Not that I’m claiming I could have done better, if I’d been born into that time, instead of this one…

    Macroscopic decoherence, a.k.a. many-worlds, was first proposed in a 1957 paper by Hugh Everett III. The paper was ignored. John Wheeler told Everett to see Niels Bohr. Bohr didn’t take him seriously.

    Crushed, Everett left academic physics, invented the general use of Lagrange multipliers in optimization problems, and became a multimillionaire.

    It wasn’t until 1970, when Bryce DeWitt (who coined the term “many-worlds”) wrote an article for Physics Today, that the general field was first informed of Everett’s ideas. Macroscopic decoherence has been gaining advocates ever since, and may now be the majority viewpoint (or not).

    But suppose that decoherence and macroscopic decoherence had been realized immediately following the discovery of entanglement, in the 1920s. And suppose that no one had proposed collapse theories until 1957. Would decoherence now be steadily declining in popularity, while collapse theories were slowly gaining steam?

    Imagine an alternate Earth, where the very first physicist to discover entanglement and superposition said, “Holy flaming monkeys, there’s a zillion other Earths out there!”

    In the years since, many hypotheses have been proposed to explain the mysterious Born probabilities. But no one has yet suggested a collapse postulate. That possibility simply has not occurred to anyone.

    One day, Huve Erett walks into the office of Biels Nohr…

    “I just don’t understand,” Huve Erett said, “why no one in physics even seems interested in my hypothesis. Aren’t the Born statistics the greatest puzzle in modern quantum theory?”

    Biels Nohr sighed. Ordinarily, he wouldn’t even bother, but something about the young man compelled him to try.

    “Huve,” says Nohr, “every physicist meets dozens of people per year who think they’ve explained the Born statistics. If you go to a party and tell someone you’re a physicist, chances are at least one in ten they’ve got a new explanation for the Born statistics. It’s one of the most famous problems in modern science, and worse, it’s a problem that everyone thinks they can understand. To get attention, a new Born hypothesis has to be… pretty darn good.”

    “And this,” Huve says, “this isn’t good?

    Huve gestures to the paper he’d brought to Biels Nohr. It is a short paper. The title reads, “The Solution to the Born Problem.” The body of the paper reads:

    When you perform a measurement on a quantum system, all parts of the wavefunction except one point vanish, with the survivor chosen non-deterministically in a way determined by the Born statistics.

    “Let me make absolutely sure,” Nohr says carefully, “that I understand you. You’re saying that we’ve got this wavefunction—evolving according to the Wheeler-DeWitt equation—and, all of a sudden, the whole wavefunction, except for one part, just spontaneously goes to zero amplitude. Everywhere at once. This happens when, way up at the macroscopic level, we ‘measure’ something.”

    “Right!” Huve says.

    “So the wavefunction knows when we ‘measure’ it. What exactly is a ‘measurement’? How does the wavefunction know we’re here? What happened before humans were around to measure things?”

    “Um…” Huve thinks for a moment. Then he reaches out for the paper, scratches out “When you perform a measurement on a quantum system,” and writes in, “When a quantum superposition gets too large.”

    Huve looks up brightly. “Fixed!”

    “I see,” says Nohr. “And how large is ‘too large’?”

    “At the 50-micron level, maybe,” Huve says, “I hear they haven’t tested that yet.”

    Suddenly a student sticks his head into the room. “Hey, did you hear? They just verified superposition at the 50-micron level.”

    “Oh,” says Huve, “um, whichever level, then. Whatever makes the experimental results come out right.”

    Nohr grimaces. “Look, young man, the truth here isn’t going to be comfortable. Can you hear me out on this?”

    “Yes,” Huve says, “I just want to know why physicists won’t listen to me.”

    “All right,” says Nohr. He sighs. “Look, if this theory of yours were actually true—if whole sections of the wavefunction just instantaneously vanished—it would be… let’s see. The only law in all of quantum mechanics that is non-linear, non-unitary, non-differentiable and discontinuous. It would prevent physics from evolving locally, with each piece only looking at its immediate neighbors. Your ‘collapse’ would be the only fundamental phenomenon in all of physics with a preferred basis and a preferred space of simultaneity. Collapse would be the only phenomenon in all of physics that violates CPT symmetry, Liouville’s Theorem, and Special Relativity. In your original version, collapse would also have been the only phenomenon in all of physics that was inherently mental. Have I left anything out?”

    “Collapse is also the only acausal phenomenon,” Huve points out. “Doesn’t that make the theory more wonderful and amazing?”

    “I think, Huve,” says Nohr, “that physicists may view the exceptionalism of your theory as a point not in its favor.”

    “Oh,” said Huve, taken aback. “Well, I think I can fix that non-differentiability thing by postulating a second-order term in the—”

    “Huve,” says Nohr, “I don’t think you’re getting my point, here. The reason physicists aren’t paying attention to you, is that your theory isn’t physics. It’s magic.”

    “But the Born statistics are the greatest puzzle of modern physics, and this theory provides a mechanism for the Born statistics!” Huve protests.

    “No, Huve, it doesn’t,” Nohr says wearily. “That’s like saying that you’ve ‘provided a mechanism’ for electromagnetism by saying that there are little angels pushing the charged particles around in accordance with Maxwell’s equations. Instead of saying, ‘Here are Maxwell’s equations, which tells the angels where to push the electrons,’ we just say, ‘Here are Maxwell’s equations’ and are left with a strictly simpler theory. Now, we don’t know why the Born statistics happen. But you haven’t given the slightest reason why your ‘collapse postulate’ should eliminate worlds in accordance with the Born statistics, rather than something else. You’re not even making use of the fact that quantum evolution is unitary—”

    “That’s because it’s not,” interjects Huve.

    “—which everyone pretty much knows has got to be the key to the Born statistics, somehow. Instead you’re merely saying, ‘Here are the Born statistics, which tell the collapser how to eliminate worlds,’ and it’s strictly simpler to just say ‘Here are the Born statistics.’ ”

    “But—” says Huve.

