Self-locating uncertainty in the Everettian multiverse

September 9, 2008

Last time I gave a brief summary of some of the positions on uncertainty in EQM, as far as I understood them, and briefly said why I didn’t like them. Prima facie, the self-locating proposal seems to have the upper hand: it involves genuine uncertainty, and the uncertainty is of a familiar kind (and much studied by philosophers.)

Here’s the most basic version of the view that should give the flavour. When a person branches (which needn’t involve EQM), rather than thinking of one person who splits into two, we think of there being *two* people all along. Before the split they were colocated, either by being colocated enduring objects, or Lewisian worms, which later come apart and are individuated by their differing futures.

Thus, in EQM, one frequently finds one self to be in one of many predicaments subjectively indistinguishable from that of your own. Thus you are frequently in a position to be uncertain about *which person you are*. Since these people only differ in their futures, you can be genuinely uncertain about what is going to happen to you. If you are about to watch an x-spin measurement, you know that you are one of two colocated people, one of which is going to see “up”, the other of which is going to see “down”.

The problem with the self-locating view, at least on this basic account, is that it does not account for uncertainty about ordinary, non indexical, sentences like “it will rain tomorrow”, as opposed to “I am going to see rain tomorrow”. (The Saunders-Wallace multiple utterance view gets around this, but I think the problems I’m interested in for the basic view are going to carry over. Uncertainty, on their view, is parasitic on this kind of self-locating uncertainty about who you are.)

Here are some examples.

(1) Suppose that I’m in the x-spin measuring scenario above – except there’s a horrible twist. If it records “up” then I will be instantaneously obliterated. What should my credence in “up” and “down” be? Assuming we just measured z-spin it should be 1/2 in each. However, on the worm view of splitting, this cannot be self locating uncertainty. If we look at my worm, it is perfectly linear – what would have been the forking off side got obliterated, leaving no temporal stub behind. With out a fork there aren’t two worms, just one, and so there is no self locating uncertainty. [I’ve just noticed this works a lot like Robbie Williams instantaneous god example here.]

[Note: you might try refining the worm view by pairing them to branches, so people are branch stage pairs, or something like this. My problem with this is I begin to lose track of what’s being explained. I don’t feel like a pair. And why should I care about what happens to these pairs, especially if they only differ over some minutest detail aeons in the future.]

(2) Again as above, except instead of obliterating me they’re going to split me in two (in the ordinary non Everettian sense.) Although the world branches in two, I branch into three. Surely the self locating uncertainty is just as much there intra-branch as it is inter-branch: I should give non-zero credence to all of my three futures. My intuition is that our credences should be distributed 1/3 each – the three way forking is pretty much symmetrical, even though the nature of the branching is different. Thus, on the multiple utterance view, if asked whether the measurement will result in “up” or “down” you should not give the standard 1/2 answer. Note that I did not ask whether you will see “up” or “down” – even on the multiple utterance view there should be three utterences in play. Note also that it does not depend on worm theory like (1) did – this is a problem for endurantists too.

(3) We might try and deny problem (1) by giving up on Lewisian metaphysics – there can be life long colocated objects. This raises a more general problem: colocation might happen for reasons unrelated to branching time. Imagine a clay statue and the lump of clay it is made of – Statue and Lump. Due to related modal paradoxes of coincidence, Statue and Lump are colocated. Similarly, presumably I have different modal properties from the matter I’m constituted of. Lets not be anthropocentric – there must be many different objects colocated with me, with varying survival conditions. And surely many of those objects are people; surely the objects that match me closely enough in modal and non-modal properties deserve to be called people too. So once again I have more self locating uncertainty than we wanted.

(4) Lastly something I roughly sketched in an earlier post: credences in self-locating propositions are governed by the Principle of Indifference. If you know that you have an exact duplicate, who is receiving exactly the same experiences as you (including knowing he has an exact duplicate) then you should divide you credence equally between you and the duplicate. After all, setting your credences otherwise means you can be certain that one of you is making a big mistake.

It is worth seeing how this conflicts with Measurement Neutrality – a central principle that allows us to get the Born rule from decision theoretic considerations. Measurement Neutrality says that we should be indifferent between two quantum bets that agree on the state being measured, the observable, and the payoffs we get for each outcome. MN sounds convincing at first, however, it requires an agent to be indifferent between bets that would result in a different number of branches being created. Roughly, the problem is: the more branches made, the more self locating uncertainty (since according to the PoI, you should divide credence equally between the branches. Note also: even if it’s vague how many branches there are, it’s still supertrue that I assign any two definite branches equal credence.)

So Measurement Neutrality is false on the view where uncertainty is self-locating uncertainty. It is like being told that we should be indifferent between getting a guaranteed £10 and being put in a Dr. Evil scenario where you are one of two duplicates, one of which will get a tenner, and the other will be horribly tortured. (I’m not entirely sure the above corresponds to a realisable quantum bet. But I think the following makes a better, but slightly more complicated analogy: you should be indifferent between being one of two people, one of which will get a tenner, the other one will have his fingers mangled, and being put in a scenario where you might be one of 9999 duplicates which receive a tenner, or one duplicate who is finger-mangled.)

