Problems with Many Worlds Interpretation

[kith]

This quote is from the introduction of the paper:

The Everett Interpretation (EI, also known as Many Worlds) [1, 2, 3] is in a sense the minimal interpretation of quantum mechanics (QM): It basically claims that only the state vector |ψ> of the universe and the global Hamilton operator H are fundamental. Everything else follows from the dynamics given by the Schrödinger equation. In particular, the state vector does not represent the state of some objects. It is the object itself.

The state vector is the universe? This sounds quite odd. I don't think this is a correct discription of MWI.

 

[Quantumental]

This quote is from the introduction of the paper:

The state vector is the universe? This sounds quite odd. I don't think this is a correct discription of MWI.

His description sounds like the typical Everettian account.
What way would you describe it differently?

 

[kith]

His description sounds like the typical Everettian account.

This is something general. We have objects and we have states of them. A state of an object can't be the object itself. Or is this just nitpicking?

What way would you describe it differently?

I have only a vague idea of the MWI. I imagine it like this: |ψ> is the state of the universe. In the beginning, the universe consisted of distinct physical systems. Their existence, states and interactions are the initial conditions of the universe. After time evolution, we have entanglement and many worlds. Maybe this is not the standard view? If so, what is it?

 

[Dmitry67]

I don't think that many adherents of MWI would agree that consciousness is the key to solve the basis problem.

Everything, absolutely everything you perceive is based on that very specific basis – your consciousness (note that it is not the same as basis of your physical brain, and many similar states of your brain can be mapped into the same state of your consciousness – consciousness is not aware of some minor movement of individual molecules, for example. So it is more like an ensemble of QM states). How can one deny a central role of it?

 

[Demystifier]

Everything, absolutely everything you perceive is based on that very specific basis – your consciousness (note that it is not the same as basis of your physical brain, and many similar states of your brain can be mapped into the same state of your consciousness – consciousness is not aware of some minor movement of individual molecules, for example. So it is more like an ensemble of QM states). How can one deny a central role of it?

Yes, but MWI people want to DERIVE everything (including consciousness) from the wave function.

 

[Demystifier]

I am probably missing something very basic, but it seems to me that the point that the vectors of the same norm all look the same is very important, at the same time he points out that the theory comes with more than just the Hilbert space, there is a distinguished operator (the Hamiltonian). That operator gives extra structure, the vectors don't look the same any more, some are eigenvectors some are not, for example. So it isn't true that the vectors look the same. This may be irrelevant for his arguments but at least as far as I read he did not make any comment on it. Also why is the factorization needed? They way I understand the MWI, very superficially, factorizations have nothing to do with the interpretation.

Later in the paper he explains that only the wave function is what matters, in the sense that if wave function at all times is given, then the Hamiltonian is irrelevant. The Hamiltonian only serves to determine wave function at all times for the case when it is not already known.

 

[Demystifier]

The state vector is the universe? This sounds quite odd. I don't think this is a correct discription of MWI.

More precisely, in MWI the state vector is the multiverse - the collection of all "universes".

 

[Demystifier]

What are your take on the paper?
Seems to be a very interesting one, but seeing as how many papers have been written about MWI I struggle to believe he has found a new "fatal" flaw

After the reading of the whole paper, I want to say that I am simply impressed.

The argument he presents is not new, but, in my opinion, nobody ever presented this argument so clearly.

In a nutshell, the argument by Jan-Markus Schwindt in
http://arxiv.org/abs/1210.8447
is this:

To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

As reasonable possibilities for the additional structure, he mentions observers of the Copenhagen interpretation and particles of the Bohmian interpretation. Consciousness which Dmitry67 likes to talk about could also be such an additional structure. But whatever the additional structure is, it is no longer pure MWI. It is MWI with an additional structure, which may be fine, but then one cannot use the typical MWI argument that it is the simplest interpretation without an additional structure, period.

 

[kith]

More precisely, in MWI the state vector is the multiverse - the collection of all "universes".

After skimming the paper, I saw that Schwindt also has commented on this. The argument for identifying the physical objects with the mathematical structure seems to be nothing inherent to the MWI but affects all self-sufficiant physical theories. So if we say that the state vector is the multiverse, we also have to say that a trajectory in phase space in classical mechanics is the particles. I don't think this is appropriate because the meaning of a mathematical structure is always given by the person who uses it to describe an already existing object. This is similar to the conclusion of Schwindt in section 6.3.

