(Warning that I may well be misunderstanding this post.)
For any well-controlled isolated system, if it starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a certain deterministic unitary operator. So far this is indisputable—you can do quantum state tomography, you can measure the interference effects, etc. Right?
OK, so then you say: “Well, a very big well-controlled isolated system could be a box with my friend Harry and his cat in it, and if the same principle holds, then there will be deterministic unitary evolution from |Ψ⟩ into U|Ψ⟩, and hey, I just did the math and it turns out that U|Ψ⟩ will have a 50⁄50 mix of ‘Harry sees his cat alive’ and ‘Harry sees his cat dead and is sad’.” This is beyond what’s possible to directly experimentally verify, but I think it should be a very strong presumption by extrapolating from the first paragraph. (As you say, “quantum computers prove larger and larger superpositions to be stable”.)
OK, and then we take one more step by saying “Hey what if I’m in the well-controlled isolated system?” (e.g. the “system” in question is the whole universe). From my perspective, it’s implausible and unjustified to do anything besides say that the same principle holds as above: if the universe (including me) starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a deterministic unitary operator.
…And then there’s an indexicality issue, and you need another axiom to resolve it. For example: “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is one such axiom, and equivalent (it turns out) to the Born rule. It’s another axiom for sure; I just like that particular formulation because it “feels more natural” or something.
I think the place anti-many-worlds-people get off the boat is this last step, because there’s actually two attitudes:
My attitude is: there’s a universe following orderly laws, and the universe was there long before there were any people around to observe it, and it will be there long after we’re gone, and the universe happened to spawn people and now we can try to study and understand it.
An opposing attitude is: the starting point is my first-person subjective mind, looking out into the universe and making predictions about what I’ll see. So my perspective is special—I need not be troubled by the fact that I claim that there are many-Harrys when Harry’s in the box and I’m outside it, but I also claim that there are not many-me’s when I’m in the box. That’s not inconsistent, because I’m the one generating predictions for myself, so the situation isn’t symmetric. If I see that the cat is dead, then the cat is dead, and if you outside the well-isolated box say “there’s a branch of the wavefunction where you saw that the cat’s alive”, then I’ll say “well, from my perspective, that alleged branch is not ‘real’; it does not ‘exist’”. In other words, when I observed the cat, I “collapsed my wavefunction” by erasing the part of the (alleged) wavefunction that is inconsistent with my indexical observations, and then re-normalizing the wavefunction.
I’m really unsympathetic to the second bullet-point attitude, but I don’t think I’ve ever successfully talked somebody out of it, so evidently it’s a pretty deep gap, or at any rate I for one am apparently unable to communicate past it.
maybe the pilot-wave model is directionally correct in the sense of informing us about the nature of knowledge?
FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
For any well-controlled isolated system, if it starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a certain deterministic unitary operator. So far this is indisputable—you can do quantum state tomography, you can measure the interference effects, etc. Right?
It will certainly be mathematically well-described by an expression like that. But when you flip a coin without looking at it, it will also be well-described by a probability distribution 0.5 H + 0.5 T, and this doesn’t mean that we insist that after the flip, the coin is Really In That Distribution.
Now it’s true that in quantum systems, you can measure a bunch of additional properties that allow you to rule out alternative models. But my OP is more claiming that the wavefunction is a model of the universe, and the actual universe is presumably the disquotation of this, so by construction the wavefunction acts identically to how I’m claiming the universe acts, and therefore these measurements wouldn’t be ruling out that the universe works that way.
Or as a thought experiment: say you’re considering a simple quantum system with a handful of qubits. It can be described with a wavefunction that assigns each combination of qubit values a complex number. Now say you code up a classical computer to run a quantum simulator, which you do by using a hash map to connect the qubit combos to their amplitudes. The quantum simulator runs in our quantum universe.
Now here’s the question: what happens if you have a superposition in the original quantum system? It turns into a tensor product in the universe the quantum computer runs in, because the quantum simulator represents each branch of the wavefunction separately.
