A case study in fooling oneself
Note: This post assumes that the Oxford version of Many Worlds is wrong, and speculates as to why this isn’t obvious. For a discussion of the hypothesis itself, see Problems of the Deutsch-Wallace version of Many Worlds.
smk asks how many worlds are produced in a quantum process where the outcomes have unequal probabilities; Emile says there’s no exact answer, just like there’s no exact answer for how many ink blots are in the messy picture; Tetronian says this analogy is a great way to demonstrate what a “wrong question” is; Emile has (at this writing) 9 upvotes, and Tetronian has 7.
My thesis is that Emile has instead provided an example of how to dismiss a question and thereby fool oneself; Tetronian provides an example of treating an epistemically destructive technique of dismissal as epistemically virtuous and fruitful; and the upvotes show that this isn’t just their problem. [edit: Emile and Tetronian respond.]
I am as tired as anyone of the debate over Many Worlds. I don’t expect the general climate of opinion on this site to change except as a result of new intellectual developments in the larger world of physics and philosophy of physics, which is where the question will be decided anyway. But the mission of Less Wrong is supposed to be the refinement of rationality, and so perhaps this “case study” is of interest, not just as another opportunity to argue over the interpretation of quantum mechanics, but as an opportunity to dissect a little bit of irrationality that is not only playing out here and now, but which evidently has a base of support.
The question is not just, what’s wrong with the argument, but also, how did it get that base of support? How was a situation created where one person says something irrational (or foolish, or however the problem is best understood), and a lot of other people nod in agreement and say, that’s an excellent example of how to think?
On this occasion, my quarrel is not with the Many Worlds interpretation as such; it is with the version of Many Worlds which says there’s no actual number of worlds. Elsewhere in the thread, someone says there are uncountably many worlds, and someone else says there are two worlds. At least those are meaningful answers (although the advocate of “two worlds” as the answer, then goes on to say that one world is “stronger” than the other, which is meaningless).
But the proposition that there is no definite number of worlds, is as foolish and self-contradictory as any of those other contortions from the history of thought that rationalists and advocates of common sense like to mock or boggle at. At times I have wondered how to place Less Wrong in the history of thought; well, this is one way to do it—it can have its own chapter in the history of intellectual folly; it can be known by its mistakes.
Then again, this “mistake” is not original to Less Wrong. It appears to be one of the defining ideas of the Oxford-based approach to Many Worlds associated with David Deutsch and David Wallace; the other defining idea being the proposal to derive probabilities from rationality, rather than vice versa. (I refer to the attempt to derive the Born rule from arguments about how to behave rationally in the multiverse.) The Oxford version of MWI seems to be very popular among thoughtful non-physicist advocates of MWI—even though I would regard both its defining ideas as nonsense—and it may be that its ideas get a pass here, partly because of their social status. That is, an important faction of LW opinion believes that Many Worlds is the explanation of quantum mechanics, and the Oxford school of MWI has high status and high visibility within the world of MWI advocacy, and so its ideas will receive approbation without much examination or even much understanding, because of the social and psychological mechanisms which incline people to agree with, defend, and laud their favorite authorities, even if they don’t really understand what these authorities are saying or why they are saying it.
However, it is undoubtedly the case that many of the LW readers who believe there’s no definite number of worlds, believe this because the idea genuinely makes sense to them. They aren’t just stringing together words whose meaning isn’t known, like a Taliban who recites the Quran without knowing a word of Arabic; they’ve actually thought about this themselves; they have gone through some subjective process as a result of which they have consciously adopted this opinion. So from the perspective of analyzing how it is that people come to hold absurd-sounding views, this should be good news. It means that we’re dealing with a genuine failure to reason properly, as opposed to a simple matter of reciting slogans or affirming allegiance to a view on the basis of something other than thought.
At a guess, the thought process involved is very simple. These people have thought about the wavefunctions that appear in quantum mechanics, at whatever level of technical detail they can muster; they have decided that the components or substructures of these wavefunctions which might be identified as “worlds” or “branches” are clearly approximate entities whose definition is somewhat arbitrary or subject to convention; and so they have concluded that there’s no definite number of worlds in the wavefunction. And the failure in their thinking occurs when they don’t take the next step and say, is this at all consistent with reality? 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? It’s the failure to ask that last question, and really think about it, which must be the oversight allowing the nonsense-doctrine of “no definite number of worlds” to gain a foothold in the minds of otherwise rational people.
If this diagnosis is correct, then at some level it’s a case of “treating the map as the territory” syndrome. A particular conception of the quantum-mechanical wavefunction is providing the “map” of reality, and the individual thinker is perhaps making correct statements about what’s on their map, but they are failing to check the properties of the map against the properties of the territory. In this case, the property of reality that falsifies the map is, the fact that it definitely exists, or perhaps the corollary of that fact, that something which definitely exists definitely exists at least once, and therefore exists with a definite, objective multiplicity.
