Even if I read the QM sequence and find the arguments compelling, I still wouldn’t feel as though I had enough subject matter expertise to rationally disagree with elite physicists with high confidence.
You don’t know what’s in the QM sequence. The whole point of it (well, one of the whole points) is to show people who wouldn’t previously believe such a thing was plausible, that they ought to disagree with elite physicists with high confidence—to break their trust in a sane world, before which nothing can begin.
The whole point of it (well, one of the whole points) is to show people who wouldn’t previously believe such a thing was plausible, that they ought to disagree with elite physicists with high confidence—to break their trust in a sane world, before which nothing can begin.
Does it worry you that people with good domain knowledge of physics(Shminux,Mitchell Porter, myself) seem to feel that your QM sequence is actually presenting a misleading picture of why some elite physicists don’t hold to many worlds with high probability?
Also, is it desirable to train rationalists to believe that they SHOULD update their belief about interpretations of quantum mechanics above a weighted sampling of domain experts based on ~50 pages of highschool level physics exposition? I would hope anyone whose sole knowledge of quantum mechanics is the sequence puts HUGE uncertainty bands around any estimate of the proper interpretation of quantum mechanics, because there is so much they don’t know (and even more they don’t know that they don’t know)
Does it worry you that people with good domain knowledge of physics(Shminux,Mitchell Porter, myself) seem to feel that your QM sequence is actually presenting a misleading picture of why some elite physicists don’t hold to many worlds with high probability?
Is there an explanation of this somewhere that you can link me to?
Does it worry you that people with good domain knowledge of physics(Shminux,Mitchell Porter, myself) seem to feel that your QM sequence is actually presenting a misleading picture of why some elite physicists don’t hold to many worlds with high probability?
Not under these circumstances, no. Part of understanding that the world is not sane, is understanding that some people in any given reference class will refuse to be persuaded by any given bit of sanity. It might be worrying if the object-level case against single-world QM were not absolutely clear-cut.
Also, is it desirable to train rationalists to believe that they SHOULD update their belief about interpretations of quantum mechanics above a weighted sampling of domain experts based on ~50 pages of highschool level physics exposition?
Depends on how crazy the domain experts are being, in this mad world of ours.
Not under these circumstances, no. Part of understanding that the world is not sane, is understanding that some people in any given reference class will refuse to be persuaded by any given bit of sanity. It might be worrying if the object-level case against single-world QM were not absolutely clear-cut.
It may be worth also observing that at least two of those users have disagreements with you about epistemology and reductionism far more fundamental than QM interpretations. When someone’s epistemic philosophy leads them to disagree about existence implications of general relativity then their epistemic disagreement about the implications of QM provides very little additional information.
When you bite the bullet and accept someone else’s beliefs based on their authority then consistency suggests you do it at the core point of disagreement, not merely one of the implications thereof. In this case that would require rather sweeping changes.
When someone’s epistemic philosophy leads them to disagree about existence implications of general relativity
I’m slightly annoyed that I just reread most of that thread in the understanding that you were linking to the disagreements in question, only to find no comments by either shminux, Mitchell Porter or EHeller and therefore feel no closer to understanding this particular subthread’s context.
I think he was referring to shminux’s non scientific-realist views, suggesting they are in conflict with such statements as “there are galaxies distant enough that we cannot see them due to lightspeed limitations.”
I’m slightly annoyed that I just reread most of that thread in the understanding that you were linking to
Never mind, that post and thread are far more interesting than the assorted related comments spread over years. Carl’s comment is correct and if you want more details about those you may have luck using Wei Dai’s script. You’d have to experiment with keywords.
Does it worry you, then, that many worlds does not generalize to Lagrangians that lead to non-linear equations of motion, and that many successful particle physics lagrangians are non-linear in the fields?
This sounds wrong. That nonlinearity is in the classical equations of motion. The quantum equations of motion will still be linear, in the sense of obeying the superposition principle. Offhand, I’m not sure how to sum up the quantum consequences of the classical nonlinearity … maybe something to do with commutators? … but I don’t see this as an argument against MWI.
edit Maybe you mean quadratic fermionic terms? Which I would agree is specifically quantum.
That nonlinearity is in the classical equations of motion.
Sure, the equation of motion are non-linear in the FIELDS, which aren’t necessarily the wavefunctions. No one has solved Yang-Mills, which is almost certainly the easiest of the non-linear lagrangians, so I don’t think we actually know about whether the quantum equations would be linear.
The standard approach is to fracture gauge symmetry and use solutions to the linearized equations of motion as wavefunctions, and treat the non-linear part as an interaction you can ignore at large times. This is actually hugely problematic because Haag’s theorem calls into question the entire framework (you can’t define an interaction picture).
It seems unlikely that you can have the classical equations of motion be non-linear in the field without the wavefunction having non-linear evolution- after all the creation operator at leading order has to obey the classical equation of motion, and you can write a single particle state as (creation*vacuum). The higher order terms would have to come together rather miraculously.
And keep in mind, its not just Yang-Mills. If we think of the standard model as the power-series of an effective field theory, it seems likely all those linear, first-order equations governing the propagator are just the linearization of the full theory.
There are many arguments against many worlds, I was simply throwing out one that I used to hear bandied about at particle physics conferences that isn’t addressed in the sequences at all. And generally, quantum field theories are still on fairly weak mathematical underpinnings. We have a nice collection of recipes that get the job done, but the underlying mathematical structure is unknown. Maybe a miracle occurs. But its a huge unknown area that is worth pointing to as “what can this mean?” Unless someone has dealt with this in the last 5 or 6 years, its been awhile since I was a physicist.
