Why does nothing happen in MWI?

[PeterDonis]

Which now sits askew on whatever basis you previously set it square on.

Not necessarily. That's the point of the Nirvana theorem. See below.

the exact meaning of the Nirvana theorem is what I was asking about.

As I understand it, the theorem says that, given a state and a Hamiltonian, we can always find a basis in which the unitary evolution induced by the Hamiltonian does nothing but phase rotate the state. In this basis, called the "Nirvana basis", nothing happens, since phase rotation does not change any physical observables.

I don't actually understand all the ins and outs of how the theorem is proved, so I may be missing something; but that's how it looks to me.

 

[craigi]

Derek,

Try to answer the following, in the conext of the MWI, to see where the problem arises.

Consider that we prepare an arbitrarily large, isolated, quantum system. Think about what happens happens within that system. Can it undergo decoherence, while isolated from the outside world? Decoherence with what? Can a meaningful measurement be made within it, while isolated from the outside world?

If yes, then how do we determine how the classical system (or environment) emerges, which the quantum subsystems can decohere with and be measured by?

If no, then how did the first classical system (or environment) emerge?

 

[Derek Potter]

Derek,
Try to answer the following, in the conext of the MWI, to see where the problem arises.

Consider that we prepare an arbitrarily large, isolated, quantum system. Think about what happens happens within that system. Can it undergo decoherence, while isolated from the outside world?
Yes

Decoherence with what?
You said "within". That means you have factorized it so the question becomes can one subsystem be decohered by another.

Can a meaningful measurement be made within it, while isolated from the outside world?
Yes

If yes, then how do we determine how the classical system (or environment) emerges, which the quantum subsystems can decohere with and be measured by?
If no, then how did the first classical system (or environment) emerge?
I don't know how we determine how, in fact I'm not sure what the question means. I can tell you how the classical system emerges. It emerges due to entanglement of the two subsystems. This then evolves into an improper mixture through decoherence.

 

[Derek Potter]

As I understand it, the theorem says that, given a state and a Hamiltonian, we can always find a basis in which the unitary evolution induced by the Hamiltonian does nothing but phase rotate the state. In this basis, called the "Nirvana basis", nothing happens, since phase rotation does not change any physical observables.

Well I'd still like to know what such a Nirvana basis looks like as I have a distinct feeling, nothing more, that the title "Nothing happens in the Universe of the Everett Interpretation" may be a slight extrapolation.

 

[PeterDonis]

I'd still like to know what such a Nirvana basis looks like

Section 3 of the paper has the key equations. He considers both a time-independent "Nirvana" factorization (in which each branch of the induced superposition phase rotates at its own frequency, but the branches don't interact) and a time-dependent one (in which each branch does not change at all).

 

[Ilja]

But what does it mean that there is a factorization in which nothing happens? What are the non-interacting subsystems like?

It means that MWI is inadequate to describe our world, because in our world something happens. Thus, MWI in this factorization is definitely false. If, now, MWI in another factorization is true, that means, MWI is incomplete without defining also the factorization, as part of the physical structure.

I have made a similar argument that the structures which MWI officially accepts are not sufficient to define physics in http://arxiv.org/abs/0901.3262

 

[Ilja]

I don't know why such an obvious, if unstated, assumption is crucial. Has someone changed the definition of MWI so that it works without physics?

MWI is supposed to be an interpretation of the most fundamental physical theory. Thus, there is no physics except the physics defined and explicitly described by MWI, or MWI does not describe what it claims to describe.

And this incompleteness is, of course, the point. It claims to be complete, argues, in particular, that dBB theory contains unnecessary additional things, a claim which would be nonsensical if MWI would not describe physics completely.

 

[Derek Potter]

MWI is supposed to be an interpretation of the most fundamental physical theory. Thus, there is no physics except the physics defined and explicitly described by MWI, or MWI does not describe what it claims to describe.

And this incompleteness is, of course, the point. It claims to be complete, argues, in particular, that dBB theory contains unnecessary additional things, a claim which would be nonsensical if MWI would not describe physics completely.

Of course MWI defines and describes all the necessary physics. The state is not merely a static ray in Hilbert space, it moves around, driven by a differential equation featuring the Hamiltonian. There's the physics that allows the state to evolve.