Trying to go further in the diagnosis, I can identify a few cognitive tendencies which may be contributing. First is the phenomenon of bundled assumptions which have never been made distinct and questioned separately. I suppose that in a few people’s heads, there’s a rapid movement from “science (or materialism) is correct” to “quantum mechanics is correct” to “Many Worlds is correct” to “the Oxford school of MWI is correct”. If you are used to encountering all of those ideas together, it may take a while to realize that they are not linked out of logical necessity, but just contingently, by the narrowness of your own experience.
Second, it may seem that “no definite number of worlds” makes sense to an individual, because when they test their own worldview for semantic coherence, logical consistency, or empirical adequacy, it seems to pass. In the case of “no-collapse” or “no-splitting” versions of Many Worlds, it seems that it often passes the subjective making-sense test, because the individual is actually relying on ingredients borrowed from the Copenhagen interpretation. A semi-technical example would be the coefficients of a reduced density matrix. In the Copenhagen interpetation, they are probabilities. Because they have the mathematical attributes of probabilities (by this I just mean that they lie between 0 and 1), and because they can be obtained by strictly mathematical manipulations of the quantities composing the wavefunction, Many Worlds advocates tend to treat these quantities as inherently being probabilities, and use their “existence” as a way to obtain the Born probability rule from the ontology of “wavefunction yes, wavefunction collapse no”. But just because something is a real number between 0 and 1, doesn’t yet explain how it manages to be a probability. In particular, I would maintain that if you have a multiverse theory, in which all possibilities are actual, then a probability must refer to a frequency. The probability of an event in the multiverse is simply how often it occurs in the multiverse. And clearly, just having the number 0.5 associated with a particular multiverse branch is not yet the same thing as showing that the events in that branch occur half the time.
I don’t have a good name for this phenomenon, but we could call it “borrowed support”, in which a belief system receives support from considerations which aren’t legitimately its own to claim. (Ayn Rand apparently talked about a similar notion of “borrowed concepts”.)
Third, there is a possibility among people who have a capacity for highly abstract thought, to adopt an ideology, ontology, or “theory of everything” which is only expressed in those abstract terms, and to then treat that theory as the whole of reality, in a way that reifies the abstractions. This is a highly specific form of treating the map as the territory, peculiar to abstract thinkers. When someone says that reality is made of numbers, or made of computations, this is at work. In the case at hand, we’re talking about a theory of physics, but the ontology of that theory is incompatible with the definiteness of one’s own existence. My guess is that the main psychological factor at work here is intoxication with the feeling that one understands reality totally and in its essence. The universe has bowed to the imperial ego; one may not literally direct the stars in their courses, but one has known the essence of things. Combine that intoxication, with “borrowed support” and with the simple failure to think hard enough about where on the map the imperial ego itself might be located, and maybe you have a comprehensive explanation of how people manage to believe theories of reality which are flatly inconsistent with the most basic features of subjective experience.
I should also say something about Emile’s example of the ink blots. I find it rather superficial to just say “there’s no definite number of blots”. To say that the number of blots depends on definition is a lot closer to being true, but that undermines the argument, because that opens the possibility that there is a right definition of “world”, and many wrong definitions, and that the true number of worlds is just the number of worlds according to the right definition.
Emile’s picture can be used for the opposite purpose. All we have to do is to scrutinize, more closely, what it actually is. It’s a JPEG that is 314 pixels by 410 pixels in size. Each of those pixels will have an exact color coding. So clearly we can be entirely objective in the way we approach this question; all we have to do is be precise in our concepts, and engage with the genuine details of the object under discussion. Presumably the image is a scan of a physical object, but even in that case, we can be precise—it’s made of atoms, they are particular atoms, we can make objective distinctions on the basis of contiguity and bonding between these atoms, and so the question will have an objective answer, if we bother to be sufficiently precise. The same goes for “worlds” or “branches” in a wavefunction. And the truly pernicious thing about this version of Many Worlds is that it prevents such inquiry. The ideology that tolerates vagueness about worlds serves to protect the proposed ontology from necessary scrutiny.
The same may be said, on a broader scale, of the practice of “dissolving a wrong question”. That is a gambit which should be used sparingly and cautiously, because it easily serves to instead justify the dismissal of a legitimate question. A community trained to dismiss questions may never even notice the gaping holes in its belief system, because the lines of inquiry which lead towards those holes are already dismissed as invalid, undefined, unnecessary. smk came to this topic fresh, and without a head cluttered with ideas about what questions are legitimate and what questions are illegitimate, and as a result managed to ask something which more knowledgeable people had already prematurely dismissed from their own minds.
In so many words you detail the disapproval of others’ reasoning, but do you ever point out what the error is?
“The error” could mean: the false thing that is being asserted; the reason why it is false; or the cognitive mistake which allows it to escape detection.
Maybe I should begin with the true thing that is being asserted! Which is that the number of ink blots can depend on definition, or on the judgment or whim of the individual observer. That is indeed true.
It also may or may not be true that the number of branches, worlds, blobs, etc., in a wavefunction is similarly undefined, or dependent on a somewhat arbitrary definition.