    Also,” says Nohr, raising his voice, “you’ve given no justification for why there’s only one surviving world left by the collapse, or why the collapse happens before any humans get superposed, which makes your theory really suspicious to a modern physicist. This is exactly the sort of untestable hypothesis that the ‘One Christ’ crowd uses to argue that we should ‘teach the controversy’ when we tell high school students about other Earths.”

    “I’m not a One-Christer!” protests Huve.

    “Fine,” Nohr says, “then why do you just assume there’s only one world left? And that’s not the only problem with your theory. Which part of the wavefunction gets eliminated, exactly? And in which basis? It’s clear that the whole wavefunction isn’t being compressed down to a delta, or ordinary quantum computers couldn’t stay in superposition when any collapse occurred anywhere—heck, ordinary molecular chemistry might start failing—”

    Huve quickly crosses out “one point” on his paper, writes in “one part,” and then says, “Collapse doesn’t compress the wavefunction down to one point. It eliminates all the amplitude except one world, but leaves all the amplitude in that world.”

    “Why?” says Nohr. “In principle, once you postulate ‘collapse,’ then ‘collapse’ could eliminate any part of the wavefunction, anywhere—why just one neat world left? Does the collapser know we’re in here?

    Huve says, “It leaves one whole world because that’s what fits our experiments.”

    “Huve,” Nohr says patiently, “the term for that is ‘post hoc.’ Furthermore, decoherence is a continuous process. If you partition by whole brains with distinct neurons firing, the partitions have almost zero mutual interference within the wavefunction. But plenty of other processes overlap a great deal. There’s no possible way you can point to ‘one world’ and eliminate everything else without making completely arbitrary choices, including an arbitrary choice of basis—”

    “But—” Huve says.

    “And above all,” Nohr says, “the reason you can’t tell me which part of the wavefunction vanishes, or exactly when it happens, or exactly what triggers it, is that if we did adopt this theory of yours, it would be the only informally specified, qualitative fundamental law taught in all of physics. Soon no two physicists anywhere would agree on the exact details! Why? Because it would be the only fundamental law in all of modern physics that was believed without experimental evidence to nail down exactly how it worked.”

    “What, really?” says Huve. “I thought a lot of physics was more informal than that. I mean, weren’t you just talking about how it’s impossible to point to ‘one world’?”

    “That’s because worlds aren’t fundamental, Huve! We have massive experimental evidence underpinning the fundamental law, the Wheeler-DeWitt equation, that we use to describe the evolution of the wavefunction. We just apply exactly the same equation to get our description of macroscopic decoherence. But for difficulties of calculation, the equation would, in principle, tell us exactly when macroscopic decoherence occurred. We don’t know where the Born statistics come from, but we have massive evidence for what the Born statistics are. But when I ask you when, or where, collapse occurs, you don’t know—because there’s no experimental evidence whatsoever to pin it down. Huve, even if this ‘collapse postulate’ worked the way you say it does, there’s no possible way you could know it! Why not a gazillion other equally magical possibilities?”

    Huve raises his hands defensively. “I’m not saying my theory should be taught in the universities as accepted truth! I just want it experimentally tested! Is that so wrong?”

    “You haven’t specified when collapse happens, so I can’t construct a test that falsifies your theory,” says Nohr. “Now with that said, we’re already looking experimentally for any part of the quantum laws that change at increasingly macroscopic levels. Both on general principles, in case there’s something in the 20th decimal point that only shows up in macroscopic systems, and also in the hopes we’ll discover something that sheds light on the Born statistics. We check decoherence times as a matter of course. But we keep a broad outlook on what might be different. Nobody’s going to privilege your non-linear, non-unitary, non-differentiable, non-local, non-CPT-symmetric, non-relativistic, a-frikkin’-causal, faster-than-light, in-bloody-formal ‘collapse’ when it comes to looking for clues. Not until they see absolutely unmistakable evidence. And believe me, Huve, it’s going to take a hell of a lot of evidence to unmistake this. Even if we did find anomalous decoherence times, and I don’t think we will, it wouldn’t force your ‘collapse’ as the explanation.”

    “What?” says Huve. “Why not?”

    “Because there’s got to be a billion more explanations that are more plausible than violating Special Relativity,” says Nohr. “Do you realize that if this really happened, there would only be a single outcome when you measured a photon’s polarization? Measuring one photon in an entangled pair would influence the other photon a light-year away. Einstein would have a heart attack.”

    “It doesn’t really violate Special Relativity,” says Huve. “The collapse occurs in exactly the right way to prevent you from ever actually detecting the faster-than-light influence.”

    “That’s not a point in your theory’s favor,” says Nohr. “Also, Einstein would still have a heart attack.”

    “Oh,” says Huve. “Well, we’ll say that the relevant aspects of the particle don’t existuntil the collapse occurs. If something doesn’t exist, influencing it doesn’t violate Special Relativity—”

    “You’re just digging yourself deeper. Look, Huve, as a general principle, theories that are actually correct don’t generate this level of confusion. But above all, there isn’t any evidence for it. You have no logical way of knowing that collapse occurs, and no reason to believe it. You made a mistake. Just say ‘oops’ and get on with your life.”

    “But they could find the evidence someday,” says Huve.

    “I can’t think of what evidence could determine this particular one-world hypothesis as an explanation, but in any case, right now we haven’t found any such evidence,” says Nohr. “We haven’t found anything even vaguely suggestive of it! You can’t update on evidence that could theoretically arrive someday but hasn’t arrived! Right now, today, there’s no reason to spend valuable time thinking about this rather than a billion other equally magical theories. There’s absolutely nothing that justifies your belief in ‘collapse theory’ any more than believing that someday we’ll learn to transmit faster-than-light messages by tapping into the acausal effects of praying to the Flying Spaghetti Monster!”

    Huve draws himself up with wounded dignity. “You know, if my theory is wrong—and I do admit it might be wrong—”

    If?” says Nohr. “Might?

