It clearly isn’t universally understood, because if all physicists understood the universe in these terms, none of them would believe in a “collapse of the wavefunction”, which is not locally related in the configuration space.
And just like that, Many-Worlds clicked for me. It’s now incredibly obvious just how preposterous waveform collapse is, and this new intuitive mental model clears up a lot of the frustrating sticking points I was having with QM. C as the speed limit of information in the universe and the notion of local causality have all been a native part of my view of the universe for a while, but it wasn’t until that sentence that I connected them to decoherence.
Edit: Wow, a lot more things just clicked, including quantum suicide. My priority of cyronics just shot up several orders of magnitude, and I’m going to sign up once I’ve graduated and start bringing in income. Eliezer, if you have never seen The Prestige, I recommend you go and watch it. It provides a nice allegory for MW/quantum suicide that I think a lot of lay-people will be able to connect to easily. Could help when you’re explaining things.
Edit2: Just read your cyronics 101, and while the RIGHT NOW message punctured through my akrasia, I looked it up and even the $310/yr is not affordable right now. However, it’s far more affordable than I had thought and in a couple months I should be in a position where this becomes sustainably possible.
By the way, thank you. You probably know this on an intuitive level, but it should be good to hear that your work may very well be saving lives.
Username, you’re having a small conversion experience here, going from “causality is local” to “wavefunction collapse is preposterous” to “I understand quantum suicide” to “I’d better sign up for cryonics once I graduate” in rapid succession. It’s a shame we can’t freeze you right now, and then do a trace-and-debug of your recent thoughts, as a case study.
This was a somewhat muddled comment from Eliezer. Local causality does not imply an upper speed limit on how fast causal influences can propagate. Then he equivocates between locality within a configuration and locality within configuration space. Then he says that if only everyone in physics thought like this, they wouldn’t have wrong opinions about how QM works. I can only guess how you personally relate all that to decoherence. And from there, you get to increased confidence in cryonics. It could only happen on Less Wrong. :-)
ETA: Some more remarks:
Locality does not imply a maximum speed. Locality just means that causes don’t jump across space to their effects, they have to cross it point by point. But that says nothing about how fast they cross it. You could have a nonrelativistic local quantum mechanics with no upper speed limit. Eliezer is conflating locality with relativistic locality, which is what he is trying to derive from the assumption of locality. (I concede that no speed limit implies a de-facto or practical nonlocality, in that the whole universe would then be potentially relevant for what happens here in the “next moment”; some influence moving at a googol light-years per second might come crashing in upon us.)
Equivocating between locality in a configuration and locality in a configuration space: A configuration is, let’s say, an arrangement of particles in space. Locality in that context is defined by distance in space. But configuration space is a space in which the “points” themselves are whole configurations. “Locality” here refers to similarity between whole configurations. It means that the amplitude for a whole configuration is only immediately influenced by the amplitudes for infinitesimally different whole configurations.
Suppose we’re talking about a configuration in which there are two atoms, A and B, separated by a light-year. The amplitude for that configuration (in an evolving wavefunction) will be affected by the amplitude for a configuration which differs slightly at atom A, and also by the amplitude for a configuration which differs slightly at atom B, a light-year away from A. This is where the indirect nonlocality of QM comes from—if you think of QM in terms of amplitude flows in configuration space: you are attaching single amplitudes to extended objects—arbitrarily large configurations—and amplitude changes can come from very different “directions” in configuration space.
Eliezer also talks about amplitudes for subconfigurations. He wants to be able to say that what happens at a point only depends on its immediate environment. But if you want to talk like this, you have to retreat from talking about specific configurations, and instead talk about regions of space, and the quantum state of a “region of space”, which will associate an amplitude with every possible subconfiguration confined to that region.
This is an important consideration for MWI, evaluated from a relativistic perspective, because relativity implies that a “configuration” is not a fundamental element of reality. A configuration is based on a particular slicing of space-time into equal-time hypersurfaces, and in relativity, no such slicing is to be preferred as ontologically superior to all others. Ultimately that means that only space-time points, and the relations between them (spacelike, lightlike, timelike) are absolute; assembling sets of points into spacelike hypersurfaces is picking a particular reference frame.
