. Well, if I like everyone in the room then I should prefer choice Two. I can make conditions on – in the bramble case I think of choices between wagers as something like choices of distributions of goods and do not think that the claim that you make that there are no principles that might constrain rational choices of distributions of goods.
[new question]
Barbour
15. I heartily agree with Jim. In Everett’s wonderful paper he makes two fantastic suggestions. One, he picks up Einstein’s argument that every theory should carry it’s complete explanation, it’s interpretation, in its bones. And it seems to me that that has failed in what you’re presenting because you’ve added the branch weights on, so far?. So I’m looking for a theory which will really do what Everett said?. And the other thing Everett said was proposing this theory to help people try to create quantum cosmology. Now, since Everett did that quite a lot of work has been done on quantum cosmology and one of the strongest hints that comes out of that ………..is that it is not really appropriate to think about time at all when you think about quantum cosmology. And if we talk about a universal wavefunction, if we’re talking about the wavefunction of the universe…and there’s a lot of indications that that will be absolutely static. And I believe that within this framework one can get actually, potentially, and explanation of the arrow of time and of Born statistical weights rather in the manner that John Bell explains in his ……..paper….. I think Bell gave the perfect explanation of quantum mechanics more-or-less in its entirety and then finished up and said but you find that solipsists after all have life insurance and seems to completely abandon it and then died before he could try and justify what he said. And I think that a very important part of this story which has not been….in any of the discussion I’ve heard is the arrow of time and the low entropy………. This I think is an essential part of the story. And Jim is quite right I think, he said it years ago and he was very much of a like mind?...we should be thinking of interpreting quantum mechanics much more like geology, where we try to find an explanation of existing records, including multiple experiments which have shown all these outcomes that…………We should be explaining the records as something static, trying to find the theory to explain that. And so I’m looking forward to Jim’s talk.
Greaves
16. The first bit was interesting, the bit about you wanted a clear interpretation we added these branch weights. This is probably something that Wayne and I would go in different directions on. I think, if you want an interpretation that does what you said you wanted, I think what you need is also to endorse the arguments that David Deutsch and David Wallace have been giving that you only need to know the structure of the quantum state and you’re guaranteed to have the Born rule. We were trying to remain neutral in this paper on the question of whether or not those arguments work and to say, look, here’s how it’s going to work: if you think that the Deutsch-Wallace arguments are successful then you’re going to think that, within the class of theories that agree on the quantum state there’s only going to be one rule for the branch weights, namely branch weights have to be amplitude squared. If you think those arguments don’t work you’re going to think there’s a larger space of possibilities, the branch weights could be the amplitudes squared or they could also be this other stuff but we thought we could remain neutral on it because, at the end of the day, it’s not going to make a difference given that in fact we’ve observed Born frequencies, because it’s going to be the ‘branch weight equals amplitude squared’ version of the theory that gets confirmed. But I think you’re right, if you really want a clear interpretation you have to commit to that stronger claim which is consistent with our programme but we didn’t commit to it in this paper.
[new question]
Albert
17. I have two brief questions, I’ll try to keep it brief but maybe I have a special privilege since it was me who was being killed [reference to Myrvold’s remark prior to his talk about it being Albert who is to be killed in Borges’ story “The Garden of Forking Paths”]. Look, first of all, I think this is along the lines of what Tim was saying but put a little differently and put specifically with regard to the question of confirmation, of updating. I’m completely puzzled along the following lines. Somebody believes in Everett, they believe in fission, okay. They know determinately their job is to choose which branching they’d like. If they do this they get this branching, if they do that they get that branching. Forget about the general worries Barry raised, which I agree with, along the lines: what could you learn from where you end up on a branching since you knew in advance everything was going to be there? Forget about that general worry. Here’s a much more specific worry: whether you learn anything from that or not, what you for sure don’t learn anything about are what branchings are going to result from what choices you make in the future. So why would you be tempted to update or to change which branchings you prefer in any way, based on what’s happened before? You know exactly, completely independent of what’s happened before, what branching is going to occur if you do this and what branching is going to occur if you do that. Your job is to choose which branching you prefer, okay, you’re clearly not going to learn anything about that because it’s just given to you deterministically by the theory; what could this updating ceremony possibly do for you?
Myrvold
18. Okay, suppose you’ve got- you’re flipping a coin and you’re doing….- and ..[goes to board]….. and you know for certain that you’re going to get that kind of branching structure. And you’re offered a choice of a dollar on heads on the second flip or a dollar on tails on the second flip, so wager One is [writing on board] and wager Two is that. Now suppose you’re uncertain about what physical theory’s right or your convinced that quantum mechanics ….uncertain? that wavefunction is right so you have two theories about branch weights, one has two-thirds here and one-third there and theory Two has it the other way round, branch weights. And you’re going to be offered the choice of the wagers here. So, T1 says each branching gives two-thirds heads and one-third tails and T2 says [writing on board: one-third heads and two-thirds tails]. If I had to make a choice here [indicating on board] I’d probably be indifferent between the two. But if I wait until I see the first one and then make a choice, okay, I’d rather have the people …heads prefernce? .go for heads and the people who are tails ….go for tails because that maximises the weight of the payoff. And so if I say that beforehand, and then I actually have the agent do that here [indicating] the agent is going to be acting as she has
Albert
19. I still don’t understand the rationale for why the agent would do that.
Myrvold
20. Alright, suppose you know for certain – perhaps people would like it more if there were more branches of equal weights so
Albert
21. That won’t matter to me
Myrvold
22. Okay, suppose you know for certain it’s two-thirds weight heads and one-third weight tails; you’d rather get a dollar here than a dollar there. Okay, here’s what I think, given our representation theorem, what it means for you to have those beliefs about branch weights is for you to prefer a dollar here to…
[cross talk]
Myrvold
23. I absolutely do not identify the weights with …..degrees of belief. Here’s the theorem, if your preferences between wagers satisfy our axioms
Albert
24. Yes, but this is a question about why they plausibly would
Myrvold
25. Okay, if they wouldn’t plausibly then tell me which one……
Albert
26. I choose ………I pick what to do next based on which branching I prefer
Myrvold
27. Exactly
Albert
28. But this isn’t going to be affected at all by my past history……Okay, we’ll continue this – I have one other quick question. This isn’t really so much a question as to highlight something you guys have already said, but that I think may come as a surprise to people and seems to me a little damaging to your case. So ……..that you want to be free of the earlier arguments which I was criticising in my talk, which select a unique weight, okay, in the quantum-mechanical case. And you want to say, look, we’re going to learn what the weights are, we’re going to learn what the relationship between the weights and the amplitudes are by seeing how our experiments come out. I think it’s worth emphasising that to the extent that you take that line you’re distinguishing between two theories both of which have the exact same quantum state evolution, okay. And the distinction between the two theories – and this is moreover a distinction that you think you can empirically distinguish between by looking at the frequencies – you’re distinguishing between two theories which make completely identical claims about the quantum state evolution but differ in the claims they make about the relationship between the amplitudes and the weights. You have a line in your paper where you say: at least for the purposes of confirmation, these are going to count as distinct theories. That seems to me a terribly heavy burden for your view to carry, that is, either these weights are additional physical facts about the world, in which case you’ve already given up the main goal of Everett which is to see the wavefunction as the whole story, or, if they’re not physical facts about the world they’re some other kind of fact which you think you’re confirming or disconfirming by observing these frequencies. I think this is a bizarre situation to be in.
Greaves
29. We had this conversation last night and I’ll give the same reply. I don’t think we’re committed to the claim that there exist two distinct and each coherent theories that agree on the amplitudes but disagree on the branch weights. The claim was, if they’re both coherent then we’re going to….
Albert
30. So the dialectical situation is as follows. If the Deutsch-Wallace proofs succeed, and there is only one coherent way to associate weights with the branches then you’re back in their programme and a lot of this gets a lot easier but I’ve already tried to raise considerations against those. To the extent that you want to hang independently of those, to the extent to which you don’t want your view to depend on those proofs, then you’re positing something extra about the world, either physical or non-physical, in the relation between the amplitudes and the branch weights and that seems like a really weird thing to …..
Myrvold
31. I think that is incoherent to have a quantum theory without extra structure that has different probabilities of branching……….Gleason’s theorem shows that if you don’t add extra structure the only probabilities that are going to fit with quantum mechanics are the Born rule probabilities. So, same thing, the onl branch weights that are going to fit with quantum mechanics without extra structure are Born rule weights. I think that’s right; if someone comes along with an Everettian version of Bohmian mechanics out of equilibrium with different branch weights, yes, it’ll add more structure and we have to empirically what it..
Albert
32. …different physical evolutions, different parameters….
Myrvold
33. Yes, absolutely
Albert
34. Yours won’t
[new question]
Hawthorne
35. I was just wondering how your dynamics of updating connects with the discussion of fission in the Sleeping Beauty literature and ……..which would suggest that – which would point to a difference between …….and gambles?. That literature would suggest that credences wouldn’t evolve in anything like the conditionalisation-theoretic way. And the two particular points I’d emphasise in the Sleeping Beauty literature are first: learning consists in representing content via … and de se modes of representation that weren’t available to your predecessors at earlier times and second: once you represent content by those de … and de se modes of representation, the way that reverberates on the rest of your credences isn’t something that can be modelled at all by conditionalisation….. You undergo fission into two subjective duplicates if tails nothing if heads then after the potential fission time you credence between heads and tails isn’t fifty-fifty any more even if it was fifty-fifty before. If orthodoxy’s right about how credences should evolve in that sort of setting then rational updating wouldn’t satisfy anything like your seven and eight.
Greaves
36. I don’t have much to say about it, I think it’s a very good question and I don’t know to what extent the analogy between the Sleeping Beauty case and the Everettian case holds.
Vaidman
37. …..Sleeping Beauty and I got one-third so I don’t see any…I have a paper on Sleeping Beauty………correct conclusion, it’s one-third. I don’t see why you believe you’d get any other result.
Hawthorne
38. …..if you do go from a half to a third ….. I’m not seeing how that kind of updating is going to be very well modelled by the dynamics of updating we’re doing here.