What I deem to be categorically false is the proposition that this is also true of “observers”, or “portions of reality that can contain observers” (which might be called worlds or branches), or even just “portions of reality like the one that I find myself in” (which is a definition not involving observers, except incidentally).
The reason that this is false, is that the arbitrariness of the number of blobs, arises from the arbitrariness of their definition. Their very existence is in some sense arbitrary, relative, observer-dependent. It is because their existence is relative, that their number is relative.
The existence of the observed portion of reality is not “relative”; it is definitely there, and it is not caused by the contingent and changeable decisions of some observer about how to divide up reality. On the contrary, the observer here is part of the branch or world; their role is simply to register the fact that it exists, not to have created it.
Why isn’t this reasoning used to criticize and rule out theories in which the existence of worlds and branches is vague and definition-dependent? This is what the post is actually about. At some level, it must be nothing more than a failure to combine fact A (this interpretation says worlds in the wavefunction are vague) with fact B (the existence of the real world can’t be vague) in order to draw the obvious conclusion (this interpretation must be wrong). But how does this work psychologically? I was hoping some believers in the “Oxford school” would describe how they arrived at their belief, but it seems I first have to communicate why this belief is so problematic.
Mitchell, you are on to an important point: Observers must be well-defined.
Worlds are not well-defined, and there is no definite number of worlds (given standard physics).
You may be interested in my proposed Many Computations Interpretation, in which observers are identified not with so-called ‘worlds’ but with implementations of computations: http://arxiv.org/abs/0709.0544
See my blog for further discussion: http://onqm.blogspot.com/
I wouldn’t characterize myself as a partisan of the Oxford Everettian school, but I do think it is, all things considered, the most compelling interpretation available. The challenges you raise are important ones, but they are ones that the Oxford Everettians have considered. Perhaps you find their responses unsatisfactory, but these questions have been addressed, even the one of which you write, “It’s the failure to ask that last question, and really think about it, which must be the oversight allowing the nonsense-doctrine of “no definite number of worlds” to gain a foothold in the minds of otherwise rational people.”
David Wallace has thought about the fuzziness of Everettian “worlds”, and the implications of this for our ordinary ontology. Here is one of a number of papers where he discusses this question: http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.2189v1.pdf
As for the claim that probabilities in the Everettian interpretation should be understood as frequencies, see Greaves: http://philsci-archive.pitt.edu/3103/2/pitei.pdf . The relevant section is 3.2.3, especially the part about the “naive counting” rule, which is what you propose. The rule is a bad one precisely because basing “world-splitting” on decoherence puts the kibosh on the idea that there is a single determinate number of worlds. If Wallace’s structuralist approach to the ontology of the wave function makes sense (and it seems to me that it does), then this response makes sense as well.
Perhaps when I have more leisure I’ll try writing a response detailing what I think are the most plausible responses to your questions, but in the interim I wanted to make sure people know that the Oxford Everettians have thought about this stuff.
That Wallace paper is a fantastic treatise on, and case study in, belief in the implied invisible.
(thanks to Nisan for pointing out the part that went missing. LW formats links with missing parts differently from reddit).
It looks like there’s something missing from your comment.
EDIT: I’m amused that the missing link turned out to be Belief in the Implied Invisible.
From the Wallace paper:
So, he basically concedes that the world counting is meaningless, except as a metaphor. What a letdown.
Wallace’s refusal to answer in any meaningful way reminded me of the following exchange in The Simple Truth:
Mark heaves a patient sigh. “Autrey, do you think you’re the first person to think of that question? To ask us how our own beliefs can be meaningful if all beliefs are meaningless? That’s the same thing many students say when they encounter this philosophy, which, I’ll have you know, has many adherents and an extensive literature.”
“So what’s the answer?” says Autrey.
“We named it the ‘reflexivity problem’,” explains Mark.
“But what’s the answer?” persists Autrey.
Mark smiles condescendingly. “Believe me, Autrey, you’re not the first person to think of such a simple question. There’s no point in presenting it to us as a triumphant refutation.”
I don’t understand this. Wallace does give an answer to the question “How many worlds?” His answer is something like “That’s not a question with a precise answer.” And he gives a number of reasons in support of this response. He doesn’t just say “Oh, I’ve thought about that question a lot. Believe me, it’s not that simple.” In what way is his response similar to Mark’s?
And why do you find his claim that world counting is meaningless a “letdown”? Why is giving a precise rule for world counting a desideratum for an Everettian interpretation?
My best understanding of the MWI’s take on the Born rule is that the ratio of the number of branches for each outcome to the total number of branches gives you the probability of each outcome. Both numbers must be finite for the division to make sense. If you cannot count branches, you cannot calculate probabilities, reducing the model into just a feel-good narrative (with the Born rule inserted by hand). Refusing to acknowledge this issue is similar to what Mark does in the story.
This is a relevant discussion of the issue.
