Why I am not an Everettian

0:00 The speaker kindly allowed me to quickly promote the Einstein conference in a month at the beginning of March. This is filling up fast, folks. If you want to have a decent audience there of profound philosophers of physics like yourself, please register. I'm passing out these. There are only 100 seats, but you should register, otherwise you won't get a seat. So that's in 4th and 5th of March, a month from now. Um, having said that, it was a great pleasure to ask Wayne Nibble, who many of you know, who's been here for six months at the University of Western Ontario, to give a talk, a fighting talk, I would say, between the scholars, um, about why I'm not pedagogic. Thank you, Wayne. Okay, thank you. First of all, I'd like to say it's a rude pleasure to be invited. Thank you for appearing by the meeting, and, um, thank you all for coming. And, um... That's why I'm going to take a little discussion with Dorothy. I don't think of this as a fighting talk because the sort of, you know, fighting metaphor makes, you know, where you take a side and start swinging, makes any progress any time anyone learns anything, you know, a lot for someone. And if I come out of this talk learning that I really do have good reasons to believe the average. I think that that would be a wonderful result, and I can add some better chances with this audience from helping anywhere else. Those of you who were there for Michael's talk know we had Ernie as a guest there. Ernie is a little tired and couldn't make it, so we have some promises. I was told the name of the elephant is Griptow Elephant, but that's not quite a definite description for me of the name. My memory doesn't fail me. I think I had a kilt book when I was a kid with a character named Everett the Elephant. So, for the purpose of the talk, this is Everett the Elephant. We start with a summary of the whole talk, and then those of you who are convinced by the summary can... First thing, we talked about interpretations of quantum mechanics. And that makes it sound like there's just one physical theory and we're differing on how to interpret it.

2:30 And I think that that's a bit misleading. And I think if you look at the various things that get called interpretations of quantum mechanics, they end up making different claims about the world. We can nevertheless agree very closely on empirical matters for a wide range of stuff, but not necessarily all of them. And I think that's particularly clear in the case of dynamical collapse theory. The dynamical collapse theory will suppress certain kinds of superstitions that Schrodinger evolution will maintain. Experiment might be very, very difficult to do in practice because it's decoherent, but at least in principle there's an empirical difference because a special class theory will say there will be no interference where experiments or equations would say there is. So we're talking about not just different ways to talk about the same theory, we're talking about different theories. And when we're faced with a choice like that, you know, which one of these physical theories do we think is true? I think our only recourse is through empirical evidence. I don't, so let me just put my empiricist cards on the table right away. I don't think we have extra empirical recourses to knowledge about the world. I think, so I'm an empiricist in that sense. There are other kinds of claims that sometimes get associated with the name empiricism, which are often very anti-empirical. A priori claim that on the basis of no evidence whatsoever, the human mind is a blank slate of past, present, and future. That, I don't think, is any part of empiricism. In fact, that's something to be compared with. Not just in discussions of the foundations of quantum mechanics, but I think... Far too often in philosophy of science in general, either explicitly or implicitly in the background, there's a notion of how empirical evidence supports theories, which I think amounts to an excessively impoverished notion of what empirical evidence can do for us, and I think that it's best to the detriment of these...

5:00 And I'll be a little more explicit about what I mean by that a little bit later. And in particular, I think that the usual way of talking, or the common way of talking about the topology of empirical support, doesn't even come close to doing justice to the empirical support for quantum mechanics itself, let alone any other theory. The quantum mechanics is getting something at least approximately right, and I'll talk later about what that something I think is. And if I do it right, I'm hoping that all of that is going to seem, what they explain what I mean is going to seem fairly non-controversial. I attend most of the talks. When you make the move to the average interpretation, you actually lose that evidence that quantum mechanics is hidden from you. Hence the title of my talk. The title is Why I Am Not the Most Ever I Am. I use the first person and the present tense not just because I'm echoing Bertrand Russell's Why I'm Not a Christian, The issue I want to address is, what I'm not going to try to do is show that the other interpretation can't possibly be right. I'm not going to try to give reasons that would dissuade a convinced essayist from his or her convictions. The question I want to address is whether someone who, like myself, was not born believing in the other interpretation, Reasons to believe that it's true. Okay, so that's the talk in a nutshell. And I hope I managed to get through that in time.

7:30 What do I mean by the average term? It's just to be very familiar to some people in the audience, not so familiar to others. I'd like to start by quoting one of the greats in the Foundation for Quantum Mechanics. And, unlike Michael, I have no drawing ability whatsoever, so I have to regard the photographs. This, as some of you know, is John S. Bell, and in one of his papers, called Are There Quantum Genes? He said, Either the wave function is given by the Schrodinger equation or not everything is written on it. Well, to what extent the Everett interpretation boils down essentially to a denial of the claim. It says that the wave function as given by the Corrosion Equation is everything and it is regular. So there are two parts to this claim. It's a denial of the two parts of Bell's Disclosure. One is the ontological claim about the state of the system. There isn't going to be anything else except the wave function or the quantum state, however you happen to choose to represent it mathematically. I don't think it makes any difference. And then the dynamical claim is you've got Schroeder's evolution in non-relativistic cases, you've got the relativistic simulation, generalization, linear, unitary, deterministic evolution of the quantum state. Okay, what the heck would John Bell claim that the least one of these claims has to be wrong? Well, that has to do with the measurement problem. If you just go the linear approach to evolution, what happens? Well, if you've got a good measuring apparatus, what happens is, and you treat the measuring apparatus as a quantum system, which you're going to have to do because of the What would you get? Well, you start out with a superposition of the available being measured. You end up with a superposition, one term of which is this eigenvalue of the observable, and this reading of the Mecklen apparatus, etc. for all those terms of the original superposition.

