Sean Carroll’s new (available in stores early September) book, Something Deeply Hidden, is a quite good introduction to issues in the understanding of quantum mechanics, unfortunately wrapped in a book cover and promotional campaign of utter nonsense. Most people won’t read much beyond the front flap, where they’ll be told:

Most physicists haven’t even recognized the uncomfortable truth: physics has been in crisis since 1927. Quantum mechanics has always had obvious gaps—which have come to be simply ignored. Science popularizers keep telling us how weird it is, how impossible it is to understand. Academics discourage students from working on the “dead end” of quantum foundations. Putting his professional reputation on the line with this audacious yet entirely reasonable book, Carroll says that the crisis can now come to an end. We just have to accept that there is more than one of us in the universe. There are many, many Sean Carrolls. Many of every one of us.

This kind of ridiculous multi-worlds woo is by now rather tired, you can find variants of it in a host of other popular books written over the past 25 years. The great thing about Carroll’s book though is that (at least if you buy the hardback) you can tear off the dust jacket, throw it away, and unlike earlier such books, you’ll be left with something well-written, and if not “entirely reasonable”, at least mostly reasonable.

Carroll gives an unusually lucid explanation of what the standard quantum formalism says, making clear the ways in which it gives a coherent picture of the world, but one quite a bit different than that of classical mechanics. Instead of the usual long discussions of alternatives to QM such as Bohmian mechanics or dynamical collapse, he deals with these expeditiously in a short chapter that appropriately explains the problems with such alternatives. The usual multiverse mania that has overrun particle theory (the cosmological multiverse) is relegated to a short footnote (page 122) which just explains that that is a different topic. String theory gets about half a page (discussed with loop quantum gravity on pages 274-5). While the outrageously untrue statement is made that string theory “makes finite predictions for all physical quantities”, there’s also the unusually reasonable “While string theory has been somewhat successful in dealing with the technical problems of quantum gravity, it hasn’t shed much light on the conceptual problems.” AdS/CFT gets a page or so (pages 303-4), with half of it devoted to explaining that its features are specific to AdS space, about which “Alas, it’s not the real world.” He has this characterization of the situation:

There’s an old joke about the drunk who is looking under a lamppost for his lost keys. When someone asks if he’s sure he lost them there, he replies, “Oh no, I lost them somewhere else, but the light is much better over here.” In the quantum-gravity game, AdS/CFT is the world’s brightest lamppost.

I found Carroll’s clear explanations especially useful on topics where I disagree with him, since reading him clarified for me several different issues. I wrote recently here about one of them. I’ve always been confused about whether I fall in the “Copenhagen/standard textbook interpretation” camp or “Everett” camp, and reading this book got me to better understanding the difference between the two, which I now think to a large degree comes down to what one thinks about the problem of emergence of classical from quantum. Is this a problem that is hopelessly hard or not? Since it seems very hard to me, but I do see that limited progress has been made, I’m sympathetic to both sides of that question. Carroll does at times too much stray into the unfortunate territory of for instance Adam Becker’s recent book, which tried to make a morality play out of this difference, with Everett and his followers fighting a revolutionary battle against the anti-progress conservatives Bohr and Heisenberg. But in general he’s much less tendentious than Becker, making his discussion much more useful.

The biggest problem I have with the book is the part referenced by the unfortunate material on the front flap. I’ve never understood why those favoring so-called “Multiple Worlds” start with what seems to me like a perfectly reasonable project, saying they’re trying to describe measurement and classical emergence from quantum purely using the bare quantum formalism (states + equation of motion), but then usually start talking about splitting of universes. Deciding that multiple worlds are “real” never seemed to me to be necessary (and I think I’m not the only one who feels this way, evidently Zurek also objects to this). Carroll in various places argues for a multiple world ontology, but never gives a convincing argument. He finally ends up with this explanation (page 234-5):

The truth is, nothing forces us to think of the wave function as describing multiple worlds, even after decoherence has occurred. We could just talk about the entire wave function as a whole. It’s just really helpful to split it up into worlds… characterizing the quantum state in terms of multiple worlds isn’t necessary – it just gives us an enormously useful handle on an incredibly complex situation… it is enormously convenient and helpful to do so, and we’re allowed to take advantage of this convenience because the individual worlds don’t interact with one another.

My problem here is that the whole splitting thing seems to me to lead to all sorts of trouble (how does the splitting occur? what counts as a separate world? what characterizes separate worlds?), so if I’m told I don’t need to invoke multiple worlds, why do so? According to Carroll, they’re “enormously convenient”, but for what (other than for papering over rather than solving a hard problem)?

In general I’d rather avoid discussions of what’s “real” and what isn’t (e.g. see here) but, if one is going to use the term, I am happy to agree with Carroll’s “physicalist” argument that our best description of physical reality is as “real” as it gets, so the quantum state is preeminently “real”. The problem with declaring “multiple worlds” to be “real” is that you’re now using the word to mean something completely different (one of these worlds is the emergent classical “reality” our brains are creating out of our sense experience). And since the problem here (classical emergence being just part of it) is that you don’t understand the relation of these two very different things, any argument about whether another “world” besides ours is “real” or not seems to me hopelessly muddled.