[new question]
Rae
39. ………….Here’s a logical sequence a physicist might make……You’re updating this business about the As and the Bs on the T-shirts and the funny transporting machine….quite clear that after you’ve done this a number of times and done all the updating that you will think that the weight for A is twice the weight for B, two-thirds/one-third, because the number of branches for A is twice the number of branches for B. Now you go to a quantum measurement; and I thought, right, he’s going to use the same logic. No, we can’t you say because the total number of branches in a quantum measurement is not determinate. Is it not determinate or is it not …….. ? You then use the word measure. Now, I’ve never heard the word ‘measure’ used in this context before since Everett’s paper so, this is the fiftieth anniversary of Everett so to use the word ‘measure’ for the first time in fifty years is perhaps a good thing (I’m sure this isn’t true………). Now it seems to me that even if the number of branches is not determinate the earlier argument shows me that the fraction of this indeterminate number must be two-to-one A and B. But it manifestly isn’t any quantum-mechanical calculation of numbers of branches and in any case if you repeat the experiment you’ll have a different indefinite number, why should that fraction stay the same? And being a simple physicist I would then go back to the………..and say which bit has been falsified, which starting point has been falsified ………..branching at all.
Myrvold
40. Okay, in the repeated transporter case you do it a lot of times and two-thirds of the time you see A, one-third of the time B, your belief can focus on the fraction of branches being two-thirds of As. What we want to say is that in the Everett, if you do a long run of sequences, a long run of experiments, you get spin-up two-thirds of the time, spin-down one-third of the time your belief will converge on there being total weight two-thirds of spin-up and total weight one-third of spin-down. And that’s what we meant by measure. These weights are a measure over the set of branches. And counting branches isn’t right. What count is total weight ..
Rae
41. Why is it right in the transporter case and not in the quantum case; I just can’t see that…..
Myrvold
42. Okay, here’s a thing about the transporter case. I included, I intended to include, as a condition of the thing that each one of those copies is counted as a part. That you’re going to treat them equivalently, there’s no difference between them – and that would go over to the Everett case as branches of equal weight.
[new question]
Brown
43. I’d just like to pick up the issue of the relationship with the….information…Your’re saying..[noise]…..[faint, poor pick-up]…that bypasses…….that stands in the middle…….and I perfectly? understand the logic of this material, you’re learning from experience in the way that we normally do……rational basis……But you seem to suggest, correct me if I’m wrong, that if you take this line? .then in particular the equivalence condition….assumption……….looks very natural………But if ……looks very natural…because you learn from experience…….is correct doesn’t it make the ……………redundant?
Myrvold
44. Here’s my attitude towards the Deutsch-Wallace type thing. …have a status similar to Gleason’s theorem in that they show that the only branch rules for probabilities that fit nicely with quantum mechanics without adding extra structure are the Born rule weights. And so …[cross talk].. yeah, it’s a premis, yea, ………..the Equivalence is a very similar kind of assumption. If you don’t agree [to someone in audience] we’ll talk about it later. Okay, so we’ve got this theory, quantum mechanics, and the only natural branch weights we can get out of quantum mechanics are the Born rule weights and you want to know whether that theory is right or some other theory that might posit different branch weights as right, and then you have to compare the observed relative frequencies with the calculated branch weights in the two theories. So a theory with different branch weights would be a different theory than quantum mechanics.
[new question]
Bacciagaluppi
45. This is related to what Harvey was saying. I’m more confused than Harvey. What I think you’ve shown is you can use the …….machinary in the branching case in every branch, it’s not something that applies to one world …………it applies to every branch. Now, ……[name of someone]……is a pure subjectivist
Myrvold
46. He claims to be
Bacciagaluppi
47. …………the way you then operate in the quantum case is, you’ve got …………which may be candidates for chances or………………you know the wave function, you do a bunch of experiments, you want to test quantum mechanics, you want to see if the frequencies you get are in any way related to the amplitudes of the wave function which …you produced and, okay. In some worlds the answer is, yes; you’ve shown you can use the de Finetti’s theorem to estimate chances ….exist. In some worlds ……..observed frequencies will? Match …….quantum mechanics; in other worlds they won’t. Now, it’s rational on the Baysian point of view to have a degree of belief given by he updating procedure. So in these deviant branches it is rational to believe that quantum mechanics is wrong. Now, according to the Deutsh-Wallace arguments, if you know what the wavefunction is it’s rational to believe that your experiments will come out with frequencies according to the quantum-mechanical weights. I see some danger? ..between what you’ve done and the Deutsch-Wallace programme for …..if the frequencies are the quantum-mechanical ones you get two different precepts of rationality …on different branches.
Wallace
48. I think the answer is that in the deviant branches you are rational to ……..but you’ve been extremely unlucky ………..you’re very, very unfortunate…..[cross talk]
11.30
Everett and evidence
Speakers: Hilary Greaves and Wayne Myrvold
Commentator: Barry Loewer
Floor speakers (in order of appearance):
Vaidman
Hartle
Maudlin
Barbour
Albert
Rae
Brown
Bacciagaluppi
55
Comment by Loewer
1. I think that Hilary and Wayne’s paper is really interesting and clever and I see it as really very interesting line of response to thought I just can’t make sense of confirmation if I thought the universe was branching, as Wayne said. And I want to first bring out some things about the branching situation and then I thought ………...and I’d like to put something else on the table that we might find relevant to the discussion. First it’s this; in thinking about this what’s the difference……a gamble where there’s a chance situation, the different is you’ve got an actual outcome and something else which is possible. In the bramble case, the branching case, both things are actual. The question is, can that difference make any difference to confirmation ……..no. And somebody who’s sceptical about this …..this is worth pushing, was to see whether or not this metaphysical difference can end up making a difference to confirmation. I want to suggest a couple of places where it might. I also wanted to bring this out; I think this is clear in the paper but to see, at least as I understand it, how confirmation would go for them. So here’s just a familiar Bayes theorem [reference to board] but with something a little unfamiliar about it, is let’s say we’re testing – P is Everettian quantum mechanics, K is some other theory, maybe it’s a quantum-mechanical theory, maybe it’s a non-quantum-mechanical theory, but it’s a chance theory, it doesn’t have branching in it. Well this is what Bayes’ theory will look like, a credence of T given some evidence is going to have these credences in it, it’s also going to have subjective weights in it, these are the numbers that they get out of the Savage representation theorem. So these are the numbers that are associated with the outputs. So they will get a subjective weight of E on T and where does that come from? Well, if we’re testing Everettian quantum mechanics then that comes from Everettian quantum mechanics……..I want my preferences, I want these numbers to come from quantum mechanics. So at this point you get this….making use of the Principal Principle. Wayne said he wasn’t going to say much about it but I’m going to say quite a bit about it in a little while.
2. So the Principal Principle …[skipped and aside clarifying background of PP] …I have two kinds of worries really. One is whether or not really conditionalisation is appropriate for them, in a branching situation, and there my worries are very familiar ones…talk about them in discussion period…..and then the status of this, the analogue to the Principal Principle. So, what about conditionalisation here? Well there’re two thoughts that people have about this, about experiments and getting information from experiments; they are old ones and I appear to be something of a troglodyte to be saying we’ve got to stick with them, but they’re really part of a law of experimentation. One is, if someone proposes an experiment and they think they know the outcome before they do the experiment then the experiment isn’t going to provide them with any information about the theory. They know the outcome beforehand. The experiment isn’t going to provide them with any information about what the experiment’s about. So an experiment which just has a particular outcome isn’t going to provide them with information. So it’s no experiment at all. So before doing the experiment, if you know what the outcome is going to be, it isn’t going to tell you anything about it. In the many-worlds case you know beforehand that you’re going to get all the outcomes, so it’s not going to tell you anything. After the experiment, there’ll be fission, there’ll be branching; think about the guys on the different branches. Well, they now, of course, will have particular evidence, particular outcomes. So you might think they should conditionalise on them but of course on the assumption that many-worlds is true it’ll follow that there’re all these other guys (there may not be guys there) with all the other outcomes. That’s their total evidence; they should conditionalise on that. But then of course they won’t get the right result either. So here’s a kind of, you know, two old principle of Baysian inference or statistical inference. One is, if an experiment doesn’t have alternatively possible outcomes, but you know for sure what the outcome is going to be, it’s not really and experiment. The other one is that you should conditionalise on the total evidence that you have, given that the theory is – on the many-worlds theory the total evidence is all the branches with all the various outcomes. So these leave me a little bit worried about conditionalisation in this context. But I don’t think these are very decisive these little objections because the reply is going to be that, well, this is a new kind of situation, a situation we haven’t thought of before, and these old rules just don’t apply, or don’t apply like that.
3. What I want to do now is look at the way the Principal Principle works and I think actually the best way for me to do it is to look at the list …[ref. to projection of page of the paper]… here’s what they’ve done on this page. What they’ve done is they’ve taken the branch weight case and the chance case and they’ve played out a complete analogy between the two. So that, as far as confirmation is concerned, chances and objective branch weights and credences and subjective weights are completely on a par, that’s the idea of the list. What I wanted to do, and I didn’t think about doing this until the discussion earlier, is to put another column on there which is a view about chance but a particular view about chance, David Lewis’s view. Probably most people here are familiar with it. I’m going to say very quickly what it is. Lewis makes a connection between what actually happens in the world and what the chances are, let me call them the L-chances. That’s tighter than the kind of chances that Wayne was talking about. It’s tighter in this way: what the chances are is that built into the laws, and the laws are given by the theory which best summarises all the facts about the world, all the fundamental facts about the world. So Lewis has an idea of there being a theory of the world which best combines simplicity and informativeness. That’s what’s meant by best summary. And one way to be very informative while staying simple is to introduce a notion of probability, a probabilistic notion. Then you have to say something about how that notion, of how those probability claims, inform about the world and the idea is that a principle connecting them to the world will tell you how it’s informing about the world. The Principal Principle is a way of making that connection. So the Lewis account has the Principal Principle, understood this way (this isn’t quite the way Lewis understood it), built right into it. Okay, so imagine that it’s in the list there.
4. If you put it in the list there too, I want to point out, this’ll be the whole of my comments really, is to point out some differences (they have all similarities) between what’s said under the Lewis account and also one difference under the chance account and the branch weight account. As far as the Lewis account is concerned, it agrees with everything that is said under chances. So Lewis chances satisfy the first thing, the theory assigns chances to possible worlds; the second, about updating; the third, there are possible worlds in which anomalous statistics occur. The next one is that a frequentist analysis of chance is untenable. That’s right for Lewis, the simple frequentist analysis is not Lewis’s, but Lewis’s is closer to an actual frequentist account because what the Lewis chances are can on the whole history, the actual facts of the world. So wereas the sort of primitivist propensities account of chance makes chances something over and above the ordinary facts of the world, Lewis’s account makes them supervenient on the categorical facts in the world. Similarly, on the branch weight case the amplitudes, which are gonna be identified with the objective weights, those are over and above the branching strucure, that is, the categorical structure. Now, you might think of the branch weights as themselves additional categorical structure, I’ll come to that in just a second. So you go through the list you see this and here is what seems to me to be some interesting differences that we might want to focus on.
