What is the problem that the Many Worlds Interpretation aims to solve?

[Quotidian]

Sean Carroll's most recent book is called Something Deeply Hidden, and is premissed on the idea that the Everett interpretation of the 'observer problem' in quantum physics is correct. Carroll, and several other prominent scientific popularisers including David Deutsche and Max Tegmark, are convinced that this interpretation, bizarre and outlandish as it sounds to many people, is correct, and that the world as we know it is constantly 'splitting' into infinite replicas, where everything that could happen, does.

Phillip Ball's essay in Quanta criticizes this idea, concluding that 'Its implications undermine a scientific description of the world far more seriously than do those of any of its rivals. The MWI tells you not to trust empiricism at all: Rather than imposing the observer on the scene, it destroys any credible account of what an observer can possibly be.'

Myself, I'm not a physicist, but I have a casual interest in philosophy, and I agree with Phillip Ball. There's an interesting Scientific American article The Many Worlds of Hugh Everett III. It says 'Everett’s scientific journey began one night in 1954, he recounted two decades later, “after a slosh or two of sherry.” He and his Princeton classmate Charles Misner and a visitor named Aage Petersen (then an assistant to Niels Bohr) were thinking up “ridiculous things about the implications of quantum mechanics.” During this session Everett had the basic idea behind the many-worlds theory, and in the weeks that followed he began developing it into a dissertation.' It recounts how when he submitted his thesis (to Wheeler), he was encouraged to play down the notion of the world dividing or splitting, but that when the idea finally became popularised by Bryce DeWitt, this aspect was very much emphasised.

So, there's a saying that 'desperate problems call for desperate solutions'. If the Many Worlds Interpretation is a solution, then what is the problem? Or, put another way, if for some unforseeable reason it was finally discovered that there couldn't actually be 'many worlds', Sean Carroll and David Deutsche would have to admit that ... .

Fill in the blank.

 

[DrChinese]

So, there's a saying that 'desperate problems call for desperate solutions'. If the Many Worlds Interpretation is a solution, then what is the problem? Or, put another way, if for some unforseeable reason it was finally discovered that there couldn't actually be 'many worlds', Sean Carroll and David Deutsche would have to admit that ... .

Fill in the blank.

There are a couple of complex issues in Quantum Mechanic that are very confusing, and MWI attempts to resolve some of those. One question is: why do we see a particular outcome to a quantum measurement (let's say spin). There is nothing in orthodox QM that explains why we see spin up (instead of spin down). MWI answers that my postulating a world where there is a spin up outcome, and another where there is a spin down outcome. We occupy one of those worlds, thereby answering the question by saying: both outcomes occur, but we are only aware of the branch we exist in.

As to whether you think the solution is more or less "desperate" than the problem: everyone has their opinion, and there is currently no experimental evidence distinguishing one interpretation from the other.

By the way, here is a recent technical summary of MWI that I am currently reading. It goes back to Everett's original work and discusses from there, you may find that interesting:

https://arxiv.org/abs/2005.04812

 

[Quotidian]

One of my other versions will have to read that paper, this version can't interpret the equations.

 

[Quotidian]

Actually, I’ll spit it out - I think that if the ‘many world’s’ interpretation was shown to be untenable, then Carroll would have to admit that the observer problem hasn’t been solved, that the Copenhagen interpretation (such as it is) is all that can be said. ‘Many worlds’ is the price you pay for clinging to realism at all costs.

 

[Minnesota Joe]

Sean Carroll's most recent book is called Something Deeply Hidden, and is premissed on the idea that the Everett interpretation of the 'observer problem' in quantum physics is correct. Carroll, and several other prominent scientific popularisers including David Deutsche and Max Tegmark, are convinced that this interpretation, bizarre and outlandish as it sounds to many people, is correct, and that the world as we know it is constantly 'splitting' into infinite replicas, where everything that could happen, does.