Finally, the last section of the book deals with attempts by Carroll to get “space from Hilbert space”, see here, which the cover flap refers to as “His [Carroll’s] reconciling of quantum mechanics with Einstein’s theory of relativity changes, well, everything.” The material in the book itself is much more reasonable, with the highly speculative nature of such ideas emphasized. Since Carroll is such a clear writer, reading these chapters helped me understand what he’s trying to do and what tools he is using. From everything I know about the deep structure of geometry and quantum theory, his project seems to me highly unlikely to give us the needed insight into the relation of these two subjects, but no reason he shouldn’t try. On the other hand, he should ask his publisher to pulp the dust jackets…

**Update**: Carroll today on Twitter has the following argument from his book for “Many Worlds”:

Once you admit that an electron can be in a superposition of different locations, it follows that person can be in a superposition of having seen the electron in different locations, and indeed that reality as a whole can be in a superposition, and it becomes natural to treat every term in that superposition as a separate “world”.

“Becomes natural” isn’t much of an argument (faced with a problem, there are “natural” things to do which are just wrong and don’t solve the problem). To me, saying one is going to “treat every term in that superposition as a separate “world”” may be natural to you, but it doesn’t actually solve any problem, instead creating a host of new ones.

**Update**: Some places to read more about these issues.

The book Many Worlds?: Everett, Quantum Theory and Reality gathers various essays, including

Simon Saunders, Introduction

David Wallace, Decoherence and Ontology

Adrian Kent, One World Versus Many

David Wallace’s book, The Emergent Multiverse.

Blog postings from Jess Riedel here and here.

This from Wojciech Zurek, especially the last section, including parts quoted here.

The thing that’s most bothersome to me about the measurement problem is whether, when I perform a Stern-Gerlach-like measurement that could produce one of two results, there is

anything at allabout the initial state of the universe that determines which result I see. Questions about whether there “really are many worlds out there” seem like they’re sort of missing the point; both Everett and Copenhagen seem like different ways of saying “no” to this question, which is what many people (including me) find unsettling regardless of any questions about ontology.This leads to something that’s confused me for a long time. It’s always seemed quite clear to me that the answer to the above question has to be “no” if (i) there is a universal wavefunction that (ii) gives a complete description of the state of the universe and (iii) evolves according to the Schrodinger equation. Some of the conversation around the “emergence of the classical from the quantum” sometimes sounds like it’s suggesting that (i-iii) are all true but somehow there ought to be some way to extract a single measurement result from it. Isn’t such a project obviously doomed?

jxd,

I share your confusion, and have never understood how invoking many worlds is supposed to answer this.

A while ago I wrote something asking a similar question here,

http://www.math.columbia.edu/~woit/wordpress/?p=10533

and learned a lot from the discussion. I’m still struck by the fact that, if you include environment + measurement apparatus, you are from the beginning dealing with mixed states and probability.

But I’d rather not start up again exactly that old discussion, unless someone really has something new to add. I’d be much more interested in hearing or getting references to a more compelling argument for many worlds than the one Carroll provides.

Are you actually talking about the cover of this book or the dust jacket? Tearing off the cover of a book seems pretty drastic, and makes the book a lot harder to hold, read, and shelve.

Peter, you seem to accept the universal wave function as a description of the “real” state of the universe. Or at least you seem to accept it as plausible. Is that correct? Then I am again confused because I don’t see the difference with the MWI, of which you are much more critical.

Could you clarify the difference between these two positions?

Also, from what I understand there is not a precise moment in MWI when a splitting “occurs.” One can “split” a universal state vectors as the sum of 2 two (or more) vectors by choosing a basis. The 2 vectors can be viewed as the state of 2 parallel universes,

and by linearity they will evolve independently. Is the issue why or how one basis is better than another to do this decomposition?

Hi Peter

Thanks for your thoughts on Sean Carroll’s book. I will get it when it is available; I enjoy SC’s podcast and his other writings…

One question and one suggestion –

Question – does the book contain lots of equations and mathematics? I ask because if not I will buy it on Kindle, and if so I won’t. I really think that publishers should state this: it is outrageous that people sell mathematical books on Kindle (frequently expensively) which are in my experience essentially unusable as mathematical text does not display legibly. (emailing PDFs to Kindle works fine if you don’t mind small fonts.)

Suggestion – when you say that you are interested in references to places that that you can go to see the strongest argument for MWI – have you read The Emergent Multiverse by David Wallace? If not then that is your answer. Do not be put off by somewhat naff title; this is the most serious and sustained presentation out there, and also has a large bibliography. I’m very interested in your take. The issue that you and jxd are discussing seems to be a variant of the concern about where the probabilities come from, which is regarded as the big challenge with MWI. Wallace and the other ‘Oxford’ school’ MWI people have a decision-theoretic argument which purports to address this. I have philosophical doubts about this argument but frankly, as someone who did physics only to UK GCSE and Maths to A-level and has recreationally self-studied beyond that I feel it is appropriate to be somewhat humble in my assessment of the arguments of trained professionals!

Peter,

I’m afraid you misunderstood Carroll’s explanation on pages 234-5. He is saying that the alternative to having multiple worlds is needing to deal with the whole universal wavefunction. That doesn’t give you a simple single-world ontology as one would want, but a hideously complex object that is nothing like a classical ontology. The most classical single-worldy ontology we can have (ironically enough) is precisely the one where we split the universal wavefunction into worlds.

The issue here is that the fundamental ontology is the universal wavefunction, the worlds are a subjectively-defined emergent ontology that we use to connect physics to our everyday experience.

An analogy would be to think of the universal wavefunction as a tree, and the worlds as the branches. Nothing forces us to think of the tree as being composed of branches, and in fact they are only an emergent ontology. They are not well-defined either, we can’t really say where one branch begins and another ends. In fact there is only a tree made up of cells. It’s just that it’s very useful to talk about the branches, so we do that.