This phenomenon, where a superposition within the system gets represented by a product outside of the system, is basically a consequence of modelling the system using wavefunctions. Contrast this to if you were just running a quantum computer with a bunch of qubits, so the superposition in the internal system would map to a superposition in the external system.
I claim that this extra product comes from modelling the system as a wavefunction, and that much of the “many worlds” aspect of the many-worlds interpretation arises from this (since products represent things that both occur, whereas things in superposition are represented with just sums).
OK, so then you say: “Well, a very big well-controlled isolated system could be a box with my friend Harry and his cat in it, and if the same principle holds, then there will be deterministic unitary evolution from |Ψ⟩ into U|Ψ⟩, and hey, I just did the math and it turns out that U|Ψ⟩ will have a 50⁄50 mix of ‘Harry sees his cat alive’ and ‘Harry sees his cat dead and is sad’.” This is beyond what’s possible to directly experimentally verify, but I think it should be a very strong presumption by extrapolating from the first paragraph. (As you say, “quantum computers prove larger and larger superpositions to be stable”.)
Yes, if you assume the wavefunction is the actual state of the system, rather than a deterministic model of the system, then it automatically follows that something-like-many-worlds must be true.
…And then there’s an indexicality issue, and you need another axiom to resolve it. For example: “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is one such axiom, and equivalent (it turns out) to the Born rule. It’s another axiom for sure; I just like that particular formulation because it “feels more natural” or something.
Huh, I didn’t know this was equivalent to the born rule. It does feel pretty natural, do you have a reference to the proof?
I’m really unsympathetic to the second bullet-point attitude, but I don’t think I’ve ever successfully talked somebody out of it, so evidently it’s a pretty deep gap, or at any rate I for one am apparently unable to communicate past it.
I agree with the former bullet point rather than the latter.
FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
For example: “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero”
What I really don’t like about this formulation is extreme vagueness of “I will find myself”, which implies that there’s some preferred future “I” out of many who is defined not only by observations he receives, but also by being a preferred continuation of subjective experience defined by an unknown mechanism.
It can be formalized as the many minds interpretation, incurring additional complexity penalty and undermining surface simplicity of the assumption. Coexistence of infinitely many (measurement operators can produce continuous probability distributions) threads of subjective experience in a single physical system also doesn’t strike me as “feeling more natural”.
there’s some preferred future “I” out of many who is defined not only by observations he receives, but also by being a preferred continuation of subjective experience defined by an unknown mechanism
I disagree with this part—if Harry does the quantum equivalent of flipping an unbiased coin, then there’s a branch of the universe’s wavefunction in which Harry sees heads and says “gee, isn’t it interesting that I see heads and not tails, I wonder how that works, hmm why did my thread of subjective experience carry me into the heads branch?”, and there’s also a branch of the universe’s wavefunction in which Harry sees tails and says “gee, isn’t it interesting that I see tails and not heads, I wonder how that works, hmm why did my thread of subjective experience carry me into the tails branch?”. I don’t think either of these Harrys is “preferred”.
I don’t think there’s any extra “complexity penalty” associated with the previous paragraph: the previous paragraph is (I claim) just a straightforward description of what would happen if the universe and everything in it (including Harry) always follows the Schrodinger equation—see Quantum Mechanics In Your Face for details.
I think we deeply disagree about the nature of consciousness, but that’s a whole can of worms that I really don’t want to get into in this comment thread.
doesn’t strike me as “feeling more natural”
Maybe you’re just going for rhetorical flourish, but my specific suggestion with the words “feels more natural” in the context of my comment was: the axiom “I will find myself in a branch of amplitude approaching 0 with probability approaching 0” “feels more natural” than the axiom “I will find myself in a branch of amplitude c with probability |c|2”. That particular sentence was not a comparison of many-worlds with non-many-worlds, but rather a comparison of two ways to formulate many-worlds. So I think your position is that you find neither of those to “feel natural”.