That book was my introduction to MWI and, even though I enjoy Carroll's writing usually, I was disappointed both at what I view to be exaggerated claims (which he might characterize as boldness) and how quickly the ideas seem to fall apart. I think quantum foundations is really important and interesting, so I don't question the motivation, but on closer examination MWI doesn't seem to solve the problems it claims to solve. I forget who on this site told me that MWI looks shiny until you examine it closely (probably multiple people), but that seems to be the case.

I doubt we could even be in a position to fill in your blank, though. It's not like I believe MWI is disprovable, but I don't have any good reason to believe it is true or even possible. Similarly, I can't disprove the claim that the universe popped into existence 5-minutes ago with all my memories included but I don't spend a lot of time worrying about it either.

 

[Minnesota Joe]

Actually, I’ll spit it out - I think that if the ‘many world’s’ interpretation was shown to be untenable, then Carroll would have to admit that the observer problem hasn’t been solved, that the Copenhagen interpretation (such as it is) is all that can be said. ‘Many worlds’ is the price you pay for clinging to realism at all costs.

Why would he have to do that when there are other realist theories available? Even Carroll thinks so.

 

[Halc]

Sean Carroll's most recent book is called Something Deeply Hidden, and is premissed on the idea that the Everett interpretation of the 'observer problem' in quantum physics is correct. Carroll, and several other prominent scientific popularisers including David Deutsche and Max Tegmark, are convinced that this interpretation, bizarre and outlandish as it sounds to many people, is correct, and that the world as we know it is constantly 'splitting' into infinite replicas, where everything that could happen, does.

I've not seen Carroll's take on the issue, but Everett's interpretation (which is RSF, not MWI) does not posit that at certain magical instances, the the world undergoes some sort of metaphysical “split” into branches. DeWitt's MWI does posit that, but that's a different interpretation.
While I don't consider DeWitt's view necessarily outlandish in itself, I think that it has some flaws as the only way a typical observer will see Born's rule is if some worlds exist more than others, which puts an unintuitive spin on what it means for a world to 'exist'.
Anyway, Tegmark and probably Deutsche push Everett's view, despite DeWitt's MWI label often being applied to the view, by these very people. Under Everett's view, whatever you call it, there is no metaphysical split. There is, was and always will be only one wavefunction, and "only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting". Tegmark's words there, not mine.

 

[PeterDonis]

Everett's interpretation (which is RSF, not MWI) does not posit that at certain magical instances, the the world undergoes some sort of metaphysical “split” into branches. DeWitt's MWI does posit that, but that's a different interpretation

I don't know that there are actually two different interpretations here. There might be a lot of different pop science claims made, but that's not the same thing.

Under Everett's view, whatever you call it, there is no metaphysical split. There is, was and always will be only one wavefunction

I don't think DeWitt's view is any different in this regard.

"only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting"

Are you claming that DeWitt's view does not agree with this? If so, please give a reference.

 

[Halc]

I don't think DeWitt's view is any different in this regard.

The indirect reference I have is to De Witt, B.S.M., 1970, ‘Quantum mechanics and Reality’, Physics Today, 23(9): 30–35.
This is linked with text " the popular “actual splitting worlds” approach in De Witt 1970" in the Stanford entry for QM-many-worlds. It is these 'actual splitting worlds' that I am referring to.

A low-quality photo-scan of the paper can be found here, but being a scan, it cannot be searched. https://physicstoday.scitation.org/doi/pdf/10.1063/1.3022331

There is a section on Maverick worlds that begins to acknowledge some of the problems I bring up about not finding ourselves in some improbable worlds, but a weak-anthropic explanation given doesn't explain away an experiment carried out just minutes ago, that somehow the worlds that must exist but with low-probability outcome cannot have observers in them.

 

[PeterDonis]

The indirect reference I have is to De Witt, B.S.M., 1970, ‘Quantum mechanics and Reality’, Physics Today, 23(9): 30–35.

Unfortunately, that's not really a good source either since it's not peer-reviewed. However, I am familiar with it as it is indeed the source most people point to as the "official" presentation of DeWitt's views.