 

[Derek Potter]

It means that MWI is inadequate to describe our world, because in our world something happens. Thus, MWI in this factorization is definitely false. If, now, MWI in another factorization is true, that means, MWI is incomplete without defining also the factorization, as part of the physical structure.

I have made a similar argument that the structures which MWI officially accepts are not sufficient to define physics in http://arxiv.org/abs/0901.3262

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post? Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

 

[atyy]

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post? Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

But if your view is BMW, then in a sense what you and Ilja are saying are the same. He is complaining about the lack of extra structure. Is it clear that your stability condition for something to become observable isn't "extra structure", especially when you consider how to implement it in detail?

 

[Derek Potter]

But if your view is BMW, then in a sense what you and Ilja are saying are the same. He is complaining about the lack of extra structure. Is it clear that your stability condition for something to become observable isn't "extra structure", especially when you consider how to implement it in detail?

It would help if there was some sort of prior agreement about what is meant by structure. Regardless of Nirvana frames it seems Ilja regards factorization as part of the physics. Factorization is a mathematical technique that applies to tensors and requires no more physics than addition. Of course my tensor theory is rubbish so I have to say if factorizability does not follow from "a vector space equipped with an inner product" then the usual "Postulate 1" of QM should be amended to include the extra structure.

Your point about stability - similarly. There is still no complete consensus about when a measurement can be said to be complete. Impatient types who insist on adding a postulate to cover the present uncertainty will no doubt also insist that the postulate is extra physics. I would take a more conservative approach. Use any criterion you like and give the result a different name each time. This doesn't add anything to the physical structure, it just defines the scenario you want to analyse. We are free to do this because MWI claims to eliminate postulates about observations and instead derive them. So instead of importing poorly-defined "observations" into the structure from everyday life, we now have complete freedom to invent different types of measurement and see which ones MWI predicts.

 

[atyy]

Use any criterion you like and give the result a different name each time. This doesn't add anything to the physical structure, it just defines the scenario you want to analyse.

So you end up with the subjective criterion of the observer. Is this any different from Copenhagen? Doesn't this leave the measurement problem open?

 

[Ilja]

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post?

Of course, the aim of any physical theory is to predict and explain what happens in the world which I observe. It is free to add something I do not observe, if there is some necessity for this. But if it does not explain anything, it can be simply rejected, and we can go back to the Bible which explains at least something - by unexplainable decisions of some guy named God.

Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

But then we are back to a theory which explains nothing. I do not need any theory to know that our particular world is logically possible - else if would be impossible for me to live in it.

 

[Derek Potter]

Of course, the aim of any physical theory is to predict and explain what happens in the world which I observe. It is free to add something I do not observe, if there is some necessity for this. But if it does not explain anything, it can be simply rejected, and we can go back to the Bible which explains at least something - by unexplainable decisions of some guy named God. .

Actually God's decisions are explained throughout the Bible - in Biblical terms. It probably isn't a good idea to jump on the fashionable bandwaggon of holding up Biblical belief as a model of irrationality. Some people might get offended. It is also against forum rules. And it might annoy God. MWI also explains itself - the particular world you experience is one of many. MWI does not single out any particular world and then put "you" in it. You are in every world. All worlds are equally real, you seem to be expecting MWI to single out one world to be more real than the others. You are free to make up an interpretation that does this, and it will certainly require extra structure, but it will not be MWI.

But then we are back to a theory which explains nothing. I do not need any theory to know that our particular world is logically possible - else if would be impossible for me to live in it.

What's that got to do with anything at all? The question isn't whether you exist but how MWI explains it.

 

[Demystifier]

Why should MWI have to justify the mathematical axiom of choice? See https://en.wikipedia.org/wiki/Axiom_of_choice

The set-theoretic axiom of choice has nothing to do with that.

 

[Demystifier]

I didn't exactly" bring up" Schwindt's paper, the thread was started by me asking for help in understanding it.

So do you now understand it better?

 

[Derek Potter]

So you end up with the subjective criterion of the observer.

If photons have subjective states then yes, why not?

Is this any different from Copenhagen?