No, the probabilities in MWI are not counting discrete worlds. A world with large amplitude is not multiple identical worlds but a single world that is more real. Leaving aside the actual interpretation, your suggestion is mathematically incoherent. You seem to be demanding that the probabilities in QM are rational numbers with bounded denominator. This is an extremely radical position. It would simplify the ontology a lot, but there is no reason to believe that quantum mechanics can be approximated by a system where the amplitudes are not infinitely divisible. More precisely, a large finite subgroup of the unitary group does not look like the unitary group, but like a torus.
Sorry, I did not get your point about the group and subgroups, or at least not its relevance to the question. I would expect that to derive Born probabilities one has to assign measures to different worlds (how else would you express mathematically that “A world with large amplitude is not multiple identical worlds but a single world that is more real.”?) I agree that counting branches is not the only way to do it, just the most obvious one. Unfortunately, none of the ways of assigning “strength” to different branches seems to work any better than this naive one in deriving the Born rule (that is to say, they do not work at all).
This is not the way the Oxford Everettians understand the Born rule. See the Hilary Greaves paper I linked to for a discussion of their decision-theoretic approach to probabilities in the MWI. This approach has its problems, but they are problems that the Everettians acknowledge and attempt to address (not entirely successfully, in my opinion). That’s very different from Mark’s attitude.
Also, the Orzel post you linked to doesn’t seem to support your contention. Where do you see him committing himself to the branch counting appproach you propose? (EDIT: Actually, I see that there is discussion of the issue in the comments to that post, which is probably what you meant.)
From the paper:
This must a bad wording, or something, otherwise why does a “rational” agent who does not believe “she lives in an Everettian multiverse” can still confirm the Born rule experimentally time after time?
The proof does not address rational agents who do not believe they are in an Everettian multiverse. They would have other reasons for using the Born rule.
Is that necessarily true?
If they are infinite, then there should at least be a well-defined way to take a limit (or one of its generalizations), which amounts to nearly the same thing, constructing a sequence of ratios of finite numbers and proving convergence.
I’m downvoting you for the tone and the constant application of insults.
And also for confused thinking. MWI advocates don’t believe that we collectively inhabit a “single” world. The first picosecond after any single quantum event I cause, surely people on the other side of the world haven’t had the time to branch yet in response to that quantum event—the light-speed barrier alone prevents them from having so branched.
So at any given time, some people have branched, and the rest of the planet hasn’t yet branched alongside them. Some of those local branches will even merge back into one, and some will not. So that alone shows there’s no “definite”, as in universal, number of branches, same way there’s no definite, as in universal frame of reference for movement or acceleration.
Your argument is effectively the analogous of saying “if the Einsteinian relativistic school of thought says there’s no definite frame of reference, only an infinite frames of reference with no definite reality in them, how is it possible for our own frame of reference to be real? You relativistists must have merely not thought this through, that’s why you believe in such obvious nonsense”
why would the light speed limit apply to quantum branching?
Because decoherence is a physically mediated process, and physical laws obey the light-speed limit.
Then restrict the discussion to “local branching”. Do you think it makes sense to say that the universe branches locally, but not into a definite number of local branches?
This post needs a much clearer explanation of what people have done wrong. I also think that a diagnosis should be a separate post from the accusation of error.
(Gee, I turn my back for ten second and LW spawns a long comment thread about me!)
My answer to smk was intending to illustrate how “world counting” worked within the Many Worlds Interpretation, not to argue which of Many Worlds (Oxford or not) or others was the correct interpretation.
Just like you can answer questions about rolling balls within the framework of Newtonian Physics, without having to launch into a diatribe about how Relativity is a better model.
I wish your post made a clearer distinction between criticism of my explanation (I think you read way too much into what I wrote), criticism of the high regard for MWI in this community, and psychoanalysis as to how my thinking supposedly went so very wrong.
I might add a link to this thread, and to wedrifid & Tetronian’s, so a reader can immediately see your response. That way, you get the right of reply, and the original diatribe is preserved.
When I wrote the “psychoanalysis” (e.g. the “imperial egos”), I was thinking more of theoretical physicists and other purveyors of comprehensive, formally expressed ontologies. They are the prime movers here, the ideologists who put the pernicious memes into circulation. The true social-psychological explanation for how “Many Vague Worlds” has managed to achieve such popularity may be quite different to what I have proposed; the whole way I got the issue out there was somewhat crudely executed. But I do regard this as a serious matter; the miasma of illogic surrounding the Oxford school is at least as bad as that surrounding the Copenhagen interpretation, yet it is getting a free pass from a community of rationalists.
You declare this, without acknowledgment of others who have considered these issues and have their rebuttals. Your alternative hybrid of string-theory and fundamental mental entities alternative described in past posts looks far more nonsensical to most. At the same time, you have never in all your posts and comments addressed the fact that all the issues with probability and personal identity in Many Worlds can apply to classical systems too, e.g. Eliezer’s Ebborians hypothetical, or this paper, or traditional philosophical hypotheticals with brain growth and surgical fission.
