Suppose we start with quantum mechanics. What is the argument that particles don’t have identity? If you start with particles in positions A and B, and end with particles in positions C and D, and you want to calculate the probability amplitude for this transition, you count histories where A goes to C and B goes to D, and histories where A goes to D and B goes to C. Furthermore, these histories can interfere destructively (e.g. this happens with fermions), which implies that the two endpoints really are the same place in configuration space, and not just outcomes that look the same.
From this it is concluded that the particles have no identity across time. According to this view, if you end up in the situation with particles at C and D, and ask if the particle at C started at A or started at B, there is simply no answer, because both types of history will have contributed to the outcome.
However, it is a curious fact that although the evolving superposition contains histories of both types, within any individual history, there is identity across time! Within an individual history in the sum over histories, A does go to strictly one of C or D.
Now I’m going to examine whether the idea of persistent particle-identity makes sense, first in single-world interpretations, then in many-world interpretations.
What do physicists actually think is the reality of a quantum particle? If we put aside the systematic attempts to think about the problem, and just ask what attitudes are implicitly at work from day to day, I see three attitudes. One is the positivistic attitude that it is pointless to talk or think about things you can’t observe. Another is the ignorance interpretation of quantum uncertainty; the particle always has definite properties, just like a classical particle, but it moves around randomly, in a way that adds up to quantum statistics. Finally, you have wavefunction realism: particles really are spread out in space or in superpositions. (The thinking of an individual physicist may combine several of these attitudes.)
The positivistic attitude is likely to dismiss the question of ‘which path the electron took’ or even ‘did the electron take a definite path’ as metaphysics and unanswerable, so it’s irrelevant to the present discussion. Wavefunction realism, pursued systematically, usually becomes a many-worlds philosophy, so I’ll save that option for the second part. So if we are asking whether electrons persist over time and follow definite paths in a single-world interpretation, we are really asking whether that is the case under an ignorance interpretation of quantum uncertainty.
I think it is obviously so. This way of thinking says that particles are just like classical particles—they always have a definite location, they always execute definite motions—except that they act randomly. If we have two particles apparently just sitting there, and we want to know whether they changed places or not, the real answer will be yes or no, even if we can never know which is right.
(A remark on the legitimacy of this way of thinking. Bell’s theorem evidently rattled a lot of people because it showed that a naive conception of how these random motions worked could not give rise to quantum mechanics—it could not produce sufficiently strong correlations at a distance. Nonetheless, it is possible to derive quantum probabilities from local random behavior, just as you can get a diffusion probability distribution from Brownian motion. The punchline is that it has to be local random motion in configuration space. In configuration space you treat the whole classical configuration as a single point in an infinite-dimensional abstract space, so “motion” in that abstract space will involve simultaneous changes to physical properties all across real space. This may sound like cheating; it means that when you go back to thinking in terms of real space, if your random motions are going to produce quantum statistics, then the randomness has to be correlated at a distance, without further cause. But some people are prepared to bite that bullet; that’s just how reality is, they’ll tell you.)
Now to many worlds. Here we are saying that superpositions are real; so the history where the particles stay where they are, and the history where they swap places, are both real, and they flow into the same world at the end. Now, surely, we cannot speak of a particle’s identity persisting over time. We started out with a world containing a particle at A and a particle at B; it evolved into a world that was a superposition (or was it a superposition of worlds?), each element of the superposition still containing two particles, but now in other positions; and it terminated in a world with a particle at C and a particle at D. Each final particle inherited a bit of amplitude from multiple predecessors, and for each there are paths heading back to A and to B. So we simply can’t say that the particle at C is the sole heir of either original particle.
However, perhaps we can say that these two particles were entangled, and that this entangled duo had a persistent identity across time! Certainly, as described, there were only ever two particles in the picture. You might object that in the real world, there would be other particles, and they would also interact with the duo, and even trade places with them in some histories, and so this notion of a locally encapsulated entanglement is false. Everything 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.
My response to that is that developing a coherent many-worlds interpretation is a lot more difficult than you might think. Many worlds has been presented here as the economical, no-collapse alternative to theories arbitrarily postulating a collapse process; but to actually find individual worlds in a universal wavefunction, you have to break it up somehow (break it up conceptually), and that is a project with a lot of hidden difficulties (significant example). The arbitrariness of the collapse postulate has its counterpart in the arbitrariness of how the worlds are defined. If a natural, non-arbitrary definition exists, it is going to have to find natural structures, such as temporarily localized entanglements; and I note Eliezer’s comment in the original article, “I’m calling you a factored subspace”. If that is so—if the idea can even make sense—then it will be that subspace which has continuity of identity across time.
So, whether you adopt a single-world or a many-world perspective, a nonpatternist theory of physical identity is viable.
We are actually talking about personal identity here, not physical identity, and that raises further issues. But if physical identity is a viable concept after all, then so too may be a concept of personal identity grounded in temporal persistence of physical identity.
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.
And what do you think? I disagree with Eliezer, and I can talk about my position, but I want to hear your opinion first.
I find Eliezer’s argument convincing.