Of course, this hasn't much to do with his mathematical argument about the factorization which is definitely interesting.

 

[Quantumental]

After the reading of the whole paper, I want to say that I am simply impressed.


To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

Ok, but why isn't David Wallace's FAPP and arguments from functionalism sufficient?
I noticed that the author mentioned something against Dennett's view of mind, so I hope his argument isn't hinging upon rejecting functionalism?

I also noticed that the author didn't cite any paper more recent than 2003, this seems to ignore all the work of Wallace and Saunders since the early 00's

 

[Fredrik]

The state vector is the universe? This sounds quite odd. I don't think this is a correct discription of MWI.

Sounds standard, but as Demystifier already mentioned, the "universe" in that sentence refers to a physical system that contains all the worlds. However, I would like to make another correction. Since ψ and cψ represent the same state for all complex numbers c, it's more accurate to say that each 1-dimensional subspace is a possible state of our world.

This is something general. We have objects and we have states of them. A state of an object can't be the object itself. Or is this just nitpicking?

When we're dealing with small subsystems of the universe that can be isolated from their environments, a state is (a mathematical representation of) an equivalence class of preparation procedures. (Two preparation procedures are considered equivalent if experiments can't determine which one was used). Some of those states (the "pure" states) can be represented by wavefunctions. So it's an interpretation-independent fact that wavefunctions can be thought of as representations of equivalence classes of preparation procedures. What this author is telling you is that a definition of an MWI includes an assumption about what else a wavefunction represents: It represents all the properties of the system, or to put it differently, it represents the system itself.

After skimming the paper, I saw that Schwindt also has commented on this. The argument for identifying the physical objects with the mathematical structure seems to be nothing inherent to the MWI but affects all self-sufficiant physical theories.

It's definitely not obvious that it makes sense to think of quantum theories this way.

So if we say that the state vector is the multiverse, we also have to say that a trajectory in phase space in classical mechanics is the particles.

What you should say is that each point in phase space (they are what correspond to the 1-dimensional subspaces of a Hilbert space) represents all the properties of all the particles in that classical particle theory.

 

[Fredrik]

To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

This is something I've been thinking for years, but I don't think I've heard anyone other than me say it.

My own interpretation of what this means is that it's wrong to assume that the 1-dimensional subspaces spanned by preferred basis vectors are the only ones that represent worlds. I think a proper definition of a MWI should start with the assumption that every 1-dimensional subspace is a world.

This changes the role of the decoherence argument that's used to identify the preferred basis associated with a given split into subsystems. I suspect that when done right, this argument will show that the basis vectors identify the worlds where the subsystems' ability to store information about each other is at a maximum. Information storage is a crucial part of consciousness, so the worlds singled out by the preferred basis are the worlds where conscious observers are the most likely to exist. So consciousness kind of has a role to play here. It doesn't actually do anything. It just gives us a reason to not care about most of the worlds. We're not particularly interested in the worlds where consciousness can't exist, because none of them is our world.

 

[kith]

What this author is telling you is that a definition of an MWI includes an assumption about what else a wavefunction represents: It represents all the properties of the system, or to put it differently, it represents the system itself.

Yes, I get this. I also get that he tries to prove that we can't get our 3D world experience out of it. What I don't get is why this should be something inherent only to the MWI. As Schwindt himself mentions in section 6.3, how do we get our 3D world experience from the point in 3n-dimensional configuration space of Bohmian mechanics? And I'd like to add: how do we get our 3D world experience from the point in 6n-dimensional phase space of classical mechanics?

Please forgive my sloppiness regarding some technical details, I appreciate your corrections. ;-)

 

[Dmitry67]

To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI.

But why do you need to separate the worlds?

Do taxons "really" exist in biology or do one need to "separate" them? Do different cat breeds exist because we, humans, assign them different labels or are they an objective reality?

Universe wavefunction evolves the same way no matter how you artificially "separate" the "worlds". In fact, it does not care how you "define" the "worlds". It does not care about "splitting"... It just evolves... I am sure you agree with me because BM shares with MWI the same wavefunction...