Copenhagen means different things to different people. I dare say it could absorb MWI and Harry Potter if it wanted to. But if you mean "does defining observations and measurements before arguing whether MWI explains them, maintain the quantum/classical cut?", then I guess the answer's obvious: it depends on the definition.

Doesn't this leave the measurement problem open?

The measurement problem *is* open. There is no consensus definition of a measurement. That's hardly MWI's fault.

There's an important principle here. Well-formed theories rest on suppositions without which the theory cannot be built up. QM is (said to be) a theory about observations - an observation postulate is required to ground the maths in consensus reality. It is there, intact and unexplained, imported from everyday experience. It hides a massive assumption: that there are measurements and that the prosaic model of someone using a tape measure and noting down the results actually means something.

MWI, however, removes the observation postulate. Instead, measurements are derived or described. But this means that the orthodox assumptions come to the surface. The tape measure is, rather appropriately, replaced by entanglement, it seems we can describe the physical process quite well in this quasi-operational way. The noting down of results is however, less clear. Is leaving a permanent record a sufficient or necessary condition? etc. Quantum erasure highlights the nee3d to be consistent in what you want MWI to explain.[/QUOTE]

 

[Demystifier]

The state is not merely a static ray in Hilbert space, it moves around, driven by a differential equation featuring the Hamiltonian.

But there is a basis in which it does not move around. The basis in which only the phase changes.

Perhaps it is easier to understand it in a classical analog:

Consider a 3-dimensional universe containing nothing but one classical pointlike particle moving around. Does anything happen in such a universe? You can consider the system in coordinates (the classical analog of basis) comoving with the particle. In these coordinates the particle does not move. So nothing happens in the universe with one particle.

How about the 3-dimensional universe with two particles? Now there is relative motion of two particles, so one may think that something really happens in the case of two particles. However, the mathematics of two particles in 3 dimensions is the same as mathematics of one particle in 6 dimensions. So mathematically, we may say that we still have one particle, only in 6 dimensions. So from that point of view nothing happens even with two particles, because they are mathematically equivalent to one particle.

How to avoid the conclusion that nothing happens in a universe with two particles? Only by saying that physically we really do have two particles (in 3 dimensions) and not one particle (in 6 dimensions). But we cannot say that only from the mathematical structure of classical mechanics. There must be some additional structure involved, something which tells us that two particles in 3 dimensions is not the same as one particle in 6 dimensions. So pure classical mechanics cannot explain why something happens.

Likewise, pure quantum mechanics (the Schrodinger equation and nothing else) also cannot explain why something happens.

 

[Derek Potter]

The set-theoretic axiom of choice has nothing to do with that.

Wikipedia - Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.
The question was If all you have is the pure state vector of the entire universe, how do you pick out the "cat" subspace? If your answer is, "well, I pick some particular basis...", then what justifies picking out that particular basis?
Seems to me the axiom is needed otherwise we can't select one space out of a collection (one in this case) of bins full of factorizations. But outside of its normal home it is so obvious that needs no recognition. Or so I thought until the question was raised. But of course if you were to insist that the axiom does not apply, I would not mind - the point still stands: why should MWI have to justify my being able to consider a cat if the existence of cats has already been established?. Come to think of it, that might be a better way of putting it.

 

[Demystifier]

Seems to me the axiom is needed otherwise we can't select one space out of a collection

The axiom of choice guarantees that you can select one member of the collection. But the physical question is - which one? The axiom of choice does not answer that crucial physical question, so that's why it is irrelevant in this context.

From the set-theoretic point of view, let me also note that the axiom of choice is really important only when there is an infinite number of collections, and you want to select one member from each of the collections. In the case of a finite number of collections, the axiom of choice is trivial.

 

[Ilja]

Actually God's decisions are explained throughout the Bible - in Biblical terms. It probably isn't a good idea to jump on the fashionable bandwaggon of holding up Biblical belief as a model of irrationality. Some people might get offended.

Sorry, but I have described it here as more rational than MWI, so there is no base for christians to be offended, SCNR. And I can refer to Romans 11,33.