    “If, I say, my theory is wrong,” Huve continues, “then somewhere out there is another world where I am the famous physicist and you are the lone outcast!”

    Nohr buries his head in his hands. “Oh, not this again. Haven’t you heard the saying, ‘Live in your own world’? And you of all people—”

    “Somewhere out there is a world where the vast majority of physicists believe in collapse theory, and no one has even suggested macroscopic decoherence over the last thirty years!”

    Nohr raises his head, and begins to laugh.

    “What’s so funny?” Huve says suspiciously.

    Nohr just laughs harder. “Oh, my! Oh, my! You really think, Huve, that there’s a world out there where they’ve known about quantum physics for thirty years, and nobody has even thought there might be more than one world?”

    “Yes,” Huve says, “that’s exactly what I think.”

    “Oh my! So you’re saying, Huve, that physicists detect superposition in microscopic systems, and work out quantitative equations that govern superposition in every single instance they can test. And for thirty years, not one person says, ‘Hey, I wonder if these laws happen to be universal.’ ”

    “Why should they?” says Huve. “Physical models sometimes turn out to be wrong when you examine new regimes.”

    “But to not even think of it?” Nohr says incredulously. “You see apples falling, work out the law of gravity for all the planets in the solar system except Jupiter, and it doesn’t even occur to you to apply it to Jupiter because Jupiter is too large? That’s like, like some kind of comedy routine where the guy opens a box, and it contains a spring-loaded pie, so the guy opens another box, and it contains another spring-loaded pie, and the guy just keeps doing this without even thinking of the possibility that the next box contains a pie too. You think John von Neumann, who may have been the highest-g human in history, wouldn’t think of it?”

    “That’s right,” Huve says, “He wouldn’t. Ponder that.”

    “This is the world where my good friend Ernest formulates his Schrödinger’s Cat thought experiment, and in this world, the thought experiment goes: ‘Hey, suppose we have a radioactive particle that enters a superposition of decaying and not decaying. Then the particle interacts with a sensor, and the sensor goes into a superposition of going off and not going off. The sensor interacts with an explosive, that goes into a superposition of exploding and not exploding; which interacts with the cat, so the cat goes into a superposition of being alive and dead. Then a human looks at the cat,’ and at this point Schrödinger stops, and goes, ‘gee, I just can’t imagine what could happen next.’ So Schrödinger shows this to everyone else, and they’re also like ‘Wow, I got no idea what could happen at this point, what an amazing paradox.’ Until finally you hear about it, and you’re like, ‘hey, maybe at thatpoint half of the superposition just vanishes, at random, faster than light,’ and everyone else is like, ‘Wow, what a great idea!’ ”

    “That’s right,” Huve says again. “It’s got to have happened somewhere.”

    “Huve, this is a world where every single physicist, and probably the whole damn human species, is too dumb to sign up for cryonics! We’re talking about the Earth where George W. Bush is President.”

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    may now be the majority viewpoint (or not).

    Or both at the same time?

    I hope the following isn't completely off-topic:

    ... if I'd been born into that time, instead of this one...
    What exactly does a hypothetical scenario where "person X was born Y years earlier" even look like? I could see a somewhat plausible interpretation of that description in periods of extremely slow scientific and technological progress, but the twentieth century doesn't qualify. In the 1920s: 1) The concept of a turing machine hadn't been formulated yet. 2) There were no electronic computers. 3) ARPANET wasn't even an idea yet, and wouldn't ... (read more)

    What if it had seemed that there was no way to get the Born rule with just simple decoherence - what if that seemed to clearly imply a uniform probability rule. Would the random collapse view seem more plausible then?

    What if it had seemed that there was no way to get the Born rule with just simple decoherence - what if that seemed to clearly imply a uniform probability rule. Would the random collapse view seem more plausible then?

    No. Eight strikes and it's out. There is no possible reason for adopting a theory that unphysical, or even spending more than thirty seconds thinking about it, without crushingly unmistakable experimental evidence that nails it down.

    If you're postulating new fundamental physics, things that don't show up microscopically but do show up macroscopically, to explain the Born statistics, there would be a hundred better possibilities that don't violate Special Relativity.

    One thing you're currently having trouble explaining is not an excuse to import magic out of nowhere and say, "Oh, that must be the explanation." Doesn't work for intelligent design and it doesn't work for collapse either.


    If MWI has no observable consequences, does it matter other than as a point of principle? Or are you going to get to ethical consequences, like the spaceship that doesn't disappear when it passes the horizon?

    I'm surprised by the last sentence. Politics is the mind-killer, and all that.

    Correct me if I am wrong, but MWI does have noticeable consequences, or at least implications: for example, interference at all length-scales and proper evaluation of the waveform equations implying the Born probabilities. Neither of these are implicit in the Copenhagen interpretation - in fact, the first is contradicted.

    03:16 was me - curse you, Typepad!

    If there really are consequences of one of the hypotheses that differ from the consequences of others, that is extremely important to know.

    I don't see how decoherence is an automatic win for MWI. Decoherence has been used in several different interpretations of quantum mechanics, notably in consistent histories and in certain hidden variable interpretations. Why should we choose MWI before those, particularly since it seems less parsimonious than consistent histories? For that matter, the language of Rovelli and Smolin's relational quantum mechanics very nearly turns decoherence into its own interpretation (if you compare papers on decoherence which shirk the metaphysical interpretation to the interpretation put forward by Rovelli, they're almost identical). Relational quantum mechanics requires much less in the way of grand assertions than MWI and is a natural framework for decoherence, so why pick MWI over relational quantum mechanics?

    Hear, hear.
    That sure is far beyond my current educational horizon but I would love to see Eliezer answer that comment. Until now I haven't even heard of Relational Quantum Mechanics. I searched LW and that comment by Dustin2 seems to be one of two comments that mention it.
    5Eliezer Yudkowsky
    As far as I can tell, the only possible coherent state of affairs corresponding to RQM - the only reality in which you can embed these systems relating to each other - is MWI. To this is added some bad amateur incoherent epistemology trying to dance around the issue without addressing it. You can quote me on the following: * RQM is MWI in denial. * Any time you might uncharitably get the impression that RQM is merely playing semantic word-games with the notion of reality, RQM is, in fact, merely playing semantic word-games with the notion of reality. * RQM's epistemology is drunk and needs to go home and sleep it off.