10:00 And if you want to say, as we would naively like to say, well that can't be right. For the most determinant outcome of the experiment, the measuring apparatus really only reads one thing at the end, then basically you have to do one of two things. You either add extra structure and take out one of those terms of the superposition as the one that actually corresponds to what actually happens, or you say, well, no, The evolution that got us to that isn't actually quite right, and somehow or another there's some kind of collapse, a dynamical collapse evolution, which suppresses what all at one time was super-threat. And so that's the usual motivation for, you know, that's Bell's motivation for making the claims that he does. Interpretational programs do the key variables. Modal interpretations take the first form of Bell's dilemma and say, yeah, the wave function is everything, and then collapse theory, so you don't know if the wave function is everything at some point. Right. What does Everett do? Well, Everett says, nope. It is everything. It is right. How, then, are we supposed to think of the post-experimental state? Well, we're supposed to think of flexibility as a branching event into branches that, because of the decoherence, subsequently evolve quasi-independently, and very often people talk about these as different worlds, hence the term world interpretation. I don't think anything I'm going to say depends crucially on whether I think of these as all branches of a way of functioning, one big world and one large force of a world. Okay. And if that's right, then the world is quite different from the way we usually think. In particular, there's all these copies of me on all these various branches.

12:30 There are branches that correspond to all sorts of possibilities in which the world is very different from the way we think it is. And this has struck some people as some kind of metaphysical extravagance. I'm just giving you an example of the sort of criticism I'm not going to raise is some kind of appeal to Hoffman's razor or simplicity or something like that. This is just sort of ruled out from the very beginning. Not the sort of theory we should seriously consider in science. And if I may quote another one of the late greats, there's Newton as the philosopher... Can I not reveal that yet? The philosopher is saying that nature does nothing in vain and it is in vain to do with more than what can be done with fewer. Nature is simple and does not indulge in the luxuries of superfluous causes. It seems that... The Everett interpretation violates this methodological principle of independence because all these extra branches except the one we are on certainly does seem superfluous and there can be more branches that are absolutely necessary to account for what we experience. There's a nice paper by David and Harvey in which they argue that actually it's not at all clear that Occam's razor actually favors other interpretations rather than the Everett interpretation. I don't want to get into that issue at all. And the reason I don't want to get into that issue at all is because if I were to ask which of these interpretations Occam's razor rules out, It would mean that I would be according, I would think, I don't believe that Occam's razor is true. I don't believe the world is simple. The best response I know of to claims like this is that the world is more complicated than it needs to be in lots of ways.

15:00 There are many things that God does with more than he could do with fewer and, you know, that's just the way it is. But do I think? Well, I think, and this is, I think in terms of, you know, criteria and simplicity, the world is simple in some ways, it's complicated in others, and it's up to what faculty are doing in science to figure out which is which. And the only way we're going to do this is through empirical evidence. And I don't think, unless you can give me some kind of account of synthetic a priori knowledge, I don't think any expert for empirical principles are going to be able to work at all. And so, their interpretation tells us that the world is very different from the way we think it is. If I can, again, lay my empiricist parts on the table. Here's my empiricist credo. I think that we should just be prepared to accept that the world is very, very different from the way we antithetically think it is if given sufficient evidence. I think that, you know, we can even gain a case that every body gravity is equal to every other one, given enough evidence. And first I want to talk about what I think is an inadequate account of the relationship between mathematics and theory. And for want of a better name, I've called this the Resultivist-Mathematical Theory, to show confirmation. And the reason for deductivist is that it focuses on deductive relations between propositions of the theory and propositions of observational consequences. You deduce from the theory in conjunction with appropriate auxiliary hypotheses some observational consequences, compare those with what you actually observe, And that leads, naturally but not inevitably, to the notion that

17:30 If I have two theories compatible with the body of evidence, then they're equally well supported by the others. Now you can refine it to avoid that, but one thing on this deductive picture you're going to get is that two theories that have the same deductive relations to the body of evidence are going to be equally well concerned by it. And that frequently leaves us with a plethora of theories that we are going to regard as equally well-concerned. This is, of course, the piece of mind-doing problem. And at this point, what do we do? Well, one thing is you can say, well, that's it, you've got all these other things. But typically people then bring in extra-empirical criteria of theory choice. Simplicity, elegance, explanatoryness, and things like that. And again, the problem with this is trying to give an account of how we can reasonably take such criteria as being with any reason to think that theory is true or more likely to be true. Of course, one way to go is to go completely anti-realist and say that it makes sense to talk about theories being true or false independently of their empirical consequences, but what I want to know is whether we have any reasons to believe that the theory is true. The least controversial thing I'm going to say is that this is a completely inadequate picture of the relationship between evidence and theory. It is simply not true that you have two hypotheses that are both compatible with the body of evidence, or equally well supported.

20:00 And it's easiest to see, in the case of overtly sarcastic hypotheses, hypotheses that contain within them some kind of statement about the chance of something occurring. The simplest example I can think of is you've got a coin and you want to know if it's a fair coin or if it's a biased coin. What are you going to do? Well, you're going to flip the coin a number of times. I actually did this. Flip the coin a thousand times, and here's the result. Actually, I did a computer simulation. And I promise you that I either did the computer simulation with a weight of one half per head or a weight of two thirds per head, and just to save you some time in my counting of those, on that there were 637 heads and 350 tails. I think most of you now have an opinion about which of those two simulations I did. And I would claim that that opinion is not an arbitrary one, but you actually have good evidence for that opinion, even though both H1 and H2 are compatible with those results, in fact, any sequence of results would be compatible with both of those hypotheses. Nevertheless, I think we do think, and more or less we should think, that this kind of result more strongly supports H2 than H1. And if we do think that, then we don't think that if you all have two hypotheses which are both compatible with the M1-3, we will support each other. I actually don't think that the deductiveness metaphysical picture works much better in the case of deterministic theories either. But that's kind of a weak point. Because we so rarely actually confront deterministic hypotheses with experiments, what we actually compare to the results of experiments is almost always some kind of statistical hypothesis.