This causes considerable problems if you want to reify quantum wavefunctions—treat them as reality, rather than as constructs akin to probability distributions—because (for any region of space bigger than a point) they are always based on a particular hypersurface, and therefore a particular notion of simultaneity; so to reify the wavefunction is to say that the reference frame in which it is defined is ontologically preferred. So then you could say, all right, we’ll just talk about wavefunctions based at a point. But building up an extended wavefunction from just local information is not a simple matter. The extended wavefunction will contain entanglement but the local information says nothing about entanglement. So the entanglement has to come from how you “combine” the wavefunctions based at points. Potentially, for any n points that are spacelike with respect to each other, there will need to be “entanglement information” on how to assemble them as part of a wavefunction for configurations.
I don’t know where that line of thought takes you. But in ordinary Copenhagen QM, applied to QFT, this just doesn’t even come up, because you treat space-time, and particular events in space-time, as the reality, and wavefunctions, superpositions, sums over histories, etc, as just a method of obtaining probabilities about reality. Copenhagen is unsatisfactory as an ontological picture because it glosses over the question of why QM works and of what happens in between one “definite event” and the next. But the attempt to go to the opposite interpretive pole, and say “OK, the wavefunction IS reality” is not a simple answer to your philosophical problems either; instead, it’s the beginning of a whole new set of problems, including, how do you reify wavefunctions without running foul of relativity?
Returning to Eliezer’s argument, which purports to derive the existence of a causal speed-limit from a postulate of “locality”: my critique is as informal and inexact as his argument, but perhaps I’ve at least shown that this is not as simple a matter as it may appear to the uninformed reader. There are formidable conceptual problems involved just in getting started with such an argument. Eliezer has the essentials needed to think about these topics rigorously, but he’s passing over crucial details, and he may thereby be overlooking a hole in his intuitions. In mathematics, you may start out with a reasonable belief that certain objects always behave in a certain way, but then when you examine specifics, you discover a class of cases which work in a way you didn’t anticipate.
What if you have a field theory with no speed limit, but in which significant and ultra-fast-moving influences are very rare; so that you have an effective “locality” (in Eliezer’s sense), with a long tail of very rare disruptions? Would Eliezer consider that a disproof of his intuitive idea, or an exception which didn’t sully the correctness of the individual insight? I have no idea. But I can say that the literature of physics is full of bogus derivations of special relativity, the Born rule, the three-dimensionality of space, etc. This derivation of “c” from Pearlian causal locality certainly has the ingredients necessary for such a bogus derivation. The way to make it non-bogus is to make it deductively valid, rather than just intuitive. This means that you have to identify and spell out all the assumptions required for the deduction.
This may or may not be the result of day 2 of modafinil. :) I don’t think it is, because I already had most of the pieces in place, it just took that sentence to make everything fit together. But that is a data point.
Hm, a trace-debug. My thought process over the five minutes that this took place was manipulation of mental imagery of my models of the universe. I’m not going to be able to explain much clearer than that, unfortunately. It was all very intuitive and not at all rigorous, the closest representation I can think of is Feynman’s thinking about balls. I’m going to have to do a lot more reading as my QM is very shakey, and I want to shore this up. It will also probably take a while until this way of thinking becomes the natural way I see the universe. But it all lines up, makes sense, and aligns with what people smarter than me are saying, so I’m assigning a high probability that it’s the correct conclusion.
An upper speed limit doesn’t matter—all that matters is that things are not instantaneous for locality to be valid.
A conversion experience is a very appropriate term for what I’m going through. I’m having very mixed emotions right now. A lot of my thoughts just clarified, which simply feels good. I’m grateful, because I live in an era where this is possible and because I was born intelligent enough to understand. Sad, because I know that most if not all of the people I know will never understand, and never sign up for cyronics. But I’m also ecstatic, because I’ve just discovered the cheat code to the universe, and it works.
I just made a long-winded addition to my comment, expanding on some of the gaps in Eliezer’s reasoning.
I’m also ecstatic, because I’ve just discovered the cheat code to the universe, and it works.
Well, you’re certainly not backing down and saying, hang on, is this just an illusory high? It almost seems inappropriate to dump cold water on you precisely when you’re having your satori—though it’s interesting from an experimental perspective. I’ve never had the opportunity to meddle with someone who thinks they are receiving enlightenment, right at the moment when it’s happening; unless I count myself.