    Some people consider it a good form to back up your accusations with examples, facts and proofs, even when discussing topics dear to their hearts. Give it a try some time.

    6Eliezer Yudkowsky
    Okay. Name a state of affairs that could correspond to RQM without being MWI. PS: Whenever you say that something is 'true relative to' B, please replace it with a state of affairs and a description of B's truth-predicate over possible states of affairs.

    Okay. Name a state of affairs that could correspond to RQM without being MWI.

    First, the onus is on you to show that the above is both relevant to your claim of "bad amateur incoherent epistemology" and that there is no such state of affairs, since it's your claim that RQM is just a word game.

    But, to indulge you, here is one example:

    different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observer at the same time, it may appear to be in a superposition of two or more states.

    Whereas in MWI, unless I misunderstand it, each interaction (after the decoherence has ran its course) irrevocably splits the world into "eigenworlds" of the interaction, and there is no observer for which the world is as yet unsplit:

    n DeWitt's formulation, the state of S after a sequence of measurements is given by a quantum superposition of states, each one corresponding to an alternative measurement history of S.

    P.S. Just to make it clear, I'm not an adherent of RQM, not until and unless it gives new testable predictions not available without it. Same applies to all other interpretations. I'm simply pointing out that MWI is not the only game in town.

    6Eliezer Yudkowsky
    So in MWI, this presumably arises when e.g. you've got 3 possible states of X, and version A of you decoheres with state 1 while version B is entangled with the superposition of 2+3. In RQM this is presumably described sagely as X being definitely-1 relative to A while X is 2+3 relative to B. Then if you ask them whether or not this statement itself is a true, objective state of affairs (where a 'yes' answer immediately yields MWI) there's a bunch of hemming and hawing.
    Ignoring your unhelpful sarcastic derision... You should know better, really. Take an EPR experiment with spatially separated observers A and B. If A measures a state of a singlet and the world is split into Aup and Adown, when does B split in this world, according to MWI? In RQM, it does not until it measures its own half of the singlet, which can be before of after A in a given frame. Its model of A is a superposition until A and B meet up and compare results (another interaction). The outcome depends on whether A actually measured anything and if so, in which basis. None of this is known until A and B interact.
    3Eliezer Yudkowsky
    I confess I'm not quite clear on your question. Local processes proceed locally with invariant states of distant entanglement. Just suppose that the global wavefunction is an objective fact which entails all of RQM's statements via the obvious truth-condition, and there you go.
    Tell me what the basis is, and where it comes from, and I will...
    I confess I'm not quite clear on your answer. Not sure what this means, at least not past "local processes proceed locally", which is certainly uncontroversial, if you mean to say that interaction is limited to light speed. "an objective fact"? As in a map from something to C? If so, what is that something? Some branching multiverse? Or what do you mean by an objective fact? You lost me here, sorry.
    I know I'm late to the party, but I couldn't help but notice that this interesting question hadn't been answered (here, at least). So here it is: as far as I know, B 'splits' immediately, but this in an unphysical question. In MWI we would have observers A and B, who could observe Aup or Adown and Bup or Bdown (and start in |Aunknown> and |Bunknown> before measuring) respectively. If we write |PAup> and |PAdown> for the wavefunctions corresponding to the particle near observer A being in the up resp. down states, and introduce similar notation for the particle near observer B, then the initial configuration is: |Aunkown> |Bunknown> (|PAup> |PBdown> - |PAdown> |PBup>) / \sqrt(2) Now if we let person A measure the particle the complete wavefunction changes to: |Bunknown> (|Aup> |PAup> |PBdown> - |Adown> |PAdown> * |PBup>) / \sqrt(2) Important is that this is a local change to the wavefunction, what happened here is merely that A measured the particle near A. Since observer A is a macroscopic object we would expect the two branches of the wavefunction above (separated by the minus sign) to be quite far apart in configuration space, so the worlds have definitely split here. But B still isn't correlated to any particular branch: from the point of A, person B is now in a superposition. In particular observer B doesn't notice anything from this splitting - as we would expect (splitting being a local process and observers A and B being far apart). This is also why I called the question as to when B splits 'unphysical' above, since it is a property known only locally at A, and in fact the answer to this question wouldn't change any of B's anticipations. This might seem a lot like RQM, and that is because RQM happens to get the answer to this question right. The problem with RQM (at least, the problem I ran into while reading the paper) was that the author claims that measurements are ontologically fundamental, and wavefunctions are only a mathematical tool. This seems
    I've since decided to not argue about what is and isn't in the territory, given how I no longer believe in the territory.
    Denying reality, and denying the reality of the .WF aren't the same thing. Suppose RQM is only doing the latter. Then, you have observers who are observing a consistent objective reality, and mapping it accurately with WFs, then their maps will agree. But that doesn't mean the terrain had all the features of the map. Accuracy is a weaker condition than identity. Consider an analogy with relativity. There is a an objective terrain of objects with locations and momenta, but to represent it an observer must supply a coordinate system which is not part of the territory.
    I am starting to get confused by RQM, I really did not get the impression that this is what was claimed. But suppose it is. To stick with the analogy of relativity, great efforts have been made there to ensure that all important physical formulas are Lorentz-invariant, i.e. do not depend on these artificial coordinate system. In an important sense the system does not depend on your coordinates, although for actual calculations (on a computer or something) such coordinates are needed. So while (General) Relativity indeed satisfies the last line you gave, it also explains exactly how (un)necessary such coordinate systems are, and explains exactly what can be expected to be shown without choosing a coordinate system. Back to RQM. Here this important explanation of which observables are still independent of the observer(/initial frame) and which formulas are universal are painfully absent. It seems that RQM as stated above is more of an anti-prediction - we accept that each observer can accurately describe his experimental outcomes using QM, and different observers agree with eachother because they are looking at the same territory, hence they should get matching maps, and finally we reject the idea that these observer-dependent representations can be combined to one global representation. Again I stuggle to combine this method of thought with the fact that humans themselves are made of atoms. If we assume that wavefunctions are only very useful tools for predicting the outcomes of experiments, but the actual territory is not made of something that would be accurately represented by a wavefunction, I run into two immediate problems: 1) In order to make this belief pay rent I would like to know what sort of thing an accurate description of the universe would look like, according to RQM. In other words, where should we begin searching for maps of a territory containing observers that make accurate maps with QM that cannot be combined to a global map? 2) What experime
    RQM may not end in an I, but it is still an interptetation. What the I in MWI means is that it is an interpretation, not a theory, and therefore neither offers new mathematical apparatus, nor testable predictions. Not exactly, RQM objects to observer independent state. You can have global state, providing it is from the perspective of a Test Observer, and you can presumably stitch multiple maps into such a picture. Or perhaps you mean that if you could write state in a manifestly basis-free way, you would no longer need to insist on an observer? I'm not sure. A lot of people are concerned about the apparent disappearance of the world in RQM. There seems to be a realistic and a non realistic version of RQM. Rovellis version was not realistic, but some have added an ontology of relations. its more of a should not than a cannot. Well, we can't distinguish between MWI and CI, either.
    Just because something is called an 'interpretation' does not mean it doesn't have testable predictions. For example, macroscopic superposition discerns between CI and MWI (although CI keeps changing its definition of 'macroscopic'). I notice that I am getting confused again. Is RQM trying to say that reality via some unknown process the universe produces results to measurements, and we use wavefunctions as something like an interpolation tool to account for those observations, but different observations lead to different inferences and hence to different wavefunctions?
    There is nothing in Copenhagen that forbids macroscopic superposition. The experimental results of macroscopic superposition in SQUIDs are usually calculated in terms of copenhagen (as are almost all experimental results).