This post isn’t about my theories. It should not take an abnormal conceptual effort to reject the proposition that “there are many worlds, but no particular number of them”. It is, on the face of it, illogical, like a round square. It doesn’t express a coherent idea. Should we spend time thinking about the possibility that true things are also false, or that reality is an elephant, or that time is actually running backwards? Maybe it’s a good cognitive workout to think about such things, and just maybe, on a very rare occasion, nonsense will turn out to be sense. But hopefully you can see my point—that this dispute is on a different level from a dispute over whether it’s reasonable to believe that there are other worlds, ten dimensions, disembodied souls, and other such hypotheses. Those hypotheses may be strange, but they are unquestionably logically well-formed. They have a meaning.
The same can not be said for “no definite number of worlds”. If something exists, it can be counted (or given a cardinality, if it is infinite). The defense of vagueness about branches rests on analogies like the ink blot, but it’s a false analogy, because the ink blot is “created” by perception, by definition, or by a rule. This is why I engaged in my speculative psychoanalysis about the imperial ego of the abstract theorist, who creates a map of reality which remains unfolded before their mind’s eye, and who never gets around to considering whether the correctness of the map is consistent with the fact of their own existence.
The existence of the world (the existence of “a” world, the existence of “this world”) is not a matter of definition, it is an elemental fact, and you can’t treat its existence as resulting from the mere mental projection of a boundary onto an underlying continuum. If your underlying-continuum theory of reality doesn’t contain objectively distinct structures, one of which corresponds to observed reality, then that is a problem for your theory, it’s not a revelation about reality.
In fact I have, but perhaps not recently. This very same reasoning also invalidates various attempts to be vague about the number of selves, or to have fractionally existing selves; but that is another unpopular conclusion (unpopular on LW), and one which perhaps experiences even more resistance than the argument against vagueness about worlds.
This is an interesting discussion, but this claim struck me as odd:
This seems like an open philosophical question. Clearly you are a finitist of some sort, but as far as I know it hasn’t been empirically verified that real numbers don’t exist. Certainly continuous functions are widely employed in physics, but whether all of physics can be cast into a finitist framework is an open question last I checked.
So your assertion above doesn’t seem firmly justified, as uncountable entities could exist. I have no informed opinion as to whether worlds must be countable or can be uncountable. It certainly seems like they ought to be countable, since the total number of particle configurations in the universe at any given moment in time seems finite, but that’s just an uneducated guess.
I am not a finitist. There are cardinals for uncountable sets. I was objecting to people who say things like (page 16) “how many worlds there are” is a “non-question”.
The inkblot is a good way to demonstrate what a “wrong question” is. The charitable (and literal) reading of his words does not attribute to that comment any particular claim about quantum mechanics.
The QM question, while it is somewhat wrong, is not one to just be dismissed as wrong. An explanation of roughly how the wavefunction works is appropriate.
Pardon me for asking another physics dummy question. Does quantum roulette still make (theoretic) sense even if the “worlds” aren’t actually distinct worlds?
I would need to know more about what you mean by “aren’t actually distinct worlds”. Also what you mean by ‘makes sense’.
Basically what Emile said about a “fuzzy continuum” and “just a high-level abstraction”. The inkblottiness.
I mean is it a coherent concept given the inkblottiness? (I don’t mean is it a sensible thing to do. I already read your post where you said “I personally consider anyone who wants to play quantum roulette to be crazy.”)
I would answer ‘yes’… QR still makes the same amount of sense under those circumstances as it ever did. (ie. It ‘works’ but gives undesirable outcomes!)
I support this interpretation. It’s a good analogy to demonstrate the concept of a wrong question, full stop.
If they do an experiment where they detect waveform collapse, and it’s repeated by other labs with different equipment, then we’ll change our opinions.
It’s common to define “world” as a blob in configuration space. It’s similar to the idea of an ink blot. It is not something ontologically fundamental. I’m told that this is the standard definition, but I don’t really know.
Another definition is a point in configuration space. As far as anyone can tell, configuration space is a continuum, and there are uncountably infinite of them. This one is precisely defined, and the answer may very well be uncountably infinite. It could even be bigger than a continuum, for that matter.
I can’t speak for the rest of us, but I follow those because each step has been pinned down extremely well.
There is no possibility. It has no inherent meaning. I suspect you’re thinking of something with specific properties. If so, the definition that compares it to ink blots isn’t that. It’s not meant to be that.
The crucial issue is whether you need to suppose the actual existence of parallel worlds (or parallel “parts-of-world”) in order to explain experiment.
Classical probability can be expressed as a sum over histories, but that is not taken as evidence that the other histories do exist or must exist. The entirety of the reason for believing in the actual existence of other quantum histories is the interference of probability amplitudes—destructive interference, as in the double-slit experiment, is especially clear. You have things that don’t happen, or that happen rarely, “because” there are two ways in which they can happen, but the amplitudes cancel.
Nonetheless, the ontological significance of this is not nailed down. One class of quantum interpretations is retrocausal: there are causal chains heading from future to past as well as from past to future. If you have classical probabilistic dependence that is bidirectional in time, can you get destructive interference? I don’t know, and I think nobody knows.
