I’ll grant that by being sufficiently clever, you can probably reconcile quantum mechanics with whatever ontology you like. But the real question is: why bother? Why not take the Schroedinger equation literally? Physics has faced this kind of issue before—think of the old episode about epicycles, for instance—and the lesson seems clear enough to me. What’s the difference here?
For what it’s worth, I don’t see the arbitrariness of collapse postulates and the arbitrariness of world-selection as symmetrical. It’s not even clear to me that we need to worry about extracting “worlds” from blobs of amplitude, but to the extent we do, it seems basically like an issue of anthropic selection; whereas collapse postulates seem like invoking magic.
But in any case you don’t really address the objection that
(e)verything is entangled with everything else, indirectly if not directly, and so all I could say is that the universe as a whole has identity across time.
Instead, you merely raise the issue of finding “individual worlds”, and argue that if you can find manage to find an individual world, then you can say that that world has an identity that persists over time. Fair enough, but how does this help you rescue the idea that personal identity resides in “continuity of substance”, when the latter may still be meaningless at the level of individual particles?
The Schroedinger equation is an assertion about a thing called Psi. “Taking it literally” usually means “believe in many worlds”. Now even if I decide to try this out, I face a multitude of questions. Am I to think of Psi as a wavefunction on a configuration space, or as a vector in a Hilbert space? Which part of Psi corresponds to the particular universe that I see? Am I to think of myself as a configuration of particles, a configuration of particles with an amplitude attached, a superposition of configurations each with its own amplitude, or maybe some other thing, like an object in Hilbert space (but what sort of object?) not preferentially associated with any particular basis? And then there’s that little issue of deriving the Born probabilities!
Once you decide to treat the wavefunction itself as ultimate physical reality, you must specify exactly which part of it corresponds to what we see, and you must explain where the probabilities come from. Otherwise you’re not doing physics, you’re just daydreaming. And when people do address these issues, they do so in divergent ways. And in my experience, when you do get down to specifics, problems arise, and the nature of the problems depends very much on which of those divergent implementations of many-worlds has been followed.
It is hard to go any further unless you tell me more about what many-worlds means to you, and how you think it works. “Take the equation literally” is just a slogan and doesn’t provide any details.
you merely raise the issue of finding “individual worlds”, and argue that if you can find manage to find an individual world, then you can say that that world has an identity that persists over time. Fair enough, but how does this help you rescue the idea that personal identity resides in “continuity of substance”, when the latter may still be meaningless at the level of individual particles?
By “world”, do you mean a universe-sized configuration, or just an element of a more localized superposition? It is another of the exasperating ambiguities of many-worlds discourse. Some people do make it clear that their worlds-in-the-wavefunction are of cosmic size, while others apparently prefer to think of the multiplicity of realities as a local and even relative thing—I think this is what “many minds” is about: the observer is in a superposition and we acknowledge that there are many distinct observers or distinct instances of the observer, but the rest of the universe is to be regarded as still in its transcendent pristine many-in-one multiverse unity… I speak sarcastically, but I do see among some many-worlders a sort of veneration of the wavefunction and a dislike for any attempt to break it up into worlds in a definite way, even though you absolutely need to do this to make contact with empirical reality.
So, anyway, I was talking about localized entanglements, or (equivalently) small factors of the total quantum state, as providing a basis for “continuity of substance” even if individual particles cannot. The relevance to personal identity is as follows. We are assuming that a person has something to do with the material world. The argument I dispute is the one that says personal identity cannot depend on the persistence through time of the person’s material parts, because there is no such thing as persistence through time of particles, because differently-braided particle histories all convey amplitude to the same configuration. And my proposition was that if you look at superpositions of these braidings and sub-braidings, you get localized entities which have ontological boundaries and persistence in time until they enter into a larger braiding; and this means you can after all talk about material parts of a person persisting in time.
“Take the equation literally” is just a slogan and doesn’t provide any details.
What it means is that you let your ontology be dictated by the mathematical structure of the equation. So for instance:
Am I to think of Psi as a wavefunction on a configuration space, or as a vector in a Hilbert space?