    That's mainly because Copenhagen never specified macrsoscopic ...but the idea of an unequivocal "cut" was at the back of a lot of copenhagenists minds, and it has been eaten away by various things over the years.
    So there are obviously a lot of different things you could mean by "Copenhagen" or "in the back of a lot of copenhagenist minds" but the way it's usually used by physicists nowadays is to mean "the Von Neumann axioms" because that is what is in 90+% of the textbooks.
    The von Neumann axioms aren't self interpreting . Physicists are trained to understand things in terms of mathematical formalisms and experimental results, but that falls over when dealing with interpretation. Interpretations canot be settled empirically, by definition,, and formulae are not self interpreting.
    My point was only that nothing in the axioms prevents macroscopic superposition.
    For some values of "wavefunction", you are going to have different observers writing different wavefunctions just because they are using different bases...that's a practical issue that's still true if you believe in, but cannot access, theOne True Basis, like a many worlder.
    By the way, your complaint here... echoed by no less than Jaynes:-
    How are you defining territory here? If the territory is 'reality' the only place where quantum mechanics connects to reality is when it tells us the outcome of measurements. We don't observe the wavefunction directly, we measure observables. I think the challenge of MWI is to make the probabilities a natural result of the theory, and there has been a fair amount of active research trying and failing to do this. RQM side steps this by saying "the observables are the thing, the wavefunction is just a map, not territory."
    To my very limited understanding, most of QM in general is completely unnatural as a theory from a purely mathematical point of view. If that is actually so, what precisely do you mean by "natural result of the theory"?
    Actually most of it is quite natural, QM is the most obvious extension that you get when you try to extend the concept of 'probability' to complex numbers, and there are some suggestions why you would want to do this (I think the most famous/commonly found explanation is that we want 'smooth' operators, for example if turning around is an operator there should also be an operator describing 'half of turning around', and another for '1/3 of turning around' etc., which for mathematical reasons immediately gives you complex numbers (try flipping a sign in two identical steps, this is the same as multiplying by i)). To my best knowledge the question of why we use wavefunctions is a chicken-and-the-egg type question - we want square integrable wavefunctions because those are the solution of Schrodingers equation, we want Schrodingers equation because it is (almost) the most general Hermitian time-evolution operator, time-evolution operators should be Hermitian because that is the only way to preserve unitarity and unitarity should be preserved because then the two-norm of the wavefunction can be interpreted as a probability. We've made a full circle. As for your second question: I think a 'natural part of the theory' is something that Occam doesn't frown upon - i.e. if the theory with the extra part takes a far shorter description than the description of the initial theory plus the description of the extra part. Informally, something is 'a natural result of the theory' if somehow the description for the added result is somehow already partly specified by the theory. Again my apologies for writing such long answers to short questions.
    Thank you, that was certainly insightful. I see now that it is some kind of natural extension of relevant concepts. I have been told however that from a formal point of view a lot of QM (maybe they were talking only about QED) makes no sense whatsoever and the only reason why the theory works is because many of the objects coming up have been redefined so as to make the theory work. I don't really know to what extent this is true, but if so I would still consider it a somewhat unnatural theory.
    See my reply to TheAncientGeek, I think it covers most of my thoughts on this matter. I don't think that your second paragraph captures the difference between RQM and MWI - the probabilities seem to be just as arbitrary in RQM as they are in any other interpretation. RQM gets some points by saying "Of course it's partially arbitrary, they're just maps people made that overfit to reality!", but it then fails to explain exactly which parts are overfitting, or where/if we would expect this process to go wrong.
    What's B? A many-worlds counterpart of A? Another observer enitrely? In rQM, if one observer measures X to be in state 1, no other observer can disagree (How may times do I have to point that out?). But they can be uiniformed as to what state it is -- ie it is superposed for them.
    By definition, interpretations don't give testable predictions. Theories give testable predictions. EDIT: having said that, rQM ontology, where information is in relations, not in relata, predicts a feature of the formalism--that when you combine Hilbert spaces, what you have is a product not a sum. That is important for understanding the advantages of quantum computation.
    Definitions can be wrong. I understand that well-meaning physics professor may have once told you that. However the various quantum mechanics interpretations do in fact pre-suppose different underlying mechanisms, and therefore result in different predictions in obscure corner cases. For example, reversible measurement of quantum phenomenon results in different probabilities on the return path in many-worlds vs the Copenhagen interpretation. (Unfortunately we lack the capability at this time to make fully reversible experimental aparatus at this scale.)
    A real testable difference between QM interpretations is a Nobel-worthy Big Deal. I doubt it will be coming.
    There are real testable differences: That page lists three ways in which MWI differs from the Copenhagen interpretation. One has to two with further constraints that MWI puts on the grand unified theory: namely that gravity must be quantized. If it turns out that gravity is not quantized, that would be strong evidence against the basic MWI explanation. The second has to do with testable predictions which could be made if it turns out that linearity is violated. Linearity is highly verified, but perhaps it does break down at high energies, in which case it could be used to communicate between or simply observe other Everett branches. Finally, there's an actual testable prediction: make a reversible device to measure electron spin. Measure one axis to prepare the electron. Measure an orthogonal axis, then reverse that measurement. Finally measure again on the first axis. You've lost your recording of the 2nd measurement, but in Copenhagen the 1st and 3rd should agree 50% of the time by random chance, because there was an intermediate collapse, whereas in MWI they agree 100% of the time, because the physical process was fully reversed, bringing the branches back into coherence. We just lack the capability to make such a device, unfortunately. But feel free to do so and win that Nobel prize.
    But such device is not physically realizable, as it would involve reversing the thermodynamic arrow of time.
    Indeed. Truly reversing the measurement would involve also forgetting what the result of the measurement was, and Copenhagenists would claim this forgotten intermediate result does not count as a "measurement" in the sense of something that (supposedly) collapses the wave function.
    ? What aspect of measuring an electron's spin is not reversible? Physics at this scale is entirely reversible.
    If you define a measurement as an the creation of a (FAPP) irreversible record....then, no.
    You can reversibly entangle an electron's spin to the state of some other small quantum system, that's not questioned by any interpretation of QM, but unless this entanglement propagates to the point of producing a macroscopic effect, it is not considered a measurement.
    It's even worse than that. Zurek's einselection relies on decoherence to get rid of non-eigenstates, and reversibility is necessarily lost in this (MWI-compatible) model of measurement. There is no size restriction, but the measurement apparatus (including the observer looking at it) must necessarily leak information to the environment to work as a detector. Thus a reversible computation would not be classically detectable.
    Which is why the experiment as described in the link I provided requires an artificial intelligence running on a reversible computing substrate to perform the experiment in order to provide the macroscopic effect.
    That is, it would require inverting the thermodynamic arrow of time.
    Actually, Nobel does not begin to cover it, whether it would be awarded or not (even J.S. Bell didn't get one, though he was nominated the year he died). Showing experimentally that, say, there is an objective collapse mechanism of some sort would probably be the biggest deal since the invention of QM.
    And even just formally applying all the complexity stuff that is alluded to in the sequences, to the question of QM interpretation, would be a rather notable deed.
    Easy: no observer-independent state. No contradictory observations. No basis problem. (Of course that isn't an empirical expectation-predicting difference, and of course there is no reason it should be, since interpretations are not theories).
    "Quantum state is in the territory" versus "state is just model" "Universal quantum state is a coherent notion" versus "universal quantum state cannot be correctly defined" "We need to get a universal basis from somewhere" versus "we don't" Etc, etc.