I haven’t fully understood your stance towards the many minds interpretation. Do you find it unnecessary?
I don’t think either of these Harrys is “preferred”.
And simultaneously you think that existence of future Harries who observe events with probabilities approaching zero is not a problem because current Harry will almost never find himself to be those future Harries. I don’t understand what it means exactly.
Harries who observe those rare events exist and they wonder how they found themselves in those unlikely situations. Harries who hadn’t found anything unusual exist too. Current Harry became all of those future Harries.
So, we have a quantum state of the universe that factorizes into states with different Harries. OK. What property distinguished a universe where “Harry found himself in a tails branch” and a universe where “Harry found himself in a heads branch”?
You have already answered it: “I don’t think either of these Harrys is “preferred”.” That is there’s no property of the universe that distinguishes those outcomes.
Let’s get back to the initial question ‘What it means that “Harry will almost never find himself to be those future Harries”?’ To answer that we need to jump from a single physical Universe (containing multitude of Harries who found themselves in branches of every possible probability) to a single one (or maybe a set) of those Harries and proclaim that, indeed, that Harry (or Harries) found himself in a usual branch of the universe and all other Harries don’t matter for some reason (their amplitudes are too low to matter despite them being fully conscious? That’s the point that I don’t understand).
The many minds interpretation solves this by proposing metaphysical threads of consciousness, thus adding a property that distinguishes outcomes where Harry observes different things. So we can say that indeed the vast majority of Harries’ threads of consciousness ended up in probable branches.
I don’t like this interpretation. Why don’t we use a single thread of consciousness that adheres to Born rule? Or why don’t we get rid of threads of consciousness altogether and just use the Copenhagen interpretation?
So, my question is how you tackle this problem? I hope I’ve made it sufficiently coherent.
My own resolution is that either collapse is objective, or due to imperfect decoherence the vast majority of branches (which also have relatively low amplitude) interfere with each other, making it impossible for conscious beings to exist in them and, consequently, observe them (it doesn’t explain billion quantum coin-flips scenario in my comment below)
I just looked up “many minds” and it’s a little bit like what I wrote here, but described differently in ways that I think I don’t like. (It’s possible that Wikipedia is not doing it justice, or that I’m misunderstanding it.) I think minds are what brains do, and I think brains are macroscopic systems that follow the laws of quantum mechanics just like everything else in the universe.
What property distinguished a universe where “Harry found himself in a tails branch” and a universe where “Harry found himself in a heads branch”?
Those both happen in the same universe. Those Harry’s both exist. Maybe you should put aside many-worlds and just think about Parfit’s teletransportation paradox. I think you’re assuming that “thread of subjective experience” is a coherent concept that satisfies all the intuitive properties that we feel like it should have, and I think that the teletransportation paradox is a good illustration that it’s not coherent at all, or at the very least, we should be extraordinarily cautious when making claims about the properties of this alleged thing you call a “thread of subjective experience” or “thread of consciousness”. (See also other Parfit thought experiments along the same lines.)
I don’t like the idea where we talk about what will happen to Harry, as if that has to have a unique answer. Instead I’d rather talk about Harry-moments, where there’s a Harry at a particular time doing particular things and full of memories of what happened in the past. Then there are future Harry-moments. We can go backwards in time from a Harry-moment to a unique (at any given time) past Harry-moment corresponding to it—after all, we can inspect the memories in future-Harry-moment’s head about what past-Harry was doing at that time (assuming there were no weird brain surgeries etc). But we can’t uniquely go in the forward direction: Who’s to say that multiple future-Harry-moments can’t hold true memories of the very same past-Harry-moment?
Here I am, right now, a Steve-moment. I have a lot of direct and indirect evidence of quantum interactions that have happened in the past or are happening right now, as imprinted on my memories, surroundings, and so on. And if you a priori picked some possible property of those interactions that (according to the Born rule) has 1-in-a-googol probability to occur in general, then I would be delighted to bet my life’s savings that this property is not true of my current observations and memories. Obviously that doesn’t mean that it’s literally impossible.