MWI also explains itself - the particular world you experience is one of many. MWI does not single out any particular world and then put "you" in it. You are in every world. All worlds are equally real, you seem to be expecting MWI to single out one world to be more real than the others. You are free to make up an interpretation that does this, and it will certainly require extra structure, but it will not be MWI.
What's that got to do with anything at all? The question isn't whether you exist but how MWI explains it.

Sorry, but this is an "explanation" which does not explain anything. It is antiscience pure. If this would be MWI, MWI should be rejected as anti-scientific. Those who argue that MWI needs more structure are, in fact, assuming that MWI is part of science, and, in particular, an interpretation of quantum theory. If one follows your variant of MWI, it should be rejected without further need of argumentation, simply as obviously anti-scientific.

It would be, in particular, in disagreement with claims that MWI gives the Born rule, because the Born rule makes differences between different worlds, assigning different probabilities to them.

 

[atyy]

The measurement problem *is* open. There is no consensus definition of a measurement. That's hardly MWI's fault.

But the point of MWI is to solve the measurement problem, so if MWI doesn't solve it, it fails.

MWI, however, removes the observation postulate. Instead, measurements are derived or described. But this means that the orthodox assumptions come to the surface. The tape measure is, rather appropriately, replaced by entanglement, it seems we can describe the physical process quite well in this quasi-operational way. The noting down of results is however, less clear. Is leaving a permanent record a sufficient or necessary condition? etc. Quantum erasure highlights the nee3d to be consistent in what you want MWI to explain.

Here you seem to be saying MWI does solve the measurement problem (remove the observation postulate). In MWI the problem is if everything happens, including seeing dead and alive cats, then MWI has to explain why we don't see such things.

One way it can do so is to say that consciousness is not possible if one does not see classical outcomes. But that is a theory of consciousness, and certainly is an additional postulate.

The other way to do it is to use the stability criterion, but then here if one is not making a statement about consciousness, then one is making a statement about what additional structure is real - ie. it exists even if there are no observers. But if one is talking about reality, the stability criterion seems to be something like Bohmian trajectotries.

 

[Derek Potter]

The axiom of choice guarantees that you can select one member of the collection. But the physical question is - which one? The axiom of choice does not answer that crucial physical question, so that's why it is irrelevant in this context.

OK, but why is the question crucial? There is nothing special about the cat factorization except that we happen to be thinking about it. Why does MWI have to explain my choice to think about cats?

Your analogy with classical phase space:

How to avoid the conclusion that nothing happens in a universe with two particles? Only by saying that physically we really do have two particles (in 3 dimensions) and not one particle (in 6 dimensions). But we cannot say that only from the mathematical structure of classical mechanics. There must be some additional structure involved, something which tells us that two particles in 3 dimensions is not the same as one particle in 6 dimensions. So pure classical mechanics cannot explain why something happens.
Likewise, pure quantum mechanics (the Schrodinger equation and nothing else) also cannot explain why something happens.

is helpful but needs fleshing out. Instead of saying "we really have two particles" we could equally well define, say a collision as a certain subspace. Since the time dependency has been removed to the coodinate system, this means that the subspace moves around and a collision happens when the subspace hits the particle. Events therefore are made possible if one defines a moving subspace in the otherwise nothing-happens frame. I think the same thing applies in QM - events only happen relative to a suitable frame but they do happen.

 

[Derek Potter]

Sorry, but this is an "explanation" which does not explain anything. It is antiscience pure. If this would be MWI, MWI should be rejected as anti-scientific. Those who argue that MWI needs more structure are, in fact, assuming that MWI is part of science, and, in particular, an interpretation of quantum theory. If one follows your variant of MWI, it should be rejected without further need of argumentation, simply as obviously anti-scientific.

That's ridiculous. I am not saying MWI requires extra structure. I am saying that a version of MWI which singles out one world would require extra structure. MWI does not single out one world. That was a requirement added by you.

It would be, in particular, in disagreement with claims that MWI gives the Born rule, because the Born rule makes differences between different worlds, assigning different probabilities to them.

Do you mean different probabilities within each world or different probabilities of each world in an ensemble - the weighting problem?

 

[Derek Potter]

But the point of MWI is to solve the measurement problem, so if MWI doesn't solve it, it fails.

