My original source was unfortunately a combination of conversations and a book I don’t remember the title of, so I can’t take you back to the original source.
I’m lost here again. The two splits happen independently at two spacelike separated points and presumably converge (at the speed of light or slower) and start interacting, somehow resulting in only two worlds at the point where the measurements are compared. If this is a bad model, what is a good one?
The thing is, they’re not truly independent because the particles were prepared so as to already be entangled—the part of Fock space you put the system (and thus yourself) in is one where the particles are already aligned relative to each other, even though no one particular absolute alignment is preferred. If you entangle yourself with one, then you find you’re already entangled with the other.
It’s just like it works the rest of the time in quantum mechanics, because that’s all that’s going on.
(†) A quick rundown of how prominent this notion is, judging by google results for ‘many worlds’: Wikipedia seemed to ignore quantity. The second hit was HowStuffWorks, which gave an abominable (and obviously pop) treatment. Third was a NOVA interview, and that didn’t give a quantitative answer but stated that the number of worlds was mind-bogglingly large. Fourth was an entry at Plato.stanford.edu, which was quasi-technical while making me cringe about some things, and didn’t as far as I could tell touch on quantity. Fifth was a very nontechnical ‘top 10’-style article which had the huge number of worlds as entries 10, 9, and 8. The sixth and seventh hits were a movie promo and a book review. Eighth was the article I linked above, in preprint form (and so no anchor link, I had to find that somewhere else).
The thing is, they’re not truly independent because the particles were prepared so as to already be entangled—the part of Fock space you put the system (and thus yourself) in is one where the particles are already aligned relative to each other, even though no one particular absolute alignment is preferred. If you entangle yourself with one, then you find you’re already entangled with the other.
Right, the two macroscopic systems are entangled once both interact with the singlet, but this is a non-local statement which acts as a curiosity stopper, since it does not provide any local mechanism for the apparent “action at a distance”. Presumably MWI would offer something better than shut-up-and-calculate, like showing how what is seen locally as a pair of worlds at each detector propagate toward each other, interact and become just two worlds at the point where the results are compared, thanks to the original correlations present when the singlet was initially prepared. Do you know of anything like that written up anywhere?
Part 1 - to your first sentence: If you accept quantum mechanics as the one fundamental law, then state information is already nonlocal. Only interactions are local. So, the way you resolve the apparent ‘action at a distance’ isn’t to deny that it’s nonlocal, but to deny that it’s an action. To be clearer:
Some events transpire locally, that determine which (nonlocal) world you are in. What happened at that other location? Nothing.
Part 2 - Same as last link, question 32., with one exception: I would say that |me(L)> and such, being macrostates, do not represent single worlds but thermodynamically large bundles of worlds that share certain common features. I have sent an email suggesting this change (but considering the lack of edits over the last 18 years, I’m not confident that it will happen).
To summarize: just forget about MWI and use conventional quantum mechanics + macrostates. The entanglement is infectious, so each world ends up with an appropriate pair of measurements.
My original source was unfortunately a combination of conversations and a book I don’t remember the title of, so I can’t take you back to the original source.
But, I found something here. (†)
Thanks! It looks like the reference equates the number of worlds with the number of microstates, since it calculates it as exp(S/k), not as the number of eigenstates of some interaction Hamiltonian, which is the standard lore. From this point of view, it is not clear how many worlds you get in, say, a single-particle Stern-Gerlach experiment: 2 or exponent of the entropy change of the detector after it’s triggered. Of course, one can say that we can coarse-grain them the usual way we construct macrostates from microstates, but then why introduce many worlds instead of simply doing quantum stat mech or even classical thermodynamics?
Anyway, I could not find this essential point (how many worlds?) in the QM sequence, but maybe I missed it. All I remember is the worlds of different “thickness”, which is sort of like coarse-graining microstates into macrostates, I suppose.
My original source was unfortunately a combination of conversations and a book I don’t remember the title of, so I can’t take you back to the original source.
But, I found something here. (†)
The thing is, they’re not truly independent because the particles were prepared so as to already be entangled—the part of Fock space you put the system (and thus yourself) in is one where the particles are already aligned relative to each other, even though no one particular absolute alignment is preferred. If you entangle yourself with one, then you find you’re already entangled with the other.
It’s just like it works the rest of the time in quantum mechanics, because that’s all that’s going on.
(†) A quick rundown of how prominent this notion is, judging by google results for ‘many worlds’: Wikipedia seemed to ignore quantity. The second hit was HowStuffWorks, which gave an abominable (and obviously pop) treatment. Third was a NOVA interview, and that didn’t give a quantitative answer but stated that the number of worlds was mind-bogglingly large. Fourth was an entry at Plato.stanford.edu, which was quasi-technical while making me cringe about some things, and didn’t as far as I could tell touch on quantity. Fifth was a very nontechnical ‘top 10’-style article which had the huge number of worlds as entries 10, 9, and 8. The sixth and seventh hits were a movie promo and a book review. Eighth was the article I linked above, in preprint form (and so no anchor link, I had to find that somewhere else).
Right, the two macroscopic systems are entangled once both interact with the singlet, but this is a non-local statement which acts as a curiosity stopper, since it does not provide any local mechanism for the apparent “action at a distance”. Presumably MWI would offer something better than shut-up-and-calculate, like showing how what is seen locally as a pair of worlds at each detector propagate toward each other, interact and become just two worlds at the point where the results are compared, thanks to the original correlations present when the singlet was initially prepared. Do you know of anything like that written up anywhere?
Part 1 - to your first sentence: If you accept quantum mechanics as the one fundamental law, then state information is already nonlocal. Only interactions are local. So, the way you resolve the apparent ‘action at a distance’ isn’t to deny that it’s nonlocal, but to deny that it’s an action. To be clearer:
Some events transpire locally, that determine which (nonlocal) world you are in. What happened at that other location? Nothing.
Part 2 - Same as last link, question 32., with one exception: I would say that |me(L)> and such, being macrostates, do not represent single worlds but thermodynamically large bundles of worlds that share certain common features. I have sent an email suggesting this change (but considering the lack of edits over the last 18 years, I’m not confident that it will happen).
To summarize: just forget about MWI and use conventional quantum mechanics + macrostates. The entanglement is infectious, so each world ends up with an appropriate pair of measurements.
Thanks! It looks like the reference equates the number of worlds with the number of microstates, since it calculates it as exp(S/k), not as the number of eigenstates of some interaction Hamiltonian, which is the standard lore. From this point of view, it is not clear how many worlds you get in, say, a single-particle Stern-Gerlach experiment: 2 or exponent of the entropy change of the detector after it’s triggered. Of course, one can say that we can coarse-grain them the usual way we construct macrostates from microstates, but then why introduce many worlds instead of simply doing quantum stat mech or even classical thermodynamics?
Anyway, I could not find this essential point (how many worlds?) in the QM sequence, but maybe I missed it. All I remember is the worlds of different “thickness”, which is sort of like coarse-graining microstates into macrostates, I suppose.
It is coarse-graining them into macrostates. Each macrostate is a bundle of a thermodynamically numerous effectively-mutually-independent worlds.