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pragmatist110

The latest attempt at a decision-theoretic account of QM probabilities is David Wallace's, here: http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.2718v1.pdf . I mention this because this proof is not susceptible to the criticisms that Barnum et al. raise against Deutsch's proof.

If we're going to be talking about the approach, it's worth getting some sense of the argument. Below, I've reproduced a very non-technical summary. I describe the decision problem, the assumptions (which Wallace thinks are intuitive constraints on rational decision-making, although I'm not sure I agree), and the representation theorem itself. It is a remarkable result. The assumptions seem fairly weak but the theorem is striking. To get the gist of the theorem, scroll down to the bolded part. If it seems that it couldn't possibly be true, look at the assumptions and think about which one you want to reject, because the theorem does follow from (appropriately formalized versions of) these assumptions.

The Decision Problem

The agent is choosing between different preparation-measurement-payment (or p-m-p) sequences (Wallace calls them acts, but this terminology is counter-intuitive, so I avoid it). In each sequence, some quantum state is prepared, then it is measured in some basis, and then rewards are doled out to the agent's future selves on the basis of the measurement outcomes in their respective branches. An example sequence: a state is prepared in the superposition 1/2 |up> + sqrt(3/4) |down>, a measurement is made in the up-down basis, then the future self of the agent in the |up> branch is given a reward and the future self in the |down> branch is not.

The agent has a preference ordering over all possible p-m-p sequences. Of course, in any particular decision problem, only some of the possible sequences will be actual options. For example, if the agent is betting on outcomes of a pre-prepared and pre-measured state, then she is choosing between sequences that only differ in the "payment" part of "preparation-measurement-payment".

The Assumptions

  1. One can always set up a p-m-p sequence where a state is prepared, measured, and then the agent is rewarded regardless of the measurement outcome.

  2. Arbitrary quantum superpositions can be prepared.

  3. After p-m-p sequence is completed, any record of the measurement outcomes can always be erased. Two different p-m-p sequences could lead to the same macroscopic states after such an erasure is performed as long as they differ only in the measurement outcomes, not in the quantum amplitudes and payments associated with those outcomes.

  4. For a given initial macrostate, the agent's preferences define a total ordering over the set of possible p-m-p sequences.

  5. The agent's preferences are diachronically consistent. Let's say a sequence U takes place between times t0 and t1. At t1, there will be branches corresponding to the different outcomes associated with U. Xi and Yi are different p-m-p sequences that could be performed at t1 in the i'th branch. If the agent in the i'th branch prefers Xi over Yi, then the pre-branching agent at time t0 prefers U followed by Xi over U followed by Yi.

  6. The agent cares only about the macroscopic state of the world. She doesn't prefer one microscopic state over another if they correspond to the same macroscopic state.

  7. The agent doesn't care about branching per se. She doesn't consider the mere multiplication of future selves in distinct macroscopic states valuable in itself.

  8. In the Everettian framework, p-m-p sequences are implemented by unitary transformations. If there are two different unitary transformations that have the same effect on the agent's branch (but differ in their effect on other branches), the agent is indifferent between them.

The Representation Theorem

The preference ordering over sequences induces a preference ordering over rewards, because for any two rewards R1 and R2, there are p-m-p sequences which lead to R1 for all branches and R2 for all branches. If any sequence of the first kind is preferred over a sequence of the second kind, then reward R1 is preferred over reward R2.

Given a preference ordering over the rewards, there is a unique (up to affine transformations) utility function over the rewards. If the agent is to use standard decision theory to reason about which p-m-p sequences to choose in order to maximize her expectation of reward utility, and we want the expected utilities of the p-m-p sequences to reflect to the agent's given preferences over those sequences, then the probability distribution over outcomes we use when calculating the expected utility of p-m-p sequences must be given by the Born rule.

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Mitchell_Porter20

Before I try to parse this argument: do you really think this line of reasoning can explain why there are dark regions in the double-slit experiment? Are you really going to explain that in terms of the utility function of a perceiving agent?!

Reply
3Nisan
I just looked at the statement of the theorem in the paper you linked. I would summarize it as: Given a preference ordering over the rewards, there is a unique (up to affine transformation) utility function over the rewards with the property that this utility function recovers the preferences over sequences leading to those rewards iff the expected utility of the sequences is calculated using the Born probabilities. Is that correct? Or does the result rule out the existence of a utility function which recovers the preferences when you calculate expected utility using that utility function and non-Born probabilities?
1pragmatist
Mitchell, in your previous post you suggested that the natural way to get probabilities in MWI is just by looking at relative frequencies of branches. Obviously if the representation theorem is correct, this strategy must be incompatible with some of the assumptions. The relevant assumptions here are (5) and (7). Wallace gives a good example illustrating why the counting rule violates (5) and (7) on page 28 of the paper I linked above.
See in context
by Mitchell_Porter
1 min read
93

5

The subject has already been raised in this thread, but in a clumsy fashion. So here is a fresh new thread, where we can discuss, calmly and objectively, the pros and cons of the "Oxford" version of the Many Worlds interpretation of quantum mechanics.

This version of MWI is distinguished by two propositions. First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence. Second, the probability law of quantum mechanics (the Born rule) is to be obtained, not by counting the frequencies of events in the multiverse, but by an analysis of rational behavior in the multiverse. Normally, a prescription for rational behavior is obtained by maximizing expected utility, a quantity which is calculated by averaging "probability x utility" for each possible outcome of an action. In the Oxford school's "decision-theoretic" derivation of the Born rule, we somehow start with a ranking of actions that is deemed rational, then we "divide out" by the utilities, and obtain probabilities that were implicit in the original ranking.