Edit: Replying to your edit, I’m thinking of any higher order terms you can throw into your lagrangian, be they quadratic fermion terms, three or four-point terms in Yang-Mills,etc. These lead to non-linear equations for the fields, and (quite likely, but unproven), the full solution to the wavefunction will be similarly non-linear. This may have implications for whether or not particle-number is a good observable, but I’m tired and don’t want to try and work it out.
Edit Again: I re-read this and its pretty clear to me I’m not communicating well (since I’m having trouble understanding what I just wrote). So- I’ll try to rephrase. The same non-linearities that crop up in Yang-Mills that require you to pick a proper gauge before you try to use the canonical relationships to write the quantum equations of motion are likely more general. You can add all kinds of non-linear terms to the lagrangian and you can’t always gauge fix them away. Most of the time they are small and you can ignore them, but on a fundamental level they are there (and at higher energies then some effective scale they probably matter). This requires modifications to linear quantum mechanics (commutation relationships become power series of which the traditional commutator is just the lowest order term, etc).
I strongly disagree that quantizing a classically nonlinear field theory should be expected to lead to a nonlinear Schrodinger equation, either at the level of the global quantum state, or at the level of the little wavefunctions which appear in the course of a calculation.
Linearity at the quantum level means that the superposition principle is obeyed—that if X1(t) and X2(t) are solutions to the Schrodinger equation, then X1(t)+X2(t) is also a solution. Nonlinear Schrodinger equations screw that up. There are sharp bounds on the degree to which that can be happening, at least for specific proposals regarding the nonlinearity.
Also, I think the “argument from Haag’s theorem” is just confused. See the discussions here. The adiabatic hypothesis and the interaction picture are heuristics which motivate the construction of a perturbative formalism. Haag’s theorem shows that the intuition behind the heuristic cannot literally be correct. But then, except for UV-complete theories like QCD, these theories all run into problems at some high energy anyway, so they don’t exist in the classic sense e.g. of von Neumann, as a specific operator algebra on a specific Hilbert space.
Instead, they exist as effective field theories. OK, what does that mean? Let’s accept the “Haagian” definition of what a true QFT or prototypical QFT should be—a quantum theory of fields that can satisfy a Hilbert-space axiomatization like von Neumann’s. Then an “effective field theory” is a “QFT-like object which only requires a finite number of parameters for its Wilsonian renormalization group to be predictive”. Somehow, this has still failed to obtain a generally accepted, rigorous mathematical definition, despite the work of people like Borcherds, Kreimer, etc. Nonetheless, effective field theories work, and they work empirically without having to introduce quantum nonlinearity.
I should also say something about how classical nonlinearity does show up in QFT—namely, in the use of solitons. But a soliton is still a fundamentally classical object, a solution to the classical equations of motion, which you might then “dress” with quantum corrections somehow.
Even if there were formally a use for quantum nonlinearity at the level of the little wavefunctions appearing along the way in a calculation, that wouldn’t prove that “ontologically”, at the level of THE global wavefunction, that there was quantum nonlinearity. It could just be an artefact of an approximation scheme. But I don’t even see a use for it at that level.
The one version of this argument that I might almost have time for, is Penrose’s old argument that gravitational superpositions are a problem, because you don’t know how to sync up the proper time in the different components of the superposition. It’s said that string theory, especially AdS/CFT, is a counterexample to this, but because it’s holographic, you’re really looking at S-matrix-like probabilities for going from the past to the future, and it’s not clear to me that the individual histories linking asymptotic past with asymptotic future, that appear in the sum over histories, do have a natural way of being aligned throughout their middle periods. They only have to “link up” at the beginning and the end, so that the amplitudes can sum. But I may be underestimating the extent to which a notion of time evolution can be extended into the “middle period”, in such a framework.
So to sum up, I definitely don’t buy these particular arguments about Haag’s theorem and nonlinearity. As you have presented them, they have a qualitative character, and so does my rebuttal, and so it could be that I’m overlooking some technicality which gives the arguments more substance. I am quite prepared to be re-educated in that respect. But for now, I think it’s just fuzzy thinking and a mistake.
P.S. In the second edit you say that the modified commutation relations “require modifications to linear quantum mechanics”. Well, I definitely don’t believe that, for the reasons I’ve already given, but maybe this is a technicality which can help to resolve the discussion. If you can find someone making that argument in detail…
edit What I don’t believe, is that the modifications in question amount to nonlinearity in the sense of the nonlinear Schrodinger equation. Perhaps the thing to do here, is to take nonlinear Schrodinger dynamics, construct the corresponding Heisenberg picture, and then see whether the resulting commutation relations, resemble the commutator power series you describe.
The whole point of it (well, one of the whole points) is to show people who wouldn’t previously believe such a thing was plausible, that they ought to disagree with elite physicists with high confidence
-1 for unjustified arrogance. The QM sequence has a number of excellent teaching points, like the discussion of how we can be sure that all electrons are identical, but the idea that one can disagree with experts in a subject matter without first studying the subject matter in depth is probably the most irrational, contagious and damaging idea in all of the sequences.
