Why do you assign identical priors to all empirically equivalent interpretations?
Why shouldn’t I? I only prefer the simpler of two stories that make everywhere and always identical predictions, because it’s more pleasant—but I can’t find it any more likely. I thought the notion of a universal prior was to normalize to the shortest equivalent description. If collapse vs. many worlds are equivalent in their predictions, then my universal prior gives the same answer for them both.
You really think there is basically no chance of a collapse or hidden variable interpretation being true? Why?
You slightly misunderstood me. As far as I understand them, they’re all equivalent with respect to any measurements I can perform. So I give them all near 100% chance of being “more or less correct”.
I thought the notion of a universal prior was to normalize to the shortest equivalent description. If collapse vs. many worlds are equivalent in their predictions, then my universal prior gives the same answer for them both.
The “equivalent” in your characterization of the universal prior does not mean “empirically equivalent”. If you read it that way, then you’re not doing Solomonoff induction.
You slightly misunderstood me. As far as I understand them, they’re all equivalent with respect to any measurements I can perform.
This is false. There are possible experiments that distinguish many worlds from its collapse and hidden variable competitors.
I wasn’t claiming to do Solomonoff induction, or claiming to use a universal prior. I think you know the definitions of those better than I do, but I’m not sure you understood that I stipulated that the competing theories be empirically equivalent everywhere and always—not just in my experience so far. I don’t know of any stronger notion of equivalence, so if you’d like to specify what equivalence you think I should be using, I’m all ears (I do know that there are syntactically verifiable equivalences, but I don’t consider those to be any stronger).
There are possible experiments that distinguish many worlds from its collapse and hidden variable competitors.
Maybe. Although I don’t completely understand QM, I’ve heard that MWI is experimentally indistinguishable from at least one other interpretation. I’d appreciate a reference to any experiment that should separate MWI from its competitors.
Consider a conspiratorial interpretation of quantum mechanics according to which the universe is genuinely local and deterministic, but the initial conditions of the universe are jerry-rigged so that all measurements made by sentient creatures fit quantum statistics (even though events in general do not). This theory is empirically equivalent to many worlds. It seems clear that there are several senses in which it is not equivalent to many worlds. And I think there is good reason to assign it substantially lower prior probability than many worlds, since one would need to specify the entire initial condition of the universe in order to predict correlations that many worlds predicts based simply on Schrodinger’s equation.
That’s a useful demonstration of the intuition behind “simpler is more plausible”. Still, if it were possible to know that your jury-rigged-setup story were everywhere and always (not just up-til-now) empirically equivalent to MWI or whatever, then I’d really bite the bullet and call it absolutely equivalent.
David Deutsch has a paper called “Three experimental implications of the Everett interpretation”. I can’t find it online, unfortunately. The experiments are infeasible with current technology, but the fact remains that many worlds makes different predictions than orthodox QM.
The basic idea is easy to grasp. Copenhagen says there are certain sorts of systems (observers, or measuring devices) that can collapse superpositions but do not themselves enter into superposed states. Many worlds says that these systems do enter into superpositions. There are possible measurements (very difficult to conduct, admittedly, given the size of these systems) that can tell us whether or not such a system is in a superposed state.
“Three experimental implications of the Everett interpretation”. The experiments are infeasible with current technology, but the fact remains that many worlds makes different predictions than orthodox QM.
Why shouldn’t I? I only prefer the simpler of two stories that make everywhere and always identical predictions, because it’s more pleasant—but I can’t find it any more likely. I thought the notion of a universal prior was to normalize to the shortest equivalent description. If collapse vs. many worlds are equivalent in their predictions, then my universal prior gives the same answer for them both.
You slightly misunderstood me. As far as I understand them, they’re all equivalent with respect to any measurements I can perform. So I give them all near 100% chance of being “more or less correct”.
The “equivalent” in your characterization of the universal prior does not mean “empirically equivalent”. If you read it that way, then you’re not doing Solomonoff induction.
This is false. There are possible experiments that distinguish many worlds from its collapse and hidden variable competitors.
I wasn’t claiming to do Solomonoff induction, or claiming to use a universal prior. I think you know the definitions of those better than I do, but I’m not sure you understood that I stipulated that the competing theories be empirically equivalent everywhere and always—not just in my experience so far. I don’t know of any stronger notion of equivalence, so if you’d like to specify what equivalence you think I should be using, I’m all ears (I do know that there are syntactically verifiable equivalences, but I don’t consider those to be any stronger).
Maybe. Although I don’t completely understand QM, I’ve heard that MWI is experimentally indistinguishable from at least one other interpretation. I’d appreciate a reference to any experiment that should separate MWI from its competitors.
Consider a conspiratorial interpretation of quantum mechanics according to which the universe is genuinely local and deterministic, but the initial conditions of the universe are jerry-rigged so that all measurements made by sentient creatures fit quantum statistics (even though events in general do not). This theory is empirically equivalent to many worlds. It seems clear that there are several senses in which it is not equivalent to many worlds. And I think there is good reason to assign it substantially lower prior probability than many worlds, since one would need to specify the entire initial condition of the universe in order to predict correlations that many worlds predicts based simply on Schrodinger’s equation.
That’s a useful demonstration of the intuition behind “simpler is more plausible”. Still, if it were possible to know that your jury-rigged-setup story were everywhere and always (not just up-til-now) empirically equivalent to MWI or whatever, then I’d really bite the bullet and call it absolutely equivalent.
Fair enough. Incidentally, if you’re looking for a rigorous justification of Occam’s razor, the best one I know of is Kevin Kelly’s.
David Deutsch has a paper called “Three experimental implications of the Everett interpretation”. I can’t find it online, unfortunately. The experiments are infeasible with current technology, but the fact remains that many worlds makes different predictions than orthodox QM.
The basic idea is easy to grasp. Copenhagen says there are certain sorts of systems (observers, or measuring devices) that can collapse superpositions but do not themselves enter into superposed states. Many worlds says that these systems do enter into superpositions. There are possible measurements (very difficult to conduct, admittedly, given the size of these systems) that can tell us whether or not such a system is in a superposed state.
Thanks. I’ll take your recollected word for it.