I reject the two propositions. "Worlds" or "branches" can't be vague if they are to correspond to observed reality, because vagueness results from an object being dependent on observer definition, and the local portion of reality does not owe its existence to how we define anything; and the upside-down decision-theoretic derivation, if it ever works, must implicitly smuggle in the premises of probability theory in order to obtain its original rationality ranking.

Some references:

"Decoherence and Ontology: or, How I Learned to Stop Worrying and Love FAPP" by David Wallace. In this paper, Wallace says, for example, that the question "how many branches are there?" "does not... make sense", that the question "how many branches are there in which it is sunny?" is "a question which has no answer", "it is a non-question to ask how many [worlds]", etc.

"Quantum Probability from Decision Theory?" by Barnum et al. This is a rebuttal of the original argument (due to David Deutsch) that the Born rule can be justified by an analysis of multiverse rationality.

Personal Blog

5

Problems of the Deutsch-Wallace version of Many Worlds
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[-]pragmatist110

The latest attempt at a decision-theoretic account of QM probabilities is David Wallace's, here: http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.2718v1.pdf . I mention this because this proof is not susceptible to the criticisms that Barnum et al. raise against Deutsch's proof.

If we're going to be talking about the approach, it's worth getting some sense of the argument. Below, I've reproduced a very non-technical summary. I describe the decision problem, the assumptions (which Wallace thinks are intuitive constraints on rational decision-making, although I'm not sure I agree), and the representation theorem itself. It is a remarkable result. The assumptions seem fairly weak but the theorem is striking. To get the gist of the theorem, scroll down to the bolded part. If it seems that it couldn't possibly be true, look at the assumptions and think about which one you want to reject, because the theorem does follow from (appropriately formalized versions of) these assumptions.

The Decision Problem

The agent is choosing between different preparation-measurement-payment (or p-m-p) sequences (Wallace calls them acts, but this terminology is counter-intuitive, so I avoid it). In each sequence... (read more)