5. In the case of propensity chances, and Lewis, but not in the case of the branches, the chances are built into the laws. The laws are the explanatory structure in the world. Some people don’t find the Lewis laws the appropriate thing to do explaining, that’s a different argument, but the Lewis account is sort of in the ball park here as an account that builds the chances and the laws in together. Whereas in the branch case that’s not so and I’m thinking, I’m wondering, if this gets at David Albert’s worry that we’re not really getting explanations from the branches of why it is that we obtain various frequencies on the various branches; why we don’t get explanations for the weights, objective weights. Next two lesser points. One is that the Lewis account as I explained it, but I think not in a way that’s very persualsive, it talkes a long story, I think the Lewis account provides an understanding, a kind of rationale, for why the principal connecting these Lewis chances and the facts of the actual world, the degrees of belief about the facts of the actual world, are connected with each other. As has been emphasised by Wayne and Hilary, and David Papineau earlier, this is just accepted as a primitive principle withing the branching account and within the chancy account. I think Lewis’s account is better off there. [noise]..was struck by the fact that Lewis’s account simply doesn’t apply to the many-worlds account, to the many-worlds ontology, because you have all of these frequencies, all of the branches, which have all of the frequencies. If you’re going to give a simple informative account of all that what it would be is the Schrodinger equation. Nothing that corresponds to probabilities would even show up there. Of course some people might respond to that by saying so much the worse for Lewis’s account. I’m mentioning it here because I think Lewis’s account is in better shape but also I’m looking for – and other people can come to some decision about these questions using the fundamental question: can you find some fundamental differences in these two kinds of cases, one where you have one actual thing happening and the others remain merely possible, and the those where you have all the outcomes being actual; some fundamental difference which makes for a difference with respect to confirmation. I’ve suggested two kinds, one having to do with these worries about conditionalisation the other having to do with this worry about making a connection between the Principal Principle and the various views about chances or weight.
Vaidman
6. …. [verbatim is difficult here, much interference – I summarise the question] … In the one world view of quantum mechanics with the Born rule if we want to get information we perform an experiment and look at the frequencies in our world. In the many-worlds view we perform an experiment and look at the frequencies in our world. Where is the difference?
7. Myrvold – Right; that’s our point. [pause, laughter] It’s not obvious that there isn’t a relevant difference there and actually I do think you have to – okay, you look at the records and the statistics perform to the Born rule – on the ordinary account by which that is confirmatory is the sort of thing we gave here, you have certain degrees of belief about chances, you update by conditionalisation and you think, okay, quantum mechanics is getting the chances right. That’s how the statistics become confirmatory for quantum mechanics, as evidence that quantum mechanics is getting the chances right. There isn’t any obvious sense in which we can talk about probability or chance in Everttian quantum mechanics; we can’t in any obvious sense take these statistics as evidence that quantum mechanics is getting the probabilities right so we have to say something a little bit more before we get to say, yes, there really isn’t a difference, the statistics confirms Everettian quantum mechanics with Born rule branch weights in exactly the same way as it confirms [non-]Everettian quantum mechanics with Born rule chances.
Vaidman
8. ………is there any other alternative in many-worlds to confirmation?
Myrvold
9. The worry is that confirmation just falls apart in that context. David [Albert] spent most of his talk trying to press that worry so think if you weren’t conviced by that I can’t do it in the next few minutes.
[next question]
Hartle
10. This is a general question which might be addressed to you all. This afternoon I’m going to give a talk in which I’m going to describe, let’s say for the sake of simplicity, how to take a particular theory of the wavefunction of the universe and calculate let’s say the microwave background ……I’m going to do that probabilistically by squaring a certain amplitude and if the probability is relatively high and I don’t see that particular high prediction I throw the theory away and look at another wavefunction of the universe. If there’s a high probability for what we observe I’m going to say that’s good and I’m going to go on to the next conditional probability that’s high and try to check that out experimentally. Now, what are you going to say? Are you going to say …….that’s a pretty…point of view and we can back you up with a theory of preferences….and that sort of work, or are you going to say that’s completely incoherent and we shouldn’t draw any conclusions?
Myrvold
11. I’m going to do neither. I’m going to say, yes, that’s exactly what you should do – if I have a theory that here’s a probability for what we observe and what we actually observe gets low probability then, yes, that’s evidence against the theory. So the ordinary way of thinking about it, yeah, we’re completely endorsing and that is the ordinary way of proceeding. What we’re adding to that is saying : even if you think of yourself as living in an Everettian branching universe and so there’s one kind of background on some branches and another kind on other ones, what you can do is, by the theory that calculates a high branch weight for what I observe then that theory is confirmed by what I observe, if the theory calculates a low branch weight for what I observe then you throw the theory away exactly as you would if you were taking amplitudes squared as probabilities.
[new question]
Maudlin
12. I don’t understand anything……actually a particular problem which maybe goes back to something David Wallace said……..So, there’s this very fundamental puzzle on the Everett picture which is easy to state but which just gets lost………which goes: as far as decision theory goes, this is decision theory under certainty, and that’s easy. It’s not a problematic thing; under certainty you have various options, each option has an outcome, you have a preference order …..that’s fine, you take the one you……..All this stuff about having an outcome space, normally I have an outcome space when? When I’m uncertain about something. Outcome spaces are the very positive………one of which I think is going to occur…[interference]……..You go back to David Papineau’s question, if you want money why do you bet to maximise expected utility? Answer: because I ………what’s going to give me money, right. There’s no puzzle about why I’m doing something other than going for what I want because I don’t know what’s going to give me what I want. ….under certainty I know what’s going to give me what I want. Now, here’s a situation………..let me just spell it out. There’s a kind of Schrodingerian ….device….I’m going to prepare an x-spin-up electron, I’m going to measure the spin near x-spin but not quite on. I’ve got two boxes, if it comes out one way one box will be filled with deadly gas, if it comes out the other way the other box will be filled with deadly gas. I’ ve got Kitty, I love Kitty, I grew up with Kitty. I have two choices in front of me. I can put Kitty in box One or I can put Kitty in box Two. From an Everett point of view it looks like I know what’s going to happen in each case; there’s no uncertainty. I put Kitty in box One, I end up with two equal-caring? .branches, one with dead Kitty, the other with Kitty surviving. If I put Kitty in the other box I’ll also? .have two branches with equal-caring?.....Now, here’s my real fundamental puzzle, and I put this in a way to David in Budapest and he gave me an he repeated, nobody else understood it, he repeated……….And I said, look, what are the………..? Just ignore the amplitudes? And he said I don’t know what you mean by ignore the amplitudes, all I’ve got is the amplitudes. So here’s what I think?. The branches decohere, what we’re told is all that matters is the structure and the structure doesn’t change if I pump up and down the relative amplitudes of the wave?. The structure doesn’t change and you’ve told me that as an Everettian all I care about is structure. So the difference between putting Kitty in…..by putting Kitty in box A or putting Kitty in box B, the only difference is the relative amplitudes of the branches and that doesn’t make any difference to the relevant structure of the branches so as far as I’m and Everettian I don’t care whether dead Kitty ends up on a high amplitude branch or a relatively low amplitude branch. And I don’t understand; Hilary can come along and say maybe I have a further, unexplained, primitive desire that I care about high-amplitude Kitty more than low-amplitude Kitty….but that seems to be smack in direct conflict with David’s talk which said what I care about is structure, and the structure’s the same. So I’d just like somebody to answer that question.
Greaves
13. Well we were fighting about who was going to answer it so we’ll probably both answer it, but let me jump in first. First a brief comment about the last thing you said and then I want to jump back to…..So, as for this stuff about structure, it’s true that adjusting relative amplitudes doesn’t affect the in-branch structure of either of the branches but it does affect the structure of the overall state and you said yourself in the earlier part of the question what you care about is this holistic thing, the state as a whole and you think that the thing you know is going to result with certainty. So I can’t see any conflict between saying on the one hand what I care about is structure and on the hand I care about amplitudes. So that’s a brief comment about the last bit. Let me go back to the thing that I think is more important. This line comes up a lot when people apply decision theory in the way that all of us have been to the Everettian case this line that, look, the decision theory for making decisions under conditions of certainty is trivial. I think this is just a mistake. Let me look at it this way. In cases of uncertainty we could if we wanted write down a trivial decision theory. It would say, your preferences over gambles have to be transitive that’s all there is to it. We can also write down a non-trivial decision theory, that’s what Savage did. Simlarly, in the Everettian case we could if we wanted write down a trivial decision theory which said that your preferences over these ‘brambles’ as Barry calls them, have to be transitive, I take it that’s the way you want to think, or you could do what we’ve been proposing which is to write down a non-trivial decision theory for preferences over brambles. So, the objection can’t be the decision theory for the branching is trivial. We have both a trivial and a non-trivial one and our argument has been the non-trivial one is just as defensible in the branching case as the non-trivial one is in the non-branching case. So, that’s my reply.
Myrvold
14. Okay, I just want to endorse that and maybe give an example. I don’t think it’s true, or it’s not obvious to me that decision-making under conditions of certainty – there’s nothing you can say about that. And here’s my example. I like everybody in this room. I have a choice, choice One makes it certain that half the people in the room are going to get a cup-cake and choice Two makes it certain that everyone in the room is going to get a cup-cake. Well, if I like everyone in the room then I should prefer choice Two. I can make conditions on – in the bramble case I think of choices between wagers as something like choices of distributions of goods and do not think that the claim that you make that there are no principles that might constrain rational choices of distributions of goods.
[new question]
Barbour
15. I heartily agree with Jim. In Everett’s wonderful paper he makes two fantastic suggestions. One, he picks up Einstein’s argument that every theory should carry it’s complete explanation, it’s interpretation, in its bones. And it seems to me that that has failed in what you’re presenting because you’ve added the branch weights on, so far?. So I’m looking for a theory which will really do what Everett said?. And the other thing Everett said was proposing this theory to help people try to create quantum cosmology. Now, since Everett did that quite a lot of work has been done on quantum cosmology and one of the strongest hints that comes out of that ………..is that it is not really appropriate to think about time at all when you think about quantum cosmology. And if we talk about a universal wavefunction, if we’re talking about the wavefunction of the universe…and there’s a lot of indications that that will be absolutely static. And I believe that within this framework one can get actually, potentially, and explanation of the arrow of time and of Born statistical weights rather in the manner that John Bell explains in his ……..paper….. I think Bell gave the perfect explanation of quantum mechanics more-or-less in its entirety and then finished up and said but you find that solipsists after all have life insurance and seems to completely abandon it and then died before he could try and justify what he said. And I think that a very important part of this story which has not been….in any of the discussion I’ve heard is the arrow of time and the low entropy………. This I think is an essential part of the story. And Jim is quite right I think, he said it years ago and he was very much of a like mind?...we should be thinking of interpreting quantum mechanics much more like geology, where we try to find an explanation of existing records, including multiple experiments which have shown all these outcomes that…………We should be explaining the records as something static, trying to find the theory to explain that. And so I’m looking forward to Jim’s talk.