    That is not a state of affairs, it is a list of questions you aren't trying to answer. I am asking for a concrete description of how the universe could possibly be that would correspond to RQM being true and MWI being false.


    Or here's another way of looking at it:

    MWI = Minkowskian spacetime. Clear objective state of affairs, observer-invariant intervals separating events.

    Single-world QM = Pre-Minkowski mysterious "Lorentz contractions" as a result of moving through the ether. The ether seems mysteriously unobservable and it's really odd that the Lorentz contractions just happen to be exactly right to make motion undetectable, when in principle the ether could be doing anything (just like it's mysterious that the worldeater eats off parts of the wavefunction according to the Born probabilities rather than something else, and only leaves one world behind). Also, since you don't know about the Lorentz transformation for time at this point in the history of physics, your equations will yield the wrong answers for extreme circumstances (just as a large enough quantum computer could contain observers who still wouldn't collapse).

    "Shut up and calculate" = Use Minkowskian spacetime but refuse to admit that your equations might refer to something.

    RQM = Relational Special Relativity = You repeatedly talk about how "motion" can only be defined relative to an observer, and it's imp... (read more)

    Reversing the direction of the analogy, what are the "invariants" of MWI? A natural, emergent multiversal basis? nah. A natural, emergent Born's law? Nah... That's actually a perfectly reasonable argument. rQM is coherent, observers can't make contradictory observations. It just isn't objective. It also isn't anything-goes philosophical subjectivism. It is an interpretation that agrees with all the results of the formalism, like any interpretation properly so called, so it does not break anything or make anything unscientific.
    Any interpretation could be called semantic word game, since the whole point is to interpret a mathematical formalism. To do that you have to use words (shock!) and discuss what things might really mean (horror!).
    Why is there so much effort spent on philosophical interpretations of QM, when there probably will be more fundamental levels of description such as string theory? Is it to be expected that the least complex interpretation of QM will also apply to the one-day victorious string theory model?

    It would be unlikely for any more fundamental theory not to be subject to the same set of evasions as QM. Roughly, we have people claiming that atoms are just theoretical figments of the imagination which merely yield good predictions, discovering neutrons isn't going to change their arguments. String theory in particular doesn't help.