(Yes, trees are also only emergent ontology, I hope the idea comes through anyway).

What does the multiverse mean in the “it from qubit” picture? If states+entanglement is everything (including the detector and the system being detected), and space and time are just how we experience this entanglement (spacetime “emerges” from entanglement); then what sense does it make to create other instances of spacetime?

If the Everettian argument is valid, one solid consequence is that the initial one-World postulate for the argument is unphysical, since we have already been cohabiting with a vast number of mutually decoherent Worlds. When the initial postulate of the Everettian argument is replaced with the vast number of mutually decoherent Worlds, contingent interferences with each of decoherent Worlds may as a whole become significant, and I suspect decoherence only slightly outperforms recoherence. (Or, is there any convincing argument over the everlasting predominance of decoherence?) If so, wavefunction collapse-like phenomena will frequently occur by the recoherence effect.

When we encounter an apparent wavefunction collapse, Everettians say it’s caused by world-branching, but it should be explained either by branching or merging of a world, and there is no way to decide which really occurred…

Edward Measure,

Thanks! When I wrote that I knew “cover” wasn’t the word I wanted, planned to go back to fix, forgot. Now done.

Dear Peter,

Are you going to review also the recent book by Smolin “Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum”?

I shall say that I much prefer what Jürg Fröhlich and colleagues are doing recently on quantum foundations (eg, https://arxiv.org/abs/1905.06603 ) rather than the Everettian approached favored mainly by cosmologists by considering that, instead of having a unique outcome from an experiment, all are realized (but only one in our Universe)…

Pascal,

1. I’m willing to consider the wavefunction of the universe, and use the word “real” to describe it (let’s call this “real-psi”). I do worry though that maybe it makes no sense to consider it to be a pure state, that it is always a mixed state.

2. In principle, one expects to somehow identify an emergent classical world corresponding to what we observe in this wavefunction. This is “real” in a different sense (the every day sense), let’s call it “real-classical”.

MWI enthusiasts make what to me seems to be the following argument. One expects that if there is one emergent classical world in the wave-function, there will be lots. Since I’ve agreed that the one we’re in is “real-classical”, and the other emergent classical worlds are part of the same “real-psi” wave function, they must also be “real-classical”. I don’t see how this follows. To be fair to Carroll, he doesn’t exactly say this. As quoted in the posting, he’s aware that these are two different versions of “real”, so you can’t argue that one implies the other. So, I’m not “forced” by logic to agree to the “reality” of these supposed other worlds, and I don’t see how agreeing to this solves any problem or does anything other than confuse the situation.

The problem with the “split” picture you give is that it doesn’t address at all the real problem of classical emergence. The best worked out theory of classical emergence that I’m aware of is Zurek’s, and as far as I can tell he also rejects 2 above while agreeing to 1 (he describes himself as an “Everettian”, see no need to describe other possible emergent classical worlds as real).

Rollo Burgess,

No equations in the book.

Yes, I’ve tried reading the Wallace book, it is the most comprehensive and serious attempt at justifying the MWI picture. I didn’t find anything convincing there on why multiple worlds must be described as “real”, but was willing to believe there was a solid argument somewhere amidst the masses of material about probability and decision theory. One reason I like Carroll’s book is that he writes and argues clearly, so you can easily follow the argument, see what he has and whether you agree or see a reason to disagree. It’s in principle possible that Wallace has a convincing argument that Carroll just decided not to present, but one wonders whether that’s really plausible.

One thing I didn’t get around to doing was adding links to the best sources I’m aware of for serious discussions of these issues, will try to do that soon.

Mateus Araujo,

I do understand that that’s the point Carroll was trying to make, and shouldn’t have been so flippant about “convenience”. My point was just that, as you and Carroll both recognize, when you move from the universal wave function to supposed emergent classical worlds, you’re discussing a very different sorts of ontology. Especially since I don’t see any convincing theory of these “branches”, I don’t see why I have to use them to build my emergent ontology.

Amitabh Lath,

I think what Carroll is doing is basically announcing that, in a fixed space-time, the problem of classical emergence is solved by MWI (except for an ongoing mopping up operation), and he’s moving ahead to also get the space-time geometry as emergent out of a pure quantum system.

The first problem for me is that I don’t think the original problem is solved. And that’s a problem where you know exactly what the quantum system is (conventional textbook Schrodinger equation). But, much more seriously, I think the emergent space-time program suffers from the problem of “emergence from what?”. Basically people doing string theory unification have given up, now are announcing that they will stop thinking about what the underlying theory is, and will derive our world as emergent from some unknown quantum theory (“it from unknown qu-something”). I don’t see how they’re going to get something from nothing here…

Stephane,

I don’t think I’ll write a review of the Smolin book, don’t really have anything interesting to say about it. As I’ve mentioned many times, I’m just not convinced by the point of view of Smolin and many others that what we don’t understand about QM indicates the need for fundamental new physics. In the case of the Carroll book, I share his basic starting point (that what we know about the world should follow, emergently, from the known QM formalism).

About the “ETH-Approach to Quantum Mechanics”, that just seems to me to be one of many sorts of programs which don’t address the basic problem, that of understanding classical emergence.

Peter,

I wouldn’t use the word “moving”. The fundamental ontology stays the same, it’s always the universal wavefunction.

But I’m very confused. Are you saying that you accept the universal wavefunction as fundamental ontology, but that you think that this is somehow compatible with a single-world emergent ontology? How? How can you even single out one of the branches as “real”? They are the same, physically speaking. Or are you saying that the universal wavefunction doesn’t have a branching structure? As far as I’m aware this point is not controversial – that decoherence splits the wavefunction into quasi-classical worlds that have effectively independent time evolution – and that people that reject Many-Worlds they also reject the universal wavefunction.