22:30 Even if you've got a deterministic theory, the model you're comparing to the actual results is going to be the deterministic predictions of the theory. Plus experimental error, where you're just going to assume you have some kind of chance of scripting about experimental error and you're going to normally just sort of do that, or you're going to get expectation value or something like that. Quine, the discretionary Quine, the new thesis, said you can defend any theory in the face of assuming you're counseling with evidence that allows you to work even through hallucinations. As a matter of fact, if you took this up to this picture, you would hardly ever have to go to such a resource because you could always put you in experimental error. It's possible that all those theories, all those statistical experiments that we take to be supporting quantum mechanics, The second account starts with the idea, Believing in a theory or any hypothesis or anything isn't an all-or-nothing affair. We can strongly believe in something, we can be very skeptical about something, we can sort of believe something else, but be weakly committed to it. And on the approach that I'm going to talk about, what we're going to say is we're going to model these degrees of belief.

25:00 Numerical degrees, of course, which already takes us out of the script of Brown. You guys don't actually all have numerical degrees fully to a million decimal places or a number of decimal places in anything at all. Analogously to deductive logic, which is a normative account, it's not a psychological account of how people actually reason, it's a normative account we can use to judge people's actual reasonings as rational or irrational or defective. The idea is to try and get canons of inductive reasoning, which is not to get as far as they want. There are arguments to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent that there are rationalities to the extent If those betting quotients don't satisfy the activities of the probability calculus, they'll be assessed as bets, each of which you individually regard as favorable to you, whose net effect is a certain loss no matter what happens. And if you think that someone in such a situation has made some kind of error in judgment, then... It follows that you think that avoiding errors in judgment means having degrees of belief that the answer is probably accurate. So, for these degrees of belief, I'm going to use CR called credences, and that's because there's a danger of multiplications of different kinds of probabilities, so these degrees of belief I'm going to call credences. All sets of credences satisfying the probability calculus are equally good, in fact I'm going to mention one particular constraint which I'm going to add.

27:30 Unlike some projects that are sometimes associated with the name logical theories and probabilities, I don't think that you can introduce a set of constraints that uniquely fit singles out of one correct probability assignment. And accounts like this often get called personal. And that makes it sound like we're rafting into some kind of psychological theory, some kind of descriptive theory, but once again, I see this as a normative account by which we would like to refine our judgments about what counts as good evidence and what doesn't count as good evidence. And I don't think the failure to single out a unique rational degree of belief means that we've made the leap from a normal theory to a discrepancy. The analogy would be, I think, with ethics, you know, ethics will tell you certain things are immoral, certain things are immoral, but could we do a range of actions within the realm of the morally acceptable? And the last element that we're going to use for this is that we're going to model a change of belief that consists of learning that a certain proposition is true and nothing else. It's going to be modeled by conditionalization problems. So your credence in a hypothesis H when we learn E is true is going to... Key terms may include, for example, mathematical physics, geometry, algebra, mathematics, algebra, I think that's it. Anyway, one of his books. He has a nice way to visualize the process of conditionalization.

30:00 What you do is you imagine the set of propositions, you visualize the set of propositions, you've got your frequencies defined by a Venn diagram, areas on the Venn diagram. You keep mud on the various areas proportional to your degree of belief in it, and conditionalization on E is just wiping off all the mud on everything that's not on E and then taking your degree of belief and then just setting the amount that's left after 1 so you normalize the results, and so within the space of things that... And there are arguments to the effect to the effect that a learning event like this ought to be modeled. I mentioned I wanted to use the word credence to create this belief. And the reason I want to do that is that I... I think if I just used the word probability there's a risk of confusing it with other things. There's a literature on interpretations of probability and that phrase interpretations of probability I think is equally as misleading as the phrase interpretations of quantum mechanics because it suggests that there's a univocal notion of probability that we're trying to capture. And that these various interpretations of probability are candidates for the correct explication of that univocal notion. And I think that that is not true. I think that there are a number of distinct and related, but related notions that we have traditionally called probabilities, or in history have been called probabilities. One is these degrees of belief, which I'm going to call creedences. Another has to do with physical chances. What do I mean by physical chances? The best way I know to explain it is to tell a story. And some of you will have heard this story before. This is, I mean, Richard Feynman's work here is helping Mr. Feynman.

32:30 Feynman tells the story of hearing that there's a person named Nick the Greek who makes his living as a professional gambler. That's impossible. He can't possibly make a living as a professional in a casino. And the reason for final skepticism is that he knows that in a casino, the odds favor the house. Even if the game is not perfect, even if it's not rigged, the casino can make lots of money because the games are so destructive, so the odds favor the house. He later meets Nick the Greek, talks with him, and realizes that he makes his living as a professional gambler not by betting against the house in the casino, but by standing around in the casino and making side bets with other patients. And since he's got this reputation as a professional gambler, he goes to Las Vegas and you tell your friends, oh, I knew. You know, I gambled with Nick Negreece. You know, this is an exciting thing to go home and tell your friends back in Peoria. So, you know, he gets lots of action that way, and so he gets offered lots of bets. And, upon talking to Nick Negreece, finally realizes, one, Nick Negreece actually understands probability theory quite well, and he knows the odds. All of these terms can be used to separate, if he could select, from all the bets that are offered him, the ones that are in fact stable for him and do quite well. What it means by fiscal chances is when Nick the Greek knows the odds, that's what he knows. And these are not the same as degrees of belief. Knowing his own degrees of belief or those of the other people around him aren't going to help him much. When he knows the odds on the chances of getting red on a roll of the roulette wheel, what a chance of getting an even number, whatever that is, that's a fact about the physical situation he's in. It's not just a fact about the roulette wheel, it's a fact about the process by which the roulette wheel steps on and the ball ends up in the thing.

