5 ms·

Carroll is a big advocate of the Many Worlds Interpretation, so it's nice to see some other interpretations getting a decent hearing in this article as well as

by n4r9 7y ago

Carroll is a big advocate of the Many Worlds Interpretation, so it's nice to see some other interpretations getting a decent hearing in this article as well as a decent treatment of some academic concerns about MWI. That's a testament to his humility as a researcher. I must admit I struggle with the MWI Born rule derivations based on rational credence. I don't see why proving that one ought to assign credence in such and such a way is sufficient to prove that that's the way nature is. It feels too much like deriving an "is" from an "ought", although in a slightly different way than what Hume objected to!

pure-awesome 7y ago
Wikipedia says > While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circular. So it seems you aren't alone in feeling this way. Edit: Forgot the link - https://en.wikipedia.org/wiki/Born_rule https://en.wikipedia.org/wiki/Born_rule
- n4r9 7y ago
  Interesting. Following through the citations, this statement seems to be based on two quite old articles which criticise a different Born rule formulation based on frequency analysis: https://link.springer.com/article/10.1007%2FBF02058273 https://link.springer.com/article/10.1007%2FBF02058273 https://arxiv.org/pdf/quant-ph/0409144.pdf https://arxiv.org/pdf/quant-ph/0409144.pdf The latter article is more recent at 2005 but as far as I can tell Carroll's self-locating uncertainty ideas weren't introduced until around 2014.
  - lisper 7y ago
    Here's a blog post I wrote about this recently: http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html http://blog.rongarret.info/2019/07/the-trouble-with-many-wor... The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also introduces an "invisible pink unicorn", i.e. a concept that, according to the theory, has physical significance but cannot be measured. In the case of MWI that concept is branch weights. [UPDATE] The critique I wrote is based on Wallace (https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718). Carroll's argument appears to be somewhat different. I'm just now working my way through his paper (https://arxiv.org/abs/1405.7577 https://arxiv.org/abs/1405.7577) but I'd be very surprised if it did not also have some untenable assumption hidden in there somewhere.
    - n4r9 7y ago
      Adrian Kent has a lengthy and detailed overview of MWIs pre-2009 which may interest you [0]. He discusses Wallace's formulation, contrasts it with other formulations and touches on branching indifference. He also has a more recent (and much more brief) article which refers to the Self-locating Uncertainty arguments [1]. I have previously come across Deutsch's formulation in terms of information flow [2], along with what seemed like a very strong criticism from Wallace and Christopher Timpson [3] that his model was not gauge-invariant. [0] https://arxiv.org/pdf/0905.0624.pdf https://arxiv.org/pdf/0905.0624.pdf [1] https://arxiv.org/abs/1408.1944 https://arxiv.org/abs/1408.1944 [2] https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf [3] http://users.ox.ac.uk/~bras2317/dhshort2.pdf http://users.ox.ac.uk/~bras2317/dhshort2.pdf
      - lisper 7y ago
        Thanks for the pointers. (This is turning into quite the little rabbit hole.)
    - Strilanc 7y ago
      What do you think of the simplified argument here: https://algassert.com/post/1902 https://algassert.com/post/1902 ? Basically: ground the definition of probability into a reversible classical circuit then use that circuit's quantum behavior to generalize the definition to quantum (while assuming as few things as possible). In this case the assumptions are "limiting to amplitude 1 must mean limiting to probability 1" and no signalling.
      - lisper 7y ago
        Thanks for bringing that to my attention. My initial reaction is that the argument appears sufficiently cogent to merit respectful consideration. I predict that if someone were to dig into it, they'd find a question-begging assumption hidden somewhere. (The alternative is that this is a major breakthrough in physics, and my Bayesian prior on that is low.) But where that assumption is hiding is not immediately obvious to me. Looking for it seems like a worthwhile exercise.
crdrost 7y ago
Yeah, I mean, at this scale you’re not going to prove how nature is from any of this. What MWI is saying is that if you admit a really difficult view of the cosmos, then you can regard the Born rule as part of Schrödinger evolution—but it is kind of only possible because you punted the details into that difficult view of the cosmos. (And then the MWI-supporters come in full force and argue that actually the view is not so “difficult” after all.) Backing up, the problem is that you have these different approaches—depending on how you count them you could maybe group them broadly and say there are 3-4, or as large as a dozen or two—that are all mathematically identical. They all predict the Born rule, but suggest different ways that Nature really fundamentally would act to produce that rule. Since they are mathematically identical, it is provable that there is no way to choose between them. As a result, the one which steps the most out of peoples’ ways to enable experimental results, has better “genes” for its own reproduction in the publication of papers. And that has just been the Copenhagen interpretation: you the experimentalist have a soul and when that soul measures the world the nice unitary evolution of the world comes crashing down with probabilities given by the Born rule. Contrast with pilot-wave theories where you