“Thread of subjective experience” was an aside (just one of the mechanisms that explains why we “find ourselves” in a world that behaves according to the Born rule), don’t focus too much on it.
The core question is which physical mechanism (everything should be physical, right?) ensures that you almost never will see a string of a billion tails after a billion quantum coin flips, while the universe contains a quantum branch with you looking in astonishment on a string with a billion tails. Why should you expect that it will almost certainly not happen, when there’s always a physical instance of you that will see it happened?
You’ll have 2^1000000000 branches with exactly the same amplitude. You’ll experience every one of them. Which physical mechanism will make it more likely for you to experience strings with roughly the same number of heads and tails?
In the Copenhagen interpretation it’s trivial: when the quantum coin flipper writes a result of the flip the universe somehow samples from a probability distribution and the rest is the plain old probability theory. You don’t expect to observe a string of a billion tails (or any other preselected string), because you who observes this string almost never exist.
I disagree with this part—if Harry does the quantum equivalent of flipping an unbiased coin, then there’s a branch of the universe’s wavefunction in which Harry sees heads and says “gee, isn’t it interesting that I see heads and not tails, I wonder how that works, hmm why did my thread of subjective experience carry me into the heads branch?”, and there’s also a branch of the universe’s wavefunction in which Harry sees tails and says “gee, isn’t it interesting that I see tails and not heads, I wonder how that works, hmm why did my thread of subjective experience carry me into the tails branch?”. I don’t think either of these Harrys is “preferred”.
This is how it works in MWI without additional postulates. But if you postulate the probability that you will find yourself somewhere, then you are postulating the difference between the case where you have found yourself there, and the case where you haven’t. Having a number for how much you prefer something is the whole point of indexical probabilities. And as probability of some future “you” goes to zero, this future “you” goes to not being the continuation of your subjective experience, right? Surely that would make this “you” dispreferred in some sense?
Where could I find the proof that “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is equivalent to the Born rule?
Quantum Mechanics In Your Face talk by Sidney Coleman, starting slide 17 near the end. The basic idea is to try to operationalize how someone might test the Born rule—they take a bunch of quantum measurements, one after another, and they subject their data to a bunch of randomness tests and so on, and then they eventually declare “Born rule seems true” or “Born rule seems false” after analyzing the data. And you can show that the branches in which this person declares “Born rule seems false” have collective amplitude approaching zero, in the limit as their test procedure gets better and better (i.e. as they take more and more measurements).
(Warning that I may well be misunderstanding this post.)
For any well-controlled isolated system, if it starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a certain deterministic unitary operator. So far this is indisputable—you can do quantum state tomography, you can measure the interference effects, etc. Right?
OK, so then you say: “Well, a very big well-controlled isolated system could be a box with my friend Harry and his cat in it, and if the same principle holds, then there will be deterministic unitary evolution from |Ψ⟩ into U|Ψ⟩, and hey, I just did the math and it turns out that U|Ψ⟩ will have a 50⁄50 mix of ‘Harry sees his cat alive’ and ‘Harry sees his cat dead and is sad’.” This is beyond what’s possible to directly experimentally verify, but I think it should be a very strong presumption by extrapolating from the first paragraph. (As you say, “quantum computers prove larger and larger superpositions to be stable”.)
OK, and then we take one more step by saying “Hey what if I’m in the well-controlled isolated system?” (e.g. the “system” in question is the whole universe). From my perspective, it’s implausible and unjustified to do anything besides say that the same principle holds as above: if the universe (including me) starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a deterministic unitary operator.
…And then there’s an indexicality issue, and you need another axiom to resolve it. For example: “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is one such axiom, and equivalent (it turns out) to the Born rule. It’s another axiom for sure; I just like that particular formulation because it “feels more natural” or something.
I think the place anti-many-worlds-people get off the boat is this last step, because there’s actually two attitudes:
My attitude is: there’s a universe following orderly laws, and the universe was there long before there were any people around to observe it, and it will be there long after we’re gone, and the universe happened to spawn people and now we can try to study and understand it.