    I once asked a QM person (who shall remain nameless) why people argue about interpretations despite their untestability, and (s)he conjectured that what they are really arguing about is ramifications of these interpretations for "hard problems" (e.g. consciousness) which was an answer that surprised me.
    It is written: a physicist does not live on instrumentalism alone.
    The way that we currently build theories in physics is to write down a classical theory, and then 'quantize it' (which involves replacing classical numbers with operators and enforcing some non-commutation. Or it involves promoting the idea that the action is extremized with a path integral over the action). String theory is no exception, you typically start with a classical string-action. Because of this, most of the underlying structure of quantum mechanics comes along for the ride. Unfortunately, this usually leads to formal problems (no one has yet developed a satisfying axiomatic quantum field theory, and the situation in string theory is even worse), but physicists ignore these issues, because such theories, while not formally developed, make the right predictions.
    There's no form of decoherence which is equivalent to ontological collapse, to actually snipping off branches. (Penrose has a nice discussion of this somewhere). So decoherence as an interpretation can't be saying anything different to what MWI says as an interpetation.. Decoeherence just gives an criterion --albeit a fuzzy and subjective one -- for world-formation.
    If you take decoherence realistically, you get something like MWI. CH is different because, like, CI, it is less realistic.

    Bravo, Eliezer, bravo. Have you sold the screen rights yet?

    Inspired by this post, I was reading some of the history today, and I learned something that surprised me: in all of his writings, Bohr apparently never once talked about the "collapse of the wavefunction," or the disappearance of all but one measurement outcome, or any similar formulation. Indeed, Huve Erett's theory would have struck the historical Bohr as complete nonsense, since Bohr didn't believe that wavefunctions were real in the first place -- there was nothing to collapse!

    So it might be that MWI proponents (and Bohmians, for that matter) underestimate just how non-realist Bohr really was. They ask themselves: "what would the world have to be like if Copenhagenism were true?" -- and the answer they come up with involves wavefunction collapse, which strikes them as absurd, so then that's what they criticize. But the whole point of Bohr's philosophy was that you don't even ask such questions. (Needless to say, this is not a ringing endorsement of his philosophy.)

    Incidentally, I'm skeptical of the idea that MWI never even occurred to Bohr, Heisenberg, Schrödinger, or von Neumann. I conjecture that something like it must have occurred to them, as an obvious reductio ad absurdum -- further underscoring (in their minds) why one shouldn't regard the wavefunction as "real". Does anyone have any historical evidence either way?

    Yes, the real CI is rather minimal and non-commital. That, not idiocy, explains its widespread adoption. Objective Reduction is a different and alter theory.

    I think you're being a bit hard on Schrödinger here. I thought the whole point of Schrödinger's cat was to point out that the "observers cause collapse" idea was kind of stupid.

    The "One Christers" are a nice SF touch.


    Nice one Eli, I haven't been able to read OB for about a month, and whith your breakneck pace it was tough to catch up, but this has been good. I enjoyed this post in particular!


    First, W Bush was just 11 in 1957. However, that does make me wonder over what fraction of the many-worlds he ended up being an idiotic asshole -- much less President now... And, wow, imagine the possible alternate world where he was a good President!

    Second, though I generally liked your post, I feel it was a bit disingenuous to not mention the hidden variable hypothesis in regard to the Copenhagen interpretation. Early 20th century physicists weren't thinking collapse was an extraordinary violation of know physics -- they thought it was a temporarily opaq... (read more)


    What the hell are the Born statistics?

    Jeeves: whaaaa?

    Smedly: the Born rule... the whole probability of what you seem to experience observing is proportional to the squared magnitude thing. ie, if you had a two state system, say a qbit, in a superposition of, say, 2/3|0> + sqrt(5)i/3*|1>, then if you take a measurement of a bunch of qbits that are independantly in that state, then you'd expect about 4/9 of them to be 0, and 5/9 of them to be 1.

    Given that QM is linear, you can see why the existance of such a rule may be a bit confusing. And given the many worlds perspective, the question o... (read more)

    Seems hard to even phrase the rule without invoking consciousness.

    Not really; anticipation seems easy enough to define without consciousness.

    Nick: anticipation of... what? Don't misunderstand, I'm not saying "oooh, Born probabilities transcend understanding" sort of thing, I just mean that I'm unsure how, in the context of many worlds, to state it. Robin's Mangled Worlds idea, if it pans out, would certainly help, but until then, I'm stumped about how to really say it in any way other than "anticipation of experience"

    Anticipation of input, which at least doesn't seem like it immediately implies conscious experience - does a minimalist Bayesian decision system feel anything?

    Nick: But... what do you mean? ie, if you have some sort of decoherence event so that one can meaningfully distinguish between world with input A occuring and world with input B occuring...

    What are we anticipating? ie, both input A occurs and input B occurs.

    If they have different amplitudes, so we square the magnitudes to figure out the anticipation... anticipation of... what? ie, both outcomes occur.

    Yet in some sense they well be "weighted" differently. What do we mean by that other than "how much do we anticipate experiencing one or the ot... (read more)

    "Anticipation of input" is the same as "anticipation of experience", but without any reference to consciousness - a non-conscious Bayesian decision system should also derive the squared-modulus law, and "anticipate" (in an qualia-free way) future "observations" (again qualia-free) to follow it. (Shouldn't it?) IMO, this is actually more confusing.

    Nick: presumably in same way it would... but I don't really see how. Remember, this is indexical uncertainty. It doesn't correspond to uncertainty about what actually happened so much as uncertainty about which branch of reality this version of you is in.

    So... There's a version of you in A, and a version of you in B.

    In A, all the computations that happen are more or less analogous to those in B, except that B uses slightly larger numbers to represent the computations...

    So exactly why would that change any anticipation of anything? I'd be unsure what a nonc... (read more)

    Meanwhile, imagine yet another alternate Earth, where the very first physicists to notice nonlocality, said, "Holy brachiating orangutans, there's a non-local force in Nature!"