Right, so MWI doesn't solve the clabbernuccle problem.
What clabbernuccle problem?
I don't know, I thought MWI was supposed to solve it. Not much use if it can't even say what it's supposed to solve.

Here you seem to be saying MWI does solve the measurement problem (remove the observation postulate). In MWI the problem is if everything happens, including seeing dead and alive cats, then MWI has to explain why we don't see such things.

Are you sure MWI has to explain anything that is specifically about us? A sensible definition of "see" would be "affected by" and "us" would be "any other system".

One way it can do so is to say that consciousness is not possible if one does not see classical outcomes. But that is a theory of consciousness, and certainly is an additional postulate.

Well it shouldn't be a theory of consciousness, it should be a theory of persistent observer states. That means we're talking about ...

The other way to do it is to use the stability criterion, but then here if one is not making a statement about consciousness, then one is making a statement about what additional structure is real - ie. it exists even if there are no observers.

MWI is generally ontic. Ontology is not mathematical nor physical structure.

But if one is talking about reality, the stability criterion seems to be something like Bohmian trajectotries.

What? Impossible to define consistently? :p

 

[Derek Potter]

OK, so this topic has bumped my post count up by 50 which suggests, correctly, that I have no life outside PF. In answer to Demystifier, No, I do not understand Schwindt's idea any better at all. I have had to clarify a few peripheral issues about the measurement problem but the thread has degenerated into wrangling about whether MWI is a viable interpretation - a long stretch from Schwindt's claim that Nothing happens in the Universe of the Everett Interpretation. Unfortunately, one must give people the benefit of the doubt and assume that what they have said is intended to be relevant and therefore must be responded to. The thread therefore branches more than a cat in MWI.

I would respectfully request that any further posts be kept on-topic and directly to the point. Thanks.

 

[Demystifier]

OK, but why is the question crucial? There is nothing special about the cat factorization except that we happen to be thinking about it. Why does MWI have to explain my choice to think about cats?

We think about cats because we observe cats. Why do we observe cats? The role of (theoretical) physics is to explain the observations,
so physics should explain why do we observe cats. If MWI cannot explain the observations, or more specifically if it cannot explain why do we observe cats, then MWI has not much to do with physics (not even with philosophy of physics). In that case, we should discuss MWI in some other forum.

Or let me put it in a different form. If MWI is the answer, then what is the question?

 

[Derek Potter]

We think about cats because we observe cats. Why do we observe cats? The role of (theoretical) physics is to explain the observations,
so physics should explain why do we observe cats. If MWI cannot explain the observations, or more specifically if it cannot explain why do we observe cats, then MWI has not much to do with physics (not even with philosophy of physics). In that case, we should discuss MWI in some other forum.

Who says MWI doesn't explain why we observe cats? That is precisely what it does do.

 

[Demystifier]

Who says MWI doesn't explain why we observe cats? That is precisely what it does do.

I think we are moving in circles:
Now I will ask - how does it explain it?
You will say - by decoherence.
I will say - but decoherence requires a split between "system" and "environment".
You will say - but the split is arbitrary made by our way of thinking, and MWI does not need to explain our thinking.
Then I will say - but we think in that way because this is what we observe.
Then you will say - MWI can explain why do we observe that.
I will ask - how?
You will say - by decoherence.
... and so on, and so on ...

Can you step out from that circle?

 

[Demystifier]

events only happen relative to a suitable frame but they do happen.

Are you really saying that all frames are real, and that "we" are just one of these frames?

If so, then in MWI "we" are just one of the branches defined by one of the frames. It does make some sense, but then the MWI reality is not merely the vector in the Hilbert space. Instead, the MWI reality is the collection of all possible decompositions of that vector in various bases. Different decompositions of the same vector are not considered equivalent. Is it what you are saying?

Very roughly, it is as if in classical physics 3 apples, 1+1+1 apples, 1+2 apples, and 2+1 apples were different things, and when you have 3 apples you really simultaneously have all these combinations as different objects.

If this is what you mean, then I can understand you. But then you should also be able to understand the paper we are discussing. In that paper the author assumes that different decompositions of the same vector are the same object. If that assumption is rejected, then his conclusions are no longer valid.

 

[Derek Potter]

Are you really saying that all frames are real, and that "we" are just one of these frames?