In the actual peer-reviewed literature on QM interpretations that I have read (and I should make clear that there is a lot of it that I have not read), I am not aware of any real difference between "relative state" and "many worlds". The key points are that the wave function is considered to be physically real, that it is the only thing that is considered to be physically real, and that there is only unitary evolution of the wave function all the time, with no actual "collapse" ever. Those points all appear to be common to both "relative state" and "many worlds". The differences seem to me to be ones of presentation and emphasis.

 

[Quotidian]

Everett's interpretation (which is RSF, not MWI) does not posit that at certain magical instances, the the world undergoes some sort of metaphysical “split” into branches.

Well, in the excerpt from Peter Byrne's bio of Everett, it is reported that it did contain these ideas, saying that in response:

Wheeler’s letter to Everett reported: “Your beautiful wave function formalism of course remains unshaken; but all of us feel that the real issue is the words that are to be attached to the quantities of the formalism.” For one thing, Wheeler was troubled by Everett’s use of “splitting” humans and cannonballs as scientific metaphors.

I know this is from popular literature, and not a scientific journal article, but scientific ideas do have a tendency of filtering into popular discourse, and this idea has deeply inflitrated culture, as this essay contends. That is the level that I'm looking at it on - as an artifact of modern culture.

Everett wrote that “From the viewpoint of the [his] theory, all elements of a superposition (all ‘branches’) are ‘actual,’ none any more ‘real’ than the rest.” Notice the scare quotes around "real". Whenever you see that, you can bet you're talking metaphysics.

I think the philosophical issue is that, according to the Copenhagen interpretation, you can't say that subatomic particles exist. You can only say what has shown up in observations, what has been registered by the apparatus. Asking what causes the observations, or what exists apart from those observations, is a meaningless question. And that's because the answer to the question 'does an electron exist?' just is the wave equation. This indicates that it only has a tendency to exist, and that tendency is described in terms of probabilities by the equation. It 'kind of' exists. And that's the kind of fundamental ambiguity that Everett couldn't tolerate. He said in correspondence that the standard (i.e. Copenhagen) interpretation was 'a philosophic monstrosity with a “reality” concept for the macroscopic world and denial of the same for the microcosm.'

It strikes me that Bohr and Heisenberg's attitude was much more philosophically mature, because it was more modest. It acknowledges that when it comes to the sub-atomic domain, even though it can be measured and predicted with extraordinary accuracy, we can't know everything about it, for the reasons that were elucidated by Heisenberg. It seems to me they had more tolerance for ambiguity.

 

[kith]

I've not seen Carroll's take on the issue, but Everett's interpretation (which is RSF, not MWI) does not posit that at certain magical instances, the the world undergoes some sort of metaphysical “split” into branches.

How do you interpret the following quote? It surely looks like Everett is saying that something is splitting at certain events. Do you object to the notion of "splitting" itself or that it is the real world which undergoes the splitting?

At this point we encounter a language difficulty. Whereas before the observation we had a single observer state afterwards there were a number of different states for the observer, all occurring in a superposition. Each of these separate states is a state for an observer, so that we can speak of the different observers described by the different states. On the other hand, the same physical system is involved, and from this viewpoint it is the same observer, which is in different states for different elements of the superposition (i.e., has had different experiences in the separate elements of the superposition). In this situation we shall use the singular when we wish to emphasize that a single physical system is involved, and the plural when we wish to emphasize the different experiences for the separate elements of the superposition. (e.g., "The observer performs an observation of the quantity A, after which each of the observers of the resulting superposition has perceived an eigenvalue.")

Source: Everett's PhD thesis, p.63, footnote 1

 

[Quotidian]

A 'language difficulty' .

You can see how the whole idea started: "What if there is no 'collapse'...?" Then, formulaize that implications of that. Hey presto! It's a gestalt. And nobody really pushes back - well, apart from Bohr - because they didn't want to discourage a 'brilliant young student' and besides, it was such an outlandish idea nobody was really sure what it meant (which remains the case). Meanwhile Everett went off to design re-entry paths for ICBM warheads and drank himself to death at age 51, leaving instructions in his will that his ashes be put out in the garbage.

And now it's part of the cultural landscape.

