The confusion on the topic of interpretations comes from the failure to answer the question, what is an “interpretation” (or, more generally, a “theory of physics”) even supposed to be? What is its type signature, and what makes it true or false?
Imagine a robot with a camera and a manipulator, whose AI is a powerful reinforcement learner, with a reward function that counts the amount of blue seen in the camera. The AI works by looking for models that are good at predicting observations, and using those models to make plans for maximizing blue.
Now our AI discovered quantum mechanics. What does it mean? What kind of model would it construct? Well, the Copenhagen interpretation does a perfectly good job. The wave function evolves via the Schrodinger equation, and every camera frame there is collapse. As long as predicting observations is all we need, there’s no issue.
It gets more complicated if you want your agent to have a reward function that depends on unobserved parameters (things in the outside world), e.g. the number of paperclips in the universe. In this case Copenhagen is insufficient, because in Copenhagen an observable is undefined when you don’t measure it. But MWI also doesn’t give an answer: our agent cares about classical observables, so how is it supposed to read their values from the wavefunction? I have some ideas about an new interpretation that solves it, but it would be its own essay.
EDIT: More precisely, given an evolving wave function Ψ(t), a classical observable O (such as the number of paperclips) and moment of time t, we can use the Born rule to get a distribution over the values of O(t). However, what we would like is to have a distribution over histories (i.e. we want an element of Δ(R→R) rather than of R→ΔR)) because our utility function might care about history in a non-trivial way, and because without being able to speak of histories it is not clear how to validate this is “the real O” (i.e. what makes this theory the right theory?). A distribution over histories is something we can get from hidden variable theories such as de Broglie-Bohm, but there are other issues with that.
I think that physics is best understood as answering the question “in what mathematical entity do we find ourselves?”—a question that Everett is very equipped to answer. Then, once you have an answer to that question, figuring out your observations becomes fundamentally a problem of locating yourself within that object, which I think raises lots of interesting anthropic questions, but not additional physical ones.
I disagree. “in what mathematical entity do we find ourselves?” is a map-territory confusion. We are not in a mathematical entity, we use mathematics to construct models of reality. And, in any case, without “locating yourself within the object”, it’s not clear how do you know whether your theory is true, so it’s very much pertinent to physics.
Moreover, I’m not sure how this perspective justifies MWI. Presumably, the wavefunction contains multiple “worlds” hence you conclude that multiple worlds “exist”. However, consider an alternative universe with stochastic classical physics. The “mathematical entity” would be a probability measure over classical histories. So it can also be said to contains “multiple worlds”. But in that universe everyone would be comfortable with saying there’s just one non-deterministic world. So, you need something else to justify the multiple worlds, but I’m not sure what. Maybe you would say the stochastic universe also has multiple worlds, but then it starts looking a like a philosophical assumption that doesn’t follow from physics.
Then what would you call reality? It sure seems like it’s well-described as a mathematical object to me.
without “locating yourself within the object”, it’s not clear how do you know whether your theory is true, so it’s very much pertinent to physics.
Put a simplicity prior over the combined difficulty of specifying a universe and specifying you within that universe. Then update on your observations.
The “mathematical entity” would be a probability measure over classical histories.
Not necessarily. You can mathematically well-define 1) a Turing machine with access to randomness that samples from a probability measure and 2) a Turing machine which actually computes all the histories (and then which one you find yourself in is an anthropic question). What quantum mechanics says, though, is that (1) actually doesn’t work as a description of reality, because we see interference from those other branches, which means we know it has to be (2).
Then what would you call reality? It sure seems like it’s well-described as a mathematical object to me.
I call it “reality”. It’s irreducible. But I feel like this is not the most productive direction to hash out the disagreement.
Put a simplicity prior over the combined difficulty of specifying a universe and specifying you within that universe. Then update on your observations.
Okay, but then the separation between “specifying a universe” and “specifying you within that universe” is meaningless. Sans this separation, your are just doing simplicity-prior-Bayesian-inference. If that’s what you’re doing, the Copenhagen interpretation is what you end up with (modulo the usual problems with Bayesian inference).