Also, the arrival statistics (interference patterns) produced in a double-slit experiment provide information about the center-of-mass motion of the object which goes through the slits. It may be possible to get double-slit behavior, even from large objects (I mean containing thousands of atoms), from something like Bohmian mechanics, in which there is an extra potential arising from the double-slit apparatus, which induces a Bohmian trajectory in the center-of-mass motion. The other degrees of freedom of the complex object would be essentially independent of this coupling. Possibly such an explanation would require a deviation from quantum mechanics; again, I don’t think this line of thought has been pursued.
Even if we reach the point of believing in many worlds, we still might want to consider something that looks like many Bohmian worlds, but in which there is no guiding wavefunction—rather, the ensemble of worlds itself would provide the guiding influence for each of the member worlds. Here you would have many worlds which were genuinely interacting with their neighbors in configuration space.
I don’t claim that this remotely exhausts the theoretical possibilities or issues that one might wish to think about. What I do claim is that there is almost no reason to consider the “possibility” that “worlds exist but they don’t definitely exist”, or however it is that one chooses to express the Oxford school’s position, because this position resists even being stated in a way that makes sense. As I just said to kilobug, it makes sense to say that there is no right definition of “blob”, but it does not make sense to say that there is no right definition of “world”, because the existence of the blob depends on the definition, but the existence of the world does not.
According to timeless physics, the past and future are just other parallel worlds. They might not actually exist, but since we can’t really do anything unless they do, we might as well assume they exist.
Even without that, Assuming that a specific path through the waveform happens is pretty silly. All of it is vital to figuring out what happens, so why assume on piece of the past exists? If I were going to assume that it was mostly just reality conforming to a random point in a waveform, I’d expect it’s one random point. Why would it be a path of them?
From what I can gather about that, it still assumes a waveform. In order for it to make the same predictions as quantum mechanics, which have been very thoroughly tested, it would have to have waveforms of huge numbers of dimensions. It would either have to have laws about how the waveform gets entangled, like the Copenhagen interpretation, or it would have to have the waveform include the position of every particle. In short, it assumes some other interpretation of quantum mechanics, and then adds particles on top of that.
Am I misunderstanding it?
One possibility I have considered is that the waveform is made of a huge number of interacting particles.
I don’t actually know what that position is. My position is that the entire waveform exists. I don’t know why the Born probabilities are what they are, but I wouldn’t know no matter what they were.
You’re reading too much into that word. The terminology is a bit misleading. It’s like a blob, not what you think of when you think “world”.
I’d say the world, in the sense of what actually happens, is the entire configuration space. I don’t know what makes us “experience” a piece of it, but it’s as much a question of neurons as it is of amplitudes.
When I saw the title of this post and your name I was hoping to read something that would challenge my beliefs about quantum physics or the hard problem of consciousness. Instead I learned three unflattering hypotheses for why people disagree with you.
By the way, I don’t know what I think about Emile’s comment, but I don’t think it’s worth making a fuss over, as it was a response to smk’s question which was basically, “How many elementary tensors make up a nonelementary tensor? Btw I don’t know math.”
But you and your whole observed reality are being identified with an elementary tensor here. If the answer to the question “How many elementary tensors make up a nonelementary tensor?” is “undefined, there is no answer, it depends on definition”, then we have just proved that the world isn’t an elementary tensor, because the existence of “you and your whole observed reality” is not just a matter of definition.
Upvoted to try to avoid deep burial of a worthwhile discussion, tone issues notwithstanding.
Decoherence according to MWI is a continuous process, not a discrete one. So it is indeed like the inkblot drawing, and you can’t actually count the worlds. The amplitudes blobs of the wavefunction in configuration space are really like the ink dots in the inkblot drawing, sometimes fully disjoint, sometimes fully connected, but also sometimes barely connected in a way that you can’t tell if they are one or two. Sure if you define a precise rule to tell apart “one blob” and “two blobs” using various metrics and a threshold, you’ll be able to count them. But that rule will be arbitrary, and i could define another and end up with another number, and both would be as valid.
That’s how I understand MWI, and if I can understand someone disagreeing with it, I really don’t see how you can call it “non-sense”.
To unambiguously count the number of blobs requires a precise rule, but you could change the rule and the number of blobs would be different according to the new rule. That much is indeed not nonsense.
But when we talk about “the branch containing this instance of you”, we are talking about something that definitely exists, and whose existence is not just the result of how you define things. That’s why it’s nonsense to treat it as if its very existence results solely from an arbitrary division of the universal wavefunction.
On the number of worlds: At least one. :)
On the wrongness of the question: It may be worth pointing out that the theory is called quantum mechanics for a reason. The number of states is countable (and invariant under a change of basis); one can presumably calculate, in principle, how many of those have a nonzero amplitude; done. No? But, that said, we are still bumping into the remaining mystery of QM, which to the best of my knowledge does not have a good answer: Why do the square amplitudes correspond to subjective probabilities?