Steven Giddings had a criticism a little while ago of the “spacetime from entanglement” business which sounds about right to me. Basically, in order to define the kind of quantity that program wishes to build spacetime out of, you first have to introduce a structure very like what you’re trying to explain.

(arXiv:1803.04973)

Mateus Araujo,

Part of the problem here is that I don’t believe anyone understands how emergence really works, so what the “branches” are, or what it even means to identify one branch as our own. I’d be much more willing to believe there could be a sensible argument for relative “emergent reality” of our branch and other branches if I felt I knew what the two different things actually were. I still don’t see why accepting “reality-psi” of the wavefunction means I have to accept “reality-classical” of supposed branches that don’t have anything to do with our “reality-classical”.

I’ve found the place where Zurek, discusses this, see the last section of

https://arxiv.org/abs/0707.2832

which starts off

“There are two key ideas in Everett’s writings. The first one is to let quantum theory dictate its own interpretation. We took this “let quantum be quantum” point very seriously. The second message (that often dominates in popular accounts) is the Many Worlds mythology. In contrast “let quantum be quantum” it is less clear what it means, so – in the opinion of this author – there is less reason to take it at face value.”

and in “Closing remarks” there is

“It is therefore not clear whether one is forced to attribute “reality” to all of the branches of the universal state vector. Indeed, such view combines a very quantum idea of a state in the Hilbert space with a very classical literal ontic interpretation of that concept. These two views of the state are incompatible. As we have emphasized, unknown quantum state cannot be found out. It can acquire objective existence only by “advertising itself” in the environment. This is obviously impossible for universal state vector – the Universe has no environment.”

jxd:

If we could predict the measurement results we would get if we measured one element of an EPR pair, we would probably be able to transmit information faster than light (although this may depend on the exact model we’re using on for how to predict these results).

Of course, this doesn’t mean that the measurement results aren’t predictable from aspects of the universe that are hidden somewhere that we can’t get at. In fact, I think Bohm’s pilot wave interpretation (which unfortunately has other problems) has this property.

Peter,

“I still don’t see why accepting “reality-psi” of the wavefunction means I have to accept “reality-classical” of supposed branches that don’t have anything to do with our “reality-classical”.”

Because there’s nothing singling out any particular branch as physical, so it’s not tenable to accept the branching picture but deny the reality of the “other” branches. Even if you define your current branch as the real one, it will split over and over again, with nothing distinguishing the future branches physically.

Incidentally, the Bohmians do have a single-world reality and a universal wavefunction, precisely by postulating these Bohmian particles that give reality to one branch of the wavefunction but not others. This is what it takes.

“Part of the problem here is that I don’t believe anyone understands how emergence really works, so what the “branches” are, or what it even means to identify one branch as our own. I’d be much more willing to believe there could be a sensible argument for relative “emergent reality” of our branch and other branches if I felt I knew what the two different things actually were.”

I’m not sure what your question is. The splitting part is the old story of decoherence, pointer states, quantum Darwinism. The “emergent” part is the arbitrary decision of when two branches have decohered enough so that their future evolution can be treated independently, and one can use the projection postulate to safely cut of other branches and focus on one’s own.

I’ve always thought of the problem with trying to extract a single classical world from an Everettian picture as one of symmetry more than anything else. If the wavefunction of the universe can be written as a sum of two terms that don’t interfere with each other and each term describes one of the two possible measurement results, you can’t pick out one of them as “the one that really happened” without introducing some extra structure to this whole picture; there’s nothing that could make one of them more “special” than the other. (And not introducing any extra structure is the whole point of the Everettian program!) The many-worlds move is to just accept this state of affairs and say, fine, then they both “really happened.” This is the strange bit; whether you want to use the word “world” to describe them doesn’t really matter.

Peter Shor: Yes, I think I agree, and that that’s what I was getting at. The question I posed — whether there’s anything about the initial state of the universe that determines which measurement result I get — is definitely an interpretation-dependent one. Everett and Copenhagen say no, Bohm (to the extent that it works) says yes.

The reason I’m confused is that some authors seem to want to extract a “yes” from unitary, collapse-free quantum mechanics with a universal wavefunction as the ultimate ontological description of reality, which seems obviously impossible to me. It would be lovely if this could happen, but as Mateus Araújo says I think it’s pretty uncontroversial that it can’t. This leaves you with either answering “no” to the above question or dropping one of the assumptions that got you there.

Mateus Araujo,

I’m just not convinced that the cartoon structure of the quantum state space as divided into “branches”, with us just characterized by a position on a branch actually captures what is going on. Part of this is skepticism that the picture of pointer states and quantum Darwinism is a complete understood answer to the classical emergence problem, neatly characterized by branches.

But also I have trouble with the idea that we’re just a point on a branch. Remember that I find myself somewhere in between Copenhagen/textbook and Everett and note that Zurek claims (in the article linked to above) “One might regard states as purely epistemic (as did Bohr) or attribute to them “existence”. Technical results described above suggest that the truth lies somewhere between these two extremes.”

It is a basic fact about the state of the world as we see it that we can’t characterize it as a pure state. As far as we can ever know, our world is at best some mixed state about which we have inherently limited information. Even in a purely classical world, I would be free to, given my limited information, decide to count as real worlds all trajectories consistent with that information, but that’s not necessarily a good idea. The quantum situation is different, with limitations of information ones of principle, but still.