have to work out a whole separate equation that doesn’t do anything which makes any further observational impact. The basic issue that we are facing is that while the notion of souls seems laughable for fashionable sciencey people, it also seems in some distressing way inevitable. You take Many Worlds for instance, you admit the reality of every single possibility of the entire universe as a much broader multiverse. An equation, the Schrödinger equation, essentially works over, say, a Planck time to create a vector field on top of this, saying “This instant is followed by that instant is followed by that instant.” In the middle of that, what uniquely qualifies my experience here and now as I know such experience must exist? I do not perceive a multiverse; I perceive a changing universe. And MWI says “well actually there are a million yous, frozen in time, all perceiving changing universes. Your experience of motion through time is actually kind of a lie.” This is not a unique problem to QM; it happened much earlier with special relativity where we discovered that you are actually a rope of worldlines thrusting through a static four-dimensional Lorentzian manifold, every part of that rope being presumably in a separate conscious state, perceiving itself as moving through time but we “on the outside” can see that there is no unique present defined such that it can wash over all of the ropes simultaneously. MWI just happens to facilitate the same basic “unrolling of time” because it has already unrolled all of possibility-space. And to fix it you need something—I’m calling it a soul, you can get fancy—which “zips along the worldline” and contains my conscious experience, or you need to argue that my experience is an illusion, or you need some “universe-soul” to act like a coherent “present moment” for all of us, or the like. It all kind of sucks. There is a nice perspective sitting in the middle of this due to Andreas O. Tell [1], and it is pleasantly agnostic while still doing something like what MWI is doing to try and derive the Born rule from normal wavefunction evolution. In brief, he says: “use the state-matrix formalism for QM, and take a completely agnostic view of what the cosmos is and how it behaves. Still if you have a local information-processing system which is embedded in the cosmos and changing, then it receives information and must update its model of the universe. Its model of the universe must necessarily come down to a list of wavefunctions with a list of weightings, but there is a freedom-of-perspective which allows you to choose the wavefunction with the highest weight as “the” one that you think the system is in. New data just forces these weights to cross in size, causing the Born rule when you try to determine whether those weights will cross over and the system will be in the new state.” In some sense then we can live in a very Copenhageny world where we are changing data-processors uniquely present in some space and time, but we can use Schrödinger evolution to derive the Born rule just the same as the many-worlds interpretation does, but rather than committing to its plethora of different universes we might be able to just remain non-committal about what is in the rest of the universe, beyond what I see in it. [1] https://arxiv.org/abs/1205.0293 https://arxiv.org/abs/1205.0293
kovrik 7y ago
I was always wondering about MWI and couldn't find the answer to one question. AFAIK Everett never mentioned Many Worlds in his paper. What he was talking about was a Universal Wave Function. In that sense, 'world' is just a 'quantum system', not 'Universe'. At what stage we started calling it Many Worlds? When scientists say Many Worlds, do they actually mean Worlds as physical 'parallel universes' that pop up into existence? Or they only mean that those are probable outcomes of our measurement (probable histories) that never actually happened (only one of them happened - the one we end up being it)?
- millstone 7y ago
  In MWI, all Worlds are physically real and may interfere with each other.
  - sliken 7y ago
    Sounds like that would be a testable hypothesis, right? How exactly would they interfere?
    - millstone 7y ago
      All QM interpretations require interference. This is demonstrated by the two-slit experiment (for example). In this experiment, an electron passing through the two-slit shield generates an interference pattern. But if you detect which slit the electron passes through, you destroy the pattern. Why? In textbook/Copenhagen interpretation, we say that when the electron passes through the slits the wavefunction has not yet been measured. But with the detector in place, you collapse the wavefunction to an eigenvector of position. By the uncertainty principle, the momentum uncertainty is now very high, so the electron shoots off in a random direction and cannot be expected to follow any pattern. In MWI, we start with the interference pattern. But adding the detector does not "collapse" anything - instead it introduces lots of degrees of freedom. The particle passes through both the left and right slits, but the degrees of freedom ensure there is no fixed relative phase delta between these possibilities. The detector turns waves into "static noise", and so any interference pattern is lost. Both options are realized, but cannot detect the other possibility: distinct Worlds. The key point is that MWI has no special role for measurement. The left-slit and right-slit worlds interfere, but with the detector in place the pattern is destroyed: the interference is uncoordinated and averages to zero, so undetectable. Whereas in textbook/Cophenhagen QM we say that the measurement results in a single outcome.