35:00 What he knows is he knows something about that actual wheel. And it's not the same as frequency in the long run or something like that. It's not the same as degrees of belief, it's not the same as long run frequency, because Nick the Greek is not at all interested in frequencies in a hypothetical infinite run. We are interested in the finite sequences which consist of all that T is going to make in its lifetime. Often our evidence about these physical chances does come from relative frequencies and large, but not infinite, sequences of repetitions. And I think that that's caused some confusion. Another point I want to make is that even though a physicist will probably want to know a lot more about the physical processes that generate those chances, if the grease doesn't have them. He doesn't have to know a lot of physics in order to do what he does. He just has to know what those chances are, however they might happen to come about. And that's a very important point. In particular, he doesn't have to know whether the underlying physical theory is deterministic or not. But I think that these physical chances could very well come in two types. One is, and it could be that at bottom, our fundamental physics theory has I think that is a perfectly intelligible concept. It doesn't seem to me any more problematic than the notion of a deterministic law of nature. Some people might disagree with these terms, but we should be brought up during this period.

37:30 And now, classically, things like throw-up-and-die and spin-over-the-wet wheel have been thought of as being generated by underlying deterministic dynamics. And the reason for variation in from spin to spin of the roulette wheel is that the initial conditions of the setup are slightly different from time to time. And moreover, you construct the setup so that someone standing around cannot possibly know enough about the initial conditions So you might say, okay, we're getting suggestive again, we're talking about ignorance, but that fact, that fact that that information is not available, the physical set up itself obscures that information, is a fact to get at about the physical situation. I mentioned relative frequencies in ensembles because there has been an attempt to develop a frequency theory of probability. The reason it doesn't get off the ground is at heart, whatever lies in our various attempts to make these frequencies of probability are various lots of large numbers that tell you that, for example, if I flip a coin, a fair coin, an infinite number of times with certainty the relative frequency of n will approach 1. The reason I can't just replace all talk of probability or chance with the long-run frequency is because when I said that, when I said with certainty, what I meant is with chance one.

40:00 And the very statement of the theory and the proof of fact theorem involves a notion of probability or chance which is distinct from the long-run theory. But nevertheless, relative frequencies and ensembles are important because they are what we use to test things and look at them. And another thing that satisfies the axioms of probabilities is on the average interpretation you've got the norm squared away for Francis. And I think... These are all intelligible concepts and I think despite us, I think they're all distinct concepts. And so I'm not going to use the word probability for any of them. You can keep a, say, a terminology distinction, you know, out in some time. I would like to. Why doesn't the book come in two Ds? Okay. Okay, okay, here's why. The dynamic is deterministic, but in the case where I'm talking about, in the Rebecca case, there are distinct outcomes on each spin of the wheel, which are due to differences in initial conditions. The better is if you don't have enough knowledge of the initial conditions to know which is which. Now when we're talking about the effort insertion, typically, it's not uncertainty about the initial state that we're talking about. Even if you know with absolutely certainty what the initial state is, when you do an experiment, it's going to divide into these various branches with different weights. So yeah, so there's a conceptual distinction. However, on the average interpretation, these guys are going to be playing much the same role as physical chances do in other things.

42:30 You didn't have that little bit about systemic stuff written down. That's what I was suggesting. Okay. Well, I'm glad you did. To provide evidence about chances on the usual interpretation. And I might be going to go through an example which might strike some of you as excessive detail. And nothing in this example is going to be new to most of you. The reason I'm going to go through it is I want it to be fresh in our minds, in the forefront of our minds, when we're talking about evidence for quantum mechanics. So I take a simple example of trying to get evidence for quantum mechanics. Again, let's go back to the coin toss. Go back to that original thing. I've got some coin toss. It's got some unknown chance of heads on each individual toss. Well, I mean, actually, this will be sort of a model for an example of how evidence is handled on the sort of picture that I'm trying to present. So you start with some kind of degrees of belief over what that is, and for any sub-interval of the unit interval, you're going to have a certain degree of belief that the actual child you've landed falls in that. So, something of the form lambda in delta, where delta is a sub-interval of the unit interval, if you do think lambda is a feature of the coin toss, then the statement that lambda is a certain element is a certain interval, then that is a statement about the physical situation, and you can have a certain degree of belief about it. Since we've got a continuous range of possibilities for lambda, we can have a density function which generates those degrees of belief. Okay, this time I actually put the point to the tenth time. That is the actual sequence I got. The tree has seven tails.

45:00 The reason I took the coin is if you're trying to make something up, you make it far too regular and you end up not having, you know, this is, this is, and I thought it'd be, you know, not such a long season to put it up to use or something like that, but anyway, that's what I did, and what I said is we're going to update our credences about those sciences by conditionalizing on that result. We need to know how we're going to assign things like this. And here comes in a statement which David Lewis calls the Principle Principle that says if you know for certain that this coin that you're about to toss has a camp head coming up, then the degree to which you believe that it's going to be head is one half. It doesn't say. Whatever the challenge. Yes, yes, yes. Whatever can't, it equals to the can. So if I know it's a fair coin, then I should agree, I believe, to agree one half is going to come up here. And applied to this means that, so for any x, if the actual value of lambda is x, What's the chance of getting this particular sequence? Well, if 1 minus x times x times x times 1 minus x becomes your independence, and so if x is the actual chance and m is the number of heads and n is the number of tails, x to the n times 1 minus x to the n is the chance of getting that sequence, and The chance that lambda is in a certain interval and we get that sequence is just that. It's the weighted average of those over the 5 plus the weighted average prior to the other chance. And so that gives us that.