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3Nisan
I just looked at the statement of the theorem in the paper you linked. I would summarize it as: Given a preference ordering over the rewards, there is a unique (up to affine transformation) utility function over the rewards with the property that this utility function recovers the preferences over sequences leading to those rewards iff the expected utility of the sequences is calculated using the Born probabilities. Is that correct? Or does the result rule out the existence of a utility function which recovers the preferences when you calculate expected utility using that utility function and non-Born probabilities?
2pragmatist
The way Wallace expresses the theorem in the paper is misleading. The theorem does rule out utility functions that recover preferences if expected utility is calculated using non-Born probabilities. I think many people, on first glance, interpret the theorem the way you did, which makes it much less impressive, and not really a justification of the Born probabilities at all. The way to read the theorem is not "... there is a unique utility function with the property that...", It is "...there is a unique utility function and it has the property that..."
0Nisan
Ah, I see. Yes, that kind of result is remarkable. I don't know what you mean, though, by "there is a unique (up to affine transformations) utility function over the rewards". If you mean there is a unique utility function on rewards that recovers the agent's preferences on rewards, that's false. But I don't know what else you could mean. EDIT: See my comment below.
1Nisan
Ah, I thought of a charitable interpretation of "there is a unique (up to affine transformations) utility function over the rewards". Given a preference ordering on sequences of rewards, there is a unique utility function on individual rewards that recovers that preference ordering. I believe this because if rewards are repeatable, the diachronicity hypothesis implies that any utility function on sequences of rewards must be additive. (We also need a hypothesis ruling out lexicographically-ordered preferences.)
0pragmatist
You're right. Diachronic consistency is required to establish the uniqueness of the utility function. Also, Wallace does include continuity axioms that rule out lexically ordered preferences, but I left them out of my summary for the sake of simplicity.
2Mitchell_Porter
Before I try to parse this argument: do you really think this line of reasoning can explain why there are dark regions in the double-slit experiment? Are you really going to explain that in terms of the utility function of a perceiving agent?!
1pragmatist
I don't think it explains why I actually see dark regions in the double slit experiment. That is explained by the Schrodinger dynamics without any need for appeal to probabilistic resources. The decision-theoretic argument does tell me why I should assign probability close to zero that the detector will show a flash in certain regions. But this is a fact about how I should set my credences, and so it's not entirely absurd that it has to do with my status as a decision-making agent.
1Mitchell_Porter
So how does it explain that? How can the imperative to maximize your expected utility, require you to "expect to see" photons to arrive in the dark zones less often than they arrive in the light zones, without it also being true that photons actually arrive in the dark zones less often than they arrive in the light zones?
3pragmatist
Sorry. I edited my post to make it clearer before I saw yours, so the part you quoted has now disappeared. Anyway, I'm not entirely on board with the Deutsch-Wallace program, so I'm not going to offer a full defense of their view. I do want to make sure it's clear what they claim to be doing. Consider a simpler case then the two-slit experiment: a Stern-Gerlach experiment on spin-1/2 particles prepared in the superposition sqrt(1/4) |up> + sqrt(3/4) |down>. Ignoring fuzzy world complications for now, the Everettian says that upon measurement of the particle, my branch will split into two branches. In one branch, a future self will observe spin-up, and in the other branch a future self will observe spin-down. All of this is determined by the Schrodinger dynamics. The Born probabilities don't enter into it. Where the Born probabilities enter is in how I should behave pre-split. As an Everettian, I am not in a genuine state of subjective uncertainty about what will happen, but I am in the weird position of knowing that I'm going to be splitting. According to Wallace (and I'm not sure I agree with this), the appropriate way to behave in this circumstance is not as if I'm going to turn into two separate people. It is basically psychologically impossible for a human being to have this attitude. Instead, I should behave as if I am subjectively uncertain about which of the two future selves is going to be me. Perhaps on some intellectual level I know that both of them will be me, but we have not evolved to account for such fission in our decision-making processes, so I have to treat it as a case where I am going to end up as just one of them, but I don't know which one. Adopting this position of faux subjective uncertainty, I should plan for the future as if maximizing expected utility. And if I am organizing my beliefs this way, the decision theoretic argument establishes that I should set my probabilities in accord with the Born rule. In this case, the probabilities do
0Mitchell_Porter