The number of particles is discrete. As far as anyone can tell, the positions aren’t. They might be if you look closer than we’ve managed, but that’s beyond the realm of quantum mechanics.
Planck distance?
Classical physics breaks down beyond this point, but the concept of distance does not. It’s not meaningful to talk about the position of something beyond this accuracy because the position is blob that’s bigger than that, but the blob itself has, as far as anyone can tell, infinite resolution.
Quantum physics is built on calculus. It doesn’t work in discrete systems.
Your first paragraph is reasonable, but quantum physics works in discrete systems. The most extreme case is quantum computation, which often uses finite dimensional Hilbert spaces. But older and more mainstream is lattice gauge theory, which I believe approximates QFT with a discrete quantum system.
You can approximate it with a discrete system. It’s just not what quantum physics uses.
Maybe lattice gauge theory isn’t what reality uses, but it’s still quantum physics.
I have advocated that. More precisely, I have said “you can think of one of those branches as stronger”, supposing one is envisioning branches of a tree (strenght here reflects the probability). I am not going to dispute its “meaninglessness”, since it is an analogy. I have provided a more detailed and more technical explanation in another comment which doesn’t speak about “strength” at all.
I wish to stress that I don’t think any metaphorical analogy is going to help one understand quantum mechanics in the important sense of having better and more precise model of the world, and overall I don’t think it is rational for somebody without technical knowledge of the field (it is, not knowing how to make predictions within a given quantum mechanical model) to investigate the interpretation of QM. Starting with the interpretation without knowing the mathematical background creates an illusion of understanding—one would say “quantum mechanics is like a branching tree” or “quantum mechanics is like Bayesian probability” or “quantum mechanics is like stains of ink” or whatever, but one should not aspire to “know” what quantum mechanics is like: one should aspire to be able to calculate the spectrum of a hydrogen atom or the results of the double-slit experiment. Quantitatively, of course.
That said, I admit that my answering in the thread was probably a mistake. One shouldn’t discuss technical topics in metaphors, ever.
(Edit: I mostly agree with the OP that the question “how many worlds” is meaningful and it isn’t a “wrong question”. The problem is that different people may have quite different understanding of what “worlds” refer to and without clearing this up, there is no sense in specifying their number.)
Good points, upvoted. But in fairness, I think the ink blot analogy is a decent one.
Imagine you asked the question about the ink blot to a philosopher in ancient Greece, how might he answer? He might say there is no definite number. Or he might say there must be some underlying reality, even though he doesn’t know for sure what it is; and the best guess says it’s based on atoms; so he might reply that he doesn’t know the answer, but hopefully it might be possible in principle to calculate it if you could count atoms.
I think that’s about where we are regarding the Born probabilities and number or measure of different worlds in MWI right now.
the ink blot analogy is not quite so good for counting worlds because it implies more ambiguity than there is.
In reality the most ambiguous amplitude-blot is the inside of a quantum computer. The difference between considering that as all one world or many not-quite-decohered worlds is at most a constant factor on the exponentially growing total number. Most different worlds are very much distinct. The amplitude blots are quite small (atom scale) and infinite-dimensional configuration space is huge. All it takes is one photon to have gone a different way and the blobs are lightyears apart.
Assuming all branches are intact and active (as implied by conservation of amplitude), the number of worlds is approximately
k*2^(r*t)wherekis your strictness of what counts as a world,ris how many decoherence events happen per time, andtis time. I chose a base of 2 because all decoherence complexes can be approximately reduced to single splits.rcan be adjusted if some other base is more natural.Is the range of possibilities for place, velocity, charge mass etc. continuous or discrete? Intuitively it seems like velocity and place are continuous, but then, what about Planck length and Planck velocity? I have no idea, but according to your post, there should be only discrete values. Did I get something wrong?
I am utterly confused about my map.
In standard QM, position is continuous. Lengths seem hard to discretize without violating Lorentz invariance. People are trying but, AFAIK, they’re not getting anywhere. The Plank velocity is the speed of light.
I can’t tell whether Mitchell is advocating a finite or infinite number of worlds.
I am advocating that the set of worlds must have a definite cardinality. It can be finite; it can be infinite; but it can’t be “undefined”.
Very good point I think. Your post was a bit tl;dr, but I think I got the idea.
We should be careful with trying to dissolve questions lest it become a fully general counter-argument.
The ink blots thing didn’t seem quite right when I saw it, but hindsight etc. Thanks for pointing it out.
How? What argument? I may very well have misunderstood the standard LW position here, so perhaps I agree with you and just don’t know it yet. But I thought Eliezer did in fact suggest we lack a precise enough definition of consciousness to locate ourselves in the quantum ink-blot picture. And he certainly wants to find a better definition.
Approaching Emile’s metaphor from this perspective, I thought it pointed out the need for better understanding of the question.
Getting consciousness confused with QM doesn’t sound like Eliezer!