47:30 What we're doing is when we conditionalize on those results using the principle-principle, our initial density function just gets multiplied by this likelihood function there, xn times 1 minus x. And what does that look like? Well, this likelihood function, not surprisingly, is peaked around the actual relative frequency of heads. And it's more sharply peaked, the larger the total number of. So for this particular example that I used, that likelihood function looks like that. If you've gotten the same relative frequency in a thousand trials, it would be peaked around the same value, but it would be a lot more sharply peaked. That's how you update your credences about the values of the chance. If, hypothetically, you started out in complete ignorance about the value of the chaos, you just have a flat density function to start with, and your final density function would end up looking like the likelihood function. If, maybe because it looks like a fair coin, no obvious asymmetries, if you initially had creases which are peaked relatively sharply around one half, Now, if you have a lot of evidence about the chance, then a few point boxes could change it too much. One of the reasons this isn't a bad way to update your increases is that now we get to apply lots and lots of large numbers and say if you do this enough, Well, if you did it an infinite number of times, then there's a chance as one that the observed relative frequency would end up converting on the actual chance and chance zero of anything else happening.

50:00 Of course, in the long run, we're all dead. But the neat thing is that for large numbers of trials, we end up with very sharply peaked credence functions. No matter where your priors start out, sufficient number of posses is going to end up you with posterior credences about the chances, which are fairly sharply peaked around the zero delta frequency. That is provided that you didn't have excessively dogmatic priors, which is some kind of probability zero to some interval in which you actually end up having to lie for that. The excessive dogmatism. I told you I wasn't going to treat all prior degrees of belief as equally reasonable. Constraint number one is the principle of principles, which isn't dictated by the acting of the problem alone. Which is, be prepared to accept what the evidence tells you, so don't start with unwarranted, dogmatic initial beliefs. Now we're talking about error. On any of the usual ways of considering probability, there just isn't any room for that on the average interpretation. If you know the initial state, you know what the final state is going to be. And, you know, there are going to be things like chances in this seminar that I've been talking about. You will certainly have degrees of both beliefs, but if you know the initial state and you know the dynamics, you don't plan to be uncertain about what the final state is.

52:30 There will be other circumstances where you are going to be uncertain about possible outcomes later. But from the end of the interpretation, we do an experiment to the initial state. There's just one possible outcome, granting of the weight function. If I'm acting on the evidence-based and asking the question, what's the probability that this result will be the result that will be observed, I think in every opinion we'll have to say, well, that video comes first. And it presupposes that one of these results is going to be the result that's observed. And the answer, I think, needs to be that, no, the results are saying it's the result that's going to be observed. Typically, when I'm doing an experiment, I will survive the experiment and hence will have successors on all these branches which count, there's nothing but the wave function, if we take a physical account of consciousness, every one of those successors is going to count as And so on one branch, my future self is an observant. On another branch, my future self is an observant. And that's the only thing that can happen. Yes. Thank you. Yes. Thank you for that qualification. Yes. And we'll talk a little more about that. Okay. We talk about this as a problem of interpreting probability in the Everett Interpretation, and that again I think is a bit misleading because it makes it sound like if I've got a probability statement like this there's some lack of things to put in for the value of the probability. And I actually think that the problem is a lack of appropriate things to be the argument of the probability function. If CI is the outcome that's going to be observed, it's just simply not true that exactly one of those is going to be an accurate description of the outcome.

55:00 Now, one thing that every professor could do is just say, well, so much that works for probability. All the topic probabilities that we had just came from a mistaken idea of what was going on in an experiment. And the reason there's a problem with that, the reason that I think that the Everett Institute should not do that, is that an awful lot of the evidence for quantum mechanics is statistical in nature, and if we abandon anything at all like probability talk, it seems that we don't get to invoke all that statistical evidence as evidence for quantum mechanics. And if we don't have evidence of quantum mechanics, we'll have to actually talk about interpretations of quantum mechanics in the first place. It's not that quantum mechanics was advanced as a sort of skeptical hypothesis by some classical physicists that we might need to study with. We're here talking about interpretations of quantum mechanics some 80 years after the inception of the theory is because we think we have Evidence that in some sense, quantum mechanics is at least approximately the right physical theory. Okay. So, decision theory for the rest of you. And I'm going to present how I see the decision theoretic, how I see the decision theoretic move. And some people in the room are probably not going to be very happy with my description of it. We'll think about that later. Unusual interpretation of an experiment. We usually think that at the end one and only one of these alternatives is obtained. Quantum mechanics gives these chances and if I attach certain values to those alternatives

57:30 If these consequences are consequences of me making a bet, then I should value that bet by the chance-weighted expectation value. And quantum mechanics by the form rule tells us how to evaluate those chances. You've got a certain outcome of the experiment, which is namely branching. We should value that certain outcome, i.e. the branch state, by the same amount. And what these weights end up being are degrees of concern for the state of affairs on various branches. If that analogy is in classical decision theory, I can always take a chance setup which has a certain value and replace it by a best of equal value where I just give you the expectation value no matter what happens. And so the idea behind this is if you do that and you value the outcomes on those various branches by amounts proportional to the funds. The non-square weights of them. They can make all the same decisions that someone would who thinks that these are actual chance events and there is a unique outcome. And that's really neat. And I think that we should not underestimate the importance of this move. I think this move goes a long way towards making sense of the evidence interpretation. Typically, in the literature so far on disorders and people talk about the special case where the quantum space and the dynamics are known with a sense of certainty. That makes perfect sense. That's a good place to start. But we don't want to end up there. Because we want to be able to extend the theory to the account of cases where you don't know the initial quantum space or certainty.

