This is an Inkhaven crosspost, and as such is fairly "off the cuff"
Among rationalists, the many worlds interpretation (MWI) of quantum mechanics is broadly accepted, and people throw around concepts like “Everett branches” to explain normal probability problems. This is substantially based on Eliezer Yudkowsky’s arguments from 2008, as well as obviously the background arguments from physicists. I don’t find this very convincing, and in this post, I begin to explain why.
TL;DR: The common-sense problems that many-worlds solves, it solves approximately equally well under classical mechanics and quantum mechanics, and it doesn’t solve them very well. The fact that many-worlds is a natural tool for thinking about probability is in my view better explained as surprising and suspicious convergence (i.e. “it’s a neat thinking tool => it is likely over-rated as an explanation relative to its actual justification”) than it being a truly natural explanation.[1]
1. Many worlds are allowed under both classical and quantum mechanics
It’s natural to adopt the concept of many worlds when working through problems involving ordinary probability: in one world a coin shows heads, in the other world the coin shows tails; you can repeat this and find that “1 out of the 4 possible worlds shows (heads, tails)”. This all goes through fine and is a lot easier than thinking “(heads, tails) occurs 1/4 of the time in the limit of a large number of trials”, or “the correct degree of belief in (heads, tails) occurring is 1/4”.
Under classical mechanics, people tend to think of this as a helpful reasoning tool, whereas under quantum mechanics people are more inclined to think there are literally 4 different worlds. I claim it’s not that obvious why these should be interpreted differently.
The reason that immediately springs to mind is “determinism”, or the idea that classical uncertainty is “purely epistemic”: In the classical case, if the observer knew all the particles’ starting position and momentum, they could calculate the outcome exactly. In the quantum case, even if the observer knew the starting wave-function, they could still not calculate the outcome exactly. However, this pre-condition “if the observer knew all the particles’ starting position and momentum” is not possible even under classical mechanics, and in fact both have irreducible uncertainty.
In the classical case, the exact particle positions/momenta are valid concepts in the theory, but the observer knowing them exactly is ruled out via the Maxwell’s Demon argument, they are confined to have a probability distribution over them. In the quantum case, the exact wave-function is a valid concept, the exact particle positions/momenta don’t appear as a concept, and the observer is still confined to having a probability distribution over the particle positions/momenta.
In both cases, the observer is confined to have a probability distribution over what they will measure. In the classical case, I believe historically it never really came up whether the underlying particle positions were “physically real” vs a calculating tool, or whether this distribution represents a multiverse vs simple “degree of belief” uncertainty. It would seem quite dramatic to suppose infinite universes to resolve this question. In the quantum case, people are concerned about whether the wave-function is “physically real”, and inclined to see this distribution as representing many different actualised universes.
Now, don’t get me wrong, I can see that these cases are different, and that the fact that quantum mechanics goes one more step removed from “exact particle positions” makes it look even less deterministic. But I don’t see the clear logical path to “and so quantum == many worlds” via non-determinism.
2. Quantum-independent problems with many worlds
Setting aside the question of whether quantum mechanics specifically motivates many worlds, there are problems with many worlds that apply regardless of which physics you’re working under.
It doesn’t solve contingency
Some people see it as a problem that the universe is contingent, that some things could happen don’t happen. Many worlds appears to do away with this problem by saying “actually, everything that could have happened did happen”. But I don’t believe this actually solves the problem, it just pushes it into “indexical uncertainty”: Instead of saying “the coin could have landed heads, but didn’t”, you say “I, the observer, could have ended up in the world where the coin landed heads, but didn’t”. To me, this seems like adding an epicycle to the problem, and it’s far more straightforward to just bite the bullet and say “some things that could happen don’t happen”.
Continuous branching creates a subjective experience and population ethics nightmare
If you take many worlds literally, then you need to deal with the fact that worlds branch continuously. If you’re morally interested in whether the number of individuals goes up as the world branches, you have two options, and both are strange. Either: every second, the moral worth in the universe exponentially increases, such that everything that happened before is completely dwarfed by what happens after. Or: there’s some constant renormalisation where, yes, there are 10 times as many people, but the degree to which each one exists is 10 times less. Even if you don’t value “moral worth” in that way, there is still an equally confusing problem wrt the amount of subjective experience generally.
Since I’m presenting Yudkowsky’s views as “the other side”: He appears to endorse “constantly renormalise”, at least implicitly (link): “There are some minor ethical implications of many-worlds itself (e.g., average utilitarianism suddenly becomes a lot more appealing” (presumably it “becomes a lot more appealing” because without it utility continuously blows up exponentially). This is quite counterintuitive to me because my subjective experience through all this branching feels like it “stays the same size” as I occupy a smaller and smaller slice of the space of possible worlds.
Single-world handles this naturally: there is one world, and the reason we count the person rolling two sixes as one-thirty-sixth is because there is a 35/36 chance that won’t happen.
The reason it was invented in quantum mechanics was to explain away the apparent collapse of the wavefunction... I also started making some quantum-specific arguments related to this, but quickly got out of my depth and have delegated them indefinitely to a future post. Quick version: QM has two main spooky properties: entanglement (”spooky action at a distance”), and the apparent collapse of the wavefunction. Many worlds does address the collapse problem, but in my view anti-addresses various entanglement paradoxes, i.e. they become even more confusing when viewed through a many-worlds lens. This isn’t covered in this post.
