The collapse of the wave function is, as far as I understand it, conjured up because the idea of a single world appeals to human intuition (even though there is no reason to believe the universe is supposed to make intuitive sense). My understanding is that regardless of the interpretation you put behind the quantum measurements you have to calculate as if there are multiple words (i.e. a subatomic particle can interfere with itself) and the collapse of the wave function is something you have to assume on top of that.
My understanding is that regardless of the interpretation you put behind the quantum measurements you have to calculate as if there are multiple worlds
You have to do this in any probabilistic calculation, especially when you have chains of dependent probabilities. The mere fact that, e.g., the behavior of a ball bouncing around on a roulette wheel can be understood in terms of branching possible worlds, is not usually interpreted as implying that those possible worlds actually exist, or that they interact with this one.
The peculiarity of quantum probability is that you can get cancellation of probability amplitudes (the complex numbers at the step just before probabilities are computed). Thus in the double slit experiment, if you try to analyze what happens in a way analogous to Galton’s Quincunx, you end up saying that particles don’t arrive in the dark areas, because the possible paths ‘cancel’ at the amplitude level. This certainly makes no sense for probabilities, which are always nonnegative and so their sum is monotonically increasing—adding a possible path to an outcome can never decrease the overall probability of that outcome occurring. Except in quantum mechanics; but that just means that we are using the wrong concepts to understand it, not that there is such a thing as a negative probability.
However, it is not as if we know that the only way to get quantum probabilities is by supposing the existence and interaction of parallel worlds in the multiverse, and in fact all the attempts to make that idea work in detail end up in a conceptual shambles (see: measure problem, relativity problem, preferred basis problem). We don’t need a multiverse explanation; we just need a single-world explanation that gives rise to the same probability distributions that are presently obtained from wavefunctions. The Nobel laureate Gerard ’t Hooft has some ideas in this direction which deserve to be much better known; they are at least as important as anything in the “famous” interpretations associated with Bohm, Everett, and Cramer.
Thanks for the additional info and explanation. I have some books about QM on my desk that I really ought to study in depth...
I should mention though that what you state about needing only a single-world is in direct contradiction to what EY asserts: “Whatever the correct theory is, it has to be a many-worlds theory as opposed to a single-world theory or else it has a special relativity violating, non-local, time-asymmetric, non-linear and non-measurepreserving collapse process which magically causes blobs of configuration space to instantly vanish [...] I don’t see how one is permitted to hold out any hope whatsoever of getting the naive single world back.”
My level of understanding is insufficient to debate QM on a serious level, but I’d be very interested in a high level exchange about QM here on LW. If you disagree with Eliezer’s views on QM I think it is a good thing to say that explicitly, because when you study the different interpretations it’s important to keep them apart (the subject is confusing[1] enough as is).
My level of understanding is insufficient to debate QM on a serious level, but I’d be very interested in a high level exchange about QM here on LW. If you disagree with Eliezer’s views on QM I think it is a good thing to say that explicitly, because when you study the different interpretations it’s important to keep them apart (the subject is confusing[1] enough as is).
I agree that such an exchange would be useful. Unfortunately it would be hard to have with Mitchell_Porter because of the reputation he has gained for his evangelism of qualia and Quantum Monadology. People who have sufficient knowledge and interest in physics to be useful in such an exchange are less likely to become significantly involved if they think they are just arguing with a crackpot (again).
I almost added this warning myself, though it would have been with a different emphasis:
Such debates about MWI as I have had here, in the past, have often not been a clean discussion of the merits of MWI versus some other interpretation, because I won’t shut up about these other issues, which are far more interesting and important. There are severe problems awaiting anyone who wants to explain consciousness in terms of interactions between distributed, coarse-grained physical states; there is an interesting possibility that it could instead be explained in terms of a single, microphysically exact entangled state; that is my preoccupation. The debate over MWI is just a sideshow.