There is still the problem that if all histories exist and if they exist equally, then the majority of them will look nothing like the real world, the shape of which depends upon some things happening more often than others. Regardless of the validity of this reasoning about "decision-making in a branch world", the characteristic experience of an agent in this sort of multiverse (where all possible histories exist equally) will be of randomness. If we think at the basic material level, agents shouldn't even exist in most branches; atoms will just disintegrate, and basic fields will do random things. If we ignore that and (inconsistently) assume enough stability to have a sequence of measurements, the measurement statistics will be wrong - if we repeat your experiment, spin up will be seen as often as spin down, because the coefficients (or the measure, if you wish) are playing no existential role. I can see a defense for Wallace: he can claim that because "there is no number of worlds", that you're not allowed to count them like I'm doing and draw the obvious conclusion, that |down,down> will exist once and |down,up> will exist once. It seems that not only are we not allowed to ask how many worlds there are, we're not even allowed to ask questions like "what is the characteristic experience of an agent in this superposition?", because implicitly that is also branch-counting. The whole thing is sounding decisively implausible at this point, since we end up requiring that all physical order somehow derives from "multiverse agent rationality", rather than from genuine microphysical cause and effect. The Born rule isn't only responsible for the Stern-Gerlach experiment turning out right; you need it in order for every material object to remain stable, rather than immediately turning into a random plasma that belongs to the majority class of physical configurations.
2pragmatist
If the decision-theoretic argument works, then a rational agent should expect to find herself in a branch which respects quantum statistics, so it should not surprise her to find herself in such a branch. Perhaps there is some measure according to which "most" observers are in branches where quantum statistics aren't respected, but that measure is not one that should guide the expectations of rational agents, so I don't see why it should be surprising that we are not typical observers in the sense of typicality associated with that measure.
1Mitchell_Porter
It's sounding like a Boltzmann brain... the observer who happens to have memories of Born-friendly statistics should still be blasted into random pieces in the next moment. I haven't pinned down the logic of it yet, but I do believe this issue - that the validity of quantum statistics is required for anything about observed reality to have any stability - seriously, even fatally, undermines Wallace's argument. Consider your assumption 2, "Arbitrary quantum superpositions can be prepared". This is the analogue, in the decision-theoretic argument, of Bohr's original assumption that there is a classical world which provides the context of quantum measurements. That assumption is unsatisfactory if we are trying to explain, solely in terms of quantum mechanics, how a "classical world" manages to exist. It looks the same for Wallace: he is presupposing the existence of a world stable enough that an agent can exist in it, interact with it, and perform actions with known outcomes. We are told that we can get this from Schrodinger dynamics alone, but Schrodinger dynamics will also produce nonzero amplitudes for all the configurations where the world has dissolved into plasma. Since we are trying to justify the Born rule interpretation of those amplitudes, we can't neglect consideration of these disintegrating-world branches just because the amplitude is small; that would be presupposing the conclusion. Also, observer selection won't help, because there will be branches where the observer survives but the apparatus disintegrates. It all sounds absurd, but this results directly from trying to talk about physical processes, without using the part of QM that gives us the probabilities. When we do use that part, we can safely say that the spontaneous disintegration of everyday objects is, not impossible, but so utterly unlikely that it is of no practical interest. When we try to describe reality without it, then all possible futures start on an equal footing, and most of them e
1pragmatist
The decision-theoretic argument is not supposed to prove everything. It's supposed to explain why agents living in environments that have so far been stable should set their credences according to the Born probabilities. So, yes, there are presuppositions involved. But I don't see how this is a devastating problem for Everettianism. You brought up Boltzmann brains. It turns out that our best cosmological models predict that most observers in the universe will be Boltzmann brains. The universe will gradually approach an eternally expanding cold de Sitter phase, and thermal fluctuations in quantum fields will produce an infinity of Boltzmann brain type observers. Do you think this is a devastating objection to cosmology? I think the appropriate tack is to recognize anthropics as an important issue that we need to work on understanding, but in the meantime proceed with using those cosmological models under the assumption that we are not Boltzmann brain type observers. Anyway, the kind of problem you're raising now is not one that Wallace's decision-theoretic argument is intended to solve. This paper by Greaves and Myrvold might be relevant to your concerns, but I haven't read it yet: http://philsci-archive.pitt.edu/4222/1/everett_and_evidence_21aug08.pdf The abstract:
1pragmatist
Mitchell, in your previous post you suggested that the natural way to get probabilities in MWI is just by looking at relative frequencies of branches. Obviously if the representation theorem is correct, this strategy must be incompatible with some of the assumptions. The relevant assumptions here are (5) and (7). Wallace gives a good example illustrating why the counting rule violates (5) and (7) on page 28 of the paper I linked above.
[-]wedrifid100

The worst thing about the Many Worlds Interpretation: The name. I mean, wtf? Everett used the perfectly sensible name "Theory of the Universal Wavefunction" which wikipedia at least acknowledges as another name for it. And 'Many Worlds' barely makes sense. It's more "It's not just one world - it's like... completely different to how we used to consider the world and to the extent there is a 'world' at all there are a bunch of them".

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[-][anonymous]80

Here are some additional sources criticizing the decision-theoretic approach by Deutsch and Wallace:

Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability? Huw Price's critique.

Probability in the Everett World: Comments on Wallace and Greaves Huw Price again

Decision Theory is a Red Herring for the Many Worlds Interpretation Jacques Mallah's thorough rebuttal of the approach by Wallace et al.

Everett and the Born Rule Alastair Rae's rebuttal.