Example followed. That is, this utterance is poor form and ironic. This charge applies far more to the parent than the grandparent. Advocacy of deference to social status rather than and despite of evidence of competence (or the lack thereof) is the most irrational, contagious and damaging idea that appears on this site. (Followed closely by the similar “but the outside view says ”.)
The whole point of it (well, one of the whole points) is to show people who wouldn’t previously believe such a thing was plausible, that they ought to disagree with elite physicists with high confidence
Elite physicists are also people. Would you say that, if exposed to your sequence, these physicists would come to see that they were mistaken in their rejection of MWI? If not, it seems that the most credible explanation of the fact that your sequence can persuade ordinary folk that elite physicists are wrong, but can’t persuade elite physicists themselves, is that there is something wrong with your argument, which only elite physicists are competent enough to appreciate.
Unfortunately, in general when someone has given a question lots of thought and come to a conclusion, it will take an absolute steamroller to get them to change their mind. Most elite physicists will have given the question that much thought. So this wouldn’t demonstrate as much as you might like.
Certainly many elite physicists were persuaded by similar arguments before I wrote them up. If MWI is wrong, why can’t you persuade those elite physicists that it’s wrong? Huh? Huh?
Certainly many elite physicists were persuaded by similar arguments before I wrote them up.
Okay, so you are saying that these arguments were available at the time elite physicists made up their minds on which interpretation of QM was correct, and yet only a minority of elite physicists were persuaded. What evidential weight do you assign to this fact? More importantly, what evidential weight should the target audience of your QM sequence assign to it? To conclude that MWI is very likely true after reading your QM sequence, from a prior position of relative agnosticism, seems to me to give excessive weight to my own ability to assess arguments, relative to the ability of people who are smarter than me and have the relevant technical expertise—most of whom, to repeat, were not persuaded by those arguments.
Some kind of community-driven kickstarter to convince a top-level physicist to read the MWI sequence (in return for a grant) and to provide an in-depth answer tailored to it would be awesome. May also be good PR.
Scott Aaronson was already reading along to it as it was published. If we paid David Deutsch to read it, I expect him to just say, “Yeah, that’s all basically correct” which wouldn’t be very in-depth.
From those who already disagree with MWI, I would expect more in the way of awful amateur epistemology delivered with great confidence. Then those who already had their trust in a sane world broken will nod and say “I expected no better.” Others will say, “How can you possibly disregard the word of so great a physicist? Perhaps he knows something you don’t!”—though they will not be able to formalize the awful amateur epistemology—and nod among themselves about how Yudkowsky failed to anticipate that so strong a reply might be made (it should be presumed to be a very strong reply since a great physicist made it, even if they can’t 100% follow themselves why it is a great refutation, or would not have believed the same words so much from a street performer). And so both will emerge strengthened in their prior beliefs, which isn’t much of a test.
The effect of authoritative validation? The difference between professional physicist qua physicist, as opposed to quantum-computing-aware computer scientist, would not be small. Even if Scott Aaronson happens to know quantum mechanics as well as Feynman, it’s difficult to validate that authority.
Job titles aside, I think you had an incorrect model of his intellectual background, and how much he knows about certain subjects (e.g. general relativity) as contrasted with others (e.g. P and NP). Also (therefore) an incorrect model of how others would view your citation of him as an authority.
That said, I think you were right to think of him as an authority here and expect him to notice any important errors in your QM sequence.
As I said in a response to a comment of Nick, I would distinguish between the median theoretical physicist at a top 5 school, and the very best people. Intellectual caliber among high status scientists at distinguished institutions varies by 100x+. Apparently elite scientists can be very unrepresentative of the best scientists. You probably haven’t had extensive exposure to the best scientists. Unless one has it, one isn’t good position to assess their epistemology.
If a great physicist were to exhibit apparently awful amateur epistemology in responding to your sequence, I would assign substantial probability mass (not sure how much) to you being right.
The issue that I take with your position is your degree of confidence. The key thing to my mind is the point that Yvain makes in Confidence levels inside and outside an argument. You have an epistemic framework that assigns a probability of < 1% (and maybe much smaller) to MWI being wrong. But given the prior established by the absence of a consensus among such smart people, 99+% confidence in the epistemic framework that you’re using is really high. I could see 80-90% confidence as being well grounded. But a 99+% confidence level corresponds to an implicit belief that you’d be using a sound epistemic framework at least 99 times if there were 100 instances analogous to the QM/MWI situation. Does this sound right?
Maybe you should just quickly glance at http://lesswrong.com/lw/q7/if_manyworlds_had_come_first/. The mysterious force that eats all of the wavefunction except one part is something I assign similar probability as I assign to God—there is just no reason to believe in it except poorly justified elite opinion, and I don’t believe in elite opinions that I think are poorly justified.
But the main (if not only) argument you make for many worlds in that post and the others is the ridiculousness of collapse postulates. Now I’m not disagreeing with you, collapses would defy a great deal of convention (causality, relativity, CPT-symmetry, etc) but even with 100% confidence in this (as a hypothetical), you still wouldn’t be justified in assigning 99+% confidence in many worlds. There exist single world interpretations without a collapse, against which you haven’t presented any arguments. Bohmian mechanics would seem to be the most plausible of these (given the LW census). Do you still assign <1% likelihood to this interpretation, and if so, why?