MWI looks bad from my ontological perspective, because I say we should take the apparent ontology of the self more seriously, as its actual ontology, whereas MWI extends the dismissal of conscious appearances further. But MWI also looks bad from a pure physics perspective, which just wants an exact mathematical description of the world that works, and cares nothing about its relationship to the “subjective world” of “lived experience”. The most shocking feature of MWI, once I really understood it, is that it cannot by itself make any correct predictions at all, because the entire predictive content of QM comes from the Born rule (or projection postulate), and no derivation of the Born rule within MWI exists. You often hear people saying “all the interpretations of QM make the same predictions”, but this is not true for MWI. You could say it makes no predictions (since it has no substitute for the Born rule), or that it makes wrong predictions (if you just count the worlds naively), but the only version of MWI which makes the same predictions as QM is the, so far imaginary, version which contains a derivation of the Born probabilities.
It’s almost comical, how new problems for MWI keep appearing, the more I discuss it with people. For example, the standard lay understanding of MWI is that there are well-defined worlds, and they split into more worlds when there are quantum events. But among the informed defenders of MWI, it’s usually considered desirable to reject the idea of a “preferred basis”, such as would be implied by a canonical division of the wavefunction into a unique set of worlds. Instead, it’s considered a feature, not a bug, that you can express a wavefunction as a superposition of basis functions in many complementary ways. But what I’ve realized is that you can extend this perspective into the interior of a person. You can consider the density matrix of my left brain hemisphere, and the density matrix of my right brain hemisphere, and you have the same freedom to choose basis functions for each of them. So, in an MWI without a preferred basis, you can’t even say that there is a specific set of copies of you in definite states, spread across the multiverse. We can describe your left hemisphere in the position basis, and the right hemisphere in the position basis, and that will produce one set of copies; or we could describe your left hemisphere in the position basis, and your right hemisphere in the momentum basis, and that will produce a differently defined set of copies.
This isn’t even a physics debate, in the sense of making calculations and comparing their results with each other and with reality. MWI exists mostly as a verbal construction by means of which people try to make sense of QM. But if you go and chase down the implications of what is being said, you end up with nonsense. Of course, the more advanced MWI advocates like Robin Hanson, David Deutsch, etc, do have something quantitative to say; though often the key to debunking them still revolves around seeing past the equations, to the plain meaning of what they are arguing or asserting. But the debate on LW isn’t at that level.
ETA: It might seem that the Gell-Mann–Hartle formalism of decoherent histories offers a derivation of the Born rule. I would argue that the procedure whereby an absolute prior for a set of decoherent histories is obtained, is an adaptation of the Born rule to the GM–H formalism, and that it faces the same problem of motivation or interpretation, as does any attempt to just add the Born rule to MWI: why do some worlds count for more than others? GM–H provides a slightly novel way to get the right probabilities, but it still hinges on attaching unequal weights to the worlds, and what this could mean, in a multiverse context where all the worlds exist equally, is left unexplained.
I have posted here, on this topic (MWI), perhaps a hundred times. There are many comments from me in the Quantum Physics sequence. Two years ago I made a top-level post in favor of the rather anodyne position that MWI is not the favored interpretation, it’s just one among many. Now I would take a much stronger line, that MWI has very little going for it. It cannot even reproduce the predictions of QM, which derive from the “Born rule” that MWI discards, in favor of having only the Schrodinger equation. Instead, the ideological stance is adopted that Only The Wavefunction Exists, and the recovery of the Born probabilities, which contain the whole of QM’s empirical content, is left for future research. Or, even worse, it’s just assumed. But this is a problem because, if you count the branches of the wavefunction, they should all count for the same, which would mean that the probabilities of all outcomes are equal, which would mean that MWI is falsified. Robin Hanson dreamed up an idea for how to get the right multiplicities of worlds, but it means that the individual worlds are somewhat messy superpositions. There are various other claims in the physics and philosophy literature of having recovered the Born rule, none of them satisfactory. One should be aware, especially in the era of arxiv.org—which is not peer-reviewed—that bad papers are available in abundance; though in this area, even good physicists produce bad papers advancing bogus arguments.
In the quotation above, Eliezer is once again assuming that wavefunctions exist and that the only alternative to MWI is wavefunction collapse. “Blobs of configuration space” don’t “vanish” if they were only ever domains in a probability distribution; see my remarks elsewhere on this page on the necessity of understanding that wavefunctions need not exist. I have made these points in the past ( 123 ).