1:00:00 Or maybe you did know the initial state with certainty, and a branching event has occurred, but you don't yet know what branch you're on. That, of course, will happen. I mean, it will happen in every experiment, because typically, the way a function has branched, the co-cranic appearance is set in before anyone actually knows what the result of the experiment is. So we didn't have time. Did we start at 2 minutes late? We did. The question is, how do we incorporate degrees of belief about, say, what branch you're on, and the quantum space. So I suppose I've just done an experiment, haven't yet looked at the results. There's a matter of, I am actually, you know, me, the consciousness is saying this, am actually determinately on one of the branches or another, and I just don't know which. We should be able to answer the question, to what degree should I believe in these various alternatives? It might seem that the answer to that question is just completely unconstrained. I'm more likely to be on a high weight branch than on a low weight branch. Does that make sense in every context? How do I deal with that? It turns out, and I'm not going to go through the details of this argument, but I've prepared a handout for that. I think that you can actually give a good argument that the average human in such a situation should assign credences about what branch he or she is on, proportionate to branches. And in a nutshell, here's the argument. If you're going to make it to the matching, compare two betting situations. One where you make a bet before the branching event and I think it's reasonable to say that for any particular value of the betting quotient, that first bet is favorable for the agent, if and only if the other one is, or the second one is.

1:02:30 And if the second bet is made according to an epistemically averaged expectation value of the weight of the unknown branch that you might be on, and the one bet is favorable if and only if the other one is, then those credences you have about which branch you're on are going to have to be proportionate to the weight. Intuitively here, I think, here's the way I think of other beliefs, and this might be a contentious way of putting it, is the ever-at-the-end thing. Well, I don't know which branch I'm on, but my subsequent actions matter more if I'm on a high-weight branch than on a low-weight branch, so I better act as if I believe more strongly I'm on a high-weight branch than on a low-weight branch. If you start out with, that was a situation where I knew the initial state and I just didn't know what branch I'm on, but similarly you might have some uncertainty about the initial state and do kind of an experiment to try and find out the information about what the initial state is, so you don't know what the initial state is, you do an experiment and you observe the results of the experiment, i.e. you find out which of those resulting branches you're on. And a similar argument shows that you should update your credences about the initial state pretty much the same way as someone who was going through conditionalizing all the evidence, like in that coin toss that I referred to. They thought the details were on the handout. Okay, now I'm getting to the point. Pretty much all we need to solve what you might think of as the evidential problem. How do I get to say that the observations we have so far count in the absence of physical chances?

1:05:00 You know, can we turn these things, these weights which interpret the carrying measures, which play much the role of physical chances in the evidence interpretation, can we argue that they can play that role in returning the observed relative frequency into the evidence that quantum mechanics is right in the first place? And, that's it. It looks like we've got a solution to the evidential problem. The argument I'm about to give I hope sounds convincing, but then I'm going to claim that we should resist the temptation to be convinced by a psychology of science. On this picture of confirmation that I've been talking about, I want to know whether body of evidence supports a hypothesis. The evidence, what would be a reasonable degree of fully in the hypothesis. And it might not be unique. It might have a certain range. And then I, so let CR be any one of those possible multitudes of previous functions in regard as reasonable for someone who doesn't know the answer. And you ask yourself, Given such a credence function, does conditionalizing on the evidence boost the credence of the hypothesis, i.e., you ask yourself, is this quantity bigger than 1, less than 1, or equal to 1? If it's equal to 1, then conditionalizing on the hypothesis doesn't change the credence. The evidence doesn't support the hypothesis at all. If it's less than one, then the evidence actually counts against the hypothesis. If it's a lot bigger than one, then we'll say the evidence strongly supports the hypothesis. And what we're interested in is comparing the relative degrees of support of two hypotheses. And by Bayes' theorem, those, I guess, will be proportional to the likelihood.

1:07:30 The credence of the evidence conditional on the hypothesis. Okay. Well, good. Let's use this to compare the degree of support quantum mechanics gets on some kind of interpretation, on something like the usual interpretation versus the degree of support that it gets on average. So, your main, say, QM average is quantum mechanics on the average interpretation. QM-chance is some big set of hypotheses, quantum mechanics, with born-rules chances, chances interpreted in the usual sense, and let E be some body of specific results within the first theory. And the usual born rule tells us what the chance of E given QM-chance is. The principal principle says that the conditional credence of the conditional intuitive enchantment is equal to that, and on any reasonable credence function, that's going to be a lot bigger than the prior degree. If you don't have that body of evidence that we take as supporting quantum mechanics, would you expect these experiments to come out exactly with quantum mechanics, that's a close, you know, with the high-cancer results? Well, no. I mean, that's why no one believed quantum mechanics prior to, you know, with evidence for it. Eight-seventeen century physicists were not, you know, people were surprised. When they had experiments, they gave different results from the last one. So, claiming that that's a lot bigger than that, hence the ratio of the two seems to be very high. If we get, all we need is the degree of credence in E conditional on QM ever is. Okay, what should that be?