by n4r9 7y ago

pure-awesome 7y ago

Wikipedia says > While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circular. So it seems you aren't alone in feeling this way. Edit: Forgot the link - https://en.wikipedia.org/wiki/Born_rule https://en.wikipedia.org/wiki/Born_rule

n4r9 7y ago
Interesting. Following through the citations, this statement seems to be based on two quite old articles which criticise a different Born rule formulation based on frequency analysis: https://link.springer.com/article/10.1007%2FBF02058273 https://link.springer.com/article/10.1007%2FBF02058273 https://arxiv.org/pdf/quant-ph/0409144.pdf https://arxiv.org/pdf/quant-ph/0409144.pdf The latter article is more recent at 2005 but as far as I can tell Carroll's self-locating uncertainty ideas weren't introduced until around 2014.
- lisper 7y ago
  Here's a blog post I wrote about this recently: http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html http://blog.rongarret.info/2019/07/the-trouble-with-many-wor... The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also introduces an "invisible pink unicorn", i.e. a concept that, according to the theory, has physical significance but cannot be measured. In the case of MWI that concept is branch weights. [UPDATE] The critique I wrote is based on Wallace (https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718). Carroll's argument appears to be somewhat different. I'm just now working my way through his paper (https://arxiv.org/abs/1405.7577 https://arxiv.org/abs/1405.7577) but I'd be very surprised if it did not also have some untenable assumption hidden in there somewhere.
  - n4r9 7y ago
    Adrian Kent has a lengthy and detailed overview of MWIs pre-2009 which may interest you [0]. He discusses Wallace's formulation, contrasts it with other formulations and touches on branching indifference. He also has a more recent (and much more brief) article which refers to the Self-locating Uncertainty arguments [1]. I have previously come across Deutsch's formulation in terms of information flow [2], along with what seemed like a very strong criticism from Wallace and Christopher Timpson [3] that his model was not gauge-invariant. [0] https://arxiv.org/pdf/0905.0624.pdf https://arxiv.org/pdf/0905.0624.pdf [1] https://arxiv.org/abs/1408.1944 https://arxiv.org/abs/1408.1944 [2] https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf [3] http://users.ox.ac.uk/~bras2317/dhshort2.pdf http://users.ox.ac.uk/~bras2317/dhshort2.pdf
    - lisper 7y ago
      Thanks for the pointers. (This is turning into quite the little rabbit hole.)
  - Strilanc 7y ago
    What do you think of the simplified argument here: https://algassert.com/post/1902 https://algassert.com/post/1902 ? Basically: ground the definition of probability into a reversible classical circuit then use that circuit's quantum behavior to generalize the definition to quantum (while assuming as few things as possible). In this case the assumptions are "limiting to amplitude 1 must mean limiting to probability 1" and no signalling.
    - lisper 7y ago
      Thanks for bringing that to my attention. My initial reaction is that the argument appears sufficiently cogent to merit respectful consideration. I predict that if someone were to dig into it, they'd find a question-begging assumption hidden somewhere. (The alternative is that this is a major breakthrough in physics, and my Bayesian prior on that is low.) But where that assumption is hiding is not immediately obvious to me. Looking for it seems like a worthwhile exercise.