Obvious rationalizations of single-world theories have no more evidence in their favor, no more reason to be believed; it’s like Deism vs. Jehovah. Sure, the class ‘Deism’ is more probable but it’s still not credible in an absolute sense (and no, Matrix Lords are not deities, they were born at a particular time, have limited domains and are made of parts). You can’t start with a terrible idea and expect to find >1% rationalizations for it. There’s more than 100 possible terrible ideas. Single-world QM via collapse/Copenhagen/shut-up was originally a terrible idea and you shouldn’t expect terrible ideas to be resurrectable on average. Privileging the hypothesis.
(Specifically: Bohm has similar FTL problems and causality problems and introduces epiphenomenal pointers to a ‘real world’ and if the wavefunction still exists (which it must because it is causally affecting the epiphenomenal pointer, things must be real to be causes of real effects so far as we know) then it should still have sentient observers inside it. Relational quantum mechanics is more awful amateur epistemology from people who’d rather abandon the concept of objective reality, with no good formal replacement, than just give up already. But most of all, why are we even asking that question or considering these theories in the first place? And again, simulated physics wouldn’t count because then the apparent laws are false and the simulations would presumably be of an original universe that would almost certainly be multiplicitous by the same reasoning; also there’d presumably be branches within the sim, so not single-world which is what I specified.)
If you can assign <1% probability to deism (the generalized abstracted class containing Jehovahism) then there should be no problem with assigning <1% probability to all single-world theories.
Given that there’s some serious fundamental physics we don’t understand yet, I find it hard to persuade myself there’s less than a 1% chance that even the framing of single-world versus many-world interpretations is incoherent.
Minor points: the generalized abstracted class containing Jehovaism is general theism, not deism. Deism is the subset of deities which do not interfere with their creation, whereas personal theism is the subset of deities which do interfere.
Also—I myself stopped with this usage but it bears mentioning—there are “gods” which were born as mortals and ascended, apotheosis-like; there are gods that can kill each other, there’s Hermes and legions of minor gods, many of them “with parts”.
It’s not trivial to draw a line that allows for killable gods of ancient times (compare Ragnarök) and thus doesn’t contradict established mythology that has lots of trivial, minor gods, but doesn’t allow for Matrix Lords to be considered gods (if not in the contemporary “triple-O Abrahamic deity” parlance). Ontologically fundamental mental powers ain’t the classifying separator, and I’m sure you’d agree that a label shouldn’t depend simply on whether we understand a phenomenon. Laws of physics with an if-clause for a certain kind of “god”-matter would still be laws of physics, and just having that description (knowing the laws), lifting the curtain, shouldn’t be sufficient to remove a “god” label.
I think the default position isn’t that MWI is wrong, but that we don’t currently have enough evidence to decide with high confidence. And you could persuade lots of physicists of that.
Elite physicists are also people. Would you say that, if exposed to your sequence, these physicists would come to see that they were mistaken in their rejection of MWI? If not, it seems that the most credible explanation of the fact that your sequence can persuade ordinary folk that elite physicists are wrong, but can’t persuade elite physicists themselves, is that there is something wrong with your argument, which only elite physicists are competent enough to appreciate.
to break their trust in a sane world, before which nothing can begin.
It seems likely to me that both “the world is insane” and “the world is sane” are incorrect, and the truth is “the world is right about some things and wrong about other things”. I like Nick’s idea of treating the opinions of people who society regards as experts as a prior and carefully updating from that as evidence warrants. I dislike treating mainstream human civilization as a faction to either align with or break from, and I dislike even more the way some people in the LW community show off by casually disregarding mainstream opinion. This seems like something that both probably looks cultish to outsiders and is legitimately cultish in a way that is bad and worth fighting.
You probably have a good point, but I found it briefly amusing to imagine it going like this:
ELIEZER: Elite scientists are usually elite for good reason, but sometimes they’re wrong. People shouldn’t blindly trust an elite’s position on a subject when they have compelling reasons to believe that that position is wrong.
STRAWMAN: I agree that there are problems with blindly trusting them. But let’s not jump straight to the opposite extreme of not blindly trusting them.
As soon as you start saying things like people need “to break their trust in a sane world, before which nothing can begin”, you know you have a problem.
As soon as you start saying things like people need “to break their trust in a sane world, before which nothing can begin”, you know you have a problem.
Deciding the world is completely untrustworthy after learning that Santa Claus is a lie seems like the wrong update to make. The right update to make seems to be “adults sometimes lie to kids to entertain themselves and the kids”. In fact, arguably society tells you more incorrect info as a kid than as an adult, so you should become more and more trusting of what society tells you the older you grow. (Well, I guess you also get smarter as you grow, so it’s a bit more complicated than that.)
Deciding the world is completely untrustworthy after learning that Santa Claus is a lie seems like the wrong update to make. The right update to make seems to be “adults sometimes lie to kids to entertain themselves and the kids”.
It would be even better to update in the direction of understanding the interaction between social status, belief, affiliation and dominance.
In fact, arguably society tells you more incorrect info as a kid than as an adult, so you should become more and more trusting of what society tells you the older you grow. (Well, I guess you also get smarter as you grow, so it’s a bit more complicated than that.)
The parenthetical is correct. The ‘arguable’ part is true only in as much as it is technically possible to argue for most things that are stupid.
You should become more trusting in the sense that what adults tell you constitutes stronger Bayesian evidence, but your own thoughts will also constitute stronger Bayesian evidence.
You should become more trusting in the sense that what adults tell you constitutes stronger Bayesian evidence, but your own thoughts will also constitute stronger Bayesian evidence.