 

[Elias1960]

‘Many worlds’ is the price you pay for clinging to realism at all costs.

Certainly not. It is the price you pay for not caring enough about interpretations making sense at all.

For those who want to preserve realism there is a large number of realist interpretations, starting with dBB and Nelsonian stochastics. Actually the best one is IMHO Caticha's entropic dynamics. This does not have any serious costs, except for accepting a hidden preferred frame in the relativistic context. (I have never understood those who look for hidden variables but have problems with a preferred frame if it is hidden.)

 

[PeterDonis]

Caticha's entropic dynamics

Do you have a good reference for this interpretation? It's not one I'm familiar with.

 

[Elias1960]

Do you have a good reference for this interpretation? It's not one I'm familiar with.

Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A 44 , 225303, arxiv:1005.2357

Caticha, A. (2019). The Entropic Dynamics approach to Quantum Mechanics. Entropy 21, 943 ; arxiv:1908.04693

 

[PeterDonis]

Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A 44 , 225303, arxiv:1005.2357

Caticha, A. (2019). The Entropic Dynamics approach to Quantum Mechanics. Entropy 21, 943 ; arxiv:1908.04693

Thanks!

 

[Halc]

How do you interpret the following quote? It surely looks like Everett is saying that something is splitting at certain events. Do you object to the notion of "splitting" itself or that it is the real world which undergoes the splitting?

At no point does Everett describe the system as anything but one system in superposition of various states, so I do not interpret his language as 'splitting' at all. There are different elements of the superposition, but never more than one system.

 

[kith]

At no point does Everett describe the system as anything but one system in superposition of various states, so I do not interpret his language as 'splitting' at all. There are different elements of the superposition, but never more than one system.

Before the measurement, there is only a single observer state. After the measurement, there are multiple observer states relative to the outcomes. In the MWI, all these observer states are equally real, so as Everett remarks "[...] we can speak of the different observers described by the different states". Your objection to use the term "splitting" for the change from one observer to these different observers seems semantic to me.

If you think that it is more than semantics, could you elaborate on the differences between your point of view and a "splitting" point of view? What exactly does someone who subscribes to "splitting" accept that you reject?

 

[Halc]

Before the measurement, there is only a single observer state. After the measurement, there are multiple observer states relative to the outcomes.

Before the measurement, there is a cat in superposition, which already might be interpreted as multiple states. After, the observer is in superposition (entangled with) the cat. In both cases, there seems to be a single observer state per observer.

In the MWI, all these observer states are equally real, so as Everett remarks "[...] we can speak of the different observers described by the different states". Your objection to use the term "splitting" for the change from one observer to these different observers seems semantic to me.

Pretty much semantic yes. There are three observers in the above scenario which respectively observe one state each: Cat in superposition, cat alive, cat dead. Calling an observation event (a point of view of sorts) a world seems to be a semantic choice.

If you think that it is more than semantics, could you elaborate on the differences between your point of view and a "splitting" point of view? What exactly does someone who subscribes to "splitting" accept that you reject?

I had thought that Wigner asserted some sort of metaphysically separate pair of worlds splitting off, but it has been pointed out to me that that was his pre-reviewed initial publication, and papers submitted since in peer-reviewed contexts seem to align more with the single system in one state of superposition of many states.

The naive metaphysical split view is something like the one expressed in the OP of another current thread: https://www.physicsforums.com/threads/single-world-or-multiple-worlds.991788/
It seems to suggest the creation of a different universe (coupled with expenditure of required resources) every time a measurement is made. That's something I reject if you want an example, but I know of no published stance that works like that.

 

[PeterDonis]

Before the measurement, there is a cat in superposition, which already might be interpreted as multiple states.

No, a superposition is not multiple states. It's one state. The one state, when the cat is in a superposition, is simply not an eigenstate of the "is the cat dead or alive" operator.

 

[Halc]

No, a superposition is not multiple states. It's one state. The one state, when the cat is in a superposition, is simply not an eigenstate of the "is the cat dead or alive" operator.