The collapse of the wave function is, as far as I understand it, conjured up because the idea of a single world appeals to human intuition (even though there is no reason to believe the universe is supposed to make intuitive sense). My understanding is that regardless of the interpretation you put behind the quantum measurements you have to calculate as if there are multiple words (i.e. a subatomic particle can interfere with itself) and the collapse of the wave function is something you have to assume on top of that.
8 minute clip of EY talking with Scott Aaronson about Schrödinger’s Cat
You have to do this in any probabilistic calculation, especially when you have chains of dependent probabilities. The mere fact that, e.g., the behavior of a ball bouncing around on a roulette wheel can be understood in terms of branching possible worlds, is not usually interpreted as implying that those possible worlds actually exist, or that they interact with this one.
The peculiarity of quantum probability is that you can get cancellation of probability amplitudes (the complex numbers at the step just before probabilities are computed). Thus in the double slit experiment, if you try to analyze what happens in a way analogous to Galton’s Quincunx, you end up saying that particles don’t arrive in the dark areas, because the possible paths ‘cancel’ at the amplitude level. This certainly makes no sense for probabilities, which are always nonnegative and so their sum is monotonically increasing—adding a possible path to an outcome can never decrease the overall probability of that outcome occurring. Except in quantum mechanics; but that just means that we are using the wrong concepts to understand it, not that there is such a thing as a negative probability.
However, it is not as if we know that the only way to get quantum probabilities is by supposing the existence and interaction of parallel worlds in the multiverse, and in fact all the attempts to make that idea work in detail end up in a conceptual shambles (see: measure problem, relativity problem, preferred basis problem). We don’t need a multiverse explanation; we just need a single-world explanation that gives rise to the same probability distributions that are presently obtained from wavefunctions. The Nobel laureate Gerard ’t Hooft has some ideas in this direction which deserve to be much better known; they are at least as important as anything in the “famous” interpretations associated with Bohm, Everett, and Cramer.
Thanks for the additional info and explanation. I have some books about QM on my desk that I really ought to study in depth...
I should mention though that what you state about needing only a single-world is in direct contradiction to what EY asserts: “Whatever the correct theory is, it has to be a many-worlds theory as opposed to a single-world theory or else it has a special relativity violating, non-local, time-asymmetric, non-linear and non-measurepreserving collapse process which magically causes blobs of configuration space to instantly vanish [...] I don’t see how one is permitted to hold out any hope whatsoever of getting the naive single world back.”
My level of understanding is insufficient to debate QM on a serious level, but I’d be very interested in a high level exchange about QM here on LW. If you disagree with Eliezer’s views on QM I think it is a good thing to say that explicitly, because when you study the different interpretations it’s important to keep them apart (the subject is confusing[1] enough as is).
[1] a property of yours truly
I agree that such an exchange would be useful. Unfortunately it would be hard to have with Mitchell_Porter because of the reputation he has gained for his evangelism of qualia and Quantum Monadology. People who have sufficient knowledge and interest in physics to be useful in such an exchange are less likely to become significantly involved if they think they are just arguing with a crackpot (again).
Yikes! Thanks for the warning.
I almost added this warning myself, though it would have been with a different emphasis:
Such debates about MWI as I have had here, in the past, have often not been a clean discussion of the merits of MWI versus some other interpretation, because I won’t shut up about these other issues, which are far more interesting and important. There are severe problems awaiting anyone who wants to explain consciousness in terms of interactions between distributed, coarse-grained physical states; there is an interesting possibility that it could instead be explained in terms of a single, microphysically exact entangled state; that is my preoccupation. The debate over MWI is just a sideshow.
MWI looks bad from my ontological perspective, because I say we should take the apparent ontology of the self more seriously, as its actual ontology, whereas MWI extends the dismissal of conscious appearances further. But MWI also looks bad from a pure physics perspective, which just wants an exact mathematical description of the world that works, and cares nothing about its relationship to the “subjective world” of “lived experience”. The most shocking feature of MWI, once I really understood it, is that it cannot by itself make any correct predictions at all, because the entire predictive content of QM comes from the Born rule (or projection postulate), and no derivation of the Born rule within MWI exists. You often hear people saying “all the interpretations of QM make the same predictions”, but this is not true for MWI. You could say it makes no predictions (since it has no substitute for the Born rule), or that it makes wrong predictions (if you just count the worlds naively), but the only version of MWI which makes the same predictions as QM is the, so far imaginary, version which contains a derivation of the Born probabilities.