From my perspective, QM is far more likely to be derived from ’t Hooft’s holographic determinism, and the idea of personal identity as a fungible pattern is just (in historical terms) a fad resulting from the incomplete state of our science, so I certainly regard your excitement as based mostly on an illusion. It’s good that you’re having exciting ideas and new thoughts, and perhaps it’s even appropriate to will yourself to believe them, because that’s a way of testing them against the whole of the rest of your experience.
But I still find it interesting how it is that people come to think that they know something new, when they don’t actually know it. How much does the thrill of finally knowing the truth provide an incentive to believe that the ideas currently before you are indeed the truth, rather than just an interesting possibility?
From experiences back when I was young and religious, I’ve learned to recognize moments of satori as not much more than a high (have probably had 2-3 prior). I enjoy the experience, but I’ve learned skepticism and try not to place too much weight on them. I was more describing the causes for my emotional states rather than proclaiming new beliefs. But to be completely honest, for several minutes I was convinced that I had found the tree of life, so I won’t completely downplay what I wrote.
How much does the thrill of finally knowing the truth provide an incentive to believe that the ideas currently before you are indeed the truth, rather than just an interesting possibility?
I suspect it has evopsych roots relating to confidence, the measured benefits of a life with purpose, and good-enough knowledge.
Reading ‘t Hooft’s paper I could understand what he was saying, but I’m realizing that the physics is out of my current depth. And I understand the argument you explained about the flaws in spatial (as opposed to configuration) locality. I’ll update my statement that ‘Many-Worlds is intuitively correct’ to ‘Copenhagen is intuitively wrong,’ which I suppose is where my original logic should have taken me—I just didn’t consider strong MWI alternatives. Determinism kills quantum suicide, so I’ll have to move down the priority of cyronics (though the ‘if MWI then quantum suicide then cyronics’ logic still holds and I still think cyronics is a good idea. I do love me a good hedge bet). But like I said, I’m not at all qualified to start assigning likelyhoods here between different QM origins. This requires more study.
I don’t see the issue with consciousness as being represented by the pattern of our brains rather than the physicality of it. You are right that we may eventually find that we can never look at a brain with high enough resolution to emulate it. But based on cases of people entering a several-hour freeze before being revived, the consciousness mechanism is obviously robust and I say this points towards it being an engineering problem of getting everything correct enough. The viability of putting it on a computer once you have a high enough resolution scan is not an issue—worst case scenario you start from something like QM and work up. Again this assumes a level of the brain’s robustness (rounding errors shouldn’t crash the mind), but I would call that experimentally proven in today’s humans.
And just like that, Many-Worlds clicked for me. It’s now incredibly obvious just how preposterous waveform collapse is, and this new intuitive mental model clears up a lot of the frustrating sticking points I was having with QM. C as the speed limit of information in the universe and the notion of local causality have all been a native part of my view of the universe for a while, but it wasn’t until that sentence that I connected them to decoherence.
Edit: Wow, a lot more things just clicked, including quantum suicide. My priority of cyronics just shot up several orders of magnitude, and I’m going to sign up once I’ve graduated and start bringing in income.
Eliezer, if you have never seen The Prestige, I recommend you go and watch it. It provides a nice allegory for MW/quantum suicide that I think a lot of lay-people will be able to connect to easily. Could help when you’re explaining things.
Edit2: Just read your cyronics 101, and while the RIGHT NOW message punctured through my akrasia, I looked it up and even the $310/yr is not affordable right now. However, it’s far more affordable than I had thought and in a couple months I should be in a position where this becomes sustainably possible.
By the way, thank you. You probably know this on an intuitive level, but it should be good to hear that your work may very well be saving lives.
Username, you’re having a small conversion experience here, going from “causality is local” to “wavefunction collapse is preposterous” to “I understand quantum suicide” to “I’d better sign up for cryonics once I graduate” in rapid succession. It’s a shame we can’t freeze you right now, and then do a trace-and-debug of your recent thoughts, as a case study.
This was a somewhat muddled comment from Eliezer. Local causality does not imply an upper speed limit on how fast causal influences can propagate. Then he equivocates between locality within a configuration and locality within configuration space. Then he says that if only everyone in physics thought like this, they wouldn’t have wrong opinions about how QM works. I can only guess how you personally relate all that to decoherence. And from there, you get to increased confidence in cryonics. It could only happen on Less Wrong. :-)
ETA: Some more remarks:
Locality does not imply a maximum speed. Locality just means that causes don’t jump across space to their effects, they have to cross it point by point. But that says nothing about how fast they cross it. You could have a nonrelativistic local quantum mechanics with no upper speed limit. Eliezer is conflating locality with relativistic locality, which is what he is trying to derive from the assumption of locality. (I concede that no speed limit implies a de-facto or practical nonlocality, in that the whole universe would then be potentially relevant for what happens here in the “next moment”; some influence moving at a googol light-years per second might come crashing in upon us.)