Kith was asking me about Everett's wording:

Whereas before the observation we had a single observer state afterwards there were a number of different states for the observer, all occurring in a superposition.

He calls them 'different states' and nevertheless 'occurring in superposition'. Is Everett wrong then, or am I using the language improperly in some way that Everett isn't? I said 'multiple', not 'different'. Did I cross a line?

 

[PeterDonis]

He calls them 'different states' and nevertheless 'occurring in superposition'. Is Everett wrong then

He is at least being sloppy in wording, since "different states" is open to an obvious interpretation under which it is simply false, namely that some sort of "splitting" process has happened that has converted a single "copy" of a quantum system into multiple "copies". Which of course is one of the key points of contention in this thread.

The inconvenient truth is that there is no good way of describing what the MWI actually says in ordinary language. Our ordinary language has implicit assumptions built into it which are violated by the MWI. Everett tries to get at this somewhat in the passage that @kith originally quoted, but I personally think his approach causes at least as much confusion as it solves.

If we step back from the MWI for a moment and just consider how we would describe an entangled state, for example two electrons in the singlet state (total spin zero), the natural description in ordinary language would be something like: neither electron has any definite state by itself; only the two-electron system does. We would not normally say that each electron is in a superposition of two different states, or that each electron is in a definite state in each term of the entangled wave function.

The natural extension of that language to the MWI would have us saying that, for example, Schrodinger's cat is not in a superposition of being alive and being dead; it is not in any definite state at all. Only the total system consisting of the radioactive atom whose decay or lack of decay causes the cat to die or not die, is in a definite state. The total system consists of the atom and the cat, entangled with each other, just as the two electrons above are entangled with each other. And if you then open the box and observe the cat, you are now entangled with the atom-cat system, so you no longer have a definite state on your own either; only the total system of atom-cat-you does.

The problem, of course, with speaking this way about the MWI is that it undermines the whole justification for the interpretation. If you are not in any definite state at all when you are entangled with the atom-cat system, then you haven't observed anything definite at all. But the MWI claims that you have--more precisely, it claims that in each "branch" of the wave function--each term in the entangled state of atom-cat-you--you have observed something definite, that the cat is either alive or dead. The MWI has to say this because otherwise it would be grossly inconsistent with observation, since we experience ourselves to have observed definite outcomes to quantum experiments--we don't experience not having observed anything definite at all. But of course that is just like saying that each electron in the two-electron singlet state has a definite state, which, as noted above, we don't normally say.

In a sense all this is about words and not physics; but words have connotations, and the MWI, by using the language Everett used, is trading on the connotations of you being in some definite state in each branch, in order to be consistent with observation, even though, IMO, those connotations are not really justified.

 

[kith]

Before the measurement, there is a cat in superposition, which already might be interpreted as multiple states. After, the observer is in superposition (entangled with) the cat. In both cases, there seems to be a single observer state per observer.

No, that's not true. Entangled states are precisely the states where you can't assign unique states to the subsystems. (Technically, we should replace "state" by "state vector" here, but I'm using the same level of rigor as Everett in his comment)

Before the measurement, the state of the combined system* is $$\left( |\text{cat dead} \rangle + |\text{cat alive} \rangle \right)\otimes|\text{observer neutral} \rangle$$ with a single state for the observer. After the measurement, the state of the combined system is $$|\text{cat dead} \rangle\otimes|\text{observer sad} \rangle + |\text{cat alive} \rangle\otimes|\text{observer happy} \rangle$$ where we see two different observer state vectors which can't be combined to give a single state for the observer alone.

After the measurement, only the combined system of cat+observer has an obviously well-defined state. As @PeterDonis notes, the best thing would be to never talk about the state of subsystems at all but in order to connect with experiments and experience, the MWI needs to assign a state to the observer. Hence the multiplicity of states of the observer which wasn't present before the measurement.
______
*: I'm simplifying a bit. Actually, we should include the quantum mechanical system which interacts with the cat as well as the environment which is present during the measurement in our description.