One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scient... (read more)

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6wedrifid
This guy has me at the title. To be honest I'd be satisfied with it even if the contents consisted of "No, realy, wtf are these guys smoking? They have this all backwards!"
0[anonymous]
Indeed. I do think Mitchell Porter (and some of these authors) are right in that you need frequency of worlds. It is very hard to see how you could make sense of probabilities without them. It's been 50 years trying to solve this problem without any succes, I think that speaks volumes.
[-]Shmi60

I think that EY has played a cruel joke (or maybe it was a rationality test for the readers), where he misrepresented an active area of physics research as an open-and-shut case of the MWI being the One True Teaching. (The alternative is an unthinkable weirdtopia: EY failed at rationality?!?!)

Were it not for the Quantum Physics sequence, the LWers would not bring the issue up as often, given the many many other active areas of (Physics) research that are just as deceptively simple to an uninitiated.

Consider, for example, an alternate universe where the gr... (read more)

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9pragmatist
Even though I'm partial to the Everettian interpretation, I've always thought Eliezer's advocacy of this interpretation was pretty overblown. Part of the problem is that he frequently represents Copenhagen (or rather, the simplified textbook version of Copenhagen) and MWI as the only available options. If that's the contest, then MWI clearly wins, but there are many many interpretations out there that are superior to Copenhagen. Perhaps Eliezer has studied these and has sound reasons for rejecting them, but I doubt it.
6CarlShulman
Many of the same arguments apply elsewhere, and Eliezer has discussed such application in the comments, e.g. going after Bohm on similar complexity grounds (real wave function vs real wave function and particles) and nonlocal FTL effects (yes, conveniently structured so that they can never be made use of).
0Peterdjones
The arguments don't apply to interpretations that don't require a real WF or real collapse, and EY has struggled with them,.
-3Peterdjones
There are interpretatiions simpler than both CI and MWI which EY has not had time to study
1pragmatist
For what it's worth, I more or less agree with Eliezer about RQM.
-2TheAncientGeek
Which ks unfortunate, since he does not understand it. He has studied N interpretation,s, and declared that MWI is the One True Interpretation , although there are others not included in his N.
8Anatoly_Vorobey
I know you're saying that ironically, but I'll take the bait and state clearly that there's nothing unthinkable or particularly astonishing about Eliezer failing at rational thinking in some instances. In my opinion, both the insistence on MWI and the heavily kool-aidish emphasis on evo-psych are examples of such failures in the sequences.
1wedrifid
This gives me a (trivial) update in the direction of MWI! (ie. A higher correlation between critics of Eliezer's rather uncontroversial evo-psych position with critics of his MW position makes the MW position slightly more plausible.)
2Anatoly_Vorobey
Is that not a species of the "Hitler was a vegetarian" argument?
0wedrifid
No. If it was then the species "Hitler was a vegetarian" would be would be valid - which would thereby make the Hitler reference a mere Godwin violation.
1[anonymous]
I think the reality is that Eliezer Yudowsky, while a very bright mind and great man in terms of rationality, has overstepped his limits when it comes to physics. He do admit that there is currently no satisfactory solution to the Born Rule issue, yet he has written several posts talking about MWI as it is "obviously true". That is quite irrational. Quantum mechanics is, after all, ALL about the probabilities predicted by Born Rule, that is the essence of QM, if a model gets these probabilities wrong, it is obviously in deep trouble. I am quite dissapointed in Yudowsky for not admitting that he may have overstepped his area of expertise and mislead people to think that the case for MWI was stronger than it ACTUALLY is. I think it might be that he thinks the only other alternative is anti-realism or indeterminism, which is wrong, I dispise and absolutely object to both antirealism and indeterminism, but thee are other realist interpretations out there and the fact that we got no quantum gravity solution nor any ToE should force even the most stubborn MWI'ers to keep their minds open and refrain from claiming that it is true.
0wedrifid
That doesn't remotely follow - at least not without a rather antagonistic interpretation of Eliezer's position. Eliezer is clearly not claiming that there is a theory that gives a good explanation for what causes the Born Rule to behave as it does. He is just claiming that supporting a theory that tries to pretend there is just one world given what we do know about physics would be batshit crazy. To precisely the same extent that the a lack of a quantum gravity should oblige people not to affiliate with general relativity.
-3Shmi
Uh, this language does not help rational discourse.
-5[anonymous]
-2wedrifid
How is this relevant? Because you think talking about Eliezer and someone else who is wrong in the same comment will make Eliezer look worse?
2prase
I assume the comment intended to provide an illustrative example of group thinking based on a contentious physical hypothesis at which the LWers can look from the outside.
0Shmi
woosh :( Because the reason the MWI is discussed here has nothing to do with rationality.
[-]Manfred50

Wait, what? This hasn't been derived yet for non-relativistic QM, and these guys claim to have done it through decision theory, not, say, probability?

Man, my calibration is way off on this.

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[-]Eliezer Yudkowsky40

Someone asked me to join the discussion, so here goes:

I don't buy the decision-theory thing. I don't think I can make a quantum coinflip come out a different way by redefining my utility function. So no, this ain't my MWI.

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[-]pragmatist120

I don't buy the decision-theory thing. I don't think I can make a quantum coinflip come out a different way by redefining my utility function.

The Oxford Everettians don't think so either. I mean, come on, Deutsch and Wallace are pretty smart people. Let's give them a little bit of credit. If your construal of their view is just blatantly absurd, the problem is probably with your construal, not their view. I tried to give some sense of Wallace's position in these comments.

The point of Wallace's argument is that no matter what your preference ordering over rewards (assuming they obey certain intuitive constraints), you will recover the Born probabilities.

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0[anonymous]
I have read your sequence on QM and MWI and you seem to support this very view of MWI, just not this derivation of Born Rule, but if you really believe in the splitting-MWI, how do you avoid this problem?
[-][anonymous]20

I find it rather interesting that Yudowsky does not participate in debates that challenge his view like this...