So I’m beginning to think the ‘uncertainty due to indeterminacy’ view actually has the upper hand. One worry that remains is that credences in indeterminate propositions might be governed by certain trumping principles (like the way that credences in self-locating propositions are governed by the Principle of Indifference – something I take to trump other principles governing credences, such as the Principal Principle.) One suggestion, by Robbie in the comments, was that my credences in p and ~p should both plummet to 0 whenever I learn p is indeterminate. He calls this ‘rejectionism’. Apparently Dempster-Shafer theory can deal with this. One thing it has to make sense of, if we’re keeping to the supervaluationist framework, is allowing Cr(p or ~p) to remain at 1. (Question: is that possible in Dempster-Shafer theory? To have Cr(p or q)=1 but Cr(p)=Cr(q)=0? Seems weird.) Talking in terms of coarse grained beliefs, rejectionism involves not believing p and not believing ~p while believing (p or ~p). Just applying some naïve conceptual analysis, this appears to be all that is required to be uncertain about whether p holds or q holds – to believe that one or the other holds, but not to believe of either one in particular that it holds. So in some sense, even rejectionism involves uncertainty.



  1. How do you know that you don’t feel like a worm-branch pair? How do you know what it feels like to be such a pair? 🙂

    The worry about why we should care about one worm-branch pair rather than another featuring similar worms and worlds I think is a more important issue. But it’s no worse than the worry about why we should care about one worm rather than another very similar one, which affects the standard multiple utterance view. And problems with rational relevance also arise on the ‘uncertainty-due-to-indeteminacy view’. How is knowing that p is indeterminate relevant to p-dependent actions?

    The way that Saunders and Wallace would deal with this worry, I think, is dogmatic – we *just are* worms (or worm-branch pairs), so worrying about such worms (or pairs) *just is* worrying about what will happen to us. And since it’s rational to worry about what will happen to us, it’s rational to worry about what will happen to worms (or to pairs).

  2. Hi Andrew,

    Dustin here from Go Grue. I’m afraid I don’t understand your point in (1). As you said above, on the view in question, “we think of their being two people all along”, one person in each branch. You need not think of these people as person-branch pairs: no, they are simply people, and there is a distinct such person in each branch. Thus, when dividing your credence, you divide among those branches which you might be in, and you do so regardless of whether each branch is a branch in which the person (who might be you) will exist after the x-spin measurement.

    I’m not sure, but it seems that you think you should divide your credence among just those branches where the person will exist after the x-spin measurement. Isn’t this just the (well-known) fallacy of Lewis’ “How Many Lives has Schroedinger’s Cat?”?

  3. Hi Alastair,

    Sorry it took me so long to reply. My worry is specifically with the ordered pair view and not the worm view. For example – I causally interact with stuff, ordered pairs don’t. I don’t have any members, ordered pairs do. Also there’s a problem saying what abstract objects is me. For example, ordered pairs can be defined lots of different ways. Which is me: the Kuratowski worm/branch pair or the Quine-Rosser worm/branch pair? Both do the job equally well, but they’re strictly different. Why does one kind of pair fit the role of people better than the other?

  4. Hi Dustin,

    Thanks for commenting!

    I’m not quite sure why there should be a different worm for each branch before the split? I take it that it is the branching of the *worm* not spacetime that accounts for there being multiple people (so it is exactly analogous to the non-EQM cases of branching.)

    To put it more vividly: suppose there were 2 worms in example (1): a and b. Now a and b overlap exactly the same objects, so by some standard mereological principles they are identical after all! Where am I going wrong?

    BTW what is the fallacy in the Lewis paper? I’m not sure I knew of this?

  5. Hi Andrew,

    I think that’s just what the view in question says. As you say in your original post:

    “When a person branches (which needn’t involve EQM), rather than thinking of one person who splits into two, we think of there being *two* people all along. Before the split they were colocated, either by being colocated enduring objects, or Lewisian worms, which later come apart and are individuated by their differing futures.”

    Surely the fact that I later branch is irrelevant to how many qualitative duplicates there are of me now. So if this holds in the case where I later branch, it should, on the view in question, hold of me now, regardless of whether I later branch.

    Re: the fallacy in Lewis’ paper. Lewis slips freely between the question of “what to expect” and the question of “what to expect to experience”. As he says, when deciding “what to expect to experience” one should divide one’s credence among just those branches where one has experiences (and thus survives). But, contra Lewis, the same does not apply when deciding “what to expect”. In that case, you should divide your credence among all the branches, regardless of whether you survive in them. The difference is just that the question “what to expect to experience” *presupposes* that you will be having experiences, whereas the question “what to expect” does not.

    See the last two sections of Lewis’ paper and you’ll see him slipping freely between these two questions.

  6. Now I think about it, Dustin seems to be right that 1) isn’t a real problem. There are two different worms available, one for each branch – a long worm in one branch and a short worm in the other. Never mind that (in some sense) the longer one includes the shorter one as a proper part. In the terms of your last comment, A and B don’t overlap exactly the same objects.