OK. Well, here’s a different perspective.
Suppose we start with quantum mechanics. What is the argument that particles don’t have identity? If you start with particles in positions A and B, and end with particles in positions C and D, and you want to calculate the probability amplitude for this transition, you count histories where A goes to C and B goes to D, and histories where A goes to D and B goes to C. Furthermore, these histories can interfere destructively (e.g. this happens with fermions), which implies that the two endpoints really are the same place in configuration space, and not just outcomes that look the same.
From this it is concluded that the particles have no identity across time. According to this view, if you end up in the situation with particles at C and D, and ask if the particle at C started at A or started at B, there is simply no answer, because both types of history will have contributed to the outcome.
However, it is a curious fact that although the evolving superposition contains histories of both types, within any individual history, there is identity across time! Within an individual history in the sum over histories, A does go to strictly one of C or D.
Now I’m going to examine whether the idea of persistent particle-identity makes sense, first in single-world interpretations, then in many-world interpretations.
What do physicists actually think is the reality of a quantum particle? If we put aside the systematic attempts to think about the problem, and just ask what attitudes are implicitly at work from day to day, I see three attitudes. One is the positivistic attitude that it is pointless to talk or think about things you can’t observe. Another is the ignorance interpretation of quantum uncertainty; the particle always has definite properties, just like a classical particle, but it moves around randomly, in a way that adds up to quantum statistics. Finally, you have wavefunction realism: particles really are spread out in space or in superpositions. (The thinking of an individual physicist may combine several of these attitudes.)
The positivistic attitude is likely to dismiss the question of ‘which path the electron took’ or even ‘did the electron take a definite path’ as metaphysics and unanswerable, so it’s irrelevant to the present discussion. Wavefunction realism, pursued systematically, usually becomes a many-worlds philosophy, so I’ll save that option for the second part. So if we are asking whether electrons persist over time and follow definite paths in a single-world interpretation, we are really asking whether that is the case under an ignorance interpretation of quantum uncertainty.
I think it is obviously so. This way of thinking says that particles are just like classical particles—they always have a definite location, they always execute definite motions—except that they act randomly. If we have two particles apparently just sitting there, and we want to know whether they changed places or not, the real answer will be yes or no, even if we can never know which is right.
(A remark on the legitimacy of this way of thinking. Bell’s theorem evidently rattled a lot of people because it showed that a naive conception of how these random motions worked could not give rise to quantum mechanics—it could not produce sufficiently strong correlations at a distance. Nonetheless, it is possible to derive quantum probabilities from local random behavior, just as you can get a diffusion probability distribution from Brownian motion. The punchline is that it has to be local random motion in configuration space. In configuration space you treat the whole classical configuration as a single point in an infinite-dimensional abstract space, so “motion” in that abstract space will involve simultaneous changes to physical properties all across real space. This may sound like cheating; it means that when you go back to thinking in terms of real space, if your random motions are going to produce quantum statistics, then the randomness has to be correlated at a distance, without further cause. But some people are prepared to bite that bullet; that’s just how reality is, they’ll tell you.)
Now to many worlds. Here we are saying that superpositions are real; so the history where the particles stay where they are, and the history where they swap places, are both real, and they flow into the same world at the end. Now, surely, we cannot speak of a particle’s identity persisting over time. We started out with a world containing a particle at A and a particle at B; it evolved into a world that was a superposition (or was it a superposition of worlds?), each element of the superposition still containing two particles, but now in other positions; and it terminated in a world with a particle at C and a particle at D. Each final particle inherited a bit of amplitude from multiple predecessors, and for each there are paths heading back to A and to B. So we simply can’t say that the particle at C is the sole heir of either original particle.
However, perhaps we can say that these two particles were entangled, and that this entangled duo had a persistent identity across time! Certainly, as described, there were only ever two particles in the picture. You might object that in the real world, there would be other particles, and they would also interact with the duo, and even trade places with them in some histories, and so this notion of a locally encapsulated entanglement is false. Everything 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.
My response to that is that developing a coherent many-worlds interpretation is a lot more difficult than you might think. Many worlds has been presented here as the economical, no-collapse alternative to theories arbitrarily postulating a collapse process; but to actually find individual worlds in a universal wavefunction, you have to break it up somehow (break it up conceptually), and that is a project with a lot of hidden difficulties (significant example). The arbitrariness of the collapse postulate has its counterpart in the arbitrariness of how the worlds are defined. If a natural, non-arbitrary definition exists, it is going to have to find natural structures, such as temporarily localized entanglements; and I note Eliezer’s comment in the original article, “I’m calling you a factored subspace”. If that is so—if the idea can even make sense—then it will be that subspace which has continuity of identity across time.
So, whether you adopt a single-world or a many-world perspective, a nonpatternist theory of physical identity is viable.
We are actually talking about personal identity here, not physical identity, and that raises further issues. But if physical identity is a viable concept after all, then so too may be a concept of personal identity grounded in temporal persistence of physical identity.
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.
All this begs the question: Is personal identity made up of the same stuff as ‘blue’?