It’s both—even when regarded purely as a mathematical object. The set of wavefunctions on a configuration space is (the unit sphere of) a Hilbert space. Specifically, as I understand it, configuration space is a measure space of some sort, and the set of wavefunctions is (the unit sphere in) L^2 of that measure space.
Am I to think of myself as a configuration of particles, a configuration of particles with an amplitude attached, a superposition of configurations each with its own amplitude, or maybe some other thing, like an object in Hilbert space (but what sort of object?) not preferentially associated with any particular basis?
It seems to me that you’re a region of configuration space. There’s a subset of the measure space that consists of configurations that represent things like “you’re in this state”, “you’re in that state”, etc. We can call this subset the “you”-region. (Of course, these states also contain information about the rest of the universe, but the information they contain about you is the reason we’re singling them out as a subset.)
And then there’s that little issue of deriving the Born probabilities!
To repeat a point made before (possibly by Eliezer himself), this isn’t an issue that distinguishes between many-worlds and collapse postulates. With many-worlds, you have to explain the Born probabilities; with collapse interpretations, you have to explain the mysterious collapse process. It seems to me far preferable, all else being equal, to be stuck with the former problem rather than the latter—because it turns the mystery into an indexical issue (“Why are we in this branch rather than another?”) rather than writing it into the laws of the universe.
you absolutely need to [break the wavefunction into worlds] to make contact with empirical reality.
Why is this?
my proposition was that if you look at superpositions of these braidings and sub-braidings, you get localized entities which have ontological boundaries and persistence in time until they enter into a larger braiding; and this means you can after all talk about material parts of a person persisting in time.
Okay, it now occurs to me that I may have been confusing “continuity of substance” (your criterion) with “identity of substance” (which is what Eliezer’s argument rules out). That’s still more problematic, in my opinion, than a view that allows for uploading and teleportation, but in any event I withdraw the claim that it is challenged by Eliezer’s quantum-mechanical argument about particle identity.
There are two issues here: many worlds, and the alleged desirability or necessity of abandoning continuity of physical existence as a criterion of identity, whether physical or personal.
Regarding many worlds, I will put it this way. There are several specific proposals out there claiming to derive the Born probabilities. Pick one, and I will tell you what’s wrong with it. Without the probabilities, you are simply saying “all worlds exist, this is one of them, details to come”.
Regarding “continuity of substance” versus “identity of substance”… If I was seriously going to maintain the view I suggested—that encapsulated local entanglements permit a notion of persistence in time—then I would try to reconceptualize the physics so that identity of substance applied. What was formerly described as three entangled particles, I would want to describe as one thing with a big and evolving state.
I’ll grant that by being sufficiently clever, you can probably reconcile quantum mechanics with whatever ontology you like. But the real question is: why bother? Why not take the Schroedinger equation literally? Physics has faced this kind of issue before—think of the old episode about epicycles, for instance—and the lesson seems clear enough to me. What’s the difference here?
For what it’s worth, I don’t see the arbitrariness of collapse postulates and the arbitrariness of world-selection as symmetrical. It’s not even clear to me that we need to worry about extracting “worlds” from blobs of amplitude, but to the extent we do, it seems basically like an issue of anthropic selection; whereas collapse postulates seem like invoking magic.
But in any case you don’t really address the objection that
Instead, you merely raise the issue of finding “individual worlds”, and argue that if you can find manage to find an individual world, then you can say that that world has an identity that persists over time. Fair enough, but how does this help you rescue the idea that personal identity resides in “continuity of substance”, when the latter may still be meaningless at the level of individual particles?
The Schroedinger equation is an assertion about a thing called Psi. “Taking it literally” usually means “believe in many worlds”. Now even if I decide to try this out, I face a multitude of questions. Am I to think of Psi as a wavefunction on a configuration space, or as a vector in a Hilbert space? Which part of Psi corresponds to the particular universe that I see? Am I to think of myself as a configuration of particles, a configuration of particles with an amplitude attached, a superposition of configurations each with its own amplitude, or maybe some other thing, like an object in Hilbert space (but what sort of object?) not preferentially associated with any particular basis? And then there’s that little issue of deriving the Born probabilities!