    The problem with underwriting the correct multiplicity of agents does arise, however, in cases of an agent’s uncertainty about events arising futurewards of his/her death. This is the motivation for bringing in the branch/worm pairs. I’ve just written up a more in-depth discussion of this problem at http://mrogblog.wordpress.com/2008/09/15/macroscopic-individuation-in-everettian-quantum-mechanics/

  7. Dustin – thanks for clearing that up. You write

    “Surely the fact that I later branch is irrelevant to how many qualitative duplicates there are of me now.”

    I think the view is that it really *is* relevant. Suppose that tomorrow you split so that your worm forms a Y shape. There are two linear worms that together compose the Y and overlap at the initial segment that includes today. So there are in fact two qualitative duplicates colocated today, which will tomorrow come apart. And it really does depend on how many times I split tomorrow, to how many qualitative duplicates of me are here *now*.

    Al – it’s true that the proper part of my worm that exists up until the world splits doesn’t ovelap exactly the same objects as my full worm (call this Andrew, and the latter Andrew-). But why does Andrew- count as a person? Clearly not all of my proper parts are people. Surely any plausible relation of personal identity between slices holds between slice of Andrew- as much as slices of Andrew- to Andrew. (Just consider causal continuity, memory, etc etc.) You need some principled reason why some proper parts count as people and others don’t. In (1) I didn’t think I was assuming any more than the Lewisian worm view, because, I took it that on the worm view people are maximal wormlike objects that stand it the appropriate personal identity relations.

  8. Whatever entitles you to say that in ‘if it records up I will be instantly obliterated’ will entitle you to say that Andrew- is a person. Take some whole continuant branch includes the apparatus reading ‘up'(there will be many such branches.) By hypothesis, any such branch includes Andrew- but includes no parts which Andrew has which but Andrew- lacks. Isn’t it obvious that such a branch includes a person which died at the measurement outcome? Just apply the normal criteria for person-persistence to the single branch in question, ignoring the others.

    I think the counter-intuitive thing which you’re trying to get at is just the result that Andrew- (the whole guy) is identical to a proper part of Andrew. Normally we don’t say that people are identical to proper parts of other people. But in the context of Everettian branching, when talking about people on different branches, this turns out true.

  9. Hmm, ok I think I agree with you now.

    But I think that leaves an interesting puzzle to do with personal identity instead. If you look at all the slices of Andrew and Andrew-, they will (surely) all stand in the personal identity relation to each other (whatever that is). This is ensured by that fact that all the slices of Andrew are so related to each other and the slices of Andrew- is a subset of those slices.

  10. I agree that it’s a corollary of the multiple-utterance proposal that thinking of personal identity as a relation between stages just doesn’t make sense – it generates puzzles just like the one you suggest.

    This does indeed seem like a potential problem for the view. We do often talk in terms of ‘the person I was then’ and ‘the person I am now’, and this kind of talk is hard to make any sense of on the multiple-utterance view. Being able to cope with this sort of talk is another good reason, I think, to individuate macroscopic objects via their branches. So maybe your original example does point in the right direction, just not quite for the reason you thought…

  11. Hi Andrew,

    As I understood the view, you should not think of things on the “Y” model–that is, you should not think of the two worms as *sharing* one and the same initial segment. Rather, you should think of things along the lines of two worms which have *qualitatively identical* initial segments. This is what I took you to mean when you said that on this view “there are two people all along”. If that’s how the view works, then, indeed, I think it is irrelevant to how many qualitative duplicates there are of me now whether my duplicates later branch. Are you familiar with Lewis’ “branching”/”diverging” distinction (“On the Plurality of Worlds”, the chapter titled “Counterparts or Double Lives”)? If so, then what I’m saying can be put in those terms: on the view in question (as I understood it), there are branching worms, not diverging worms.

  12. Oops! I got Lewis’ terminology backwards. Using Lewis’ terms, what I’m trying to say is that on the view in question (as I understood it), there are diverging worms, not branching worms. (See p. 206 of “On the Plurality of Worlds” (1986 edition)

  13. Hi Dustin,

    I agree with you that if we can recover a ‘diverging worms’ picture from Everettian QM that is the best direction in which to take this view.

    The worry is that there isn’t any straight-forward way to underwrite this in the fundamental metaphysics. Saunders and Wallace seem to give an account of material objects as aggregates of temporal parts, allowing that these parts can be part of more than one worm. This leads to big problems, as I argue in my most recent blog entry.

    If you have reason for thinking either that some metaphysical account is available to underwrite divergence on the Everettian view, or that we don’t need any such account, I’d be delighted to hear it!

    As far as Saunders/Wallace exegesis goes, I think the view in their 2008 BJPS paper is that the difference between branching and divergence is irrelevant, or ‘purely formal’. I don’t think this is the case – to recover normal thought about the future, we need divergence, and not branching. The difference shows up when it comes to ‘post-mortem’ future contingents.

  14. […] fallacies of selfhood we would cease to be ourselves and revert to observers observing the machinations of the unknowable, manifold expressions of energy and […]

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