An opposing attitude is: the starting point is my first-person subjective mind, looking out into the universe and making predictions about what I’ll see. So my perspective is special—I need not be troubled by the fact that I claim that there are many-Harrys when Harry’s in the box and I’m outside it, but I also claim that there are not many-me’s when I’m in the box. That’s not inconsistent, because I’m the one generating predictions for myself, so the situation isn’t symmetric. If I see that the cat is dead, then the cat is dead, and if you outside the well-isolated box say “there’s a branch of the wavefunction where you saw that the cat’s alive”, then I’ll say “well, from my perspective, that alleged branch is not ‘real’; it does not ‘exist’”. In other words, when I observed the cat, I “collapsed my wavefunction” by erasing the part of the (alleged) wavefunction that is inconsistent with my indexical observations, and then re-normalizing the wavefunction.
I’m really unsympathetic to the second bullet-point attitude, but I don’t think I’ve ever successfully talked somebody out of it, so evidently it’s a pretty deep gap, or at any rate I for one am apparently unable to communicate past it.
FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
Based off the abstracts of these papers:
QFT as pilot-wave theory of particle creation and destruction,
Bohmian Mechanics and Quantum Field Theory,
Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics,
Making nonlocal reality compatible with relativity,
Time in relativistic and non relativistic quantum mechanics,
and the Wikipedia page on de Broglie Bohm’s section on QFT, it seems like this claim is wrong. I haven’t read these papers yet, but someone I was talking to said Bohmian QFT is even more unnecessarily complicated than Bohmian QM.
I don’t know if anyone has re-constructed the Standard Model in this framework as of yet.
EDIT: Changed “standard Bohmian QFT” → “Bohmian QM”
It will certainly be mathematically well-described by an expression like that. But when you flip a coin without looking at it, it will also be well-described by a probability distribution 0.5 H + 0.5 T, and this doesn’t mean that we insist that after the flip, the coin is Really In That Distribution.
Now it’s true that in quantum systems, you can measure a bunch of additional properties that allow you to rule out alternative models. But my OP is more claiming that the wavefunction is a model of the universe, and the actual universe is presumably the disquotation of this, so by construction the wavefunction acts identically to how I’m claiming the universe acts, and therefore these measurements wouldn’t be ruling out that the universe works that way.
Or as a thought experiment: say you’re considering a simple quantum system with a handful of qubits. It can be described with a wavefunction that assigns each combination of qubit values a complex number. Now say you code up a classical computer to run a quantum simulator, which you do by using a hash map to connect the qubit combos to their amplitudes. The quantum simulator runs in our quantum universe.
Now here’s the question: what happens if you have a superposition in the original quantum system? It turns into a tensor product in the universe the quantum computer runs in, because the quantum simulator represents each branch of the wavefunction separately.
This phenomenon, where a superposition within the system gets represented by a product outside of the system, is basically a consequence of modelling the system using wavefunctions. Contrast this to if you were just running a quantum computer with a bunch of qubits, so the superposition in the internal system would map to a superposition in the external system.
I claim that this extra product comes from modelling the system as a wavefunction, and that much of the “many worlds” aspect of the many-worlds interpretation arises from this (since products represent things that both occur, whereas things in superposition are represented with just sums).
Yes, if you assume the wavefunction is the actual state of the system, rather than a deterministic model of the system, then it automatically follows that something-like-many-worlds must be true.
Huh, I didn’t know this was equivalent to the born rule. It does feel pretty natural, do you have a reference to the proof?
I agree with the former bullet point rather than the latter.
Someone in the comments of the last thread claimed maybe some people found out how to generalize pilot-wave to QFT. But I’m not overly attached to that claim; pilot-wave theory is obviously directionally incorrect with respect to the ontology of the universe, and even if it can be forced to work with QFT, I can definitely see how it is in tension with it.