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[-]Douglas_Knight20

I think that the fuzziness of the worlds is much more popular both on LW and among physicists than the decision-theoretic derivation of the Born rule. For example, the decoherence literature is about fuzzy worlds. I don't think it is helpful to talk about the two together.

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-1Mitchell_Porter
If you can't count the worlds, you can't derive the Born rule from counting... and if you can count the worlds, then there must be something exact about them. So there is a natural affiliation between Many Vague Worlds and non-frequentist derivations of the Born rule. Most of the physics literature on decoherence is not about fuzzy worlds. The view from Copenhagen is that decoherence is a process affecting probabilities in a single world. But I do agree that fuzziness or vagueness about worlds is tolerated much more widely than "Born rule from decision theory".
2Douglas_Knight
No one derives the Born rule from counting.
2Mitchell_Porter
Robin Hanson tries, and so do a few others. But yes, in general people don't think this is necessary, and (here I go) that is greatly to the discredit of MWI's advocates. If ever I wanted a simple way to categorize all the different shades of opinion about MWI, while also demonstrating that almost all of them have deep problems, I need only organize them according to how they think about the Born rule and the origin of quantum probabilities. Perhaps the most reputable version of MWI is Gell-Mann and Hartle's consistent histories formalism. This formalism gives you a prior for the different histories, but no attempt is made to "ontologically interpret" these probabilities. Then we have a "no-collapse wavefunction-realist" interpretation which centers on decoherence and on the appearance of probability-like numbers in reduced density matrices. This is a "folk interpretation" among working physicists, and like all folk theories, it does not come in an authoritative official form, usually hasn't been thought through, and so it's hard to simply rebut. Instead you would have to ask questions like, is there a preferred basis?, and, what makes those numbers probabilities?, and see how the individual physicist responds. Then we have people who say that there's one world for each possible outcome, but that some worlds "exist more" than other worlds, or are "more real" than other worlds. I wonder if that answer has ever been tried in a court of law? "Mr Casino Owner, the ball keeps landing on double-zero more often than it ought to." "No, that's not true! It lands on all outcomes equally, but the double-zero outcome is more real than the others." It's an expression rendered meaningless by self-contradiction, like the round square; the result of trying to reconcile an ontological commitment to the equal reality of all outcomes with the inconvenient fact that they don't occur equally often. Then we have the "decision theory" approach to deriving the probabilities, which I'm
6wedrifid
Jurors not having intuitions based on advanced physics has very little bearing on the details of quantum mechanics. This is an absolutely pathetic argument by local standards!
-1Mitchell_Porter
It is an attempt to show the absurdity of what is being said, by transposing it to an everyday situation. But perhaps this line of argument will appeal more to the LW sensibility.
5ArisKatsaris
Perhaps it's because I'm a programmer, not a physicist, that I don't see what's the problem with this position. If I e.g. have a static cache map that maps to already instantiated instances of a class, to retrieve them as appropriate, then some of these will be retrieved more often than others, but the rarely-called and the often-called will still have one instance of each. If I have many-clients connecting to many-servers (depending on the configurations/location of each), then some servers will be connected-to more often, and some servers not at all. And if we change from a client-server architecture to a peer-to-peer architecture, the concept of a definite number of servers vs a definite number of clients collapses, as each atomic entity functions a bit like each. Though I can't know if this analogy has anything to do with the physical world, I don't think you can condemn it on the basis of absurdity.
-1Mitchell_Porter
You can always count how many instances of something exist in a digital computer. The physical state of the computer is made of a definite number of definite states. There is certainly never any need to say that something exists "more than" something else exists, that's just sloppy language. You can count how many times a function is called, you can count the number of instances of a token, you can count the number of copies of a piece of code; at the level of bits, you can even distinguish between instances of an object and pointers to an object, even if they function similarly within a program, because at the level of bits, a genuine instance contains all the bits in the original, whereas a pointer just contains an address where the original may be found. So yes, I do condemn as absurd this talk of "A existing more than B", as if that could mean something other than "there are more copies of A than there are copies of B".
2wedrifid
Genuinely curious: Would you have a problem with the idea that that the relative weighting of instances only existing as a real number? (Either at the level we are able to detect or actually, if that is the way reality happens to be implemented?)
0Mitchell_Porter
I do not have a problem with it in principle; but it would imply that there are uncountably many. The reason you can't think of a superposition as just a sort of continuum without genuine parts, is that the part of reality we're observing here is objectively differentiated from what it is not. Even if the specific branch you see around you is just part of a continuum, it must be a continuum made of parts that each have a distinct enough existence to, e.g., host an observer in a definite state. This means they can be counted (or have a cardinality), and so the only way to get a real-valued weighting is if there are continuum-many of them. Something that I strongly suspect, but which I'm not 100% sure about, is that if branch A is supposed to be x times more likely than branch B, x not a rational number, then there must be uncountably many copies of A, and uncountably many copies of B, with the A-set being x times bigger than the B-set, according to some natural measure. The alternative would be to say that A exists once, B exists once; they're both embedded in a continuum of branches, every member of which only exists once; but the measure is non-uniform for some reason. But I think this is another version of the "A exists more than B exists" fallacy. Formally we can write down a non-uniform measure, but what it actually means is that we are counting some branches for more than others, and the only way to justify that is to suppose that the branches in question are duplicated, in proportion to the extra factor. Uncountably many distinct branches, each duplicated uncountably many times - at least it meets my criteria for a well-formed multiverse theory (the branches can be objectively individuated, and they have a cardinality), but it's very extravagant metaphysically. I'm planning a post on forms of Many Worlds that I do think are well-defined, that will focus on approaches which I consider to be much better motivated than that one.
2wedrifid
Yes, those two things seem roughly equivalent. I'm not entirely sure where you are going with this objective difference thing. The difference seems to just be that this is the part where the configurations that are us happen to be. Let's see... say the universal wave function was represented with rock's in an infinitely large desert. There are (assuming a non-obfuscated wave function representation) some rocks which, if moved, would change the part of the representation which is us. There are others which when moved wouldn't change us at all - they'd change other stuff. The universe emulator could go paint those rocks a different color if he was so inclined. That's the only 'objective' difference that I expect or require. Do you require more than that? (I sincerely do not understand what you mean by objective here and so wonder if that would satisfy you.) That seemed well formed. I'm not sure that it is extravagant metaphysically. It just seems like math that could be how the universe is. The extravagance all seems to be in the stories we try to tell ourselves about the math based on our intuitions. That is, it doesn't seem like an especially complicated way for reality to be - it just seems weird to us because of the simplified models that we've been working with for convenience up till now. I'd be curious. No doubt there would be some folks complaining that lesswrongians are overstepping their bounds again into physics territory that is off limits to them but I'd enjoy reading anyhow.
-2ArisKatsaris
You seem to me to be talking about two different things -- (a) - You argue that worlds must have a definite number, because you argue that everything that exists needs have a definite number (b)- You say that this cardinality must be all that determines the probability of a world being "observed". Both of these claims are highly suspect to me. (a) a fuzzy non-fundamental concept needn't have a definite number, and "world" is such a fuzzy non-fundamental concept (b) I don't see why the number of how many times something exists must equal how many times something is observed. As I said an instance may exist once but be retrieved many times, while another instance may exist once and retrieved less times. I don't like it being called "existing more" either -- since that's not how the verb "to exist" is typically used, but "observed more" or "experienced more" are good enough for me.
-1Mitchell_Porter
Those numbers don't have to be equal. They only have to be equal in a "many minds" version of "many worlds", where observations are all that exists anyway. More precisely, in Many Minds, the only branching you care about is the branching of observers, and the only "parts of the whole" that are given existential status, are parts of the wavefunction which correspond to experiences. So you never speak of just having "an electron in a spin-up state", but only of "someone observing an electron in a spin-up state". Clearly a viable many-worlds theory must at least have the latter - it must at least say that branches exist in which observers are having distinct and definite experiences - or else it makes no connection to reality at all. But to ascribe reality only to observer-branching, and not to the branching of lesser physical systems, is a remarkably observer-centric ontology; it's hard to see what advantage it has over "consciousness collapses the wavefunction". In any case, the real point here is that you can't defend the "no definite number" argument by constructing a contrast between observation and existence, because observers and experiences themselves exist. In a Many-Worlds context, the observer is not outside of physics. The observer has a physical state, the experience is a physical state. You use the expression, "how many times something is observed". How can that expression have meaning, unless observations exist, and exist distinctly enough to be counted? So if you're in a Many-Worlds ontology and counting experiences, but you insist that worlds can't be counted, then what exactly are you counting? Where are these distinct countable experiences located? If A is observed, then A has an observer; when you say A is "observed more" than B, you are saying that the observer of A "exists more" than the observer of B.
1wedrifid
Is this theory one that is advocated by actual physicists? If so that is scary!
0Douglas_Knight
Yes, Robin Hanson does, but his theory is a collapse theory so don't hold it against MWI. ETA: actually, no, I do not agree that Robin Hanson does counting.
0Mitchell_Porter
If I google "mangled worlds", I am told: "Describes a variation on the many worlds interpretation in which the Born probability rule can be derived via finite world counting."
0Douglas_Knight
I reached the opposite conclusion from that page.
[-]Oscar_Cunningham20