All these problems with the "worlds", "splitting", "preferred basis" etc are artificial because this is how our human mind works - we want to stay on a solid ground, we got used to split reality into pieces and to give these pieces names and definitions... But once again, our common sense reasoning is wrong...

P.S.
Another example. Go back to the very beginning, say, 10^-20sec after the Big Bang. Hot quark plasma filled the whole Universe. No solid objects, no separate systems... Can you separate "worlds" in that chaos? What "preferred basis" can you choose in hot plasma? If you have to work without these notions at 10^-20sec, why do you think they become obligatory in colder Universe? (Note that my approach with consciousness doesn't have any problems with world at t=10^-20s)

 

[Fredrik]

Yes, I get this. I also get that he tries to prove that we can't get our 3D world experience out of it. What I don't get is why this should be something inherent only to the MWI. As Schwindt himself mentions in section 6.3, how do we get our 3D world experience from the point in 3n-dimensional configuration space of Bohmian mechanics? And I'd like to add: how do we get our 3D world experience from the point in 6n-dimensional phase space of classical mechanics?

I don't know Bohmian mechanics well enough to comment about that, but each point in the phase space of a classical particle theory specifies the position and momentum of each particle. So if you know the point (and the Hamiltonian, which determines the time evolution), you have a very clear picture of what's happening in the world described by the theory.

QM doesn't tell us (unambiguously) what is actually happening to physical systems. It just associates probabilities with possible results of experiments. The MWI on the other hand claims that the wavefunction (or rather the 1-dimensional subspace it spans) is a description of what's actually happening to a physical system that's large enough to include the observers. The problem is that this description involves superpositions, and we know that observers never experience superpositions directly. So how can the MWI's claim be true?

This is why it will be hard to take the MWI seriously unless it can explain what sort of experiences the observers can have. At the very least, it should be able to explain why an observer always perceives a cat to be either dead or alive, and never |dead> + |alive>.

 

[kith]

I don't know Bohmian mechanics well enough to comment about that, but each point in the phase space of a classical particle theory specifies the position and momentum of each particle.

How do you deduce how much particles you have and how do you know they act in 3D space given only a state in abstract phase space? You have to add the knowledge that the corresponding experiment is done by an observer in 3 dimensions. So if we can't deduce this from a classical state, is it really reasonable to demand that we can deduce it from the state vector/ray in the MWI?

This is only about the factorization question and not about the emergence of a preferred basis once we know how to factorize our Hilbert space, about the ermergence of probabilities or about the emergence of single outcomes.

 

[Darwin123]

Hello,

While the majority of physicists embrace the Many Worlds interpretation of quantum decoherence, I am holding out hope for the Copenhagen interpretation or better yet, a undiscovered interpretation.

I am a retired physicist. I haven't met any physicist who promotes that Many Worlds interpretation of quantum decoherence. That is to say, in my universe there are very few physicists that endorse the Many World's interpretation of Quantum mechanics.

Most physics students in my universe learn the Copenhagen interpretation of quantum mechanics. I have met many other physicists in my universe that endorse the Copenhagen interpretation of quantum mechanics. My opinion is that there are better interpretations of quantum mechanics. I am really interested in Quantum Decoherence explanations of the so called wave collapse. For a while, I was really interested in the Stochastic Electrodynamics explanations of quantum mechanics. Recent experiments have shown that stochastic electrodynamics may not be a valid theory. However, I keep hoping.

Most of your objections to the multiworld interpretation are really objections to quantum mechanics. In the multiworld interpretation, for instance, there is a universe somewhere where someone very much like you has already turned into a sun. You are not that universe or you wouldn't be reading this. However, in the Copenhagen view there was always a very small probability that you would turn into a sun. You are lucky it didn't happen, or you couldn't read this.

The turning into a sun scenario is a type of quantum tunneling. You are suggesting that the atoms of your body have a finite probability of tunneling from a low density quantum state (you right now) into a high density quantum state (a sun). This is a possibility no matter what interpretation you pick. The probability is astronomically small, but one can estimate it with quantum mechanics. I hope that I didn't frighten you!

Quantum tunneling has been proven in many, many experiments on a small scale. How one interprets it is epistomology. However, the phenomenon has been observed. Caclulating the odds that an object like you will turn into a sun within the next 5 minutes involves extrapolating from a small scale to a large scale. Maybe extrapolating it doesn't work. However, the interpretation doesn't change the theory.