 

[Jarvis323]

No, that's not true. Entangled states are precisely the states where you can't assign unique states to the subsystems. (Technically, we should replace "state" by "state vector" here, but I'm using the same level of rigor as Everett in his comment)

Before the measurement, the state of the combined system* is $$\left( |\text{cat dead} \rangle + |\text{cat alive} \rangle \right)\otimes|\text{observer neutral} \rangle$$ with a single state for the observer. After the measurement, the state of the combined system is $$|\text{cat dead} \rangle\otimes|\text{observer sad} \rangle + |\text{cat alive} \rangle\otimes|\text{observer happy} \rangle$$ where we see two different observer state vectors which can't be combined to give a single state for the observer alone.

After the measurement, only the combined system of cat+observer has an obviously well-defined state. As @PeterDonis notes, the best thing would be to never talk about the state of subsystems at all but in order to connect with experiments and experience, the MWI needs to assign a state to the observer. Hence the multiplicity of states of the observer which wasn't present before the measurement.
______
*: I'm simplifying a bit. Actually, we should include the quantum mechanical system which interacts with the cat as well as the environment which is present during the measurement in our description.

Is it the case that measurement produces classical information about the quantum system? And the difference between "branch's/worlds" is only relevant to classical information, which is observer dependent? If something like that were the case, then couldn't entropy somehow be a reflection of the body of measurements that have taken place, and the heat death of the universe would be something like the case where the potential classical information possible about the quantum system is saturated?

 

[entropy1]

The naive metaphysical split view is something like the one expressed in the OP of another current thread: https://www.physicsforums.com/threads/single-world-or-multiple-worlds.991788/
It seems to suggest the creation of a different universe (coupled with expenditure of required resources) every time a measurement is made. That's something I reject if you want an example, but I know of no published stance that works like that.

I am the author of that topic. I am not advertising multiple worlds, but instead argue for a single world with a diverging superposition (my words), meaning that not only the outcomes would differ, but the environments too. Just exactly as the equation given at the top. This quote describes it in other words:

At no point does Everett describe the system as anything but one system in superposition of various states, so I do not interpret his language as 'splitting' at all. There are different elements of the superposition, but never more than one system.

 

[Jarvis323]

But the branches break a single closed system into multiple non-interacting closed systems as far as any obervable laws of physics or cause and effect are concerned. I would think that this would be the main sense that you would consider them separate, they don't interact.

 

[entropy1]

The problem, of course, with speaking this way about the MWI is that it undermines the whole justification for the interpretation. If you are not in any definite state at all when you are entangled with the atom-cat system, then you haven't observed anything definite at all. But the MWI claims that you have--more precisely, it claims that in each "branch" of the wave function--each term in the entangled state of atom-cat-you--you have observed something definite, that the cat is either alive or dead. The MWI has to say this because otherwise it would be grossly inconsistent with observation, since we experience ourselves to have observed definite outcomes to quantum experiments--we don't experience not having observed anything definite at all.

I don't know if I get your right, but I would say we ARE in superposition in that case, albeit a superposition of observed outcomes paired with matching environments, which is still a superposition I think.

 

[entropy1]

But the branches break a single closed system into multiple non-interacting closed systems as far as any obervable laws of physics or cause and effect are concerned. I would think that this would be the main sense that you would consider them separate, they don't interact.

Yes, perhaps in that sense you could call it "seperate worlds". If it would be a matter of preference, I might prefer a superposition in one and the same world (and that would probably imply the reality of the wave function).

 

[Halc]

[Everett] is at least being sloppy in wording, since "different states" is open to an obvious interpretation under which it is simply false, namely that some sort of "splitting" process has happened that has converted a single "copy" of a quantum system into multiple "copies".

Maybe Everett's actual meaning would be less open to loose interpretation if the whole paper is considered instead of one snippet that you find less than ideally worded in hindsight. The language of this sort of thing was totally new with the introduction of this paper and the precise way we might express it today was unknown at the time.
No, given the paper as a whole, it does not seem open to interpretation that new 'copies' are being generated.