Greaves
16. The first bit was interesting, the bit about you wanted a clear interpretation we added these branch weights. This is probably something that Wayne and I would go in different directions on. I think, if you want an interpretation that does what you said you wanted, I think what you need is also to endorse the arguments that David Deutsch and David Wallace have been giving that you only need to know the structure of the quantum state and you’re guaranteed to have the Born rule. We were trying to remain neutral in this paper on the question of whether or not those arguments work and to say, look, here’s how it’s going to work: if you think that the Deutsch-Wallace arguments are successful then you’re going to think that, within the class of theories that agree on the quantum state there’s only going to be one rule for the branch weights, namely branch weights have to be amplitude squared. If you think those arguments don’t work you’re going to think there’s a larger space of possibilities, the branch weights could be the amplitudes squared or they could also be this other stuff but we thought we could remain neutral on it because, at the end of the day, it’s not going to make a difference given that in fact we’ve observed Born frequencies, because it’s going to be the ‘branch weight equals amplitude squared’ version of the theory that gets confirmed. But I think you’re right, if you really want a clear interpretation you have to commit to that stronger claim which is consistent with our programme but we didn’t commit to it in this paper.
[new question]
Albert
17. I have two brief questions, I’ll try to keep it brief but maybe I have a special privilege since it was me who was being killed [reference to Myrvold’s remark prior to his talk about it being Albert who is to be killed in Borges’ story “The Garden of Forking Paths”]. Look, first of all, I think this is along the lines of what Tim was saying but put a little differently and put specifically with regard to the question of confirmation, of updating. I’m completely puzzled along the following lines. Somebody believes in Everett, they believe in fission, okay. They know determinately their job is to choose which branching they’d like. If they do this they get this branching, if they do that they get that branching. Forget about the general worries Barry raised, which I agree with, along the lines: what could you learn from where you end up on a branching since you knew in advance everything was going to be there? Forget about that general worry. Here’s a much more specific worry: whether you learn anything from that or not, what you for sure don’t learn anything about are what branchings are going to result from what choices you make in the future. So why would you be tempted to update or to change which branchings you prefer in any way, based on what’s happened before? You know exactly, completely independent of what’s happened before, what branching is going to occur if you do this and what branching is going to occur if you do that. Your job is to choose which branching you prefer, okay, you’re clearly not going to learn anything about that because it’s just given to you deterministically by the theory; what could this updating ceremony possibly do for you?
Myrvold
18. Okay, suppose you’ve got- you’re flipping a coin and you’re doing….- and ..[goes to board]….. and you know for certain that you’re going to get that kind of branching structure. And you’re offered a choice of a dollar on heads on the second flip or a dollar on tails on the second flip, so wager One is [writing on board] and wager Two is that. Now suppose you’re uncertain about what physical theory’s right or your convinced that quantum mechanics ….uncertain? that wavefunction is right so you have two theories about branch weights, one has two-thirds here and one-third there and theory Two has it the other way round, branch weights. And you’re going to be offered the choice of the wagers here. So, T1 says each branching gives two-thirds heads and one-third tails and T2 says [writing on board: one-third heads and two-thirds tails]. If I had to make a choice here [indicating on board] I’d probably be indifferent between the two. But if I wait until I see the first one and then make a choice, okay, I’d rather have the people …heads prefernce? .go for heads and the people who are tails ….go for tails because that maximises the weight of the payoff. And so if I say that beforehand, and then I actually have the agent do that here [indicating] the agent is going to be acting as she has
Albert
19. I still don’t understand the rationale for why the agent would do that.
Myrvold
20. Alright, suppose you know for certain – perhaps people would like it more if there were more branches of equal weights so
Albert
21. That won’t matter to me
Myrvold
22. Okay, suppose you know for certain it’s two-thirds weight heads and one-third weight tails; you’d rather get a dollar here than a dollar there. Okay, here’s what I think, given our representation theorem, what it means for you to have those beliefs about branch weights is for you to prefer a dollar here to…
[cross talk]
Myrvold
23. I absolutely do not identify the weights with …..degrees of belief. Here’s the theorem, if your preferences between wagers satisfy our axioms
Albert
24. Yes, but this is a question about why they plausibly would
Myrvold
25. Okay, if they wouldn’t plausibly then tell me which one……
Albert
26. I choose ………I pick what to do next based on which branching I prefer
Myrvold
27. Exactly
Albert
28. But this isn’t going to be affected at all by my past history……Okay, we’ll continue this – I have one other quick question. This isn’t really so much a question as to highlight something you guys have already said, but that I think may come as a surprise to people and seems to me a little damaging to your case. So ……..that you want to be free of the earlier arguments which I was criticising in my talk, which select a unique weight, okay, in the quantum-mechanical case. And you want to say, look, we’re going to learn what the weights are, we’re going to learn what the relationship between the weights and the amplitudes are by seeing how our experiments come out. I think it’s worth emphasising that to the extent that you take that line you’re distinguishing between two theories both of which have the exact same quantum state evolution, okay. And the distinction between the two theories – and this is moreover a distinction that you think you can empirically distinguish between by looking at the frequencies – you’re distinguishing between two theories which make completely identical claims about the quantum state evolution but differ in the claims they make about the relationship between the amplitudes and the weights. You have a line in your paper where you say: at least for the purposes of confirmation, these are going to count as distinct theories. That seems to me a terribly heavy burden for your view to carry, that is, either these weights are additional physical facts about the world, in which case you’ve already given up the main goal of Everett which is to see the wavefunction as the whole story, or, if they’re not physical facts about the world they’re some other kind of fact which you think you’re confirming or disconfirming by observing these frequencies. I think this is a bizarre situation to be in.
Greaves
29. We had this conversation last night and I’ll give the same reply. I don’t think we’re committed to the claim that there exist two distinct and each coherent theories that agree on the amplitudes but disagree on the branch weights. The claim was, if they’re both coherent then we’re going to….
Albert
30. So the dialectical situation is as follows. If the Deutsch-Wallace proofs succeed, and there is only one coherent way to associate weights with the branches then you’re back in their programme and a lot of this gets a lot easier but I’ve already tried to raise considerations against those. To the extent that you want to hang independently of those, to the extent to which you don’t want your view to depend on those proofs, then you’re positing something extra about the world, either physical or non-physical, in the relation between the amplitudes and the branch weights and that seems like a really weird thing to …..
Myrvold
31. I think that is incoherent to have a quantum theory without extra structure that has different probabilities of branching……….Gleason’s theorem shows that if you don’t add extra structure the only probabilities that are going to fit with quantum mechanics are the Born rule probabilities. So, same thing, the onl branch weights that are going to fit with quantum mechanics without extra structure are Born rule weights. I think that’s right; if someone comes along with an Everettian version of Bohmian mechanics out of equilibrium with different branch weights, yes, it’ll add more structure and we have to empirically what it..
Albert
32. …different physical evolutions, different parameters….
Myrvold
33. Yes, absolutely
Albert
34. Yours won’t
[new question]
Hawthorne
35. I was just wondering how your dynamics of updating connects with the discussion of fission in the Sleeping Beauty literature and ……..which would suggest that – which would point to a difference between …….and gambles?. That literature would suggest that credences wouldn’t evolve in anything like the conditionalisation-theoretic way. And the two particular points I’d emphasise in the Sleeping Beauty literature are first: learning consists in representing content via … and de se modes of representation that weren’t available to your predecessors at earlier times and second: once you represent content by those de … and de se modes of representation, the way that reverberates on the rest of your credences isn’t something that can be modelled at all by conditionalisation….. You undergo fission into two subjective duplicates if tails nothing if heads then after the potential fission time you credence between heads and tails isn’t fifty-fifty any more even if it was fifty-fifty before. If orthodoxy’s right about how credences should evolve in that sort of setting then rational updating wouldn’t satisfy anything like your seven and eight.
Greaves
36. I don’t have much to say about it, I think it’s a very good question and I don’t know to what extent the analogy between the Sleeping Beauty case and the Everettian case holds.
Vaidman
37. …..Sleeping Beauty and I got one-third so I don’t see any…I have a paper on Sleeping Beauty………correct conclusion, it’s one-third. I don’t see why you believe you’d get any other result.
Hawthorne
38. …..if you do go from a half to a third ….. I’m not seeing how that kind of updating is going to be very well modelled by the dynamics of updating we’re doing here.
[new question]
Rae
39. ………….Here’s a logical sequence a physicist might make……You’re updating this business about the As and the Bs on the T-shirts and the funny transporting machine….quite clear that after you’ve done this a number of times and done all the updating that you will think that the weight for A is twice the weight for B, two-thirds/one-third, because the number of branches for A is twice the number of branches for B. Now you go to a quantum measurement; and I thought, right, he’s going to use the same logic. No, we can’t you say because the total number of branches in a quantum measurement is not determinate. Is it not determinate or is it not …….. ? You then use the word measure. Now, I’ve never heard the word ‘measure’ used in this context before since Everett’s paper so, this is the fiftieth anniversary of Everett so to use the word ‘measure’ for the first time in fifty years is perhaps a good thing (I’m sure this isn’t true………). Now it seems to me that even if the number of branches is not determinate the earlier argument shows me that the fraction of this indeterminate number must be two-to-one A and B. But it manifestly isn’t any quantum-mechanical calculation of numbers of branches and in any case if you repeat the experiment you’ll have a different indefinite number, why should that fraction stay the same? And being a simple physicist I would then go back to the………..and say which bit has been falsified, which starting point has been falsified ………..branching at all.
Myrvold
40. Okay, in the repeated transporter case you do it a lot of times and two-thirds of the time you see A, one-third of the time B, your belief can focus on the fraction of branches being two-thirds of As. What we want to say is that in the Everett, if you do a long run of sequences, a long run of experiments, you get spin-up two-thirds of the time, spin-down one-third of the time your belief will converge on there being total weight two-thirds of spin-up and total weight one-third of spin-down. And that’s what we meant by measure. These weights are a measure over the set of branches. And counting branches isn’t right. What count is total weight ..