I'll copy my comment from the other thread:

That is, if a quantum world is something whose existence is fuzzy and which doesn't even have a definite multiplicity - that is, we can't even say if there's one, two, or many of them - if those are the properties of a quantum world, then is it possible for the real world to be one of those?

The real world is a single point in configuration space (there are uncountably many such points). So what's the point of keeping track of the blobs? It's because the Hilbert space is so vast that it's very unlikely that tw... (read more)

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0Mitchell_Porter
That can't be what they think in Oxford, or else they would agree with argumzio, who says there are uncountably many worlds. In the Oxford version of MWI, the real world is one of those "blobs", therefore it's partly a matter of definition, and that's why there's no exact number of worlds.
4Oscar_Cunningham
Yes they call the blobs "worlds" but that doesn't mean that they think the "real world" or "individually observed world" is a exactly one of the blobs.
3pragmatist
The "real world", in the Oxford MWI, is the entire wavefunction, not just one branch. That is the fundamental ontology of the interpretation. There's no sense in which one blob is more "real" than any other.
0Mitchell_Porter
But the individually observed portion of reality is just part of the wavefunction, yes? So, what sort of part?
4wedrifid
Why does it need a special name? There's a wavefunction. Part of that wavefunction represents a Mitchell_Porter observing stuff. It's that part of the wavefunction.
-3Mitchell_Porter
That's no good if I'm trying to evaluate MWI as a physical theory. Those are just words. You can try to extract a "branch" from a wavefunction or a state vector in a variety of ways. You might focus on a specific classical configuration (then we might have to quibble about whether you mean the point in configuration space that is labeled by that configuration, or whether you mean the delta function peaked at that point in configuration space). Or we might be talking about some other sort of basis function in terms of which a wavefunction might be decomposed (momentum eigenfunctions, wavelets, eigenfunctions of other observables). We might be talking about reduced density matrices rather than pure states... If someone wants to insist that, in their version of MWI, there is a locally specific reality only for the region of the observer's brain corresponding to conscious observation, they can dodge some of the details by saying we don't know enough neuroscience yet. But they should be able to make precise statements about what sort of mathematical vivisection is going to be performed on the local wavefunction in order to get the "part of the wavefunction... observing stuff". Otherwise, they don't yet have a physical theory, just a vague hope that some version of Many Minds will work out. And by the way, if we are not saying that branches correspond to universe-wide configurations, but rather just to local configurations, what's responsible for tying together a million different information-processing events into a single mind-state? Every neighboring molecule in the brain ought to be locally branching, constantly, and independently of branchings on the other side of the skull. How could you ever justify speaking about "the" state of someone's brain, even just as one branch of an Everett multiverse? The cognitive state will have to "supervene" on something which, from an atomic and subatomic level, is already a very intricate superposition.
5wedrifid
No, you have this backwards. You're looking for some words. I'm telling you there are just numbers. The numbers are all we need to be evaluating here.
-1Mitchell_Porter
Fine, let's talk about numbers. If you tell me that reality is one big wavefunction, and that observable reality is made of states of neurons, then you need to tell me how to get "state of neuron" from "wavefunction". Which set of numbers do I use? Is it the coefficients of the wavefunction, expressed in a global configuration basis? Is it the coefficients of the wavefunction, expressed in some other basis? Or should I be looking at the matrix elements of reduced density matrices? Also, if we talk about the configuration basis, should I regard the numbers specifying a particular configuration as part of reality? From a Hilbert-space geometric perspective, a "wavefunction" is actually a state vector, so it's just a ray in Hilbert space, and the associated configuration is just a label for that ray, like the "x" attached to a coordinate axis. A basis function is a different object to a density matrix, and the coefficient of a basis vector is a different sort of quantity to the quantities appearing in the label of the basis vector (that is, the eigenvalues associated with the vector). I need to know which of the various types of number that can be associated with a quantum state, are supposed to be related to observable reality.
[-]WrongBot20

To clarify: does the Deutsch-Wallace school hold that worlds/branches are like real numbers, in that if you pick any two worlds, you can always pick a world that lies "between" them? Or is it some confused alternative?

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0Mitchell_Porter
See my response to Oscar. Branches (according to Oxford) are like the blobs in configuration space (or like the ink blots on Emile's illustration!), they're an approximate construct that depends on definition. Which is an absolutely untenable position, if you want to identify the observed portion of reality with a branch, because the observed portion of reality does not owe its existence to our definitions. If people cared about this issue of vagueness, they could seek objective definitions of world (apart from "a point in configuration space"). For example, they could look at maxima, minima, and other turning points in the wavefunction. The blob could be exactly identified by the maximum that it contains, rather than fuzzily identified by its edges. There might be a dual description of the wavefunction in terms of a topological object in configuration space, rather than a complex-valued function, in which specifying the maxima, minima, etc., carries all the same information. That sort of investigation would be much healthier.
[-]timtyler10

This seems to be one of the main Deutsch papers on the topic: Quantum Theory of Probability and Decisions.

Deutsch sets out to demonstrate that "No probabilistic axiom is required in quantum theory." - which seems to be reasonable enough.

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0[anonymous]
Check the critiques of this approach in my earlier comment
5timtyler
I think you are probably on the wrong side of this argument. However, there's currenly no scientific consensus on the issue.
-1[anonymous]
There is rarely consensus in the philosophical aspects of physics, but the vast majority who think these issues through definitely reject MWI due to, among other things, the Born rule issue
4timtyler
I am skeptical. There have been surveys and the MWI came out pretty well. The Born rule Wikipedia page has this citation for a derivation from decision theory: Armando V.D.B. Assis (2011). On the nature of a'kak and the emergence of the Born rule. Annalen der Physik, 2011.
2[anonymous]
Well you are citing a HIGHLY unscientific and invalid poll. For instance this: Gell-Mann does not support Many Worlds and he never did, he is a proponent of something called Consistent Histories. Stephen Hawking is not a supporter of MWI either, it was taken out of context in a interview, he has later cleared this up. I have personally asked Steven Weinberg and he says he has changed his position due to the probability issue, he actualy mentions this in a interview from earlier this year, but more importanty in his most recent paper from somewhere around Sept-Oct. The author of that FAQ has an almost religious view of MWI, he is still weekly updating the wiki site and it seems his best arguments are an appeal to authority, which I've just shown is a false authority as they do not share his views. Even David Deutsch, the strongest proponent of MWI, admits that he estimates that less than 5% of those working on quantum foundations accepts Many Worlds and within that group there are atleast 10 different "many worlds" views that are at odds with each other. As for the Born Rule paper, well I have certainly never heard of it before, if it indeed was a vaid derivation of Born Rule within a Many Worlds context I am pretty sure it would be huge news within the foundations community, which it has not. It is listed with a "wavefunction collapse" tag, so I doubt he is talking about Many Worlds.
0timtyler
More polls on the topic are listed here. By now it looks as though you don't have much good evidence for your claim that "the vast majority who think these issues through definitely reject MWI".
2[anonymous]
Please read that link you just posted, it supports my statement 100%. Also take a look at the "talk section" and you will see that there are several people criticizing the biased presentation of MWI's popularity, eventhough it clearly says the vast majority rejects MWI. so it's even wose than presented. Next time read your own sources before using them to advocate for your own position. Also the fact that there are several people who consider MWI to be a nice mental model to use while doing physics, but ultimately not the fundamental representation of reality, these people will often vote "yes". This is the reason for Tegmark sometimes starting his presentations by taking a poll of the audience and then go on to say "now out of those who support MWI, how many believe these worlds REALLY exists and this represents reality?" Then usually quite a few takes their hands down and no longer should be counted as "pro-MWI", Martin Gardner explains this somewhat in the link you gave above... Lastly there are yet 2 more factors affecting these results, when a proponent of MWI decides to take a poll, it is highly likely that his audience is not a nonbiased random sample of the physics community, it's highly likely that other MWI sympathizers show up to his talk because they already share his views. This is why it's always emphasized that it is a "highly unscientific poll" Last but not least you've got to realize that there are somewhere around 10 different Many worlds interpretations and 5 different Many Minds interpretations, all of these people would say "yes" when asked "do you support MWI?" when in reality they are not in agreement on very important details at all...
[-]lessdazed00

I would very much appreciate critical feedback on this comment, as I have no math background.