1:10:00 I think if you imagine yourself, you know, the experiments have been performed, but you just haven't looked at the results, and I've never read any of you, the degree to which you believe that these are the particular results are going to be the degree to which you believe which branch you're on. What you know is that when all these experiments were performed, the wave functions branched into all these different waves. You have to look at the results, but you don't yet know which one of those branches you're on, and you want to know what degree of belief should you believe that you're on the branch, and what's this particular result. Well, what it said was that the ever-repeating Shutterstein Credence is proportional to the weights of the branches in pretty much the same way that someone who thinks of these weights is given chances of unique results. On the average interpretation, the weights of these branches are interpretive of degrees to which we should be concerned about. On the more standard interpretations, those weights of branches are the interpretative chances that that will be the unique outcome of the experiment. But an argument can be made that the apparition on a certain boat would grant you one should the sign was created proportionately late. Okay, well if that's true, then... The degree to which this body of evidence supports ever-riding quantum mechanics is exactly as high as the degree to which this body of evidence supports quantum mechanics on the Newton-Chamberlain area, which I already said is very high. Yay forever! I said, okay, I called that the siren song. I hope this sounds like a plausible argument to people, but I think that we should reduce the temptation to come to that conclusion.

1:12:30 A key point, when I said, well, how am I going to evaluate this, I asked myself, to what degree would an Averagian believe it, should an Averagian believe it or not. And that means treating that quantity, treating the neconditional unquantum evidence as something like the degree of belief I would have if I were to accept the Averagian interpretation. But that's not what that means, what I'm going to show. Way back when, I defined conditional probability just as credence of a conditional on b is just the credence of a and b divided by a and b. And they aren't going to be evaluated with respect to a credence function that someone who already accepts the average interpretation. We're imagining someone who doesn't yet know this evidence, who doesn't yet believe quantum mechanics, to what extent, what kind of credence functions do we regard as reasonable in those situations. And knowing what an Everettian would assign to these ideas doesn't tell us anything at all about what the values of these are. And in particular, there doesn't seem to be any reason to say that it's probably not right that a conditional degree of credence for someone who doesn't yet believe in quantum mechanics is equal to what the decision-theoretic approach to Everettian quantum mechanics tells us, and Everettian, I think, is a pretty good question.

1:15:00 And this is what that argument depended on. You might say, okay, that argument didn't work, but maybe I can do better. Well, maybe. Let me tell you why I'm a little bit skeptical. I think there's a deep-seated problem with turning those observed relative frequencies into evidence for quantum mechanics on the average interpretation. I said earlier that Nick Degree can know the odds, know the chances of outcomes without knowing much about the physics involved. And that's important. Chances, as we saw in the coin talking example, can be measured independently of any knowledge about physical theory that underlies them. The relationship between chances, the board rule can be experimentally confirmed or disconfirmed because I can measure these guys' chances of outcomes from experiments independently in quantum mechanics. I might use a lot of theory to interpret the results, but I don't have to use the theory of testing to interpret the results. That's why Kansas at least is normally construed and replaces them with these degrees to which a rational agent should care, and that's just not something that you can intelligently talk about being measured independently of the theory. In fact, the argument that Bilodar in fact agrees to which a rational agent should care about the branches These aren't arguments on empirical grounds but are arguments on normal grounds. The argument is the relationship between those quantum weights and degrees to which an irrational agent should care about the branches are meant to be arguments on the basis of conditions of pure rationality.

1:17:30 They presuppose the Everett Interpretation, their arguments about what an agent who is convinced of the quantum mechanics on the Everett Interpretation should do. And that makes them very different from the chances on the standard interpretation, which you can imagine... But compiling all this statistical evidence without saying, well, here, when you do this, you get this chance of this outcome, this chance of this outcome, we know this experimentally, darn it, we should come up with a theory to get those chances right and try to construct quantum mechanics. That means that you're thinking of these chances as features of the world that quantum mechanics is getting right, and because quantum mechanics is getting them right, We think that some of those measured values have a support for quantum mechanics. It's not clear to me what an Everettian can offer in this place. You know, is there some fact about the world? You know, quantum science is a degree to which every relation should care about these outcomes. So we can actually say, yes, now we have a theory to get those right. I have no idea. I have no idea who raised their hands first, but I think Simon did. Do I get to choose? You get to choose. I'm sorry, I meant to leave lots of time for discussion, and I'm sorry I didn't, but I suspect that this is a discussion that is not going to end today. I'm glad that we had a decent discussion. And I can't actually, I think I may not even address the most important point of it, but if I can give a gut response, it's that I don't quite understand the view that there aren't objective chances, that there are only rational degrees of caring.

1:20:00 And I think it's a very different point of view, which says that sure, there are objective chances. Ratios and weights, branches and so forth. And that's what probabilities are, you know. This is what people have turned out to be, a stroke or something like that. But then there's the further question about mathematical deliberation, judgment and so forth. And all of that is addressing the question of, well, good grief, that's just so unlike what we thought chances would turn out to be. There's a credibility problem here. And that's what the decision-making stuff is really addressing. Now, I guess where this starts to get a grip on your talk is actually fairly early on, in that you made the point, the question, what is the probability that C.R. Newton's result will be observed, you know, in answer to just a badly posed question to everyone. Well, I don't think it's that badly posed. I mean, it's just that it needs to be unpacked a little bit, and it's irrelational. This is my take on it anyway. When we ask what is a probability of something, there's an implicit context relative to what context. And the answer is different depending on the context. And if we're talking about time-like related events, then the answer is a probability of two and so forth. So, you know, it's just not that we're forced to this view of what we're talking about in actual judgment. We're just talking about physical planets. There's no real difference there. It then comes in a very special context, the context of skepticism, that those things can't be political. Now, what I thought you were doing in your talk was leveraging off there being nothing but national deliberation here, and now everyone's coming in the bunk because various ways in which you normally approach physical chances aren't available and so forth. And I think that's my immediate take. Oh, okay. Let me take a few brief remarks to what you said. First of all, about the chances, you may have noticed at several points I said chances as usually conceived.

