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 glad to see is being met with some incredulity, here on a site where people care about decision theory and know something about how it works; but which nonetheless has somehow acquired a reputation as a serious and important approach to the question.
There would be still other schools of opinion on this matter. And then finally, hardly noticed, off in a corner by themselves, are the MWI rogues and renegades who are trying to explain the predictions of quantum mechanics regarding the frequencies of events in the multiverse, by exhibiting a description of the multiverse in which the frequencies of events do in fact match the probabilities! (And then we have the “MWI public”, who naively think that Many Worlds means that there are many worlds, and who don’t know what a mess the interpretation is in, when you look at its technicalities.)
I would say that explaining quantum probabilities in terms of event frequencies in the multiverse, is the only sensible way to seek a multiverse explanation of QM; the fact that “deriving the Born rule from counting” is very much a minority concern in the real world of MWI studies, is a symptom of something very wrong with the whole “field”.
ETA I include deriving the Born rule from a measure, as a form of “deriving the Born rule from counting”. But note, talking about measure is not the same thing as explaining its form. Saying that “measure is concentrated at this world” doesn’t explain why it’s concentrated there, or what measure is.
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.”
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!
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.
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?
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.
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”.
You can always count how many instances of something exist in a digital computer.
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?)
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.
I do not have a problem with it in principle; but it would imply that there are uncountably many.
Yes, those two things seem roughly equivalent.
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.
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.)
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.
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’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.
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.
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.
I don’t see why the number of how many times something exists must equal how many times something is observed.
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?
I don’t like it being called “existing more” either … but “observed more” or “experienced more” are good enough for me.
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.
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.
Is this theory one that is advocated by actual physicists? If so that is scary!
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.”
No one derives the Born rule from counting.
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 glad to see is being met with some incredulity, here on a site where people care about decision theory and know something about how it works; but which nonetheless has somehow acquired a reputation as a serious and important approach to the question.
There would be still other schools of opinion on this matter. And then finally, hardly noticed, off in a corner by themselves, are the MWI rogues and renegades who are trying to explain the predictions of quantum mechanics regarding the frequencies of events in the multiverse, by exhibiting a description of the multiverse in which the frequencies of events do in fact match the probabilities! (And then we have the “MWI public”, who naively think that Many Worlds means that there are many worlds, and who don’t know what a mess the interpretation is in, when you look at its technicalities.)
I would say that explaining quantum probabilities in terms of event frequencies in the multiverse, is the only sensible way to seek a multiverse explanation of QM; the fact that “deriving the Born rule from counting” is very much a minority concern in the real world of MWI studies, is a symptom of something very wrong with the whole “field”.
ETA I include deriving the Born rule from a measure, as a form of “deriving the Born rule from counting”. But note, talking about measure is not the same thing as explaining its form. Saying that “measure is concentrated at this world” doesn’t explain why it’s concentrated there, or what measure is.
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!
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.
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.
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”.
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?)
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.
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.
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.
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.
Is this theory one that is advocated by actual physicists? If so that is scary!
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.
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.”
I reached the opposite conclusion from that page.