Rae
41. Why is it right in the transporter case and not in the quantum case; I just can’t see that…..
Myrvold
42. Okay, here’s a thing about the transporter case. I included, I intended to include, as a condition of the thing that each one of those copies is counted as a part. That you’re going to treat them equivalently, there’s no difference between them – and that would go over to the Everett case as branches of equal weight.
[new question]
Brown
43. I’d just like to pick up the issue of the relationship with the….information…Your’re saying..[noise]…..[faint, poor pick-up]…that bypasses…….that stands in the middle…….and I perfectly? understand the logic of this material, you’re learning from experience in the way that we normally do……rational basis……But you seem to suggest, correct me if I’m wrong, that if you take this line? .then in particular the equivalence condition….assumption……….looks very natural………But if ……looks very natural…because you learn from experience…….is correct doesn’t it make the ……………redundant?
Myrvold
44. Here’s my attitude towards the Deutsch-Wallace type thing. …have a status similar to Gleason’s theorem in that they show that the only branch rules for probabilities that fit nicely with quantum mechanics without adding extra structure are the Born rule weights. And so …[cross talk].. yeah, it’s a premis, yea, ………..the Equivalence is a very similar kind of assumption. If you don’t agree [to someone in audience] we’ll talk about it later. Okay, so we’ve got this theory, quantum mechanics, and the only natural branch weights we can get out of quantum mechanics are the Born rule weights and you want to know whether that theory is right or some other theory that might posit different branch weights as right, and then you have to compare the observed relative frequencies with the calculated branch weights in the two theories. So a theory with different branch weights would be a different theory than quantum mechanics.
[new question]
Bacciagaluppi
45. This is related to what Harvey was saying. I’m more confused than Harvey. What I think you’ve shown is you can use the …….machinary in the branching case in every branch, it’s not something that applies to one world …………it applies to every branch. Now, ……[name of someone]……is a pure subjectivist
Myrvold
46. He claims to be
Bacciagaluppi
47. …………the way you then operate in the quantum case is, you’ve got …………which may be candidates for chances or………………you know the wave function, you do a bunch of experiments, you want to test quantum mechanics, you want to see if the frequencies you get are in any way related to the amplitudes of the wave function which …you produced and, okay. In some worlds the answer is, yes; you’ve shown you can use the de Finetti’s theorem to estimate chances ….exist. In some worlds ……..observed frequencies will? Match …….quantum mechanics; in other worlds they won’t. Now, it’s rational on the Baysian point of view to have a degree of belief given by he updating procedure. So in these deviant branches it is rational to believe that quantum mechanics is wrong. Now, according to the Deutsh-Wallace arguments, if you know what the wavefunction is it’s rational to believe that your experiments will come out with frequencies according to the quantum-mechanical weights. I see some danger? ..between what you’ve done and the Deutsch-Wallace programme for …..if the frequencies are the quantum-mechanical ones you get two different precepts of rationality …on different branches.
Wallace
48. I think the answer is that in the deviant branches you are rational to ……..but you’ve been extremely unlucky ………..you’re very, very unfortunate…..[cross talk]
Transcript discussion Deutsch
July 20 15.00
Apart from universes
Speaker: David Deutsch
Floor speakers (in order of appearance):
Vaidman
Wallace
Saunders
Ladyman
Hemmo
Barbour
69
[questions only]
Vaidman
1. I’m certainly very much with you that Everett’s is by far the best interpretation, that it’s correct and it’s a miracle why it’s not understandable until now. I’m trying to think why and I think you may be partly responsible. The first reason is the biggest; it’s many-world and you said they’re really separate and it looks like your multiverse, which had before been given different names, you consider theories of the multiverse. And I think Everett means, and especially Schrodinger, it’s a single physical universe. I don’t think multiverse, it’s not a theory of multiverse, the important thing is no collapse, that’s the main point. And the other thing, and you made a big contribution which put it forward, but you also didn’t ask things which can be achieved which might be not, and I think Everett was the first to say that you can get probability out of many-worlds, if he didn’t say so I think now it would be accepted because this was not proven at that time, it’s not proven until today. And when ………show that this doesn’t work they kill the whole theory. But the main thing is there’s no collapse and that does not contradict our experience. This is Everett’s theory. If you would not add some other things which are maybe not achievable then it would be accepted.
Deutsch
2. Okay, two things there. First of all, I think what you say about universe/multiverse, I don’t care about the terminology, I’m quite happy to call the multiverse the universe and the universe a branch, in fact I did that in one paper. I don’t care. Certainly the point of Everett’s theory is that we don’t need collapse and that quantum theory can be regarded as a complete theory of the universe. As for probability, I agree with you that the objection to Everett that it didn’t describe probability properly was always a mistake. What was happening there was that there is a problem at the foundations of probability theory which was obscured by silly interpretations. But in Everett’s interpretation you could actually see that problem. It wasn’t a problem with Everett’s interpretation, it’s something that you could see through Everett’s interpretation and then, we believe, solve. If we hadn’t solved it it would be no argument against Everett.
[new question]
Wallace
3. It’s a sort of friendly amendment I suppose. You had your particle, a single particle in space, this classical multiverse approximation breaks down. It seems to me that it’s a retrograde move to describe that thing as multiversal in the sense of describing it as living in different universes at different points. Those sorts of position-basis eigenstates are there and…….by all means, but calling them universes doesn’t seem to me to be necessarily that helpful. There not autonomous, they’re not that sort of thing, they’re just….
Deutsch
4. Yes, I entirely agree with that and if only we had a proper mathematical description of the multiverse then I’d be very happy to say that what’s actually happening with a single particle is so-and-so and you can see than you can’t then make the universe approximation and have that be accurate. Yeah, I agree.
Saunders
5. When you say we don’t have a proper understanding of the multiverse what sort of understanding do you want? Is it mathematical, is it….
Deutsch
6. There’s a mathematical physics issue and also a philosophical issue. The mathematical physics issue is that we don’t know what mathematical object the equations of quantum theory are supposed to apply to. We know how to get answers out of them and we know how to describe something about this object in emergent approximations but we don’t have an exact theory of it. We don’t have a theory of it that’s in principle exact. For instance, in that work I did on time travel with – going back in time and coming back in a different universe, I had a diagram there where there’s a spacetime and the loop in spacetime gets unfolded into a – I don’t know if any of you are familiar with that work, but anyway the point is that that manifold which is a sort of hybrid conception of a relativity thing with a quantum thing – there’s no mathematical object that I can say that’s an approximation to. There ought to be. So that’s the mathematical physics part of it, I think we need that in order to make progress in certain directions. There’s also the philosophical thing that we don’t have a vocabulary and a language. We have a vocabulary to talk about situations where and observable is sharp, and we have vocabulary to talk about parallel universes but most of the multiverse isn’t like that and we don’t have a good way of talking about what that is like, even in the case of a single particle. So, those are the two things that are lacking.
[new question]
Ladyman
7. I thought you overstated the argument against anti-realism and also you ran together two distinct things. An anti-realist about science doesn’t have to deny that there’s an objective reality, they can just deny that we’re finding out about it, so you shouldn’t run those things together because obviously one’s much less plausible than the other. I’m not personally an anti-realist but it is an intelligible view to take about science as is exemplified by the attitude a lot of people take towards Newtonian mechanics; you can think it’s a wonderful theory, use it every day, predict lots of stuff with it, don’t believe that there really are Newtonian action-at-a-distance forces, that’s not a crazy view to have of the world so someone might think about quantum mechanics just like that: it’s a good theory to use but I don’t see why I should believe it to be telling me the truth about unobservables.
Deutsch
8. First of all, I’m glad you’re not an anti-realist because it’s very hard to argue with someone who denies that they exist. About whether I was too hard on anti-realism, all I said about it was – you say it could be that there is a reality but our science doesn’t have access to it – all I said about it was that if you take that view then science isn’t about anything, apart from your own mind, and I think that would be true of the person that you outlined as well. Now, as for explanation, the trouble is, if you regard a theory as being purely a set of observable predictions then you must, logically, be thinking of observations as unanalysable primitive things and that is incompatible with having a universal scientific theory. Also there’s the fact that explanation – there are infinitely many interpretations of those things which make different predictions for the future, then you’ll run into the problem of induction and so on. I’d have to refer you to ‘The Fabric of Reality’ for why science has to be explanatory.
[new question]
Hemmo
9. We had a discussion this morning about….probability
Deutsch
10. Sorry, I wasn’t there for that
Hemmo
11. and many people …………………….derivation?..of the Born rule is not based solely on rationality…..[faint voice obscured by noises]….and second it might not even be possible to justify that in the context of many-world theory.
Deutsch
12. At the moment all I can say - I think they are justified but all I can say about that at the moment is the same as my reply to Lev’s question: if it turns out that there is a hidden assumption there, and we have to admit that there have been …[crosstalk]…if this really is an assumption over and above rationality then it’s no argument against Everett’s theory, it’s simply says that there’s a remaining puzzle about what probability really is. And, as I say, we have to admit that all previous attempts for whatever it is, three hundred years, to solve this problem of deriving a “tends-to” from a “does” have contained hidden assumptions and it could be that we’re wrong as well. We’re not.
[new question]
Barbour
13. David, you’ve completely persuaded me that the central task is to find the mulitverse, what it is like, would you agree with me in Popperian lines that ultimately someone’s got to conjecture what it’s like and then we’ve got to take…
Deutsch
14. Absolutely, I agreed entirely with what you said about that yesterday. Yes, they’ve got to conjecture an explanation, that is, an assertion about what the reality’s like, observed and unobserved, and then that has to be tested.
Barbour
15. As a follow-up to that: there is an argument for saying that science actually progresses in small steps so I wouldn’t be quite so quick in dismissing the ghost within the thing because that’s really actually - the classical ghost within the quantum - it’s a bit disliking not making a giant leap rather than a series of small leaps and to some extent I have made a conjecture about what the multiverse is like, I think it’s probably, almost certainly, too naïve and will be wrong, but that is essentially what Brice deWitt conjectured forty years ago, so I wouldn’t totally dismiss that as a possibility
Deutsch
16. I said it was worth trying heuristically, and it has been tried but it seems to be running out of steam. There seems to be an obvious explanation for why it’s running out of steam.