First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence.

Some stuff can no longer influence other stuff due to distance and the locality of physics, whereas in the past it could. As time goes on, this is true of more and more things. For each bit of stuff and each other bit, the question of whether they are or are not in range has a definite answer, whether we know it... (read more)

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[-]DuncanS00

The question here is which is the correct / best interpretation of quantum mechanics.

The key word in this is interpretation. The actual predictions of what we should actually observe are the same for all the various interpretations of quantum mechanics - this should be no surprise, because we are not discussing the actual mathematics of quantum mechanics, nor its predictions.

We are in fact discussing the unobservable aspects of quantum mechanics. If I perceive a random quantum event, is there also a counterpart of me that perceives the other outcome of tha... (read more)

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1Peterdjones
MWI adds a privileged basis that is also unnecessary. MWI adds a universal quantum state that is not , and cannot be, observed.
0Mitchell_Porter
You are missing MWI's problem with the Born rule. If each "branch" exists only once, then all outcomes are equally probable, which is empirically wrong.
2pragmatist
You keep asserting this, but you have not provided any good reason to believe it. Your assumption seems to be that the counting rule is the natural understanding of probability in MWI. I don't see this at all. As far as I can tell, there is no "natural" way to interpret probability in MWI. Consider an analog: a Parfit-esque case of fission, where your body is disintegrated and, instantaneously, two atom-for-atom duplicates are produced in different parts of the world. Call these duplicates Mitchell-1 and Mitchell-2. It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1. I fail to see why that would be the default position. The appropriate default position seems to be that probabilities are irrelevant here. I think that is the right default position in the MWI case as well, and it is incumbent on all proponents of probabilities in MWI to justify why one should be talking about probabilities at all. I can understand the criticism that talk of probabilites in MWI is incoherent, but I really don't understand the criticism that probabilities in MWI must be branch frequencies. As far as I can see, the only way to justify talk of probabilities in the fission case (and, by extension, in MWI) is to think about it from the perspective of the agent's decision-making process prior to the fission. Perhaps even this is insufficient to get us any coherent notion of probabilities, but it seems like the only semi-plausible candidate. If you're going to justify the counting rule, you need to tell me why it would make sense for an agent in an Everettian world to organize expectations in accord with the counting rule. And this justification should not sneak in prior probabilistic ideas (like the idea that the agent is equally likely to end up in each future branch). Wallace claims to have provided such a justification for the Born rule. If you want me to take the counting rule seriously, I'd like to see an attempt
1Mitchell_Porter
Let's suppose I am to be disintegrated as you suggest, to be replaced with these atomic duplicates, Mitchell-1 and Mitchell-2. But we add that Mitchell-1 will be gunned down, and Mitchell-2 will not be. Now suppose you ask me, before this disintegration, "what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?" The answer is 50%. But this is analogous to the situation in Many Worlds, before a branching. I, here, now, will cease to be; in my place will be a variety of distinct successors. Why is it illegitimate to reason about them in exactly the same way?
0pragmatist
This is true, but irrelevant. There is no random selection going on. By the same token I could say that if you asked "What are the odds that a future self selected according to the Born rule will observe spin-up in this experiment?" you'd recover quantum statistics. But then you'd rightly challenge me by asking why this particular question should matter. Well, I can ask the same of your random selection question. Here's one way random selection might be relevant in the fission case. Perhaps, pre-split, the agent should reason as if in a position of complete subjective uncertainty about which future branch is him. If this is right, then it seems reasonable that in a classical world he should assign a maximum entropy distribution over future selves, and so he should reason as if his future self is being randomly selected from all the future duplicates. This sort of argument might justify the random selection assumption. But Wallace makes exactly this sort of argument for the quantum case, except he claims that there are symmetry considerations involved in that case which make it more reasonable to use the Born distribution when one is in a state of complete subjective uncertainty. The other potential justification I can see for the random selection assumption is that you are using some anthropic selection rule like Bostrom's Self Sampling Assumption. I think it is far from clear that the SSA is the right way to reason anthropically. In any case, Bostrom himself modifies the SSA to fit Born statistics in his discussion of MWI in his book.
0Mitchell_Porter
My question was constructed in order to completely sidestep questions of persistent identity (i.e., which future duplicate, if any, is me?). It could have been phrased as follows: "What percentage of my future duplicates will be gunned down?" The answer is 50%, because by hypothesis, there are two duplicates, one is shot, the other isn't. There is nothing there about random selection or any other sort of selection. There is also no uncertainty about which future copy "is me"; that's not what I'm asking; a future entity counts for such a question if it is a duplicate of me, and by hypothesis there are two of them. So why can I not reason in exactly this way about my quantum successors according to MWI? I am not asking "What should I expect to see?"; I am asking, "How many of my decohered successors will have a certain property?"
1pragmatist
If that's the question you're asking, then it's obvious frequencies are the way to go. But why is this a problem for the MWI?
1ArisKatsaris
You keep making this claim, and it keeps not making sense. It isn't even true for classical mechanics. A coin can have two sides, and it can still be made to favor one side more than the other.
0Mitchell_Porter
This resembles the misleading dichotomy between "observation" and "existence", discussed elsewhere. If you want to talk about bias in the coin, then we should be talking about the existence and the number of coin flips.
[-]lavalamp-10

This is much clearer than your last post, thank you.

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