The main objection to Multiworld Interpretation isn't on your list. It isn't even wave interference, per se. It is the uniqueness of the basis. The set of possible universes seems to be set by the experimental apparatus in one universe. This is more mathematics than physics.

The Fourier decomposition isn't unique. The basis functions of the Fourier transform are not unique. Yet, the basis functions define the set of universes. This is a logical paradox, not just something that appears to be improbable. So very few physicists subscribe to the Multiworld's approximation.

I conjecture there is a way around this objection. In any case, I have lost interest in the Multiple World's interpretation of quantum mechanics because it is not mathematically consistent. There still seems to be a type of "multiworld theory" in general relativity and cosmology. I have a mild interest in this because there are hypothetical experiments that can be done, and may someday be done. However, this subset of general relativity theory is just an analogue of the multiworlds theory of quantum mechanics.

I am really interested in what made you think that multiworld interpretation was a commonly accepted theory by physicists.

There are a lot of physicist want to bees. Depak Chopra is not a physicist. Timothy Leary was not a physicist. Carlos Castenada was not a physicist. Gene Roddenbury was not a physicist.

 

[Hurkyl]

Dynamics is nothing but a unitary transformation from one point in the Hilbert space to another. As long as all points in the Hilbert space look the same (which is one of central claims in the paper), such dynamics does not bring anything interesting.

But we can distinguish between symmetries that preserve the laws of physics and those that do not. This is the most important idea behind a symmetry based analysis of physical theories.

 

[bohm2]

In case others haven't come across the papers, note that Schwindt does mention and references 2 authors (M. Dugic and J. Jeknic-Dugic) that made the same argument. On of the papers by these 2 authors was posted previously in this thread. I believe that Ilja Schmelzer also makes a similar argument in some of his papers.

 

[Demystifier]

Ok, but why isn't David Wallace's FAPP and arguments from functionalism sufficient?

I don't see how functionalism can resolve the basis problem.

 

[Demystifier]

Yes, I get this. I also get that he tries to prove that we can't get our 3D world experience out of it. What I don't get is why this should be something inherent only to the MWI. As Schwindt himself mentions in section 6.3, how do we get our 3D world experience from the point in 3n-dimensional configuration space of Bohmian mechanics? And I'd like to add: how do we get our 3D world experience from the point in 6n-dimensional phase space of classical mechanics?

Please forgive my sloppiness regarding some technical details, I appreciate your corrections. ;-)

Yes, that's an important question to answer.

Note that he discusses Bohmian mechanics (BM) in TWO contexts. First at page 18 where he explains why BM does not have the basis problem. Second at page 21 where he suggests that it might. So which argument is correct? Both!

Namely, the second argument is a CONDITIONAL argument, valid only if one "takes mathematical universe serious" (see the end of page 20). Indeed, the title of section starting at page 20 is "Is the world a mathematical structure?". He correctly points out that if it is, then Bohmian mechanics also has a problem. But so has classical mechanics in configuration or phase space. Yet this is not really a problem for Bohmians, or for classical physicists, because they typically don't think that "the world is a mathematical structure". Such thinking is more typical for many-world people.

 

[Demystifier]

But why do you need to separate the worlds?

To explain the illusion of wave-function collapse, which, indeed, is the main motivation for studying many worlds in the first place.

 

[Demystifier]

But we can distinguish between symmetries that preserve the laws of physics and those that do not. This is the most important idea behind a symmetry based analysis of physical theories.

He discusses that issue as well. What matters in MWI is not the Hamiltonian (with its symmetries), but the wave function (as a function of time). If you know the wave function, you don't need the Hamiltonian. A wave function is a particular solution, and in general it does not have any symmetries which the Hamiltonian does.

 

[Dmitry67]

BTW, what is the current position of BM with the issue about the cosmology. AFAIK, there is a hidden rest frame in BM, right? But in expanding Universe no objects 'at rest' in some frame can have timelike worldlines globally. For example, let's say that here, on Earth, the hidden rest frame is the same as 'rest to CMB'. So we have a 'hidden' center of the universe in BM :) But outside of our Hubble space the 'NOW' in the hidden rest frame, normally spacelike, becomes timelike.