Apart from universes
Speaker: David Deutsch
Floor speakers (in order of appearance):
Vaidman
Wallace
Saunders
Ladyman
Hemmo
Barbour
69
[questions only]
Vaidman
1. I’m certainly very much with you that Everett’s is by far the best interpretation, that it’s correct and it’s a miracle why it’s not understandable until now. I’m trying to think why and I think you may be partly responsible. The first reason is the biggest; it’s many-world and you said they’re really separate and it looks like your multiverse, which had before been given different names, you consider theories of the multiverse. And I think Everett means, and especially Schrodinger, it’s a single physical universe. I don’t think multiverse, it’s not a theory of multiverse, the important thing is no collapse, that’s the main point. And the other thing, and you made a big contribution which put it forward, but you also didn’t ask things which can be achieved which might be not, and I think Everett was the first to say that you can get probability out of many-worlds, if he didn’t say so I think now it would be accepted because this was not proven at that time, it’s not proven until today. And when ………show that this doesn’t work they kill the whole theory. But the main thing is there’s no collapse and that does not contradict our experience. This is Everett’s theory. If you would not add some other things which are maybe not achievable then it would be accepted.
Deutsch
2. Okay, two things there. First of all, I think what you say about universe/multiverse, I don’t care about the terminology, I’m quite happy to call the multiverse the universe and the universe a branch, in fact I did that in one paper. I don’t care. Certainly the point of Everett’s theory is that we don’t need collapse and that quantum theory can be regarded as a complete theory of the universe. As for probability, I agree with you that the objection to Everett that it didn’t describe probability properly was always a mistake. What was happening there was that there is a problem at the foundations of probability theory which was obscured by silly interpretations. But in Everett’s interpretation you could actually see that problem. It wasn’t a problem with Everett’s interpretation, it’s something that you could see through Everett’s interpretation and then, we believe, solve. If we hadn’t solved it it would be no argument against Everett.
[new question]
Wallace
3. It’s a sort of friendly amendment I suppose. You had your particle, a single particle in space, this classical multiverse approximation breaks down. It seems to me that it’s a retrograde move to describe that thing as multiversal in the sense of describing it as living in different universes at different points. Those sorts of position-basis eigenstates are there and…….by all means, but calling them universes doesn’t seem to me to be necessarily that helpful. There not autonomous, they’re not that sort of thing, they’re just….
Deutsch
4. Yes, I entirely agree with that and if only we had a proper mathematical description of the multiverse then I’d be very happy to say that what’s actually happening with a single particle is so-and-so and you can see than you can’t then make the universe approximation and have that be accurate. Yeah, I agree.
Saunders
5. When you say we don’t have a proper understanding of the multiverse what sort of understanding do you want? Is it mathematical, is it….
Deutsch
6. There’s a mathematical physics issue and also a philosophical issue. The mathematical physics issue is that we don’t know what mathematical object the equations of quantum theory are supposed to apply to. We know how to get answers out of them and we know how to describe something about this object in emergent approximations but we don’t have an exact theory of it. We don’t have a theory of it that’s in principle exact. For instance, in that work I did on time travel with – going back in time and coming back in a different universe, I had a diagram there where there’s a spacetime and the loop in spacetime gets unfolded into a – I don’t know if any of you are familiar with that work, but anyway the point is that that manifold which is a sort of hybrid conception of a relativity thing with a quantum thing – there’s no mathematical object that I can say that’s an approximation to. There ought to be. So that’s the mathematical physics part of it, I think we need that in order to make progress in certain directions. There’s also the philosophical thing that we don’t have a vocabulary and a language. We have a vocabulary to talk about situations where and observable is sharp, and we have vocabulary to talk about parallel universes but most of the multiverse isn’t like that and we don’t have a good way of talking about what that is like, even in the case of a single particle. So, those are the two things that are lacking.
[new question]
Ladyman
7. I thought you overstated the argument against anti-realism and also you ran together two distinct things. An anti-realist about science doesn’t have to deny that there’s an objective reality, they can just deny that we’re finding out about it, so you shouldn’t run those things together because obviously one’s much less plausible than the other. I’m not personally an anti-realist but it is an intelligible view to take about science as is exemplified by the attitude a lot of people take towards Newtonian mechanics; you can think it’s a wonderful theory, use it every day, predict lots of stuff with it, don’t believe that there really are Newtonian action-at-a-distance forces, that’s not a crazy view to have of the world so someone might think about quantum mechanics just like that: it’s a good theory to use but I don’t see why I should believe it to be telling me the truth about unobservables.
Deutsch
8. First of all, I’m glad you’re not an anti-realist because it’s very hard to argue with someone who denies that they exist. About whether I was too hard on anti-realism, all I said about it was – you say it could be that there is a reality but our science doesn’t have access to it – all I said about it was that if you take that view then science isn’t about anything, apart from your own mind, and I think that would be true of the person that you outlined as well. Now, as for explanation, the trouble is, if you regard a theory as being purely a set of observable predictions then you must, logically, be thinking of observations as unanalysable primitive things and that is incompatible with having a universal scientific theory. Also there’s the fact that explanation – there are infinitely many interpretations of those things which make different predictions for the future, then you’ll run into the problem of induction and so on. I’d have to refer you to ‘The Fabric of Reality’ for why science has to be explanatory.
[new question]
Hemmo
9. We had a discussion this morning about….probability
Deutsch
10. Sorry, I wasn’t there for that
Hemmo
11. and many people …………………….derivation?..of the Born rule is not based solely on rationality…..[faint voice obscured by noises]….and second it might not even be possible to justify that in the context of many-world theory.
Deutsch
12. At the moment all I can say - I think they are justified but all I can say about that at the moment is the same as my reply to Lev’s question: if it turns out that there is a hidden assumption there, and we have to admit that there have been …[crosstalk]…if this really is an assumption over and above rationality then it’s no argument against Everett’s theory, it’s simply says that there’s a remaining puzzle about what probability really is. And, as I say, we have to admit that all previous attempts for whatever it is, three hundred years, to solve this problem of deriving a “tends-to” from a “does” have contained hidden assumptions and it could be that we’re wrong as well. We’re not.
[new question]
Barbour
13. David, you’ve completely persuaded me that the central task is to find the mulitverse, what it is like, would you agree with me in Popperian lines that ultimately someone’s got to conjecture what it’s like and then we’ve got to take…
Deutsch
14. Absolutely, I agreed entirely with what you said about that yesterday. Yes, they’ve got to conjecture an explanation, that is, an assertion about what the reality’s like, observed and unobserved, and then that has to be tested.
Barbour
15. As a follow-up to that: there is an argument for saying that science actually progresses in small steps so I wouldn’t be quite so quick in dismissing the ghost within the thing because that’s really actually - the classical ghost within the quantum - it’s a bit disliking not making a giant leap rather than a series of small leaps and to some extent I have made a conjecture about what the multiverse is like, I think it’s probably, almost certainly, too naïve and will be wrong, but that is essentially what Brice deWitt conjectured forty years ago, so I wouldn’t totally dismiss that as a possibility
Deutsch
16. I said it was worth trying heuristically, and it has been tried but it seems to be running out of steam. There seems to be an obvious explanation for why it’s running out of steam.
Transcript discussion Vaidman
July 20 15.45
The time-symmetric QW and the MWI
Speaker: Lev Vaidman
Floor speakers (in order of appearance):
Bacciagaluppi
Wallace
Lehner
73
[questions only]
Bacciagaluppi
1. [extended question as had prepared to be commentator] Apart from your speculation at the end you were saying maybe we should opt for the trivial?..two-states?..for the universe and your argument was otherwise we would get effects from the ABL?..rule. Now, I’m just wondering about a slightly different way of seeing things which - I won’t insist on it but it may be something to have a look at. So if we take a different psi-final [going to board] and have a psi-initial which are different, there is a natural way of trying to define a many-worlds interpretation would be following …Gell-Mann, Kent and Hartle by setting up a two-vector decoherence condition so, real part on a trace of psi-f, v-alpha n of t-n….[continuing description of expression being written on board]..this thing different - equal to zero for different histories. Now, by the way, Gell-Mann and Hartle show that if the initial and final state are pure this is a very restrictive condition so they suggest to consider mixed states. But I’m also wondering if one shouldn’t try the following. Especially in a many-worlds interpretation in which probabilities should be understood along the lines of Deutsch and Wallace as guiding the acts of agents that are branching - is it the case that we should expect in general an agent to have access both to psi-initial and psi-final? Should we expect the probabilities to be well-defined according to this rule, defined by a psi-initial and psi-final or shouldn’t we rather expect that we might have different kinds of agents with different arrows of time and then have something like: it’s only the marginals of the probabilities that should be defined for different kinds of agents and we don’t really worry if we don’t have decoherence with respect to two states. So, the idea would be that if we are initial observers we average over the final state and vice versa. Something like that; just two small comments, of course it would be difficult to study this in complete generality but maybe in bi-partite systems we’ve got Alice and Bob and Alice and Bob only have a classical communcation channel and they have…..directions of time…well-known by Barnum et al, the most general probability measure for setups of this kind are more general than the quantum states and that may be related to the possibility of different arrows of time and anyway I think this would be a good setting to study it.
Vaidman
2. I was trying to tailor - looking at a simple example with one beam-splitter this boundary condition in the future which are different from just …..And I saw how many disasters they caused. So, it’s really not simple to get a single time error and still have something non-trivial different in the future. Maybe I should mention one example which is not proper for this conference because it’s really to make a single world out of this theory, and this is Ahronov’s conjecture that there is…………..quantum states, a very special one. It’s really this one [indicating on board]: we go to the end of the universe, we go to a particular branch and we take one of it and we put it backwards in time. The picture will not be like this, there’ll be many red things going on all over but the overlap, he believes, and fits the time is not too long, we really single-out one trajectory, our world, and by fiat we’ll have right probabilities, everything is correct, and I think it’s better than collapse, I don’t think it’s better than the many-worlds interpretation because it’s very special, I take a very special final condition. So, unless you take a mixture, for a mixture everything goes, you take a mixture from here, a mixture from there, everything correct comes together and it does not……our experience. Maybe it’s a little too much because it takes everything, not only all many-worlds, multiple worlds, you can split them in different ways; in a mixture you can do whatever, like teleportation. You can teleport one state it’s free to several?..worlds, you can teleport another state and it makes…..in many other worlds.
[new question]
Wallace
3. A quick comment. You gave good reasons for not wanting two vectors for the whole universe……if I’ve got this right, the difference between a forward and backward-evolving vector is the forward-evolved vector we evolve from the measurement forward and then shift?..the backwards is the other way. And also the whole universe………measurements……in this context, in the case of the whole universe we’ve got no measurement so the initial state evolves forwards to the end of time and the second?..state evolves back to the beginning of time and of course the Schrodinger equation is time-symmetric, the Schrodinger equation doesn’t come with a little arrow built in, so actually, if we had two states of the whole universe we really just have two states both evolving through time in whatever direction together and there………something redundant about what’s going on there. So I think the naturalness of making this forward/backward-evolving thing does rely on these……unusual?..steps.