What would a mixed state for the universe mean? A universal wavefunction would describe a pure state. We could have a proper mixture instead but that is usually understood to reflect our “classical” ignorance about the true quantum state (like in the case of an ensemble of systems where we only have statistical knowledge of their individual states); it is not really a fundamental property of the system.

I am on the same page as Mateus and (I think) jxd. But I have a small quibble with one sentence in the comment by jxd:

“If the wavefunction of the universe can be written as a sum of two terms that don’t interfere…”

By linearity of evolution, if you write the universal state vector Psi as Psi_1+Psi_2

the we have U(Psi) = U(Psi_1) + U(Psi_2), i.e., the 2 universes evolve “independently”

for *any* choice of the decomposition Psi = Psi_1+Psi_2. This means that “non inteference” is not a useful criterion to decide on which way to split Psi.

I think non-interference is a notion which makes sense only in the setting of

QM+projection postulate and not in purely linear QM.

Peter,

“It is a basic fact about the state of the world as we see it that we can’t characterize it as a pure state. As far as we can ever know, our world is at best some mixed state about which we have inherently limited information. Even in a purely classical world, I would be free to, given my limited information, decide to count as real worlds all trajectories consistent with that information, but that’s not necessarily a good idea. The quantum situation is different, with limitations of information ones of principle, but still.”

You are making the usual map-territory confusion. A mixed state is a description of your ignorance, not of what the world is. All our fundamental theories are formulated in terms of pure states; mixed states are introduced as derived concept, either to describe the statistics from local measurements on an entangled state, or to make probabilistic assignments of (pure) states to a not fully known system. The world itself is in a pure state, our ignorance of it doesn’t make a difference.

“But also I have trouble with the idea that we’re just a point on a branch. Remember that I find myself somewhere in between Copenhagen/textbook and Everett and note that Zurek claims (in the article linked to above) “One might regard states as purely epistemic (as did Bohr) or attribute to them “existence”. Technical results described above suggest that the truth lies somewhere between these two extremes.””

Żurek’s statement makes no sense. Quantum states are either ontic or epistemic, the is no middle ground where to compromise. And the epistemicist program has taken quite a beating throughout history, I might add.

“I’m just not convinced that the cartoon structure of the quantum state space as divided into “branches”, with us just characterized by a position on a branch actually captures what is going on. Part of this is skepticism that the picture of pointer states and quantum Darwinism is a complete understood answer to the classical emergence problem, neatly characterized by branches.”

Well, that’s just the best we got. Sure, as all theories it is limited and subject to change, but until we find something better that’s what I’m going with.

Glitch notification: There’s an extraneous “~woit/wordpress/?p=11128#comments” just after the second blockquote.

Carlos Ungil,

Sorry, I think my reference to a “mixed state” and universal wave function in that response to Pascal was confused, best to ignore that.

Blake Stacey,

Thanks, fixed.

Mateus Araujo,

Thanks! Right now, while I have learned a lot, all of this is causing my brain to hurt, and I have other things to do, may or may not find time soon to think some more. I do wish someone could get Zurek to say more about this. He’s thought deeply about what seems to me the core of the problem, but the thing I quoted is one of the few places he has written about why he is skeptical about “Many Worlds” (in some other places he refers to this one).

Pascal,

This is a point that often confuses people. The situation you describe is precisely one where the terms do interfere, and do not evolve independently. Let |0> be the upper path of an interferometer, and |1> the lower path. Then if the photon is in the state |0> + |1>, and passes through a beam splitter, the effect is H|0> + H|1> = |0>, the paradigmatic case of interference.

Now suppose we made a (non-demolition) measurement on the photon, entangling its position with the outside world |W>, ending up with the state |0>|W_0> + |1>|W_1>. Now these terms do not interfere anymore (as long as |W_0> and |W_1> are orthogonal), meaning that any whichever unitaries U,V one applies to the photon, getting U|0>|W_0> + V|1>|W_1>, will not make one term disappear as in the example above. In fact the evolution of both terms is now completely independent of each other.

An interference is only possible if one acts with an entangling unitary on the whole system at once. For a large enough system this is practically impossible, so it is far to regard |0>|W_0> + |1>|W_1> as a sum of two terms that don’t interfere.

There is a basic problem with the idea of “branching” that is too rarely mentioned. The number of brnaches really cannot ever change, simply as a consequence of unitarity. There are never “new” branches. In some sense, the universe is just static, and the psi function and, indirectly, probability just sloshes around among the eternal branches.

All of us take this for granted when we do actual QM problems: e.g., resolving the spin of an eletron along different axes. But, somehow life gets more romantic when people think about MWI in the large.

David Deutsch takes this to its logical conclusion where there is no time either (try to do MWI in GR: the “problem of time” hits you). So, there is, Deutsch has said, just one eternal unchanging wave function with no actual time at all.

Like Peter, this makes my head hurt. Enough that I am willing to consider the possibility that just maybe QM is not the last word.

Peter,

I’m glad you enjoyed the discussion. I think Żurek’s relative silence about this is because he doesn’t find Many-Worlds so objectionable. As he put it in his contribution to the “Many Worlds?” volume, his results “fit well within Everett’s relative states framework, but do not require ‘many worlds’ per se”.

Mateus, is this table in wiki comparing QM interpretations accurate? It seems roughly split evenly between real wavefunction and not.