You could blame Robin, of course. But the part about consciousness doesn’t actually look like confusion to me:
I alluded to this in the quantum-randomized memory discussion, when I said the configurations we were talking about all seemed to have equal amplitude. (So if we find ourselves definitively living in one of them through observation, Mangled Worlds does not appear to change that earlier question). Then another commenter suggested I read about Mangled Worlds. So clearly someone’s missed something.
from my understanding of MW, the question of how many worlds can be answered pretty well by ~2 to the power of the average number of decoherence events since the beginning. Unless there’s some wierdness with a lot of worlds getting terminated or still-lifed early.
The difference between counting the states in a quantum computer (for example) as one world or many is at most a constant factor, so the fuzziness on our concept of “world” isn’t actually that much of a big deal. (I chose a quantum computer because it is probably the most definition-stretching phenomenon).
barring weird stuff like quantum computers, branches get very separate very fast, so I don’t think it’s all that weird to talk about number of worlds.
Deocherence evernts aren’t well defined .. they are always FAPP. That;s the source of the problem.
Eliezer’s objection is more about his distaste for infinite sets than about any mysterious properties of consciousness; he feels that the universe should be a large but finite thing rather than a continuum, and thus the granularity of that finite thing becomes an issue.
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 two blobs will ever interact again. We care about which blob we’re in because it comprises all the amplitude that can actually affect us. Furthermore, the blobs often split into chunks that we care about (achieving this is the point of experiment?), for instance one blob with the cat alive, one blob with it dead.
As for the question about frequencies, I have no idea.
EDIT: I copied this response to the other thread where it seemed more appropriate. Here.
Isn’t this essentially true, though?
What is there apart from computations and the substrate being computed?
Uncountably many is the correct answer, and yet it’s one of the down-voted posts. In another thread, my posts were also down-voted, despite their well-reasoned bases.
Personally, I think the voting system is corrupt, and – especially given that one can create an account, get a few votes, and start wreaking havoc with the presumed perception of posts – LW will only be more wrong than anything I might imagine. Is LW supposed to be a popularity contest, where gang affiliation is measured in the “karma” one has gained by not stepping on the toes of those who might down-vote (whatever that is supposed to suggest; one guesses 1= “yay” and −1=”boo”) something they either dislike or don’t comprehend (and don’t want to admit they don’t comprehend)? If so, I’m already counting the days I continue “participating”.
The measure of a post should consist in its merits, but the way LW invites censors, I hardly think the improvement of the “art of human rationality” will manifest. After all, an excellent exercise of rational thought is to show in what way faults are present in specific claims, not the arbitrary employment of “yay” or “boo” ascriptions.
(This was edited a few times after initial posting.)
I can assure you that stepping on toes doesn’t interfere with karma gain all that much.
That sounds believable. My post has already been down-voted. Why? Who knows.
I downvoted you for the troll speak—that is, the billigerent defiance of the negative perception of your own behavior and the generalization of the defiance of karma to all cases, not just a specific disagreement.
I never generalized. I asked a question. Read the post again, if you care to.
What? Where is that, exactly? The behavior isn’t negative, but the perception of it is, therefore I’m unjustified in being quite disgusted by it? It still seems to be a popularity contest that consists in an arbitrary ascription that generates nothing useful in an “art of rationality” setting.
And suggesting that someone is a troll is by far the most bathetic exercise of non-rational discourse. But, go ahead, down-vote this, too, if you feel better by it.
I express disgust with specific instances of voting. I downvote generalised defiance and “I’m going to leave” bluster. It’s not a big deal—I just prefer that people don’t make comments like that and so I downvote them.
The specific comment contained trollspeak—you are not a troll.
Okay, I see your point. But the way the voting system is set up, it generalizes across one’s presence on the website, hence “karma”.
To be clear, I wasn’t being “defiant”. I asked a very specific question, expecting specific input, not a down-vote and being told (in a “put up or shut up” fashion) that I am just wrong. Well, LW is looking less inviting as a place for truly “rational discourse”. But I digress.
I thought it was clear that if the question was answered in the affirmative (with clear reasoning), then it would be reasonable for someone to leave such a forum. I stand by that, too, because it would be a waste of my time to put thought into posts and to have them down-voted out of existence. It is wise for a community (if that’s what it is) to consider its own nature from a meta-stand point. Is LW a treasure trove of instances of “fooling oneself”? A case study leads to many others.
Yes, but that post didn’t just contain the words “uncountably many”, it also contained babble like “it is absurd to suppose there is a universe in which something, if there be anything, does not exist. ” which even if perceived in the context of Tegmark IV which argues for the existence of all mathematical objects, it has nothing to do with the Many-Worlds Interpretation that the original poster was asking about, and which is Tegmark III, not Tegmark IV.
So 95% of that post was utterly irrelevant to the question asked, and yet pretending to be relevant. A horrible signal-to-noise ratio.
And yet you complain that it currently has a −1 downvote? It was probably worthy of atleast a −4 or thereabouts.
How do you know that? Feel free to link to a mathematically sound reference.
I’m fairly certain no such references exist.
Prase and I contend in the other thread that Argumzio’s comments are not well-reasoned.
And wrongly contend at that.