The inconvenient truth is that there is no good way of describing what the MWI actually says in ordinary language. Our ordinary language has implicit assumptions built into it which are violated by the MWI.

Physics has always had to deal with that. Ordinary language for instance is very A-series making it awkward to discuss a system only in terms devoid of references to the present. Similarly, the language has all kinds of implicit assumptions about identity, of say 'the observer', all of which fall apart under MWI and must be expressed in new terms. Common language needs upgrades to discuss new frameworks, and the pain of doing so does not in any way serve as evidence for or against the framework.

The natural extension of that language to the MWI would have us saying that, for example, Schrodinger's cat is not in a superposition of being alive and being dead; it is not in any definite state at all.

Not sure about 'not in superposition'. If dead is a valid solution to the cat's wave function, and so is alive, then dead and alive is also a solution. Seems to be a language nit, not a disagreement with what you're saying here.

Only the total system consisting of the radioactive atom whose decay or lack of decay causes the cat to die or not die, is in a definite state. The total system consists of the atom and the cat, entangled with each other, just as the two electrons above are entangled with each other. And if you then open the box and observe the cat, you are now entangled with the atom-cat system, so you no longer have a definite state on your own either; only the total system of atom-cat-you does.

Except you're declaring the atom-cat-you to be a system, but if you take the wave function from further back, the current atom-cat-you system is now only one solution to that wave function, not a definite state at all. Sure, it's a definite state relative to the atom-cat-you system, but the dead cat is also in a definite state relative to the guy observing a dead cat.
I think in relational terms, so I have a hard time conveying any concept of and objective 'definite state'. I'm not an MWI guy, but I admire the cleanliness of it.

The problem, of course, with speaking this way about the MWI is that it undermines the whole justification for the interpretation. If you are not in any definite state at all when you are entangled with the atom-cat system, then you haven't observed anything definite at all.

Depends on your definition of 'you'. The common language one is totally out the window here, but that doesn't mean you can't define a new one. I've gone through all that identity stuff. Quotidian balks at MWI because this assault to the intuitive view of personal identity conflicts with his eastern-dualistic beliefs. But I do have a definition of identity that works, something like "'I' am an event, coupled my worldline leading up to that event". The definition seems to work with MWI and RQM. Using that definition, 'I' cannot measure anything, 'I' cannot collapse a wave function. 'I' can only have measured things, in which case it is entirely consistent to be observing a dead cat.

But the MWI claims that you have--more precisely, it claims that in each "branch" of the wave function--each term in the entangled state of atom-cat-you--you have observed something definite, that the cat is either alive or dead.

Yep.

No, that's not true. Entangled states are precisely the states where you can't assign unique states to the subsystems. (Technically, we should replace "state" by "state vector" here, but I'm using the same level of rigor as Everett in his comment)

Before the measurement, the state of the combined system* is $$\left( |\text{cat dead} \rangle + |\text{cat alive} \rangle \right)\otimes|\text{observer neutral} \rangle$$ with a single state for the observer. After the measurement, the state of the combined system is $$|\text{cat dead} \rangle\otimes|\text{observer sad} \rangle + |\text{cat alive} \rangle\otimes|\text{observer happy} \rangle$$ where we see two different observer state vectors which can't be combined to give a single state for the observer alone.

Agree with all this, with comments above about the combined system not being fully combined with other outcomes from some system in the past where we might never have decided to put the cat in this predicament.

After the measurement, only the combined system of cat+observer has an obviously well-defined state.

This seems self contradictory. If dead-cat+observer-of-dead-cat is not a well defined state, then neither can be the cat+observer state, pre-measurement. (Almost) all pre-measurement states are post-some-other-measurement, and thus not an 'obviously well-defined state'. See my point? If all entangled states are needed to define the actual state, then you have a system that is indistinguishable from no state at all. So at some point you have to talk about are these states as systems of their own.Disclaimer: Not claiming to be any authority on what Everett or another proponent says. I'm just pointing out what I see as being inconsistencies with what is being posted here. Clarification is always welcome. I'm not too stubborn to learn.

 

[PeterDonis]

Physics has always had to deal with that.