Adults also have more incentive to lie and deceive you when your decisions have enough power to influence their outcomes.
You must be strawmanning “the world is insane” if you think it’s not compatible with “the world is right about some things and wrong about other things”. EY knows pretty well that the world isn’t wrong about everything.
This seems circular :-) (I should use an inside view of your sequence to update the view that I shouldn’t give too much weight to my inside view of your sequence...?) But I’ll check out your sequence.
This seems circular :-) (I should use an inside view of your sequence to update the view that I shouldn’t give too much weight to my inside view of your sequence...?)
That isn’t circular. Choosing to limit your use of reasoning to a specific subset of valid reasoning (the assertion of a reference class that you have selected and deference to analogies thereto—‘outside view’) is a quirk of your own psychology, not a fact about what reasoning is valid or circular. You don’t have to believe reasoning that isn’t based on the outside view but this is very different from that reasoning being circular. Using arguments that will not convince the particular audience is futile, not fallacious.
The above holds regardless of whether your particular usage of outside view reasoning is sound with respect to the subject discussed in this context. “Circular” is an incorrect description even if Eliezer is wrong.
You don’t know what’s in the QM sequence. The whole point of it (well, one of the whole points) is to show people who wouldn’t previously believe such a thing was plausible, that they ought to disagree with elite physicists with high confidence—to break their trust in a sane world, before which nothing can begin.
Does it worry you that people with good domain knowledge of physics(Shminux,Mitchell Porter, myself) seem to feel that your QM sequence is actually presenting a misleading picture of why some elite physicists don’t hold to many worlds with high probability?
Also, is it desirable to train rationalists to believe that they SHOULD update their belief about interpretations of quantum mechanics above a weighted sampling of domain experts based on ~50 pages of highschool level physics exposition? I would hope anyone whose sole knowledge of quantum mechanics is the sequence puts HUGE uncertainty bands around any estimate of the proper interpretation of quantum mechanics, because there is so much they don’t know (and even more they don’t know that they don’t know)
Is there an explanation of this somewhere that you can link me to?
This might be relevant.
Not under these circumstances, no. Part of understanding that the world is not sane, is understanding that some people in any given reference class will refuse to be persuaded by any given bit of sanity. It might be worrying if the object-level case against single-world QM were not absolutely clear-cut.
Depends on how crazy the domain experts are being, in this mad world of ours.
It may be worth also observing that at least two of those users have disagreements with you about epistemology and reductionism far more fundamental than QM interpretations. When someone’s epistemic philosophy leads them to disagree about existence implications of general relativity then their epistemic disagreement about the implications of QM provides very little additional information.
When you bite the bullet and accept someone else’s beliefs based on their authority then consistency suggests you do it at the core point of disagreement, not merely one of the implications thereof. In this case that would require rather sweeping changes.
I’m slightly annoyed that I just reread most of that thread in the understanding that you were linking to the disagreements in question, only to find no comments by either shminux, Mitchell Porter or EHeller and therefore feel no closer to understanding this particular subthread’s context.
I think he was referring to shminux’s non scientific-realist views, suggesting they are in conflict with such statements as “there are galaxies distant enough that we cannot see them due to lightspeed limitations.”
Thanks.
Never mind, that post and thread are far more interesting than the assorted related comments spread over years. Carl’s comment is correct and if you want more details about those you may have luck using Wei Dai’s script. You’d have to experiment with keywords.
Does it worry you, then, that many worlds does not generalize to Lagrangians that lead to non-linear equations of motion, and that many successful particle physics lagrangians are non-linear in the fields?
This sounds wrong. That nonlinearity is in the classical equations of motion. The quantum equations of motion will still be linear, in the sense of obeying the superposition principle. Offhand, I’m not sure how to sum up the quantum consequences of the classical nonlinearity … maybe something to do with commutators? … but I don’t see this as an argument against MWI.
edit Maybe you mean quadratic fermionic terms? Which I would agree is specifically quantum.
Sure, the equation of motion are non-linear in the FIELDS, which aren’t necessarily the wavefunctions. No one has solved Yang-Mills, which is almost certainly the easiest of the non-linear lagrangians, so I don’t think we actually know about whether the quantum equations would be linear.
The standard approach is to fracture gauge symmetry and use solutions to the linearized equations of motion as wavefunctions, and treat the non-linear part as an interaction you can ignore at large times. This is actually hugely problematic because Haag’s theorem calls into question the entire framework (you can’t define an interaction picture).
It seems unlikely that you can have the classical equations of motion be non-linear in the field without the wavefunction having non-linear evolution- after all the creation operator at leading order has to obey the classical equation of motion, and you can write a single particle state as (creation*vacuum). The higher order terms would have to come together rather miraculously.
And keep in mind, its not just Yang-Mills. If we think of the standard model as the power-series of an effective field theory, it seems likely all those linear, first-order equations governing the propagator are just the linearization of the full theory.
There are many arguments against many worlds, I was simply throwing out one that I used to hear bandied about at particle physics conferences that isn’t addressed in the sequences at all. And generally, quantum field theories are still on fairly weak mathematical underpinnings. We have a nice collection of recipes that get the job done, but the underlying mathematical structure is unknown. Maybe a miracle occurs. But its a huge unknown area that is worth pointing to as “what can this mean?” Unless someone has dealt with this in the last 5 or 6 years, its been awhile since I was a physicist.