Wasn’t this the assumption originally used by Everret to recover Born statistics in his paper on MWI?
What I really don’t like about this formulation is extreme vagueness of “I will find myself”, which implies that there’s some preferred future “I” out of many who is defined not only by observations he receives, but also by being a preferred continuation of subjective experience defined by an unknown mechanism.
It can be formalized as the many minds interpretation, incurring additional complexity penalty and undermining surface simplicity of the assumption. Coexistence of infinitely many (measurement operators can produce continuous probability distributions) threads of subjective experience in a single physical system also doesn’t strike me as “feeling more natural”.
I disagree with this part—if Harry does the quantum equivalent of flipping an unbiased coin, then there’s a branch of the universe’s wavefunction in which Harry sees heads and says “gee, isn’t it interesting that I see heads and not tails, I wonder how that works, hmm why did my thread of subjective experience carry me into the heads branch?”, and there’s also a branch of the universe’s wavefunction in which Harry sees tails and says “gee, isn’t it interesting that I see tails and not heads, I wonder how that works, hmm why did my thread of subjective experience carry me into the tails branch?”. I don’t think either of these Harrys is “preferred”.
I don’t think there’s any extra “complexity penalty” associated with the previous paragraph: the previous paragraph is (I claim) just a straightforward description of what would happen if the universe and everything in it (including Harry) always follows the Schrodinger equation—see Quantum Mechanics In Your Face for details.
I think we deeply disagree about the nature of consciousness, but that’s a whole can of worms that I really don’t want to get into in this comment thread.
Maybe you’re just going for rhetorical flourish, but my specific suggestion with the words “feels more natural” in the context of my comment was: the axiom “I will find myself in a branch of amplitude approaching 0 with probability approaching 0” “feels more natural” than the axiom “I will find myself in a branch of amplitude c with probability |c|2”. That particular sentence was not a comparison of many-worlds with non-many-worlds, but rather a comparison of two ways to formulate many-worlds. So I think your position is that you find neither of those to “feel natural”.
I haven’t fully understood your stance towards the many minds interpretation. Do you find it unnecessary?
And simultaneously you think that existence of future Harries who observe events with probabilities approaching zero is not a problem because current Harry will almost never find himself to be those future Harries. I don’t understand what it means exactly.
Harries who observe those rare events exist and they wonder how they found themselves in those unlikely situations. Harries who hadn’t found anything unusual exist too. Current Harry became all of those future Harries.
So, we have a quantum state of the universe that factorizes into states with different Harries. OK. What property distinguished a universe where “Harry found himself in a tails branch” and a universe where “Harry found himself in a heads branch”?
You have already answered it: “I don’t think either of these Harrys is “preferred”.” That is there’s no property of the universe that distinguishes those outcomes.
Let’s get back to the initial question ‘What it means that “Harry will almost never find himself to be those future Harries”?’ To answer that we need to jump from a single physical Universe (containing multitude of Harries who found themselves in branches of every possible probability) to a single one (or maybe a set) of those Harries and proclaim that, indeed, that Harry (or Harries) found himself in a usual branch of the universe and all other Harries don’t matter for some reason (their amplitudes are too low to matter despite them being fully conscious? That’s the point that I don’t understand).
The many minds interpretation solves this by proposing metaphysical threads of consciousness, thus adding a property that distinguishes outcomes where Harry observes different things. So we can say that indeed the vast majority of Harries’ threads of consciousness ended up in probable branches.
I don’t like this interpretation. Why don’t we use a single thread of consciousness that adheres to Born rule? Or why don’t we get rid of threads of consciousness altogether and just use the Copenhagen interpretation?
So, my question is how you tackle this problem? I hope I’ve made it sufficiently coherent.