 

[Demystifier]

In case others haven't come across the papers, note that Schwindt does mention and references 2 authors (M. Dugic and J. Jeknic-Dugic) that made the same argument. On of the papers by these 2 authors was posted previously in this thread. I believe that Ilja Schmelzer also makes a similar argument in some of his papers.

As I said, his (Schwindt's) argument is not new, but in my opinion, nobody before presented this argument in such a clear form.

In particular, his analogies (with Minkowski space in strange coordinates, as well as with classical phase space) are brilliant. Also, his terminology (nirvana and samara basis) is fun.

 

[Dmitry67]

To explain the illusion of wave-function collapse, which, indeed, is the main motivation for studying many worlds in the first place.

Demystifier, could you explain it in more details?

Decoherence shows that taking some basis and somehow isolating somehow 2 systems (observer and the cat), we can explain what an observer perceive.

I am putting a stress on the words some/somehow, because in fact, these parameters are free, decoherence doesn't put any constraint to limit your choice (expect the observer must have high number degrees of freedom).

WHY do you need any constrains on these parameters?

 

[Demystifier]

BTW, what is the current position of BM with the issue about the cosmology. AFAIK, there is a hidden rest frame in BM, right? But in expanding Universe no objects 'at rest' in some frame can have timelike worldlines globally. For example, let's say that here, on Earth, the hidden rest frame is the same as 'rest to CMB'. So we have a 'hidden' center of the universe in BM :) But outside of our Hubble space the 'NOW' in the hidden rest frame, normally spacelike, becomes timelike.

You misunderstood something about general relativity. In the fame in which CMB is homogeneous and isotropic, there is no center of the Universe, there is no horizon, and the notion of "hubble space" does not make sense.

 

[Demystifier]

Demystifier, could you explain it in more details?

Decoherence shows that taking some basis and somehow isolating somehow 2 systems (observer and the cat), we can explain what an observer perceive.

I am putting a stress on the words some/somehow, because in fact, these parameters are free, decoherence doesn't put any constraint to limit your choice (expect the observer must have high number degrees of freedom).

WHY do you need any constrains on these parameters?

The point is that you have to do it somehow. (Unlike you, I emphasize the word "have"). On the other hand, MWI in its minimal form (i.e., without the additional structure) tells you that you shouldn't, because otherwise you ruin the mathematical structure of MWI. That is the problem.

 

[Dmitry67]

You misunderstood something about general relativity. In the fame in which CMB is homogeneous and isotropic, there is no center of the Universe, there is no horizon, and the notion of "hubble space" does not make sense.

Of course I understand it - you had probably misunderstood my post.
But I've heard that BM has a special rest frame, is it true?

 

[Dmitry67]

The point is that you have to do it somehow. (Unlike you, I emphasize the word "have"). On the other hand, MWI in its minimal form (i.e., without the additional structure) tells you that you shouldn't, because otherwise you ruin the mathematical structure of MWI. That is the problem.

No, it doesn't say that you shouldn't.
It says that you can do it any way you want
Feel the difference.

 

[Demystifier]

But I've heard that BM has a special rest frame, is it true?

Some variants do, some variants don't.

 

[Dmitry67]

Some variants do, some variants don't.

Hm...
Then how many flavors of BM exist,
and are all of them compatible?
Of course, I am interested only in relativistic BM

 

[Demystifier]

No, it doesn't say that you shouldn't.
It says that you can do it any way you want
Feel the difference.

Yes, Schwindt discusses that variant of MWI too. In second paragraph of Sec. 5 he says:
"The Many World Interpretation is therefore rather a No World Interpretation (accord-
ing to the simple factorization), or a Many Many Worlds Interpretation (because each of
the arbitrary more complicated factorizations tells a different story about Many Worlds
[7])."

But the many-many world interpretation is certainly not how most MWI experts see MWI, because they typically believe that decoherence fixes the basis. What Schwindt shows is that it doesn't.

 

[Demystifier]

Hm...
Then how many flavors of BM exist,
and are all of them compatible?
Of course, I am interested only in relativistic BM

There are a few of them. They are not intrinsically equivalent, but they all reproduce standard measurable predictions of relativistic quantum theory.

 

[Dmitry67]

Exactly! But one story is special for you, because of your consciousness.
So we have a constructive disagreement - our axioms are different, I assume a special role of consciousness aka 'qualia'.