This is an Inkhaven crosspost, and as such is fairly "off the cuff"
Among rationalists, the many worlds interpretation (MWI) of quantum mechanics is broadly accepted, and people throw around concepts like “Everett branches” to explain normal probability problems. This is substantially based on Eliezer Yudkowsky’s arguments from 2008, as well as obviously the background arguments from physicists. I don’t find this very convincing, and in this post, I begin to explain why.
TL;DR: The common-sense problems that many-worlds solves, it solves approximately equally well under classical mechanics and quantum mechanics, and it doesn’t solve them very well. The fact that many-worlds is a natural tool for thinking about probability is in my view better explained as surprising and suspicious convergence (i.e. “it’s a neat thinking tool => it is likely over-rated as an explanation relative to its actual justification”) than it being a truly natural explanation.[1]
1. Many worlds are allowed under both classical and quantum mechanics
It’s natural to adopt the concept of many worlds when working through problems involving ordinary probability: in one world a coin shows heads, in the other world the coin shows tails; you can repeat this and find that “1 out of the 4 possible worlds shows (heads, tails)”. This all goes through fine and is a lot easier than thinking “(heads, tails) occurs 1/4 of the time in the limit of a large number of trials”, or “the correct degree of belief in (heads, tails) occurring is 1/4”.
Under classical mechanics, people tend to think of this as a helpful reasoning tool, whereas under quantum mechanics people are more inclined to think there are literally 4 different worlds. I claim it’s not that obvious why these should be interpreted differently.
The reason that immediately springs to mind is “determinism”, or the idea that classical uncertainty is “purely epistemic”: In the classical case, if the observer knew all the particles’ starting position and momentum, they could calculate the outcome exactly. In the quantum case, even if the observer knew the starting wave-function, they could still not calculate the outcome exactly. However, this pre-condition “if the observer knew all the particles’ starting position and momentum” is not possible even under classical mechanics, and in fact both have irreducible uncertainty.
In the classical case, the exact particle positions/momenta are valid concepts in the theory, but the observer knowing them exactly is ruled out via the Maxwell’s Demon argument, they are confined to have a probability distribution over them. In the quantum case, the exact wave-function is a valid concept, the exact particle positions/momenta don’t appear as a concept, and the observer is still confined to having a probability distribution over the particle positions/momenta.
In both cases, the observer is confined to have a probability distribution over what they will measure. In the classical case, I believe historically it never really came up whether the underlying particle positions were “physically real” vs a calculating tool, or whether this distribution represents a multiverse vs simple “degree of belief” uncertainty. It would seem quite dramatic to suppose infinite universes to resolve this question. In the quantum case, people are concerned about whether the wave-function is “physically real”, and inclined to see this distribution as representing many different actualised universes.
Now, don’t get me wrong, I can see that these cases are different, and that the fact that quantum mechanics goes one more step removed from “exact particle positions” makes it look even less deterministic. But I don’t see the clear logical path to “and so quantum == many worlds” via non-determinism.
2. Quantum-independent problems with many worlds
Setting aside the question of whether quantum mechanics specifically motivates many worlds, there are problems with many worlds that apply regardless of which physics you’re working under.
It doesn’t solve contingency
Some people see it as a problem that the universe is contingent, that some things could happen don’t happen. Many worlds appears to do away with this problem by saying “actually, everything that could have happened did happen”. But I don’t believe this actually solves the problem, it just pushes it into “indexical uncertainty”: Instead of saying “the coin could have landed heads, but didn’t”, you say “I, the observer, could have ended up in the world where the coin landed heads, but didn’t”. To me, this seems like adding an epicycle to the problem, and it’s far more straightforward to just bite the bullet and say “some things that could happen don’t happen”.
Continuous branching creates a subjective experience and population ethics nightmare
If you take many worlds literally, then you need to deal with the fact that worlds branch continuously. If you’re morally interested in whether the number of individuals goes up as the world branches, you have two options, and both are strange. Either: every second, the moral worth in the universe exponentially increases, such that everything that happened before is completely dwarfed by what happens after. Or: there’s some constant renormalisation where, yes, there are 10 times as many people, but the degree to which each one exists is 10 times less. Even if you don’t value “moral worth” in that way, there is still an equally confusing problem wrt the amount of subjective experience generally.
Since I’m presenting Yudkowsky’s views as “the other side”: He appears to endorse “constantly renormalise”, at least implicitly (link): “There are some minor ethical implications of many-worlds itself (e.g., average utilitarianism suddenly becomes a lot more appealing” (presumably it “becomes a lot more appealing” because without it utility continuously blows up exponentially). This is quite counterintuitive to me because my subjective experience through all this branching feels like it “stays the same size” as I occupy a smaller and smaller slice of the space of possible worlds.
Single-world handles this naturally: there is one world, and the reason we count the person rolling two sixes as one-thirty-sixth is because there is a 35/36 chance that won’t happen.
The reason it was invented in quantum mechanics was to explain away the apparent collapse of the wavefunction... I also started making some quantum-specific arguments related to this, but quickly got out of my depth and have delegated them indefinitely to a future post. Quick version: QM has two main spooky properties: entanglement (”spooky action at a distance”), and the apparent collapse of the wavefunction. Many worlds does address the collapse problem, but in my view anti-addresses various entanglement paradoxes, i.e. they become even more confusing when viewed through a many-worlds lens. This isn’t covered in this post.