Edit: Replying to your edit, I’m thinking of any higher order terms you can throw into your lagrangian, be they quadratic fermion terms, three or four-point terms in Yang-Mills,etc. These lead to non-linear equations for the fields, and (quite likely, but unproven), the full solution to the wavefunction will be similarly non-linear. This may have implications for whether or not particle-number is a good observable, but I’m tired and don’t want to try and work it out.
Edit Again: I re-read this and its pretty clear to me I’m not communicating well (since I’m having trouble understanding what I just wrote). So- I’ll try to rephrase. The same non-linearities that crop up in Yang-Mills that require you to pick a proper gauge before you try to use the canonical relationships to write the quantum equations of motion are likely more general. You can add all kinds of non-linear terms to the lagrangian and you can’t always gauge fix them away. Most of the time they are small and you can ignore them, but on a fundamental level they are there (and at higher energies then some effective scale they probably matter). This requires modifications to linear quantum mechanics (commutation relationships become power series of which the traditional commutator is just the lowest order term, etc).
I strongly disagree that quantizing a classically nonlinear field theory should be expected to lead to a nonlinear Schrodinger equation, either at the level of the global quantum state, or at the level of the little wavefunctions which appear in the course of a calculation.
Linearity at the quantum level means that the superposition principle is obeyed—that if X1(t) and X2(t) are solutions to the Schrodinger equation, then X1(t)+X2(t) is also a solution. Nonlinear Schrodinger equations screw that up. There are sharp bounds on the degree to which that can be happening, at least for specific proposals regarding the nonlinearity.
Also, I think the “argument from Haag’s theorem” is just confused. See the discussions here. The adiabatic hypothesis and the interaction picture are heuristics which motivate the construction of a perturbative formalism. Haag’s theorem shows that the intuition behind the heuristic cannot literally be correct. But then, except for UV-complete theories like QCD, these theories all run into problems at some high energy anyway, so they don’t exist in the classic sense e.g. of von Neumann, as a specific operator algebra on a specific Hilbert space.
Instead, they exist as effective field theories. OK, what does that mean? Let’s accept the “Haagian” definition of what a true QFT or prototypical QFT should be—a quantum theory of fields that can satisfy a Hilbert-space axiomatization like von Neumann’s. Then an “effective field theory” is a “QFT-like object which only requires a finite number of parameters for its Wilsonian renormalization group to be predictive”. Somehow, this has still failed to obtain a generally accepted, rigorous mathematical definition, despite the work of people like Borcherds, Kreimer, etc. Nonetheless, effective field theories work, and they work empirically without having to introduce quantum nonlinearity.
I should also say something about how classical nonlinearity does show up in QFT—namely, in the use of solitons. But a soliton is still a fundamentally classical object, a solution to the classical equations of motion, which you might then “dress” with quantum corrections somehow.
Even if there were formally a use for quantum nonlinearity at the level of the little wavefunctions appearing along the way in a calculation, that wouldn’t prove that “ontologically”, at the level of THE global wavefunction, that there was quantum nonlinearity. It could just be an artefact of an approximation scheme. But I don’t even see a use for it at that level.
The one version of this argument that I might almost have time for, is Penrose’s old argument that gravitational superpositions are a problem, because you don’t know how to sync up the proper time in the different components of the superposition. It’s said that string theory, especially AdS/CFT, is a counterexample to this, but because it’s holographic, you’re really looking at S-matrix-like probabilities for going from the past to the future, and it’s not clear to me that the individual histories linking asymptotic past with asymptotic future, that appear in the sum over histories, do have a natural way of being aligned throughout their middle periods. They only have to “link up” at the beginning and the end, so that the amplitudes can sum. But I may be underestimating the extent to which a notion of time evolution can be extended into the “middle period”, in such a framework.
So to sum up, I definitely don’t buy these particular arguments about Haag’s theorem and nonlinearity. As you have presented them, they have a qualitative character, and so does my rebuttal, and so it could be that I’m overlooking some technicality which gives the arguments more substance. I am quite prepared to be re-educated in that respect. But for now, I think it’s just fuzzy thinking and a mistake.
P.S. In the second edit you say that the modified commutation relations “require modifications to linear quantum mechanics”. Well, I definitely don’t believe that, for the reasons I’ve already given, but maybe this is a technicality which can help to resolve the discussion. If you can find someone making that argument in detail…
edit What I don’t believe, is that the modifications in question amount to nonlinearity in the sense of the nonlinear Schrodinger equation. Perhaps the thing to do here, is to take nonlinear Schrodinger dynamics, construct the corresponding Heisenberg picture, and then see whether the resulting commutation relations, resemble the commutator power series you describe.
Given EHeller’s appeal to your authority to support his position in this context this is an interesting development.
We’ll have to see what he had in mind—I may have had the wrong interpretation.
-1 for unjustified arrogance. The QM sequence has a number of excellent teaching points, like the discussion of how we can be sure that all electrons are identical, but the idea that one can disagree with experts in a subject matter without first studying the subject matter in depth is probably the most irrational, contagious and damaging idea in all of the sequences.
Example followed. That is, this utterance is poor form and ironic. This charge applies far more to the parent than the grandparent. Advocacy of deference to social status rather than and despite of evidence of competence (or the lack thereof) is the most irrational, contagious and damaging idea that appears on this site. (Followed closely by the similar “but the outside view says ”.)