My own resolution is that either collapse is objective, or
due to imperfect decoherence the vast majority of branches (which also have relatively low amplitude) interfere with each other, making it impossible for conscious beings to exist in them and, consequently, observe them(it doesn’t explain billion quantum coin-flips scenario in my comment below)I just looked up “many minds” and it’s a little bit like what I wrote here, but described differently in ways that I think I don’t like. (It’s possible that Wikipedia is not doing it justice, or that I’m misunderstanding it.) I think minds are what brains do, and I think brains are macroscopic systems that follow the laws of quantum mechanics just like everything else in the universe.
Those both happen in the same universe. Those Harry’s both exist. Maybe you should put aside many-worlds and just think about Parfit’s teletransportation paradox. I think you’re assuming that “thread of subjective experience” is a coherent concept that satisfies all the intuitive properties that we feel like it should have, and I think that the teletransportation paradox is a good illustration that it’s not coherent at all, or at the very least, we should be extraordinarily cautious when making claims about the properties of this alleged thing you call a “thread of subjective experience” or “thread of consciousness”. (See also other Parfit thought experiments along the same lines.)
I don’t like the idea where we talk about what will happen to Harry, as if that has to have a unique answer. Instead I’d rather talk about Harry-moments, where there’s a Harry at a particular time doing particular things and full of memories of what happened in the past. Then there are future Harry-moments. We can go backwards in time from a Harry-moment to a unique (at any given time) past Harry-moment corresponding to it—after all, we can inspect the memories in future-Harry-moment’s head about what past-Harry was doing at that time (assuming there were no weird brain surgeries etc). But we can’t uniquely go in the forward direction: Who’s to say that multiple future-Harry-moments can’t hold true memories of the very same past-Harry-moment?
Here I am, right now, a Steve-moment. I have a lot of direct and indirect evidence of quantum interactions that have happened in the past or are happening right now, as imprinted on my memories, surroundings, and so on. And if you a priori picked some possible property of those interactions that (according to the Born rule) has 1-in-a-googol probability to occur in general, then I would be delighted to bet my life’s savings that this property is not true of my current observations and memories. Obviously that doesn’t mean that it’s literally impossible.
“Thread of subjective experience” was an aside (just one of the mechanisms that explains why we “find ourselves” in a world that behaves according to the Born rule), don’t focus too much on it.
The core question is which physical mechanism (everything should be physical, right?) ensures that you almost never will see a string of a billion tails after a billion quantum coin flips, while the universe contains a quantum branch with you looking in astonishment on a string with a billion tails. Why should you expect that it will almost certainly not happen, when there’s always a physical instance of you that will see it happened?
You’ll have 2^1000000000 branches with exactly the same amplitude. You’ll experience every one of them. Which physical mechanism will make it more likely for you to experience strings with roughly the same number of heads and tails?
In the Copenhagen interpretation it’s trivial: when the quantum coin flipper writes a result of the flip the universe somehow samples from a probability distribution and the rest is the plain old probability theory. You don’t expect to observe a string of a billion tails (or any other preselected string), because you who observes this string almost never exist.
What happens in MWI?
This is how it works in MWI without additional postulates. But if you postulate the probability that you will find yourself somewhere, then you are postulating the difference between the case where you have found yourself there, and the case where you haven’t. Having a number for how much you prefer something is the whole point of indexical probabilities. And as probability of some future “you” goes to zero, this future “you” goes to not being the continuation of your subjective experience, right? Surely that would make this “you” dispreferred in some sense?
I wrote “flipping an unbiased coin” so that’s 50⁄50.
Where could I find the proof that “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is equivalent to the Born rule?
Quantum Mechanics In Your Face talk by Sidney Coleman, starting slide 17 near the end. The basic idea is to try to operationalize how someone might test the Born rule—they take a bunch of quantum measurements, one after another, and they subject their data to a bunch of randomness tests and so on, and then they eventually declare “Born rule seems true” or “Born rule seems false” after analyzing the data. And you can show that the branches in which this person declares “Born rule seems false” have collective amplitude approaching zero, in the limit as their test procedure gets better and better (i.e. as they take more and more measurements).
I was assigned this reading for a class once but only skimmed it—now I wish I’d read it more closely!