I think we are in agreement here that interacting with the detector initially creates a messy entangled object. If one believes Zurek, it then decoheres/relaxes into a superposition of eigenstates through einselection, while bleeding away all other states into the “environment”. Zurek seems to be understandably silent on whether a single eigenstate survives (collapse) or they all do (MWI).
What I was pointing out with the spontaneous emission example is that there are no discrete eigenstates there, thus all possible emission times and directions are on an equal footing. If you are OK with this being described as MWI, I have no problem with that. I have not seen it described this way, however. In fact, I do not recall seeing any treatment of spontaneous emission in the MWI context. I wonder why.
Another, unrelated issue I have not seen addressed by MWI (or objective collapse) is how in the straight EPR experiment on a singlet and two aligned detectors one necessarily gets opposite spin measurements, even though each spacelike-separated interaction produces “two worlds”, up and down. Apparently these 2x2 worlds somehow turn into just 2 worlds (updown and downup), with the other two (upup and downdown) magically discarded to preserve the angular momentum conservation. But I suppose this is a discussion for another day.
In fact, I do not recall seeing any treatment of spontaneous emission in the MWI context. I wonder why.
Peculiar. That was one of the first examples I ever encountered. Not the first two, but it was one of the earlier ones. It was emphasized that there is a colossal number of ‘worlds’ coming out of this sort of event, and the two-way splits in the previous examples were just simplest-possible cases.
… in the straight EPR experiment on a singlet and two aligned detectors one necessarily gets opposite spin measurements, even though each spacelike-separated interaction produces “two worlds”, up and down
How can you cut a pizza twice and get only two slices? By running the pizza cutter over the same line again. Same deal here. By applying the same test to the two entangled particles, they get the same results. Or do you mean, how can MWI keep track of the information storage aspects of quantum mechanics? Well, we live in Fock space.
That was one of the first examples I ever encountered.
I’d appreciate some links.
By applying the same test to the two entangled particles, they get the same results.
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?
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.
I think we are in agreement here that interacting with the detector initially creates a messy entangled object. If one believes Zurek, it then decoheres/relaxes into a superposition of eigenstates through einselection, while bleeding away all other states into the “environment”. Zurek seems to be understandably silent on whether a single eigenstate survives (collapse) or they all do (MWI).
What I was pointing out with the spontaneous emission example is that there are no discrete eigenstates there, thus all possible emission times and directions are on an equal footing. If you are OK with this being described as MWI, I have no problem with that. I have not seen it described this way, however. In fact, I do not recall seeing any treatment of spontaneous emission in the MWI context. I wonder why.
Another, unrelated issue I have not seen addressed by MWI (or objective collapse) is how in the straight EPR experiment on a singlet and two aligned detectors one necessarily gets opposite spin measurements, even though each spacelike-separated interaction produces “two worlds”, up and down. Apparently these 2x2 worlds somehow turn into just 2 worlds (updown and downup), with the other two (upup and downdown) magically discarded to preserve the angular momentum conservation. But I suppose this is a discussion for another day.
Peculiar. That was one of the first examples I ever encountered. Not the first two, but it was one of the earlier ones. It was emphasized that there is a colossal number of ‘worlds’ coming out of this sort of event, and the two-way splits in the previous examples were just simplest-possible cases.
How can you cut a pizza twice and get only two slices? By running the pizza cutter over the same line again. Same deal here. By applying the same test to the two entangled particles, they get the same results. Or do you mean, how can MWI keep track of the information storage aspects of quantum mechanics? Well, we live in Fock space.
I’d appreciate some links.
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?
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.