Elite physicists are also people. Would you say that, if exposed to your sequence, these physicists would come to see that they were mistaken in their rejection of MWI? If not, it seems that the most credible explanation of the fact that your sequence can persuade ordinary folk that elite physicists are wrong, but can’t persuade elite physicists themselves, is that there is something wrong with your argument, which only elite physicists are competent enough to appreciate.
Unfortunately, in general when someone has given a question lots of thought and come to a conclusion, it will take an absolute steamroller to get them to change their mind. Most elite physicists will have given the question that much thought. So this wouldn’t demonstrate as much as you might like.
Certainly many elite physicists were persuaded by similar arguments before I wrote them up. If MWI is wrong, why can’t you persuade those elite physicists that it’s wrong? Huh? Huh?
Okay, so you are saying that these arguments were available at the time elite physicists made up their minds on which interpretation of QM was correct, and yet only a minority of elite physicists were persuaded. What evidential weight do you assign to this fact? More importantly, what evidential weight should the target audience of your QM sequence assign to it? To conclude that MWI is very likely true after reading your QM sequence, from a prior position of relative agnosticism, seems to me to give excessive weight to my own ability to assess arguments, relative to the ability of people who are smarter than me and have the relevant technical expertise—most of whom, to repeat, were not persuaded by those arguments.
Some kind of community-driven kickstarter to convince a top-level physicist to read the MWI sequence (in return for a grant) and to provide an in-depth answer tailored to it would be awesome. May also be good PR.
Scott Aaronson was already reading along to it as it was published. If we paid David Deutsch to read it, I expect him to just say, “Yeah, that’s all basically correct” which wouldn’t be very in-depth.
From those who already disagree with MWI, I would expect more in the way of awful amateur epistemology delivered with great confidence. Then those who already had their trust in a sane world broken will nod and say “I expected no better.” Others will say, “How can you possibly disregard the word of so great a physicist? Perhaps he knows something you don’t!”—though they will not be able to formalize the awful amateur epistemology—and nod among themselves about how Yudkowsky failed to anticipate that so strong a reply might be made (it should be presumed to be a very strong reply since a great physicist made it, even if they can’t 100% follow themselves why it is a great refutation, or would not have believed the same words so much from a street performer). And so both will emerge strengthened in their prior beliefs, which isn’t much of a test.
Scott Aaronson is not a physicist!
I’d expect him to notice math errors and he specializes in the aspect of QM that I talk about, regardless of job titles.
Still, it diminishes the effect.
Nnnoo it doesn’t, IMO.
The effect of authoritative validation? The difference between professional physicist qua physicist, as opposed to quantum-computing-aware computer scientist, would not be small. Even if Scott Aaronson happens to know quantum mechanics as well as Feynman, it’s difficult to validate that authority.
Job titles aside, I think you had an incorrect model of his intellectual background, and how much he knows about certain subjects (e.g. general relativity) as contrasted with others (e.g. P and NP). Also (therefore) an incorrect model of how others would view your citation of him as an authority.
That said, I think you were right to think of him as an authority here and expect him to notice any important errors in your QM sequence.
As I said in a response to a comment of Nick, I would distinguish between the median theoretical physicist at a top 5 school, and the very best people. Intellectual caliber among high status scientists at distinguished institutions varies by 100x+. Apparently elite scientists can be very unrepresentative of the best scientists. You probably haven’t had extensive exposure to the best scientists. Unless one has it, one isn’t good position to assess their epistemology.
If a great physicist were to exhibit apparently awful amateur epistemology in responding to your sequence, I would assign substantial probability mass (not sure how much) to you being right.
The issue that I take with your position is your degree of confidence. The key thing to my mind is the point that Yvain makes in Confidence levels inside and outside an argument. You have an epistemic framework that assigns a probability of < 1% (and maybe much smaller) to MWI being wrong. But given the prior established by the absence of a consensus among such smart people, 99+% confidence in the epistemic framework that you’re using is really high. I could see 80-90% confidence as being well grounded. But a 99+% confidence level corresponds to an implicit belief that you’d be using a sound epistemic framework at least 99 times if there were 100 instances analogous to the QM/MWI situation. Does this sound right?
Maybe you should just quickly glance at http://lesswrong.com/lw/q7/if_manyworlds_had_come_first/. The mysterious force that eats all of the wavefunction except one part is something I assign similar probability as I assign to God—there is just no reason to believe in it except poorly justified elite opinion, and I don’t believe in elite opinions that I think are poorly justified.
But the main (if not only) argument you make for many worlds in that post and the others is the ridiculousness of collapse postulates. Now I’m not disagreeing with you, collapses would defy a great deal of convention (causality, relativity, CPT-symmetry, etc) but even with 100% confidence in this (as a hypothetical), you still wouldn’t be justified in assigning 99+% confidence in many worlds. There exist single world interpretations without a collapse, against which you haven’t presented any arguments. Bohmian mechanics would seem to be the most plausible of these (given the LW census). Do you still assign <1% likelihood to this interpretation, and if so, why?
Obvious rationalizations of single-world theories have no more evidence in their favor, no more reason to be believed; it’s like Deism vs. Jehovah. Sure, the class ‘Deism’ is more probable but it’s still not credible in an absolute sense (and no, Matrix Lords are not deities, they were born at a particular time, have limited domains and are made of parts). You can’t start with a terrible idea and expect to find >1% rationalizations for it. There’s more than 100 possible terrible ideas. Single-world QM via collapse/Copenhagen/shut-up was originally a terrible idea and you shouldn’t expect terrible ideas to be resurrectable on average. Privileging the hypothesis.
