p1: Many Worlds says that the only dynamical rule is Schrodinger’s equation acting on a real wavefunction (not numerically ‘real’). That’s the end of it. If you hold that, you end up with many worlds whether you like it (or realize it) or not. People may feel unsatisfied with that and add more explanation, but when it comes down to it, that is what MWI is.
See, there are (at least?) two kinds of postulates. I don’t know of names for them so I’m going to call them types 1 and 2. Type 1 says what the system does. Type 2 is how you map the system onto our perceptions.
Like, in Newtonian mechanics, Newton’s 3rd law is a type 1 postulate. The mapping of the xyz coordinate parameters onto our 3-dimensional space is a type 2 postulate. Alternately, on a world map, the projection used is type 2 (or if you’re using a globe then that fact is also of type 2).
Copenhagen-style objective collapse treats the Born rule as a type 1 postulate. MWI treats the Born rule as a type 2. Anyone else who introduces the Born rule as a type 2 rule somehow and doesn’t add any other dynamical rules, ends up with a flavor of MWI. Their arguments, reasoning, etc. are irrelevant.
P2,3: Those sound like flavors of MWI. If they add dynamical rules then they’re not. If they don’t use the Born rule (unlikely) then they’re not, except that in the many minds interpretation I suppose we could introduce a correction for differences in numbers of minds by way of anthropic reasoning, but that depends how you put the question.
P4: Not all postulates are created equal. Euclid’s 5th is far uglier than the 1st to 4th, for instance. If you take one tine of the fork in a Gödel sentence, that’s going to be waaaay uglier still. And generally speaking, it’s fair to weight type 1 and type 2 differently.
In the globe analogy, the MWI family is the equivalent of using a globe to represent the Earth, while Copenhagen is the equivalent of flattening it by the two-point equidistant projection onto a billion-piece jigsaw puzzle and eating the 99.999% of the pieces that don’t include anything we can see. And with an ontologically real collapse, then that’s what you think the Earth is actually doing (minus your personally eating it) - you’re not even keeping the globe in the back of your mind.
Sure, it’s the same number of postulates, and it ends up describing our experiences as well. Must be just as good!
Your p1: Thats simply not true. Consistent histories, for instance is definitely NOT many worlds, and yet it only has the one dynamical rule. Similarly, Ballentine’s ensemble interpretation has only one world,but only the one dynamical rule (it denies the “reality” of the wavefunction to get there).
Your p2: I’m not sure your two kinds of postulates are distinct categories. Consider the standard quantum postulate: All observables are associated with Hermitian operators. Is this type 1 or 2? It defines what we measure, but its also defining the system. Can you list a type 2 postulate for me that isn’t the measurement postulate?
Your p4: In my mind (and in most literature I’m familiar with) many worlds means specifically Everett’s intepretation. In Everett’s interpretation: you don’t take measurement as EITHER a type 1 or a type 2 postulate, and people like Wallace insist that you can deduce the “type 2” of the theory from the dynamics.
I’d be willing to extend the term “many worlds” to any interpretations that insist on the existence of multiple “worlds”, but to suggest consistent histories or Ballentine’s ensemble are many worlds variants is to weaken the term to the point of meaningless. Neither have any kind of multiple worlds! Consistent histories, for instance, is most often described (by Omnes, for instance) as Copenhagen made more precise.
P penultimate:I haven’t discussed copenhagen in the comments in this chain,or any objective collapse intepretations. This whole paragraph seems off point. Your choices aren’t only between many worlds and Copenghagen (unless you continue with your definition of many worlds as ‘anything not Copenhagen’). There are many other modern interpretations.
I’ve seen variants of MWI that were explicitly MWI, so what you’re calling MWI would be straight Everettian MWI. But really, here, I’m asking: “Does this theory have multiple worlds in it?” I care significantly less what it’s called.
For instance, Consistent Histories looks at things quite differently, but if you ask the critical questions of it, it looks like it has many worlds in it. It primes you to zero in on one of them, but if you’re going to stick with the wavefunction being real then the histories you don’t observe are going to be equally real, just less relevant. On the other hand if you say it’s just a trick for finding the probabilities, well, then it’s just a formalized ontological collapse and not MWI. I don’t see any middle ground or ground off to the side here (aside from throwing your hands in the air and saying you don’t know, which is perfectly legitimate but it isn’t an interpretation).