Equivocating between locality in a configuration and locality in a configuration space: A configuration is, let’s say, an arrangement of particles in space. Locality in that context is defined by distance in space. But configuration space is a space in which the “points” themselves are whole configurations. “Locality” here refers to similarity between whole configurations. It means that the amplitude for a whole configuration is only immediately influenced by the amplitudes for infinitesimally different whole configurations.
Suppose we’re talking about a configuration in which there are two atoms, A and B, separated by a light-year. The amplitude for that configuration (in an evolving wavefunction) will be affected by the amplitude for a configuration which differs slightly at atom A, and also by the amplitude for a configuration which differs slightly at atom B, a light-year away from A. This is where the indirect nonlocality of QM comes from—if you think of QM in terms of amplitude flows in configuration space: you are attaching single amplitudes to extended objects—arbitrarily large configurations—and amplitude changes can come from very different “directions” in configuration space.
Eliezer also talks about amplitudes for subconfigurations. He wants to be able to say that what happens at a point only depends on its immediate environment. But if you want to talk like this, you have to retreat from talking about specific configurations, and instead talk about regions of space, and the quantum state of a “region of space”, which will associate an amplitude with every possible subconfiguration confined to that region.
This is an important consideration for MWI, evaluated from a relativistic perspective, because relativity implies that a “configuration” is not a fundamental element of reality. A configuration is based on a particular slicing of space-time into equal-time hypersurfaces, and in relativity, no such slicing is to be preferred as ontologically superior to all others. Ultimately that means that only space-time points, and the relations between them (spacelike, lightlike, timelike) are absolute; assembling sets of points into spacelike hypersurfaces is picking a particular reference frame.
This causes considerable problems if you want to reify quantum wavefunctions—treat them as reality, rather than as constructs akin to probability distributions—because (for any region of space bigger than a point) they are always based on a particular hypersurface, and therefore a particular notion of simultaneity; so to reify the wavefunction is to say that the reference frame in which it is defined is ontologically preferred. So then you could say, all right, we’ll just talk about wavefunctions based at a point. But building up an extended wavefunction from just local information is not a simple matter. The extended wavefunction will contain entanglement but the local information says nothing about entanglement. So the entanglement has to come from how you “combine” the wavefunctions based at points. Potentially, for any n points that are spacelike with respect to each other, there will need to be “entanglement information” on how to assemble them as part of a wavefunction for configurations.
I don’t know where that line of thought takes you. But in ordinary Copenhagen QM, applied to QFT, this just doesn’t even come up, because you treat space-time, and particular events in space-time, as the reality, and wavefunctions, superpositions, sums over histories, etc, as just a method of obtaining probabilities about reality. Copenhagen is unsatisfactory as an ontological picture because it glosses over the question of why QM works and of what happens in between one “definite event” and the next. But the attempt to go to the opposite interpretive pole, and say “OK, the wavefunction IS reality” is not a simple answer to your philosophical problems either; instead, it’s the beginning of a whole new set of problems, including, how do you reify wavefunctions without running foul of relativity?
Returning to Eliezer’s argument, which purports to derive the existence of a causal speed-limit from a postulate of “locality”: my critique is as informal and inexact as his argument, but perhaps I’ve at least shown that this is not as simple a matter as it may appear to the uninformed reader. There are formidable conceptual problems involved just in getting started with such an argument. Eliezer has the essentials needed to think about these topics rigorously, but he’s passing over crucial details, and he may thereby be overlooking a hole in his intuitions. In mathematics, you may start out with a reasonable belief that certain objects always behave in a certain way, but then when you examine specifics, you discover a class of cases which work in a way you didn’t anticipate.
What if you have a field theory with no speed limit, but in which significant and ultra-fast-moving influences are very rare; so that you have an effective “locality” (in Eliezer’s sense), with a long tail of very rare disruptions? Would Eliezer consider that a disproof of his intuitive idea, or an exception which didn’t sully the correctness of the individual insight? I have no idea. But I can say that the literature of physics is full of bogus derivations of special relativity, the Born rule, the three-dimensionality of space, etc. This derivation of “c” from Pearlian causal locality certainly has the ingredients necessary for such a bogus derivation. The way to make it non-bogus is to make it deductively valid, rather than just intuitive. This means that you have to identify and spell out all the assumptions required for the deduction.