If so, then in MWI "we" are just one of the branches defined by one of the frames. It does make some sense, but then the MWI reality is not merely the vector in the Hilbert space. Instead, the MWI reality is the collection of all possible decompositions of that vector in various bases. Different decompositions of the same vector are not equivalent. Is it what you are saying?

Very roughly, it is as if in classical physics 3 apples, 1+1+1 apples, 1+2 apples, and 2+1 apples were different things, and when you have 3 apples you really simultaneously have all these combinations as different objects.

If this is what you mean, then I can understand you. But then you should also be able to understand the paper we are discussing. In that paper the author assumes that different decompositions of the same vector are the same object. If that assumption is rejected, then his conclusions are no longer valid.

That is exactly how I see it. If Schwindt makes that assumption then he must have a very strange idea of what comprises an object! The amplitude of |dog> in a Schrodinger's cat experiment may be extremely small, but it is a valid basis vector in the DOG decomposition. Schrodinger's cat is a dog!

 

[Ilja]

That's ridiculous. I am not saying MWI requires extra structure. I am saying that a version of MWI which singles out one world would require extra structure. MWI does not single out one world. That was a requirement added by you.

You have misunderstood. MWI requires additional structure to recover the laws of physics. This is the argument of the paper discussed here, that without additional structure MWI would be compatible with Nirvana, which is obviously very different physics, and it was also my argument in http://arxiv.org/abs/0901.3262 that without additional structure it would be compatible with very different physics. You have, AFAIU, not questioned these arguments themself.

So, if you reject additional structure, the argument is not about singling out a particular world, but about singling out a particular set of general laws of physics.

 

[Derek Potter]

You have misunderstood. MWI requires additional structure to recover the laws of physics. This is the argument of the paper discussed here, that without additional structure MWI would be compatible with Nirvana, which is obviously very different physics, and it was also my argument in http://arxiv.org/abs/0901.3262 that without additional structure it would be compatible with very different physics. You have, AFAIU, not questioned these arguments themself.

So, if you reject additional structure, the argument is not about singling out a particular world, but about singling out a particular set of general laws of physics.

Oh. Well something you said did seem to suggest that but I thought it was too far-fetched for you to really mean it. I don't think you're right in your interpretation of Schwindt. I think Schwindt assumes normal physics, the unitary evolution under a Hamiltonian law which *is* all relevant physics. He creates a Nirvana frame with normal physics driving the evolution of the state. I am not really interested in any wild claims that MWI can derive the magnitude of electric charge and the mass of the fundamental particles purely from tensor theorems.

 

[Ilja]

Oh. Well something you said did seem to suggest that but I thought it was too far-fetched for you to really mean it. I don't think you're right in your interpretation of Schwindt. I think Schwindt assumes normal physics, the unitary evolution under a Hamiltonian law which *is* all relevant physics. He creates a Nirvana frame with normal physics driving the evolution of the state. I am not really interested in any wild claims that MWI can derive the magnitude of electric charge and the mass of the fundamental particles purely from tensor theorems.

Of course it is not the job of MWI to deifne particle masses. But it is the job to to allow for sufficient structure to define fixed laws of physics. And in this sense, MWI is insufficient. Say, classical mechanics is fine with defineing that there is some abstract configuration space - with some examples for illustration - together with a minimum principle for some Lagrangian. This specifies what you have to define to specify the complete theory.

 

[Demystifier]

That is exactly how I see it.

OK, it's good to know that now we understand each other.

If Schwindt makes that assumption then he must have a very strange idea of what comprises an object!

I would put it differently. He takes that assumption not because he likes it, but because he thought it is assumed by those who pursue MWI. And then he (correctly) shows that such an assumption is not consistent with the existence of physical objects. So at the very least, he has proved a no-go theorem which shows how MWI should not be understood: In MWI, the reality is not the vector in the Hilbert space.

He does not say what is the reality in MWI, but now the compact answer seems to be: the set of all possible decompositions of the vector in the Hilbert space.

So, what to say about such an interpretation of QM? First, I think it is logically and mathematically consistent. Second, I think it is very inelegant. So I don't reject it, but I also don't like it.