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]