You can mathematically well-define 1) a Turing machine with access to randomness that samples from a probability measure and 2) a Turing machine which actually computes all the histories (and then which one you find yourself in is an anthropic question). What quantum mechanics says, though, is that (1) actually doesn’t work as a description of reality, because we see interference from those other branches, which means we know it has to be (2).
I don’t see how you get (2) out of quantum mechanics.
The confusion on the topic of interpretations comes from the failure to answer the question, what is an “interpretation” (or, more generally, a “theory of physics”) even supposed to be? What is its type signature, and what makes it true or false?
Imagine a robot with a camera and a manipulator, whose AI is a powerful reinforcement learner, with a reward function that counts the amount of blue seen in the camera. The AI works by looking for models that are good at predicting observations, and using those models to make plans for maximizing blue.
Now our AI discovered quantum mechanics. What does it mean? What kind of model would it construct? Well, the Copenhagen interpretation does a perfectly good job. The wave function evolves via the Schrodinger equation, and every camera frame there is collapse. As long as predicting observations is all we need, there’s no issue.
It gets more complicated if you want your agent to have a reward function that depends on unobserved parameters (things in the outside world), e.g. the number of paperclips in the universe. In this case Copenhagen is insufficient, because in Copenhagen an observable is undefined when you don’t measure it. But MWI also doesn’t give an answer: our agent cares about classical observables, so how is it supposed to read their values from the wavefunction? I have some ideas about an new interpretation that solves it, but it would be its own essay.
EDIT: More precisely, given an evolving wave function Ψ(t), a classical observable O (such as the number of paperclips) and moment of time t, we can use the Born rule to get a distribution over the values of O(t). However, what we would like is to have a distribution over histories (i.e. we want an element of Δ(R→R) rather than of R→ΔR)) because our utility function might care about history in a non-trivial way, and because without being able to speak of histories it is not clear how to validate this is “the real O” (i.e. what makes this theory the right theory?). A distribution over histories is something we can get from hidden variable theories such as de Broglie-Bohm, but there are other issues with that.
I think that physics is best understood as answering the question “in what mathematical entity do we find ourselves?”—a question that Everett is very equipped to answer. Then, once you have an answer to that question, figuring out your observations becomes fundamentally a problem of locating yourself within that object, which I think raises lots of interesting anthropic questions, but not additional physical ones.
I disagree. “in what mathematical entity do we find ourselves?” is a map-territory confusion. We are not in a mathematical entity, we use mathematics to construct models of reality. And, in any case, without “locating yourself within the object”, it’s not clear how do you know whether your theory is true, so it’s very much pertinent to physics.
Moreover, I’m not sure how this perspective justifies MWI. Presumably, the wavefunction contains multiple “worlds” hence you conclude that multiple worlds “exist”. However, consider an alternative universe with stochastic classical physics. The “mathematical entity” would be a probability measure over classical histories. So it can also be said to contains “multiple worlds”. But in that universe everyone would be comfortable with saying there’s just one non-deterministic world. So, you need something else to justify the multiple worlds, but I’m not sure what. Maybe you would say the stochastic universe also has multiple worlds, but then it starts looking a like a philosophical assumption that doesn’t follow from physics.
Then what would you call reality? It sure seems like it’s well-described as a mathematical object to me.
Put a simplicity prior over the combined difficulty of specifying a universe and specifying you within that universe. Then update on your observations.
Not necessarily. You can mathematically well-define 1) a Turing machine with access to randomness that samples from a probability measure and 2) a Turing machine which actually computes all the histories (and then which one you find yourself in is an anthropic question). What quantum mechanics says, though, is that (1) actually doesn’t work as a description of reality, because we see interference from those other branches, which means we know it has to be (2).
I call it “reality”. It’s irreducible. But I feel like this is not the most productive direction to hash out the disagreement.
Okay, but then the separation between “specifying a universe” and “specifying you within that universe” is meaningless. Sans this separation, your are just doing simplicity-prior-Bayesian-inference. If that’s what you’re doing, the Copenhagen interpretation is what you end up with (modulo the usual problems with Bayesian inference).
I don’t see how you get (2) out of quantum mechanics.