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison

All our fundamental theories are formulated in terms of pure states; mixed states are introduced as derived concept, either to describe the statistics from local measurements on an entangled state, or to make probabilistic assignments of (pure) states to a not fully known system. The world itself is in a pure state, our ignorance of it doesn’t make a difference.I would argue that we formulate our theories in the simplest possible terms, which is why we formulate it in terms of pure states, but we simply don’t know if the world is a pure state or not. Since the mathematical formalism works just as well either way, and since there is no experimental way to determine whether the world is in a pure state or not, “the world is in a pure state” is not a scientific statement.

I think the issue is that a theory that describes

(1) the state of the world and

(2) what an observer observes at a particular time

is fundamentally incomplete. It also needs to explain

(3) how many, and which, observers exist.

Otherwise we would not be able to explain why any observers exist at all, nor why we find ourselves on Earth instead of on another planet or in empty space, nor answer whether other humans feel pain as we do.

If you accept that the universal wave function satisfying unitary evolution is fundamental, and everything else must derive from this, then you run into a problem with quantum measurements. It’s alright to say that an observer, me, exists, and after performing the experiment, I either observed outcome 1 with 60% probability or observed outcome 2 with 40% probability. The problem is that there is nothing in the wave function to distinguish the observer who observed outcome 1 from the observer who observed outcome 2. So if one exists, then both must exist.

If you accept that both exists then I think you essentially accept many worlds. If before performing the experiment there are two scientists Alice and Bob, and afterwards there are Alice-1 and Bob-1 who both observed Outcome 1, and then observed each other discussing it, writing it down, etc., and also Alice-2 and Bob-2 who both observed Outcome 2. etc. etc., then it seems fair to say that Alice-1 and Bob-1 are in some kind of world together and Alice-2 and Bob-2 are in a different world together.

To believe that Alice-1 exists but not Alice-2 you have to believe in some extra information beyond the wave function that helps determine which observers exist. If you want to believe that Alice-1 and Bob-1 exist but not Alice-2 and Bob-2, or vice versa, but never any other combination, it seems like you have to believe in something like objective collapse or Bohmian mechanics.

Anonyrat,

Yes, I think the Wikipedia table is roughly accurate. What’s your point, though? Nobody is disputing that there are interpretations that consider the wavefunction to be real and interpretations that do not.

“I would argue that we formulate our theories in the simplest possible terms, which is why we formulate it in terms of pure states, but we simply don’t know if the world is a pure state or not. Since the mathematical formalism works just as well either way, and since there is no experimental way to determine whether the world is in a pure state or not, “the world is in a pure state” is not a scientific statement.”

So you want to ignore the historical development of our theories, and the fact that mixed states were introduced explicitly to be linear on the probabilities, to consider whether mixed states might be fundamental?

Fine, it is mathematically possible. It doesn’t change the fact that the mixedness that Peter was talking about – the one caused by our ignorance of the precise state and environment – is explicitly a property of the observer, not of the world. Again, map versus territory.

And what if we still end up with a mixed state after removing this subjective mixedness? As you say, there is no experimental way to test whether the state of the universe is pure or mixed. We might as well use Occam’s razor and take it to be pure.

I really appreciate the conversation this post has generated; it’s clarified my thinking on a lot of these interpretation questions. I’m trained as a mathematician, not a physicist, and maybe relatedly I can sometimes find these questions really exasperating to read about. Over and over I’ve had the experience of reading some paragraph that purports to be explaining someone’s favorite interpretation of quantum mechanics and realizing at the end that the paragraph didn’t contain any content at all that I could meaningfully extract. (Żurek’s discussion of what he thinks the wavefunction means is a good example.)

I especially feel this way about the epistemic interpretations I’ve tried to read about; I understand that they want to interpret the wavefunction as an expression of someone’s knowledge, but I can never tell what this knowledge is supposed to be knowledge

of. I know this might be off-topic, but can anyone point to a clear exposition of one of these approaches?Breaking headline: “ICE Opens Interdimensional Detention Center to Indefinitely Imprison Immigrants Across Infinite Number of Multiverses.”

(from The Onion, https://www.theonion.com/ice-opens-interdimensional-detention-center-to-indefini-1837476700 )

(Sorry for being OT….a bit…)

“… an electron can be in a superposition of different locations …” – Sure.

“… it follows that person can be in a superposition of having seen the electron in different locations …” – Maybe.

” … that reality as a whole can be in a superposition …” – Doesn’t follow at all.

” … it becomes natural to treat every term in that superposition as a separate ‘world’.” – Really? In what world?

jxd,

You might enjoy this review by Matt Leifer: arXiv:1409.1570. He gives some toy models of what the “ontic states” might look like in a psi-epistemic theory i.e. what objective reality the wavefunction is supposed to encode knowledge about. They don’t reproduce ordinary quantum mechanics though (well except for the trivial one ontic states = vectors in Hilbert space).

Realist psi-epistemic theories are awkward but it’s interesting to see if they are possible. Personally, studying them has pushed me further towards a realist interpretation of the wavefunction.

jxd,

The standard reference about epistemic versus ontic states is Harrigan and Spekkens. I find it quite clear.

People sometimes confuse epistemic quantum states with subjective quantum states. The former represents an observer’s (lack of) knowledge about an underlying reality. The latter represents an observer’s beliefs, without connection to an underlying reality. It is the point of view of QBism and similar subjectivist interpretations.

So you want to ignore the historical development of our theories, and the fact that mixed states were introduced explicitly to be linear on the probabilities, to consider whether mixed states might be fundamental?I fail to see how the historical development of our theories tells us anything about the subject of our theories, unless the history of the theory is part of the subject of the theory. Presumably if it is a good theory then some other culture/civilization/AI/alien species will arrive at the theory (or one isomorphic to it) with an entirely different history.