The associations of the hermitian operators corresponding to observable quantities are very type-2. We should feel about as justified using them as using the Born rule.
The point of mentioning objective collapse in the last 2 paragraphs was as a reference point for the non-equality of type-2 postulates. I know it’s terrible, and you know it’s terrible—that’s the point.
But really, here, I’m asking: “Does this theory have multiple worlds in it?” I care significantly less what it’s called
Right- in consistent histories there is 1 world. When you make a measurement, you get one answer. In ensemble quantum mechanics there is 1 world. Remember- the creators of consistent histories (Hartle, for instance) consider it a formalized and clarified copenhagen variant (though inspired by many worlds). Maybe think about it like Bohmian mechanics- the “world” that the Bohmian particle actually sits in is the ‘real’ one. Similarly, in consistent histories, the answer you get picks out a set of projection operators as “real.”
Side question- do you know a many worlds variant (in the sense of more than one world) that makes explicit what its “type 2” postulate is? The only variant I know of is many minds, which I find sort of abhorrent and disregard out of hand. The reason I insist that “many worlds” is incomplete is that the only formalized version I know is Everettian many worlds (which we both seem to agree IS incomplete).
The associations of the hermitian operators corresponding to observable quantities are very type-2.
But also type 1, because it defines the system (hermitian operators on a Hilbert space). What would you consider the type 2 postulates of Newtonian mechanics? What would you consider the type 2 postulates of GR?
In that case, Consistent Histories is both not WMI and I didn’t say it was, because it doesn’t consider the wavefunction fully real in its own right (there were two criteria, not just one, in that sentence)*. Just as Bohm isn’t, on the same grounds.
Type 1 vs type 2: Normally we don’t even talk about these types—if it were a matter of discussion, we wouldn’t be using these terms! With the observables, using them in the theory is type 1. Associating each one to a part of the world we experience is type 2.
As for the incompleteness of Everett, I hold that you can deduce that the Born Rule is one possible way of finding sapience within wavefunctions. I am not at all sure that you can prove that there aren’t others, so barring such a proof, a postulate is necessary to exclude them—“The way of getting to a perceivable world from this theory is… THIS one, not any others.”
ETA: and in this case Consistent Histories deserves every bit of scorn that Eliezer heaped on Copenhagen in the ‘what does it have to do, kill a puppy’ rant.
p1: Many Worlds says that the only dynamical rule is Schrodinger’s equation acting on a real wavefunction (not numerically ‘real’). That’s the end of it. If you hold that, you end up with many worlds whether you like it (or realize it) or not. People may feel unsatisfied with that and add more explanation, but when it comes down to it, that is what MWI is.
See, there are (at least?) two kinds of postulates. I don’t know of names for them so I’m going to call them types 1 and 2. Type 1 says what the system does. Type 2 is how you map the system onto our perceptions.
Like, in Newtonian mechanics, Newton’s 3rd law is a type 1 postulate. The mapping of the xyz coordinate parameters onto our 3-dimensional space is a type 2 postulate. Alternately, on a world map, the projection used is type 2 (or if you’re using a globe then that fact is also of type 2).
Copenhagen-style objective collapse treats the Born rule as a type 1 postulate. MWI treats the Born rule as a type 2. Anyone else who introduces the Born rule as a type 2 rule somehow and doesn’t add any other dynamical rules, ends up with a flavor of MWI. Their arguments, reasoning, etc. are irrelevant.
P2,3: Those sound like flavors of MWI. If they add dynamical rules then they’re not. If they don’t use the Born rule (unlikely) then they’re not, except that in the many minds interpretation I suppose we could introduce a correction for differences in numbers of minds by way of anthropic reasoning, but that depends how you put the question.
P4: Not all postulates are created equal. Euclid’s 5th is far uglier than the 1st to 4th, for instance. If you take one tine of the fork in a Gödel sentence, that’s going to be waaaay uglier still. And generally speaking, it’s fair to weight type 1 and type 2 differently.
In the globe analogy, the MWI family is the equivalent of using a globe to represent the Earth, while Copenhagen is the equivalent of flattening it by the two-point equidistant projection onto a billion-piece jigsaw puzzle and eating the 99.999% of the pieces that don’t include anything we can see. And with an ontologically real collapse, then that’s what you think the Earth is actually doing (minus your personally eating it) - you’re not even keeping the globe in the back of your mind.
Sure, it’s the same number of postulates, and it ends up describing our experiences as well. Must be just as good!