1:22:30 Because I don't want to argue about the word chance. And I think there is a distinction between chances as usually conceived and... And he waits on the other interpretations. And sure, if someone says to me, you know, you've been thinking those chances wrong. There are no such things in the world as chances as you've been thinking about them, what there are of these other things that play the same role. My response is, well, okay, I'll accept that if I have good evidence that that is the case. I'm quite willing to accept that those things are different from the way I view them, and please do me a favor and teach them. And this I think speaks to the last thing. I wasn't trying to say, error comes when I'm stuck. I don't want to dissuade someone who already believes in the average interpretation saying, no, you've got an incoherent view. What I want to say is I don't see what counts as reasons for accepting the average interpretation in the first place. When you make the move to the Everett interpretation, it is the usual interpretation of these experiments with chance set-ups revealing the values of these chances, measured independently of any theory about them, and it doesn't seem to me that they're being replaced with anything that It turns those things into evidence for quantum mechanics for somebody who doesn't already believe in quantum mechanics and doesn't already believe in the other interpretations. Yeah, I guess I didn't get the lesson. I'm completely not set with it, actually. Why is it that the experiments no longer reveal chances? Why is that? And what is the anteceding and the discrimination of what chances are anyway that evidence replaces them? I didn't understand that idea. I think that the way we met I had a good idea about it.

1:25:00 See, that's why I brought up the story about Nathan Creech. That strikes me as a perfectly intelligible story. How does it change genetics? I don't think the notion of physical chance is obscure at all. We might not know the underlying physics behind it, but people have been measuring chances for thousands of years, actually. Math doesn't change. Thank you. I can imagine someone who doesn't believe, you've never heard of quantum mechanics, looking at these experiments and thinking these are giving us results, giving us both chances of results in different situations, and then suddenly learning quantum mechanics. Reconceptualize both results and the weights of branches become degrees to which an Everettian should be concerned about things. And that test doesn't seem to me a sort of thing that even makes sense to talk about being measured independently of having any idea upon mechanics or the Everettian interpretation. And again, I don't want to quibble over the word chance. If you want to say, on the average interpretation, these weights play a role in the decisions the chances that traditionally could be, have, and should be called chances, I'm fine with that.

1:27:30 But nevertheless, they are conceptually different from chances of being traditionally conceived, because as traditionally conceived, when you do something, when you roll a die, there is a unique event, a unique outcome of that die, of the roll of the die. We ask the question, what does it count as this, rather than this will be the outcome. So, maybe I can let someone else go in. Okay, now in fact, if I may, I'm going to suggest that we give special prominence to those who I believe are on the collective front, who are only here for today. So Matthew Darnell, Michael Davidson, and then David Walters. Okay, well... Instead of saying why I'm not a Maravoldian, I'll try and say why I am an Everettian. I'm not sure what we count as being Maravoldian. You started off by saying our only source of knowledge about the world is empirical evidence. Well, as a mathematician, I tend to think that our main source of evidence about the foundations of physics is mathematics. Therefore, we have to deal with the Schrodinger equation. If the Schrodinger equation is wrong, we have to find something else. So, you know, you can't say you're not an Everettian unless you're producing some other theory, and I don't know of any other theories which are coherent and complete and compatible with special relativity. I went on to say, well, the Everettian interpretation of the Schrodinger equation is everything. Well, after that, you started talking about branches. My disagreement with the Oxford School of Everettians is that they are sufficiently clear about what a branch is. My feeling about probability is that the reason that we might believe Everett is because we have a whole body of knowledge and then we have a theory. And then we look at what that theory has produced and we say, okay, if Everett is right and if my definition of a branch is right, then I'm typical according to that theory.

1:30:00 Now, typical, you know, what does that mean? Well, it means something like the fact that if you stuck up a set of heads and tails that came from your computer and it had simply been a bunch of heads, well, we would have just as deeply programmed your computer wrong. Whether or not you had, whether or not the computer was working, seems to me, to give a suitable definition of branch, provides us with a sense in which we have turned out to be typical so far. But there's nothing else we can say about the justification of Everett or the meaning of probability. I mean, all this stuff about decision theory is all very well, but it doesn't tell us why we should be typical. Physical probabilities. The first one was a stochastic theory and the second one was initial conditions. It seems to me that to differentiate between Everett and a stochastic physical theory on the grounds that the main difference between them seems to be that on the stochastic physical theory lots of things don't happen, that we don't see. That doesn't seem to be a good reason for believing in that, rather than lots of things do happen that we don't see. There are three points you made there, Hannah. I wanted to address the middle one first, the typical. Perhaps to address that point explicitly in the talk, Essentially, making a model of quantum information both more deductible to a stochastic theory and expected to be typical. And I ask, well, why should we expect to be typical? And, you know, this role of ten heads, you know, trees, is that a typical result or not? I don't know.

1:32:30 But when you get to really long strings, the distinction between typical and not typical gets a lot sharper because the camps could get really, really deep. So you can not go far off by replacing this sort of probabilistic reasoning where you update, you conditionalize on the evidence. By guessing, if you get atypical results, you've got to predict the theory, and that's very often what statistics textbooks, which want to make everything look like more cookbooks, do. And then you ask, well, why should I expect that my results are typical? Well, I think the answer is, there's a very high chance that they'll be typical in that sense, and a low chance that they won't be. And so, we're not really getting away from this probabilistic notion of confirmation, but anyway, and so that's one thing. Mathematics is good, but find another. Okay, find another. So you have to be beforehand, before the talk, what do you believe?