As you say, there is no experimental way to test whether the state of the universe is pure or mixed. We might as well use Occam’s razor and take it to be pure.Occam’s razor would say, don’t state an assumption either way. E.g., if there is no experimental way to determine whether God exists or not, Occam’s razor says don’t include God in your theory, and not “Might as well assume God exists” or “Might as well assume God does not exist”.

Just to draw your attention to a table of QM interpretations in A. Cabello. Interpretations of quantum theory: A map of madness. arXiv:1509.04711 and a Venn diagram (Figure 1.1) in J.B. Ruebeck, Understanding sequential measurements in psi-epistemic ontological models ( https://uwspace.uwaterloo.ca/bitstream/handle/10012/14845/Ruebeck_Joshua.pdf?sequence=3 )

It corrected my misimpression that psi-ontic and psi-epistemic was a complete classification of QM interpretations.

Mateus Araújo,

The discussion here has been illuminating, causing the following evolution in my thinking:

1. When I wrote this posting I saw no problem with accepting the “universal wave-function” as what you get if you ask what is the description of the state of the world given by our best theory, QM. Now I realize that there’s a big jump from what we know QM says about the world (which includes the fact we can’t ever know the state of the world, so don’t know if it is described by a pure state) to postulating a universal pure state wavefunction.

2. I remain confused about how the idea of multiple classical “worlds” is supposed to work and explain anything. What would really explain things is a detailed understanding of classical emergence. The best effort towards that I can find is the program of working to understand decoherence, the preferred basis problem and perhaps quantum Darwinism. Do the results of this program imply the “reality” of many worlds? Since I don’t understand exactly how this is all supposed to work, I can’t tell. That Carroll and most “Many Worlders” don’t address this and seem rather uninterested in the details of classical emergence, while Zurek, who is interested , calls Many Worlds “mythology” doesn’t encourage me towards the “Many Worlds are real” view.

In particular, Carroll only deals with the preferred basis/pointer state question in a single sentence (page 244-45): “the preferred-basis states are those that describe coherent objects in space, because such objects interact consistently with their environments.” I’m not sure what this means, and he gives no references for it, not even a reference explaining what the “preferred basis” problem is. Among the many references in the book to more technical material, the only relevant one to classical emergence is to Zeh’s 1970 decoherence paper (there are several attempts to derive the Born rule referenced, including Carroll’s own).

As far as I can tell, Carroll’s interest in the preferred basis problem is limited to the argument that the fact that interactions are local in space makes the position-space basis distinguished. I guess it is this that he wants to claim as somehow important for his attempt to find a theory of quantum gravity by identifying space inside a more generic quantum system (his version of “it from qubit”). As mentioned in the posting, I don’t see any evidence you can do this with the tools and concepts available.

Mateus, I am still not sure what “interference” means in this context since my point that U(Psi_1+Psi_2)=U(Psi_1)+U(Psi_2) for any Psi_1, Psi_2 is certainly valid.

Instead I propose the following toy model.

The state space is a finite dimensional Hilbert state and the unitary U represents time evolution (time is discrete; for continuous time we would need an infinite dimensional Hilbert space).

The goal is to single out some “classical states” or in another terminology a “preferred basis”.

We would like these states to enjoy some kind of stability property under the action of U.

So I propose that in a preferred basis, U should be simply (maybe up to a phase) a permutation matrix. “Up to a phase” means that the entries of the permutation matrix may be multiplied by arbitrary complex numbers of modulus 1.

This is a model of a cyclic universe: after a while we come back (up to a phase) to our initial state.

In this setting a “preferred basis” will be an orthonormal basis in which U becomes (up to a phase) a permutation matrix. This is a non-trivial constraint: not all bases satisfy this property.

This is unfortunately not enough to single out a unique “preferred basis”. For instance, given any permutation matrix one can always (like for any unitary) choose a basis of eigenvectors,

And if the initial state is an eigenvector there will be (up to a phase) no time evolution at all!

I will hazard the suggestion that the only way to single out a unique “preferred basis” may lie in the initial condition of the universe (which would be an element of that basis).

Again, there is no escaping the fact that if we start from an eigenstate there is no time evolution at all. But if we decompose the eigenvector in another of these “preferred bases” we may obtain a superposition of “universes”, each enjoying some time evolution even though there is no global time evolution in the multiverse (whose state is the eigenvector, if you have followed me up to this point).

Does this look like something that has been studied in decoherence or MWI ?

Anonyrat,

“I fail to see how the historical development of our theories tells us anything about the subject of our theories, unless the history of the theory is part of the subject of the theory. Presumably if it is a good theory then some other culture/civilization/AI/alien species will arrive at the theory (or one isomorphic to it) with an entirely different history.”

It is important. We take seriously conjectures that are well-motivated, not conjectures whose only thing going for it is that “it hasn’t been proven false”.

“Occam’s razor would say, don’t state an assumption either way. E.g., if there is no experimental way to determine whether God exists or not, Occam’s razor says don’t include God in your theory, and not “Might as well assume God exists” or “Might as well assume God does not exist”.”

Not, Anonyrat, Russell’s teapot is just not there. We are not respectfully agnostic about unfalsifiable hypotheses, we mercilessly eliminate extraneous entities. And a state of the for |\psi> is much simpler than a state of the form p|\psi><\psi'|.