Agreed, but I think the MWI is a particularly difficult case.

Not sure about 'not in superposition'. If dead is a valid solution to the cat's wave function, and so is alive, then dead and alive is also a solution.

But the total system is not just the cat. The total system (if we leave out the observer) is atom plus cat. And the atom plus cat system is entangled; there is no way of expressing its state as the product of an atom state and a cat state. So neither the atom nor the cat is in any definite state at all.

Whether or not the atom plus cat system is in a superposition depends on your choice of basis. Yes, in the "atom decayed or not decayed" plus "cat dead or alive" basis, the entangled state is a superposition. But one can always change basis to one in which the particular state of atom plus cat is one of the basis vectors, and in this basis, the atom plus cat state is not in a superposition.

Saying that the cat itself is in a "superposition" is therefore misleading, since the cat is entangled with the atom.

Similar remarks apply when we include you, the observer, in the system and describe the interaction between you and the atom plus cat system when you open the box to look at the cat.

you're declaring the atom-cat-you to be a system

I'm not "declaring" that; that's simply a fact of the scenario. The atom, cat, and you all interact during the scenario; that means you have to consider them as one complete system. Interaction causes entanglement, and you cannot treat an entangled system as multiple isolated systems.

I think in relational terms, so I have a hard time conveying any concept of and objective 'definite state'.

If you want to say that, relationally speaking, no subsystem in an entangled, interacting system is in a definite state, that's fine. If you want to draw a distinction between "objective definite state", which is what no subsystem in an entangled, interacting system is in, and "relational definite state", which has some other meaning, then you should at least attach the "relational" qualifier to the term" definite state", since the ordinary language meaning of "definite state" is "objective definite state". With that choice of language, you would say that none of the atom, cat, and you are in an "objective definite state" after the experiment, but all of them are in "relational definite states" in each branch.

I understand the "relational" viewpoint; I'm just not sure it actually makes sense. In fact that would be a way of rephrasing my previous objections that might make it more evident to you what I am objecting to.

I do have a definition of identity that works, something like "'I' am an event, coupled my worldline leading up to that event". The definition seems to work with MWI and RQM.

No, this definition does not work with MWI and RQM, since in those interpretations, nothing has a single definite worldline. The only single definite trajectory that exists in MWI and RQM is the single definite trajectory of the whole system (atom plus cat plus you, in the scenario we are discussing) in the state space of the system, which is not ordinary spacetime. The "you" in a particular branch of the overall wave function cannot point to a trajectory in spacetime that distinguishes that "you" from the other "yous" in other branches.

If dead-cat+observer-of-dead-cat is not a well defined state, then neither can be the cat+observer state, pre-measurement.

I didn't say dead cat + observer-of-dead-cat is not a well-defined state. It is. But the total cat + observer system being in that state does not mean either the cat or the observer, by themselves, is in a well-defined state.

The cat + observer state pre-measurement is not entangled (but note that you are leaving out the atom that either decayed or didn't decay, so what you are calling "cat" is actually an entangled state of atom + cat), so the cat (entangled atom + cat) and the observer are in well-defined states by themselves pre-measurement, and the cat + observer state is just a product state. The interaction involved in you observing the cat entangles the cat and observer subsystems, so the cat + observer system evolves into an entangled state.

(Almost) all pre-measurement states are post-some-other-measurement, and thus not an 'obviously well-defined state'.

Yes, that's why I pointed out above that what you were calling "cat" is actually "atom + cat" in an entangled state. And the atom, cat, and you have all interacted with other things in the past, so yes, from the MWI point of view the most likely thing is that nothing in the universe is in a definite state by itself; everything is entangled. Only the whole universe will be in a definite state on this view.

If your response to that is "that doesn't seem like it would work", welcome to the club of people who don't think the MWI works.

If all entangled states are needed to define the actual state, then you have a system that is indistinguishable from no state at all.

No, you don't. A system with $10^{123}$ (to throw out some kind of number for the whole universe) degrees of freedom that are all entangled is very different from nothing at all, which has zero degrees of freedom.