Vaidman
4. First, it’s kind of tricky. The measurements are inside, everything is unitary so measurement is just macroscopic objects coming to microscopic objects and separating microscopic…..distances or states. So, in fact I first put this argument that I have to put another source and then I said my probabilities are wrong. I’m not very strong about this probability wrong, because probably if put some different final states it will kind of wash out and I will not know now, the probability might come out correct because we have this macro?scopic object in each branch, this wave function is the same so it’s not completely clear but anyway it’s very difficult to tailor consistently the…middle?.state, what about the error of time. So it’s not simple; the only thing which I know it works it’s a complete mixture or a single branch probably.
[new question]
Lehner
5. An interesting way I think you can think about that is in terms of Everett’s relative state picture, that the backwards vector in time is just a relative state of subsequent observation. That there’s nothing sort of unnatural about ascribing - there’s nothing that tells us in the Everett story which of the two relative states we really should pick for the description of anything that happens in between, so you also get that symmetry. In Everett’s case, what takes care of the….that there is a sort of inherent time asymmetry in the description of the observer. I mean the observer is supposedly this Turing machine and so has some inherent time asymmetry. Do you see that as a plausible way of looking at that or do you think that’s something that we’d better avoid?
Vaidman
6. I think first that there’s no conceptual difference between the Everett way and this way. Everett just wanted to consider one observer and that’s what his world?.proved?. Every macroscopic object he is in contact with should be in a well-defined state……….......superposition. So I think you’re correct, it’s easier and more natural just to discuss this vector……quantum states which are close to observers. There are many events far away, it’s just a waste of time to think about them. So I think………..even better, more natural when you consider just local things, you just consider quantum systems which influence you and it’s relative state, of course the same story. Given the experiment, you will consider your forward and backward states for micro-particles.
The time-symmetric QW and the MWI
Speaker: Lev Vaidman
Floor speakers (in order of appearance):
Bacciagaluppi
Wallace
Lehner
73
[questions only]
Bacciagaluppi
1. [extended question as had prepared to be commentator] Apart from your speculation at the end you were saying maybe we should opt for the trivial?..two-states?..for the universe and your argument was otherwise we would get effects from the ABL?..rule. Now, I’m just wondering about a slightly different way of seeing things which - I won’t insist on it but it may be something to have a look at. So if we take a different psi-final [going to board] and have a psi-initial which are different, there is a natural way of trying to define a many-worlds interpretation would be following …Gell-Mann, Kent and Hartle by setting up a two-vector decoherence condition so, real part on a trace of psi-f, v-alpha n of t-n….[continuing description of expression being written on board]..this thing different - equal to zero for different histories. Now, by the way, Gell-Mann and Hartle show that if the initial and final state are pure this is a very restrictive condition so they suggest to consider mixed states. But I’m also wondering if one shouldn’t try the following. Especially in a many-worlds interpretation in which probabilities should be understood along the lines of Deutsch and Wallace as guiding the acts of agents that are branching - is it the case that we should expect in general an agent to have access both to psi-initial and psi-final? Should we expect the probabilities to be well-defined according to this rule, defined by a psi-initial and psi-final or shouldn’t we rather expect that we might have different kinds of agents with different arrows of time and then have something like: it’s only the marginals of the probabilities that should be defined for different kinds of agents and we don’t really worry if we don’t have decoherence with respect to two states. So, the idea would be that if we are initial observers we average over the final state and vice versa. Something like that; just two small comments, of course it would be difficult to study this in complete generality but maybe in bi-partite systems we’ve got Alice and Bob and Alice and Bob only have a classical communcation channel and they have…..directions of time…well-known by Barnum et al, the most general probability measure for setups of this kind are more general than the quantum states and that may be related to the possibility of different arrows of time and anyway I think this would be a good setting to study it.
Vaidman
2. I was trying to tailor - looking at a simple example with one beam-splitter this boundary condition in the future which are different from just …..And I saw how many disasters they caused. So, it’s really not simple to get a single time error and still have something non-trivial different in the future. Maybe I should mention one example which is not proper for this conference because it’s really to make a single world out of this theory, and this is Ahronov’s conjecture that there is…………..quantum states, a very special one. It’s really this one [indicating on board]: we go to the end of the universe, we go to a particular branch and we take one of it and we put it backwards in time. The picture will not be like this, there’ll be many red things going on all over but the overlap, he believes, and fits the time is not too long, we really single-out one trajectory, our world, and by fiat we’ll have right probabilities, everything is correct, and I think it’s better than collapse, I don’t think it’s better than the many-worlds interpretation because it’s very special, I take a very special final condition. So, unless you take a mixture, for a mixture everything goes, you take a mixture from here, a mixture from there, everything correct comes together and it does not……our experience. Maybe it’s a little too much because it takes everything, not only all many-worlds, multiple worlds, you can split them in different ways; in a mixture you can do whatever, like teleportation. You can teleport one state it’s free to several?..worlds, you can teleport another state and it makes…..in many other worlds.
[new question]
Wallace
3. A quick comment. You gave good reasons for not wanting two vectors for the whole universe……if I’ve got this right, the difference between a forward and backward-evolving vector is the forward-evolved vector we evolve from the measurement forward and then shift?..the backwards is the other way. And also the whole universe………measurements……in this context, in the case of the whole universe we’ve got no measurement so the initial state evolves forwards to the end of time and the second?..state evolves back to the beginning of time and of course the Schrodinger equation is time-symmetric, the Schrodinger equation doesn’t come with a little arrow built in, so actually, if we had two states of the whole universe we really just have two states both evolving through time in whatever direction together and there………something redundant about what’s going on there. So I think the naturalness of making this forward/backward-evolving thing does rely on these……unusual?..steps.
Vaidman
4. First, it’s kind of tricky. The measurements are inside, everything is unitary so measurement is just macroscopic objects coming to microscopic objects and separating microscopic…..distances or states. So, in fact I first put this argument that I have to put another source and then I said my probabilities are wrong. I’m not very strong about this probability wrong, because probably if put some different final states it will kind of wash out and I will not know now, the probability might come out correct because we have this macro?scopic object in each branch, this wave function is the same so it’s not completely clear but anyway it’s very difficult to tailor consistently the…middle?.state, what about the error of time. So it’s not simple; the only thing which I know it works it’s a complete mixture or a single branch probably.
[new question]
Lehner
5. An interesting way I think you can think about that is in terms of Everett’s relative state picture, that the backwards vector in time is just a relative state of subsequent observation. That there’s nothing sort of unnatural about ascribing - there’s nothing that tells us in the Everett story which of the two relative states we really should pick for the description of anything that happens in between, so you also get that symmetry. In Everett’s case, what takes care of the….that there is a sort of inherent time asymmetry in the description of the observer. I mean the observer is supposedly this Turing machine and so has some inherent time asymmetry. Do you see that as a plausible way of looking at that or do you think that’s something that we’d better avoid?
Vaidman
6. I think first that there’s no conceptual difference between the Everett way and this way. Everett just wanted to consider one observer and that’s what his world?.proved?. Every macroscopic object he is in contact with should be in a well-defined state……….......superposition. So I think you’re correct, it’s easier and more natural just to discuss this vector……quantum states which are close to observers. There are many events far away, it’s just a waste of time to think about them. So I think………..even better, more natural when you consider just local things, you just consider quantum systems which influence you and it’s relative state, of course the same story. Given the experiment, you will consider your forward and backward states for micro-particles.
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.
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.
Transcript discussion Albrecht
July 20 17.45
Probability without time
Speaker: Andreas J. Albrecht
Floor speakers (in order of appearance):
Barbour
Saunders
Brown
Maudlin
Albert
Hartle
83
[questions only]
Barbour
1. I’m going to attack you head-on right at the start, I think you’ve got the totally wrong idea of what a clock is. I think the whole idea of an internal theory for a clock has been a total and utter disaster. You only have to look back over a century to see how astronomers solved the problem of determining what time is to see that the internal time idea is just nonsense. When the astronomers had a problem with the motion of the moon there were two alternatives: one, the theory of gravity was wrong, the other was that the Earth wasn’t rotating uniformly. And they guessed that it was the second. So then they said where do we find a reliable clock? And they said we are going to assume that the solar system is a closed dynamical system and they realised that there was only one single sensible time variable they could choose, it’s the time variable that conserves the energy of the solar system. And that actually in 1937?.was confirmed as the only sensible one and for two decades that was actually the official standard of time. Now, when you say that clock is a localised system that is completely true, but it is a very special localised system to make sure that it keeps time with that time that is defined by the solar system and for finding what is a good clock, the definition of a good clock is that you must have clocks that keep in step with each other, and it’s got to be, ultimately, the complete universe that is going to provide the standard of time. And in any individual degree of freedom or subset of it can never do it. Therefore I think the whole programme with internal time was misguided from the start, and Brice was I think the first person to introduce this with his paper in ’67, and I’ve twice asked Brice “What is a good clock?” and he said to me it’s what the National Bureau of Standards tells me keeps time to a good accuracy, and I said to Brice: it’s your job as a theoretician to tell the experimentalists what a good clock is, not vice versa.
Albrecht
2. But once I’ve got?..my future I’ve got clocks coming out of my ears so that’s not a problem. So the way to attack this is to find something wrong with the premises because this is what everyone does
Barbour
3. ……[short phrase]..
Albrecht
4. No, no, but poke a hole in it.
Barbour
5. I already have done because you’re not defining clocks properly.
Albrecht
6. What you’ve described is some…..co-ordinate of the physical state and then you can carry the rest with it
Barbour
7. …chosen very carefully..
Albrecht
8. I’m totally into choosing it carefully, that’s what half this talk is about.
Saunders
9. …choose it randomly!
Albrecht
10. Well, then it lucked out that I could choose it randomly and still get my field theory out. I didn’t even expect that. That’s a really remarkable thing. I thought I’d choose it randomly, get a bunch of crap and then say okay, well, but that’s such a terrible clock and I’m going to throw out most of the random things I see and then hunker down and choose some good ones and take it from there, but remarkably just random junk is giving a field theory as much as I seem - so I think that’s a remarkable result.
Brown
11. This reminds me of the issue………….[faint]……Julian’s saying that when you choose subsystems as clocks you choose them very carefully. If you don’t choose them carefully you can still do physics, it just becomes horribly complicated but that doesn’t threaten the nature of physics itself, it just means that you’ve chosen clocks that make the equations look very, very complicated. And what I’m trying to understand is: this threat that you raise when you show that there’s this ambiguity in the choice of clocks, is it any worse than the issue that …[name]….was raising?