crdrost 7y ago

Yeah, I mean, at this scale you’re not going to prove how nature is from any of this. What MWI is saying is that if you admit a really difficult view of the cosmos, then you can regard the Born rule as part of Schrödinger evolution—but it is kind of only possible because you punted the details into that difficult view of the cosmos. (And then the MWI-supporters come in full force and argue that actually the view is not so “difficult” after all.) Backing up, the problem is that you have these different approaches—depending on how you count them you could maybe group them broadly and say there are 3-4, or as large as a dozen or two—that are all mathematically identical. They all predict the Born rule, but suggest different ways that Nature really fundamentally would act to produce that rule. Since they are mathematically identical, it is provable that there is no way to choose between them. As a result, the one which steps the most out of peoples’ ways to enable experimental results, has better “genes” for its own reproduction in the publication of papers. And that has just been the Copenhagen interpretation: you the experimentalist have a soul and when that soul measures the world the nice unitary evolution of the world comes crashing down with probabilities given by the Born rule. Contrast with pilot-wave theories where you have to work out a whole separate equation that doesn’t do anything which makes any further observational impact. The basic issue that we are facing is that while the notion of souls seems laughable for fashionable sciencey people, it also seems in some distressing way inevitable. You take Many Worlds for instance, you admit the reality of every single possibility of the entire universe as a much broader multiverse. An equation, the Schrödinger equation, essentially works over, say, a Planck time to create a vector field on top of this, saying “This instant is followed by that instant is followed by that instant.” In the middle of that, what uniquely qualifies my experience here and now as I know such experience must exist? I do not perceive a multiverse; I perceive a changing universe. And MWI says “well actually there are a million yous, frozen in time, all perceiving changing universes. Your experience of motion through time is actually kind of a lie.” This is not a unique problem to QM; it happened much earlier with special relativity where we discovered that you are actually a rope of worldlines thrusting through a static four-dimensional Lorentzian manifold, every part of that rope being presumably in a separate conscious state, perceiving itself as moving through time but we “on the outside” can see that there is no unique present defined such that it can wash over all of the ropes simultaneously. MWI just happens to facilitate the same basic “unrolling of time” because it has already unrolled all of possibility-space. And to fix it you need something—I’m calling it a soul, you can get fancy—which “zips along the worldline” and contains my conscious experience, or you need to argue that my experience is an illusion, or you need some “universe-soul” to act like a coherent “present moment” for all of us, or the like. It all kind of sucks. There is a nice perspective sitting in the middle of this due to Andreas O. Tell [1], and it is pleasantly agnostic while still doing something like what MWI is doing to try and derive the Born rule from normal wavefunction evolution. In brief, he says: “use the state-matrix formalism for QM, and take a completely agnostic view of what the cosmos is and how it behaves. Still if you have a local information-processing system which is embedded in the cosmos and changing, then it receives information and must update its model of the universe. Its model of the universe must necessarily come down to a list of wavefunctions with a list of weightings, but there is a freedom-of-perspective which allows you to choose the wavefunction with the highest weight as “the” one that you think the system is in. New data just forces these weights to cross in size, causing the Born rule when you try to determine whether those weights will cross over and the system will be in the new state.” In some sense then we can live in a very Copenhageny world where we are changing data-processors uniquely present in some space and time, but we can use Schrödinger evolution to derive the Born rule just the same as the many-worlds interpretation does, but rather than committing to its plethora of different universes we might be able to just remain non-committal about what is in the rest of the universe, beyond what I see in it. [1] https://arxiv.org/abs/1205.0293 https://arxiv.org/abs/1205.0293

kovrik 7y ago

I was always wondering about MWI and couldn't find the answer to one question. AFAIK Everett never mentioned Many Worlds in his paper. What he was talking about was a Universal Wave Function. In that sense, 'world' is just a 'quantum system', not 'Universe'. At what stage we started calling it Many Worlds? When scientists say Many Worlds, do they actually mean Worlds as physical 'parallel universes' that pop up into existence? Or they only mean that those are probable outcomes of our measurement (probable histories) that never actually happened (only one of them happened - the one we end up being it)?

millstone 7y ago
In MWI, all Worlds are physically real and may interfere with each other.
- sliken 7y ago
  Sounds like that would be a testable hypothesis, right? How exactly would they interfere?
  - millstone 7y ago
    All QM interpretations require interference. This is demonstrated by the two-slit experiment (for example). In this experiment, an electron passing through the two-slit shield generates an interference pattern. But if you detect which slit the electron passes through, you destroy the pattern. Why? In textbook/Copenhagen interpretation, we say that when the electron passes through the slits the wavefunction has not yet been measured. But with the detector in place, you collapse the wavefunction to an eigenvector of position. By the uncertainty principle, the momentum uncertainty is now very high, so the electron shoots off in a random direction and cannot be expected to follow any pattern. In MWI, we start with the interference pattern. But adding the detector does not "collapse" anything - instead it introduces lots of degrees of freedom. The particle passes through both the left and right slits, but the degrees of freedom ensure there is no fixed relative phase delta between these possibilities. The detector turns waves into "static noise", and so any interference pattern is lost. Both options are realized, but cannot detect the other possibility: distinct Worlds. The key point is that MWI has no special role for measurement. The left-slit and right-slit worlds interfere, but with the detector in place the pattern is destroyed: the interference is uncoordinated and averages to zero, so undetectable. Whereas in textbook/Cophenhagen QM we say that the measurement results in a single outcome.