(Specifically: Bohm has similar FTL problems and causality problems and introduces epiphenomenal pointers to a ‘real world’ and if the wavefunction still exists (which it must because it is causally affecting the epiphenomenal pointer, things must be real to be causes of real effects so far as we know) then it should still have sentient observers inside it. Relational quantum mechanics is more awful amateur epistemology from people who’d rather abandon the concept of objective reality, with no good formal replacement, than just give up already. But most of all, why are we even asking that question or considering these theories in the first place? And again, simulated physics wouldn’t count because then the apparent laws are false and the simulations would presumably be of an original universe that would almost certainly be multiplicitous by the same reasoning; also there’d presumably be branches within the sim, so not single-world which is what I specified.)
If you can assign <1% probability to deism (the generalized abstracted class containing Jehovahism) then there should be no problem with assigning <1% probability to all single-world theories.
Given that there’s some serious fundamental physics we don’t understand yet, I find it hard to persuade myself there’s less than a 1% chance that even the framing of single-world versus many-world interpretations is incoherent.
Minor points: the generalized abstracted class containing Jehovaism is general theism, not deism. Deism is the subset of deities which do not interfere with their creation, whereas personal theism is the subset of deities which do interfere.
Also—I myself stopped with this usage but it bears mentioning—there are “gods” which were born as mortals and ascended, apotheosis-like; there are gods that can kill each other, there’s Hermes and legions of minor gods, many of them “with parts”.
It’s not trivial to draw a line that allows for killable gods of ancient times (compare Ragnarök) and thus doesn’t contradict established mythology that has lots of trivial, minor gods, but doesn’t allow for Matrix Lords to be considered gods (if not in the contemporary “triple-O Abrahamic deity” parlance). Ontologically fundamental mental powers ain’t the classifying separator, and I’m sure you’d agree that a label shouldn’t depend simply on whether we understand a phenomenon. Laws of physics with an if-clause for a certain kind of “god”-matter would still be laws of physics, and just having that description (knowing the laws), lifting the curtain, shouldn’t be sufficient to remove a “god” label.
Thanks. I read this some years ago, but will take another look.
I think the default position isn’t that MWI is wrong, but that we don’t currently have enough evidence to decide with high confidence. And you could persuade lots of physicists of that.
Elite physicists are easy to persuade in the abstract. You wait till the high status old people die.
It seems likely to me that both “the world is insane” and “the world is sane” are incorrect, and the truth is “the world is right about some things and wrong about other things”. I like Nick’s idea of treating the opinions of people who society regards as experts as a prior and carefully updating from that as evidence warrants. I dislike treating mainstream human civilization as a faction to either align with or break from, and I dislike even more the way some people in the LW community show off by casually disregarding mainstream opinion. This seems like something that both probably looks cultish to outsiders and is legitimately cultish in a way that is bad and worth fighting.
You probably have a good point, but I found it briefly amusing to imagine it going like this:
ELIEZER: Elite scientists are usually elite for good reason, but sometimes they’re wrong. People shouldn’t blindly trust an elite’s position on a subject when they have compelling reasons to believe that that position is wrong.
STRAWMAN: I agree that there are problems with blindly trusting them. But let’s not jump straight to the opposite extreme of not blindly trusting them.
As soon as you start saying things like people need “to break their trust in a sane world, before which nothing can begin”, you know you have a problem.
I take it you grew up in an atheist or liberal-Christian community?
For example, you may be talking to a child whose parents are still lying to him.
Deciding the world is completely untrustworthy after learning that Santa Claus is a lie seems like the wrong update to make. The right update to make seems to be “adults sometimes lie to kids to entertain themselves and the kids”. In fact, arguably society tells you more incorrect info as a kid than as an adult, so you should become more and more trusting of what society tells you the older you grow. (Well, I guess you also get smarter as you grow, so it’s a bit more complicated than that.)
It would be even better to update in the direction of understanding the interaction between social status, belief, affiliation and dominance.
The parenthetical is correct. The ‘arguable’ part is true only in as much as it is technically possible to argue for most things that are stupid.
You should become more trusting in the sense that what adults tell you constitutes stronger Bayesian evidence, but your own thoughts will also constitute stronger Bayesian evidence.
Adults also have more incentive to lie and deceive you when your decisions have enough power to influence their outcomes.
You must be strawmanning “the world is insane” if you think it’s not compatible with “the world is right about some things and wrong about other things”. EY knows pretty well that the world isn’t wrong about everything.
This seems circular :-) (I should use an inside view of your sequence to update the view that I shouldn’t give too much weight to my inside view of your sequence...?) But I’ll check out your sequence.
That isn’t circular. Choosing to limit your use of reasoning to a specific subset of valid reasoning (the assertion of a reference class that you have selected and deference to analogies thereto—‘outside view’) is a quirk of your own psychology, not a fact about what reasoning is valid or circular. You don’t have to believe reasoning that isn’t based on the outside view but this is very different from that reasoning being circular. Using arguments that will not convince the particular audience is futile, not fallacious.
The above holds regardless of whether your particular usage of outside view reasoning is sound with respect to the subject discussed in this context. “Circular” is an incorrect description even if Eliezer is wrong.