Albrecht
12. Well, it’s worse because you name a perfect Hamiltonian that has a well-defined time and I can pull it out of this junk. And it can be completely different from the one everyone’s working hard with particle accelerators to find, and it’s on a completely equal basis to that one, and it’s just as good. So, yes, there’s lots of junk and the remarkable thing, a little bit distracting, is that is seems like it’s easy to find something interesting in almost all the junk. But that set aside, even if that’s too-naïve an account of what I’ve just shown you, even if most of the junk is just junk, there’s still all the good stuff that’s in there. You name good Hamiltonians, it’s all in there, apparently on an equal basis to the one we’re working so hard to construct in our attempts to understand the world around us.
Maudlin
13. I think this is the same question, let try to do it from a different angle. You said there was a big disaster…………….So, Galileo needed a good clock, right, for doing his inclined-plane experiments; I’ve heard different stories, sometimes it’s said that he used………..water clocks and stuff and when I hear the beginning part of your story it sounds like here’s a really horrible…………clock, suppose you chose a hamster and then you had a bunch of hamster states……when the hamster does this it will be time 1 and when the hamster does that it’ll be time 2 and you started rolling a ball down a plane and said, hey, I’ve got nothing here, right….
Albrecht
14. That’s the same question and I’ll give you the same answer
Maudlin
15. But I don’t understand the answer, it doesn’t seem like there was ever such a disaster, the only disaster would be, I mean, Einstein used to say it was a mistake, or incorrect, to believe you could have a theory in which measuring instruments, clocks and rods, were primitives…..Now it sounds like you’re saying, well, I’m not going to……….I’m going to choose a brain and see what happens, and then you get, of course some disaster….I guess the question I have is: that disaster seems no surprise at all, I thought there was a disaster I never thought of…….when you choose a …..you’ll get a mess
Albrecht
16. You will get good clocks when you choose, and you’ll have a chance to get good clocks; I’ve argued it’s a better chance than I thought it would be…..chance of getting very good clocks and, when you do so all possible good Hamiltonians, very accurate, well-behaved laws of physics are seen to be on an equal footing. All the garbage is in there too but the good stuff is good regardless of what results you get from CERN..
Maudlin
17. You’re telling me there’s some weird clock that if I use it I’ll get good-looking results, but I have no reason whatsoever for choosing.
Albrecht
18. Right, so you can take a very anthropic view and say: I’m just going to look at this Hamiltonian, look at this random process of defining my physical world and just throw things out unless they match exactly what I see, so you’re just fixing all the parameters based on data that you have and that’s that. I think you can do that but I think this is saying that..
Albert
19. Isn’t the name of that ‘…..from our experience’? …..
Albrecht
20. But you want predictability, you want……this is my Hamiltonian and then you say there’s this extra term, you say, no, it’s not that, it’s not my theory of physics but in fact………one of the extra terms waiting to be pulled out; it’s all sitting in there in the theory waiting to - they’re all on an equal footing, the question is: do you have any principles of physics that inform the kind of theory you can build and if you don’t then you’re just fitting data and it’s fine, everyone’s happy, but this undermines having principles of physics like field theories and so on that constrain how you build your model; it removes all constraint from how you build your model.
[new question]
Hartle
21. I just thought the usual definition in classical physics, the definition of a ……as something that is correlated with the time supply of my metric in spacetime. I would have thought the definition of a clock in quantum mechanics was………….mechanical system that was correlated with some……….This is somehow different from that?
Albrecht
22. Well, it’s saying that in your super-space, if you dig around for good clocks in that sense, no matter how hard you try to set up your super-space to reflect the laws of physics as we know it, with standard model, blah, blah, blah, the process of finding the clocks wouldn’t give any preference to that model that you put in. That you just as well get O3 model out or another model out. So that’s it.
Probability without time
Speaker: Andreas J. Albrecht
Floor speakers (in order of appearance):
Barbour
Saunders
Brown
Maudlin
Albert
Hartle
83
[questions only]
Barbour
1. I’m going to attack you head-on right at the start, I think you’ve got the totally wrong idea of what a clock is. I think the whole idea of an internal theory for a clock has been a total and utter disaster. You only have to look back over a century to see how astronomers solved the problem of determining what time is to see that the internal time idea is just nonsense. When the astronomers had a problem with the motion of the moon there were two alternatives: one, the theory of gravity was wrong, the other was that the Earth wasn’t rotating uniformly. And they guessed that it was the second. So then they said where do we find a reliable clock? And they said we are going to assume that the solar system is a closed dynamical system and they realised that there was only one single sensible time variable they could choose, it’s the time variable that conserves the energy of the solar system. And that actually in 1937?.was confirmed as the only sensible one and for two decades that was actually the official standard of time. Now, when you say that clock is a localised system that is completely true, but it is a very special localised system to make sure that it keeps time with that time that is defined by the solar system and for finding what is a good clock, the definition of a good clock is that you must have clocks that keep in step with each other, and it’s got to be, ultimately, the complete universe that is going to provide the standard of time. And in any individual degree of freedom or subset of it can never do it. Therefore I think the whole programme with internal time was misguided from the start, and Brice was I think the first person to introduce this with his paper in ’67, and I’ve twice asked Brice “What is a good clock?” and he said to me it’s what the National Bureau of Standards tells me keeps time to a good accuracy, and I said to Brice: it’s your job as a theoretician to tell the experimentalists what a good clock is, not vice versa.
Albrecht
2. But once I’ve got?..my future I’ve got clocks coming out of my ears so that’s not a problem. So the way to attack this is to find something wrong with the premises because this is what everyone does
Barbour
3. ……[short phrase]..
Albrecht
4. No, no, but poke a hole in it.
Barbour
5. I already have done because you’re not defining clocks properly.
Albrecht
6. What you’ve described is some…..co-ordinate of the physical state and then you can carry the rest with it
Barbour
7. …chosen very carefully..
Albrecht
8. I’m totally into choosing it carefully, that’s what half this talk is about.
Saunders
9. …choose it randomly!
Albrecht
10. Well, then it lucked out that I could choose it randomly and still get my field theory out. I didn’t even expect that. That’s a really remarkable thing. I thought I’d choose it randomly, get a bunch of crap and then say okay, well, but that’s such a terrible clock and I’m going to throw out most of the random things I see and then hunker down and choose some good ones and take it from there, but remarkably just random junk is giving a field theory as much as I seem - so I think that’s a remarkable result.
Brown
11. This reminds me of the issue………….[faint]……Julian’s saying that when you choose subsystems as clocks you choose them very carefully. If you don’t choose them carefully you can still do physics, it just becomes horribly complicated but that doesn’t threaten the nature of physics itself, it just means that you’ve chosen clocks that make the equations look very, very complicated. And what I’m trying to understand is: this threat that you raise when you show that there’s this ambiguity in the choice of clocks, is it any worse than the issue that …[name]….was raising?
Albrecht
12. Well, it’s worse because you name a perfect Hamiltonian that has a well-defined time and I can pull it out of this junk. And it can be completely different from the one everyone’s working hard with particle accelerators to find, and it’s on a completely equal basis to that one, and it’s just as good. So, yes, there’s lots of junk and the remarkable thing, a little bit distracting, is that is seems like it’s easy to find something interesting in almost all the junk. But that set aside, even if that’s too-naïve an account of what I’ve just shown you, even if most of the junk is just junk, there’s still all the good stuff that’s in there. You name good Hamiltonians, it’s all in there, apparently on an equal basis to the one we’re working so hard to construct in our attempts to understand the world around us.
Maudlin
13. I think this is the same question, let try to do it from a different angle. You said there was a big disaster…………….So, Galileo needed a good clock, right, for doing his inclined-plane experiments; I’ve heard different stories, sometimes it’s said that he used………..water clocks and stuff and when I hear the beginning part of your story it sounds like here’s a really horrible…………clock, suppose you chose a hamster and then you had a bunch of hamster states……when the hamster does this it will be time 1 and when the hamster does that it’ll be time 2 and you started rolling a ball down a plane and said, hey, I’ve got nothing here, right….
Albrecht
14. That’s the same question and I’ll give you the same answer
Maudlin
15. But I don’t understand the answer, it doesn’t seem like there was ever such a disaster, the only disaster would be, I mean, Einstein used to say it was a mistake, or incorrect, to believe you could have a theory in which measuring instruments, clocks and rods, were primitives…..Now it sounds like you’re saying, well, I’m not going to……….I’m going to choose a brain and see what happens, and then you get, of course some disaster….I guess the question I have is: that disaster seems no surprise at all, I thought there was a disaster I never thought of…….when you choose a …..you’ll get a mess
Albrecht
16. You will get good clocks when you choose, and you’ll have a chance to get good clocks; I’ve argued it’s a better chance than I thought it would be…..chance of getting very good clocks and, when you do so all possible good Hamiltonians, very accurate, well-behaved laws of physics are seen to be on an equal footing. All the garbage is in there too but the good stuff is good regardless of what results you get from CERN..
Maudlin
17. You’re telling me there’s some weird clock that if I use it I’ll get good-looking results, but I have no reason whatsoever for choosing.
Albrecht
18. Right, so you can take a very anthropic view and say: I’m just going to look at this Hamiltonian, look at this random process of defining my physical world and just throw things out unless they match exactly what I see, so you’re just fixing all the parameters based on data that you have and that’s that. I think you can do that but I think this is saying that..
Albert
19. Isn’t the name of that ‘…..from our experience’? …..
Albrecht
20. But you want predictability, you want……this is my Hamiltonian and then you say there’s this extra term, you say, no, it’s not that, it’s not my theory of physics but in fact………one of the extra terms waiting to be pulled out; it’s all sitting in there in the theory waiting to - they’re all on an equal footing, the question is: do you have any principles of physics that inform the kind of theory you can build and if you don’t then you’re just fitting data and it’s fine, everyone’s happy, but this undermines having principles of physics like field theories and so on that constrain how you build your model; it removes all constraint from how you build your model.
[new question]
Hartle
21. I just thought the usual definition in classical physics, the definition of a ……as something that is correlated with the time supply of my metric in spacetime. I would have thought the definition of a clock in quantum mechanics was………….mechanical system that was correlated with some……….This is somehow different from that?
Albrecht
22. Well, it’s saying that in your super-space, if you dig around for good clocks in that sense, no matter how hard you try to set up your super-space to reflect the laws of physics as we know it, with standard model, blah, blah, blah, the process of finding the clocks wouldn’t give any preference to that model that you put in. That you just as well get O3 model out or another model out. So that’s it.
Subscribe to:
Posts (Atom)