It’s almost comical, how new problems for MWI keep appearing, the more I discuss it with people. For example, the standard lay understanding of MWI is that there are well-defined worlds, and they split into more worlds when there are quantum events. But among the informed defenders of MWI, it’s usually considered desirable to reject the idea of a “preferred basis”, such as would be implied by a canonical division of the wavefunction into a unique set of worlds. Instead, it’s considered a feature, not a bug, that you can express a wavefunction as a superposition of basis functions in many complementary ways. But what I’ve realized is that you can extend this perspective into the interior of a person. You can consider the density matrix of my left brain hemisphere, and the density matrix of my right brain hemisphere, and you have the same freedom to choose basis functions for each of them. So, in an MWI without a preferred basis, you can’t even say that there is a specific set of copies of you in definite states, spread across the multiverse. We can describe your left hemisphere in the position basis, and the right hemisphere in the position basis, and that will produce one set of copies; or we could describe your left hemisphere in the position basis, and your right hemisphere in the momentum basis, and that will produce a differently defined set of copies.
This isn’t even a physics debate, in the sense of making calculations and comparing their results with each other and with reality. MWI exists mostly as a verbal construction by means of which people try to make sense of QM. But if you go and chase down the implications of what is being said, you end up with nonsense. Of course, the more advanced MWI advocates like Robin Hanson, David Deutsch, etc, do have something quantitative to say; though often the key to debunking them still revolves around seeing past the equations, to the plain meaning of what they are arguing or asserting. But the debate on LW isn’t at that level.
ETA: It might seem that the Gell-Mann–Hartle formalism of decoherent histories offers a derivation of the Born rule. I would argue that the procedure whereby an absolute prior for a set of decoherent histories is obtained, is an adaptation of the Born rule to the GM–H formalism, and that it faces the same problem of motivation or interpretation, as does any attempt to just add the Born rule to MWI: why do some worlds count for more than others? GM–H provides a slightly novel way to get the right probabilities, but it still hinges on attaching unequal weights to the worlds, and what this could mean, in a multiverse context where all the worlds exist equally, is left unexplained.
I have posted here, on this topic (MWI), perhaps a hundred times. There are many comments from me in the Quantum Physics sequence. Two years ago I made a top-level post in favor of the rather anodyne position that MWI is not the favored interpretation, it’s just one among many. Now I would take a much stronger line, that MWI has very little going for it. It cannot even reproduce the predictions of QM, which derive from the “Born rule” that MWI discards, in favor of having only the Schrodinger equation. Instead, the ideological stance is adopted that Only The Wavefunction Exists, and the recovery of the Born probabilities, which contain the whole of QM’s empirical content, is left for future research. Or, even worse, it’s just assumed. But this is a problem because, if you count the branches of the wavefunction, they should all count for the same, which would mean that the probabilities of all outcomes are equal, which would mean that MWI is falsified. Robin Hanson dreamed up an idea for how to get the right multiplicities of worlds, but it means that the individual worlds are somewhat messy superpositions. There are various other claims in the physics and philosophy literature of having recovered the Born rule, none of them satisfactory. One should be aware, especially in the era of arxiv.org—which is not peer-reviewed—that bad papers are available in abundance; though in this area, even good physicists produce bad papers advancing bogus arguments.
In the quotation above, Eliezer is once again assuming that wavefunctions exist and that the only alternative to MWI is wavefunction collapse. “Blobs of configuration space” don’t “vanish” if they were only ever domains in a probability distribution; see my remarks elsewhere on this page on the necessity of understanding that wavefunctions need not exist. I have made these points in the past ( 1 2 3 ).
Let me unearth a few other discussions for you… Counterfactual measurement. A supposed derivation of the Born rule. MWI’s problem with relativity, shared with Bohmian mechanics. MWI’s non-problem with conservation of energy. An example of how string theory might explain QM. Further observations.