    In the years since, the theory has been successfully extended to encompass every observed phenomenon. The biggest mystery in physics is the relationship between nonlocality and relativity. The basic equations have a preferred reference frame, but it's undetectable. Everyone thinks that there must be a relativistic way to write the equations, but no-one knows how to do it.

    On... (read more)

    In bohmian mechanics, the particles are purely epiphenomenal. Everything is indeed contained in the pilot wave. (If this weren't true, it would not be a mere interpretation -- it would have different predictions.)

    I'm a chemist; we actually have to use quantum physics on a routine basis. The main reason many-worlds never got traction is that it doesn't make a testable prediction. Most physicists realize that making a model of reality that predicts experiment (as far as possible) is, well, science; BSing about what the implications are is more of a late night and beer thing.

    In other words, if the model implies that there may be other worlds, but they can't conceivably be detected, then who cares?

    One last thing: there's some pretty good evidence of nonlocal physics ... (read more)

    If resources (including mental ones) are being spent fighting for a less plausible theory, isn't that enough?
    What are you referring to? The kind of non-locality exhibited in the EPR paradox is consistent with special relativity - or at least there's an elegant way of looking at this in which it is consistent. So are you talking about something totally different? Something incompatible with GR but not SR? Or both?

    The main reason many-worlds never got traction is that it doesn't make a testable prediction.

    I am not sure that it is possible to interpret this sentence without admitting to what amounts to Eliezer's position. In other words, for this to be either right or wrong, Eliezer has to be right.

    This sentence is most plausibly unpacked as assuming that the Copenhagen Interpretation and MWI are consistent with all findings, and that pride of place is naturally given to the first interpretation that makes predictions no other interpretation has. Science may not be wrong to, in general and as a heuristic, only accept new theories that make better predictions than the old. After all, even creationism or magic faerieism can be molded to be consistent with all known observations, whatever they are.

    Eliezer simply asserts that MWI is simpler. He appeals to the Occam's razor heuristic, not the "new testable predictions" one, as reason for the reader to accept MWI. (If you caught it, MWI is making a prediction - that no quantum superposition will be too small to cause a result interpreted as a collapse under CI - but that's relatively small potatoes, since MWI is succeeding where CI is... (read more)

    Great work.
    It sounds like you are mocking the post, not expressing genuine amusement. I imagine that wasn't your actual intent, though; judging tone over the internet is notoriously difficult. Your comment follows the same format as other mocking posts, so I'd avoid it - i.e. starting off with "haha", "scream with laughter", it comes off as sarcasm.
    0David Althaus
    In addition to that, my comment was badly written and not really insightful.

    Hilarious and 100% true! Thank you! The only thing I might add to this is that in Huve's theory, information is created out of nowhere.

    Eliezer, don't you have a whole post about why you shouldn't use examples from politics if you can possibly avoid it?


    This is a very nice essay attacking the Copenhagen interpretation, and other objective collapse models. But I think that the way it is written seems to imply that if I don't believe in objective collapse, that the only alternative is to believe the equally insane idea that I live in a world that is constantly locally branching into millions of alternative worlds, only one of which is, even in principle, observable to me.

    There are many alternatives. I think Qubism is a mix of a genuine solution, and a  kind of a slight-of-hand that hides the problem. M... (read more)

    Why is it called Many-Worlds? AIUI (which may be completely wrong, as I know nothing of quantum mechanics) there is a single, deterministically evolving wave function. No splitting. The puzzle is why no-one ever perceives a system to be in a superposition. Suppose that a particle is flying towards a pair of detectors, in a superposition of states that will trigger one of them or the other. I will only perceive one of the detectors firing, never a superposition of both of them firing. From the point of view of the universal wave function, I am in a superpos... (read more)

    Many worlders are pointing at something in the physics and saying "that's a world"... but whether it qualifies as a world is a separate question , and a separate kind of question, from whether it is really there in the physics. A successful MWI needs to jump both hurdles. The issue is not whether superpositions exist, but whether they qualify as worlds.. it's a conceptual issue. There is an approach to MWI based on coherent superpositions, and a version based on decoherence. These are incompatible opposites, but are treated as interchangeable in Yudkowsky's writings. Deutsch uses the coherence based approach, while most other many worlders use the decoherence based approach. He absolutely does establish that quantum computing is superior to classical computing, and therefore that underlying reality is not classical. But showing that reality is not a single classical world is not the same as showing that it consists of a number of quasi classical worlds in superposition. Superposed states lack a number of features that one would typically associate with a world: objectivity, size, causal isolation, and permanence. Decoherence has the opposite problem: decoherent worlds can be large, can be objective, can be permanent for all practical, purposes, are causally isolated by definition. But there is no obvious mechanism for decoherence within core QM. A coherent quantum state that evolves according to the Schrodinger wave equation remains coherent. Some additional mechanism for decoherence is required, and the complexity of the that mechanism must be factored into an assessment of which theory is simplest. (Why assume a coherent starting state? Well, maybe the universe started in a decohered state.. that's actually a popular suggestion ... but it requires its own explanation and adds own complexities).
    They're not opposites, they're two different ways of analyzing the same situation. Examining the local density matrices at various places, we may find decoherence has occurred, even while the global state is in a coherent superposition.
    Local decoherence with global coherence is hardly many worlds. Global decoherence with local coherence would be a much better fit.
    Many minds is a thing ...But appealing to special properties of of observers is one of the main things many worlders are trying to getaway from them.

    Macroscopic decoherence, a.k.a. many-worlds, was first proposed in a 1957 paper by Hugh Everett III

    No, he didn't call it "many worlds", and he didn't base it on decoherence.

    About a few of the violations of the collapse postulate: this wouldn't be the only phenomenon with a preferred reference frame of simultaneity - the CMB also has that. Maybe a little less fundamental, but nonetheless a seemingly general property of our universe. This next part I'm less sure about, but locality implies that Nature also has a preferred basis for wavefunctions, i.e. the position basis (as opposed to, say, momentum). Acausal - since nothing here states that the future affects the past, I assume it's a rehash of the special relativity violation... (read more)