Once you decide to treat the wavefunction itself as ultimate physical reality, you must specify exactly which part of it corresponds to what we see, and you must explain where the probabilities come from. Otherwise you’re not doing physics, you’re just daydreaming. And when people do address these issues, they do so in divergent ways. And in my experience, when you do get down to specifics, problems arise, and the nature of the problems depends very much on which of those divergent implementations of many-worlds has been followed.
It is hard to go any further unless you tell me more about what many-worlds means to you, and how you think it works. “Take the equation literally” is just a slogan and doesn’t provide any details.
By “world”, do you mean a universe-sized configuration, or just an element of a more localized superposition? It is another of the exasperating ambiguities of many-worlds discourse. Some people do make it clear that their worlds-in-the-wavefunction are of cosmic size, while others apparently prefer to think of the multiplicity of realities as a local and even relative thing—I think this is what “many minds” is about: the observer is in a superposition and we acknowledge that there are many distinct observers or distinct instances of the observer, but the rest of the universe is to be regarded as still in its transcendent pristine many-in-one multiverse unity… I speak sarcastically, but I do see among some many-worlders a sort of veneration of the wavefunction and a dislike for any attempt to break it up into worlds in a definite way, even though you absolutely need to do this to make contact with empirical reality.
So, anyway, I was talking about localized entanglements, or (equivalently) small factors of the total quantum state, as providing a basis for “continuity of substance” even if individual particles cannot. The relevance to personal identity is as follows. We are assuming that a person has something to do with the material world. The argument I dispute is the one that says personal identity cannot depend on the persistence through time of the person’s material parts, because there is no such thing as persistence through time of particles, because differently-braided particle histories all convey amplitude to the same configuration. And my proposition was that if you look at superpositions of these braidings and sub-braidings, you get localized entities which have ontological boundaries and persistence in time until they enter into a larger braiding; and this means you can after all talk about material parts of a person persisting in time.
What it means is that you let your ontology be dictated by the mathematical structure of the equation. So for instance:
It’s both—even when regarded purely as a mathematical object. The set of wavefunctions on a configuration space is (the unit sphere of) a Hilbert space. Specifically, as I understand it, configuration space is a measure space of some sort, and the set of wavefunctions is (the unit sphere in) L^2 of that measure space.
It seems to me that you’re a region of configuration space. There’s a subset of the measure space that consists of configurations that represent things like “you’re in this state”, “you’re in that state”, etc. We can call this subset the “you”-region. (Of course, these states also contain information about the rest of the universe, but the information they contain about you is the reason we’re singling them out as a subset.)
To repeat a point made before (possibly by Eliezer himself), this isn’t an issue that distinguishes between many-worlds and collapse postulates. With many-worlds, you have to explain the Born probabilities; with collapse interpretations, you have to explain the mysterious collapse process. It seems to me far preferable, all else being equal, to be stuck with the former problem rather than the latter—because it turns the mystery into an indexical issue (“Why are we in this branch rather than another?”) rather than writing it into the laws of the universe.
Why is this?
Okay, it now occurs to me that I may have been confusing “continuity of substance” (your criterion) with “identity of substance” (which is what Eliezer’s argument rules out). That’s still more problematic, in my opinion, than a view that allows for uploading and teleportation, but in any event I withdraw the claim that it is challenged by Eliezer’s quantum-mechanical argument about particle identity.
There are two issues here: many worlds, and the alleged desirability or necessity of abandoning continuity of physical existence as a criterion of identity, whether physical or personal.
Regarding many worlds, I will put it this way. There are several specific proposals out there claiming to derive the Born probabilities. Pick one, and I will tell you what’s wrong with it. Without the probabilities, you are simply saying “all worlds exist, this is one of them, details to come”.
Regarding “continuity of substance” versus “identity of substance”… If I was seriously going to maintain the view I suggested—that encapsulated local entanglements permit a notion of persistence in time—then I would try to reconceptualize the physics so that identity of substance applied. What was formerly described as three entangled particles, I would want to describe as one thing with a big and evolving state.