This may or may not be the result of day 2 of modafinil. :) I don’t think it is, because I already had most of the pieces in place, it just took that sentence to make everything fit together. But that is a data point.
Hm, a trace-debug. My thought process over the five minutes that this took place was manipulation of mental imagery of my models of the universe. I’m not going to be able to explain much clearer than that, unfortunately. It was all very intuitive and not at all rigorous, the closest representation I can think of is Feynman’s thinking about balls. I’m going to have to do a lot more reading as my QM is very shakey, and I want to shore this up. It will also probably take a while until this way of thinking becomes the natural way I see the universe. But it all lines up, makes sense, and aligns with what people smarter than me are saying, so I’m assigning a high probability that it’s the correct conclusion.
An upper speed limit doesn’t matter—all that matters is that things are not instantaneous for locality to be valid.
A conversion experience is a very appropriate term for what I’m going through. I’m having very mixed emotions right now. A lot of my thoughts just clarified, which simply feels good. I’m grateful, because I live in an era where this is possible and because I was born intelligent enough to understand. Sad, because I know that most if not all of the people I know will never understand, and never sign up for cyronics. But I’m also ecstatic, because I’ve just discovered the cheat code to the universe, and it works.
I just made a long-winded addition to my comment, expanding on some of the gaps in Eliezer’s reasoning.
Well, you’re certainly not backing down and saying, hang on, is this just an illusory high? It almost seems inappropriate to dump cold water on you precisely when you’re having your satori—though it’s interesting from an experimental perspective. I’ve never had the opportunity to meddle with someone who thinks they are receiving enlightenment, right at the moment when it’s happening; unless I count myself.
From my perspective, QM is far more likely to be derived from ’t Hooft’s holographic determinism, and the idea of personal identity as a fungible pattern is just (in historical terms) a fad resulting from the incomplete state of our science, so I certainly regard your excitement as based mostly on an illusion. It’s good that you’re having exciting ideas and new thoughts, and perhaps it’s even appropriate to will yourself to believe them, because that’s a way of testing them against the whole of the rest of your experience.
But I still find it interesting how it is that people come to think that they know something new, when they don’t actually know it. How much does the thrill of finally knowing the truth provide an incentive to believe that the ideas currently before you are indeed the truth, rather than just an interesting possibility?
From experiences back when I was young and religious, I’ve learned to recognize moments of satori as not much more than a high (have probably had 2-3 prior). I enjoy the experience, but I’ve learned skepticism and try not to place too much weight on them. I was more describing the causes for my emotional states rather than proclaiming new beliefs. But to be completely honest, for several minutes I was convinced that I had found the tree of life, so I won’t completely downplay what I wrote.
I suspect it has evopsych roots relating to confidence, the measured benefits of a life with purpose, and good-enough knowledge.
Reading ‘t Hooft’s paper I could understand what he was saying, but I’m realizing that the physics is out of my current depth. And I understand the argument you explained about the flaws in spatial (as opposed to configuration) locality. I’ll update my statement that ‘Many-Worlds is intuitively correct’ to ‘Copenhagen is intuitively wrong,’ which I suppose is where my original logic should have taken me—I just didn’t consider strong MWI alternatives. Determinism kills quantum suicide, so I’ll have to move down the priority of cyronics (though the ‘if MWI then quantum suicide then cyronics’ logic still holds and I still think cyronics is a good idea. I do love me a good hedge bet). But like I said, I’m not at all qualified to start assigning likelyhoods here between different QM origins. This requires more study.
I don’t see the issue with consciousness as being represented by the pattern of our brains rather than the physicality of it. You are right that we may eventually find that we can never look at a brain with high enough resolution to emulate it. But based on cases of people entering a several-hour freeze before being revived, the consciousness mechanism is obviously robust and I say this points towards it being an engineering problem of getting everything correct enough. The viability of putting it on a computer once you have a high enough resolution scan is not an issue—worst case scenario you start from something like QM and work up. Again this assumes a level of the brain’s robustness (rounding errors shouldn’t crash the mind), but I would call that experimentally proven in today’s humans.