"Just to draw your attention to a table of QM interpretations in A. Cabello. Interpretations of quantum theory: A map of madness. arXiv:1509.04711 and a Venn diagram (Figure 1.1) in J.B. Ruebeck, Understanding sequential measurements in psi-epistemic ontological models ( https://uwspace.uwaterloo.ca/bitstream/handle/10012/14845/Ruebeck_Joshua.pdf?sequence=3 )

It corrected my misimpression that psi-ontic and psi-epistemic was a complete classification of QM interpretations."

Yeah, you can always reject an objective reality, and then anything goes. There's also no point in talking about it.

Peter,

1 – I don’t see what’s the point of this discussion about whether the quantum state of the universe is pure or mixed. You still have many worlds either way, the important thing is that there is a quantum state for the whole universe.

2 – It’s not as if many worlds are postulated to explain anything, rather they are the consequence of applying the laws of quantum mechanics to the whole universe.

Peter, Re Many Worlds vs Decoherence:

Everett’s starting point was von Neumann’s analysis of measurement in his Grundlagen. According to von Neumann, a “measurement” is a physical process that converts a pure quantum state into a mixed state. Pretty clearly von Neumann is thinking here of QM as a description of ensembles, and arguably this is nothing more than a mathematised version of the Born rule. The evidence for the Born rule, of course, is the fact that measurements on quantum systems give definite results, even when the original state is known to be in a superposition*, and after the measurement no further superposition can be demonstrated (or, per the analysis in the Feynman lectures, if you *can* demonstrate superposition you have not really made a measurement).

Everett applies von Neumann’s analysis to a single quantum system, and in effect asks: how should we interpret the plus signs when we write out the mixture as a sum (or integral) of terms corresponding to particular outcomes? Should we read “plus” as “and” or as “or”? Conventional QM goes for “or” but MWI goes for “and”, and it is hard to argue that this is not the only consistent interpretation of the mathematics.

A decade after Everett, decoherence theory explained in some detail how measurement-like processes, that is, interactions with “environments” containing a macroscopic number of degrees of freedom, could indeed convert a pure state into a state that effectively acts as a mixture, once the environmental degrees of freedom are traced out. Given the practical impossibility of designing an apparatus that took the environment into account in full detail, Zurek in particular claimed at the time that this “solved” the measurement problem and provided a complete interpretation of QM. However, it does not at all address the “and/or” question for mixtures and I believe that Zurek’s views have evolved over time on this. Most MWI people are very grateful to decoherence theory for providing a detailed account of “branching”, but would argue that we always knew that branching must take place thanks to the existence of our perceived classical world. And if you have every tried to explain decoherence at a popular level (or even to advanced undergraduates), you would have sympathy with Carroll for not delving into this in depth.

* Superposition of eigenstates of whatever is being measured.

Paddy,

I don’t object to Carroll’s decision not to discuss decoherence theory in detail. In a popular book one’s ability to discuss more technical issues is very limited. My reference was to the very specific issue of the “preferred basis” problem. Note that he’s doing something very questionable with this book: he moves on from the old claim that MWI solves interpretational problems to the claim that it somehow is involved in telling you how to reconcile QM and GR. The hinge of this argument is that the “preferred basis” is the space coordinate basis,. Because this is both a huge problem for MWI and at the center of his argument, some sort of reference backing it up would have been a good idea.

I started looking a bit at how the MWI people treat the preferred basis problem, specifically at David Wallace’s discussion of it, and it seems to me that there’s not much argument besides the assumption that however classical emergence happens, it solves the problem. This is where I have a problem with Mateus’s point number 2. Besides Zurek, I just am not finding places where MWI people actually come to grips with classical emergence (in particular the preferred basis aspect of it), so the argument that the way classical emergence happens implies Many Worlds seems to me possibly empty.

Peter,

I agree that Zurek seems to have put more serious work into the preferred basis problem than anyone else I know of. To be honest, I have not read his work on this point with enough care to claim that I fully understand how einselection is supposed to work, but I have extracted the idea that states expressed in certain bases are relatively stable because of the way the corresponding operators feature in the Hamiltonian, which seems extremely plausible (also, it sounds like what Carroll is referring to in the sentence you quote). If true it solves one of the two deep problems for MWI, the other being the probability issue, which I guess is why Wallace’s book focuses on that.

I’m no expert on any of this, but I just want to comment on:

“A mixed state is a description of your ignorance, not of what the world is. All our fundamental theories are formulated in terms of pure states; mixed states are introduced as derived concept, either to describe the statistics from local measurements on an entangled state, or to make probabilistic assignments of (pure) states to a not fully known system.”

This kind of glib statement is repeated everywhere. But I don’t see how matters can be that simple.

If pure states are a description of the world, and mixed states just a description of incomplete knowledge, then we would model mixed states by *probability measures on the space of pure states*. Instead, mixed states are modelled by density operators: but there are infinitely many probability measure which give the same density operator. (E.g., for the qubit, the space of density matrices is a 3 dimensional ball, but the space of probability measures on pure states (a 2 sphere) is infinite.)

It seems to be a magical property of QM that for practical purposes almost all of the information about our incomplete knowledge can be ignored, and we can work entirely with mixed states (density operators). This seems like something which deserves an explanation in any account of an interpretation of quantum mechanics.

Of course, one way to respond to this is to suppose that there is something incomplete in our understanding of QM, which I think is a point of view Penrose takes in some of his big weird books.

It seems more economical to just suppose that mixed states can be a description of the world, exactly on par with pure states, a point of view which seems supported by the fact that the mathematical description of QM is at least as clean (if not cleaner) using mixed states as it is using pure states. Does anything go wrong if we just suppose that the world can be described by mixed states? I don’t see how.