Your p1: Thats simply not true. Consistent histories, for instance is definitely NOT many worlds, and yet it only has the one dynamical rule. Similarly, Ballentine’s ensemble interpretation has only one world,but only the one dynamical rule (it denies the “reality” of the wavefunction to get there).
Your p2: I’m not sure your two kinds of postulates are distinct categories. Consider the standard quantum postulate: All observables are associated with Hermitian operators. Is this type 1 or 2? It defines what we measure, but its also defining the system. Can you list a type 2 postulate for me that isn’t the measurement postulate?
Your p4: In my mind (and in most literature I’m familiar with) many worlds means specifically Everett’s intepretation. In Everett’s interpretation: you don’t take measurement as EITHER a type 1 or a type 2 postulate, and people like Wallace insist that you can deduce the “type 2” of the theory from the dynamics.
I’d be willing to extend the term “many worlds” to any interpretations that insist on the existence of multiple “worlds”, but to suggest consistent histories or Ballentine’s ensemble are many worlds variants is to weaken the term to the point of meaningless. Neither have any kind of multiple worlds! Consistent histories, for instance, is most often described (by Omnes, for instance) as Copenhagen made more precise.
P penultimate:I haven’t discussed copenhagen in the comments in this chain,or any objective collapse intepretations. This whole paragraph seems off point. Your choices aren’t only between many worlds and Copenghagen (unless you continue with your definition of many worlds as ‘anything not Copenhagen’). There are many other modern interpretations.
I’ve seen variants of MWI that were explicitly MWI, so what you’re calling MWI would be straight Everettian MWI. But really, here, I’m asking: “Does this theory have multiple worlds in it?” I care significantly less what it’s called.
For instance, Consistent Histories looks at things quite differently, but if you ask the critical questions of it, it looks like it has many worlds in it. It primes you to zero in on one of them, but if you’re going to stick with the wavefunction being real then the histories you don’t observe are going to be equally real, just less relevant. On the other hand if you say it’s just a trick for finding the probabilities, well, then it’s just a formalized ontological collapse and not MWI. I don’t see any middle ground or ground off to the side here (aside from throwing your hands in the air and saying you don’t know, which is perfectly legitimate but it isn’t an interpretation).
The associations of the hermitian operators corresponding to observable quantities are very type-2. We should feel about as justified using them as using the Born rule.
The point of mentioning objective collapse in the last 2 paragraphs was as a reference point for the non-equality of type-2 postulates. I know it’s terrible, and you know it’s terrible—that’s the point.
Right- in consistent histories there is 1 world. When you make a measurement, you get one answer. In ensemble quantum mechanics there is 1 world. Remember- the creators of consistent histories (Hartle, for instance) consider it a formalized and clarified copenhagen variant (though inspired by many worlds). Maybe think about it like Bohmian mechanics- the “world” that the Bohmian particle actually sits in is the ‘real’ one. Similarly, in consistent histories, the answer you get picks out a set of projection operators as “real.”
Side question- do you know a many worlds variant (in the sense of more than one world) that makes explicit what its “type 2” postulate is? The only variant I know of is many minds, which I find sort of abhorrent and disregard out of hand. The reason I insist that “many worlds” is incomplete is that the only formalized version I know is Everettian many worlds (which we both seem to agree IS incomplete).
But also type 1, because it defines the system (hermitian operators on a Hilbert space). What would you consider the type 2 postulates of Newtonian mechanics? What would you consider the type 2 postulates of GR?
In that case, Consistent Histories is both not WMI and I didn’t say it was, because it doesn’t consider the wavefunction fully real in its own right (there were two criteria, not just one, in that sentence)*. Just as Bohm isn’t, on the same grounds.
Type 1 vs type 2: Normally we don’t even talk about these types—if it were a matter of discussion, we wouldn’t be using these terms! With the observables, using them in the theory is type 1. Associating each one to a part of the world we experience is type 2.
As for the incompleteness of Everett, I hold that you can deduce that the Born Rule is one possible way of finding sapience within wavefunctions. I am not at all sure that you can prove that there aren’t others, so barring such a proof, a postulate is necessary to exclude them—“The way of getting to a perceivable world from this theory is… THIS one, not any others.”
ETA: and in this case Consistent Histories deserves every bit of scorn that Eliezer heaped on Copenhagen in the ‘what does it have to do, kill a puppy’ rant.