A Does the MWI require "creation" of multiple worlds?

[A. Neumaier]

Does the MWI require "creation" of multiple worlds?

Unitary evolution, postulated in MWI, implies that the wave function is that of the universe, since the universe is the only isolated system that exists - the effective (observable) dynamics of nonisolated systems is always dissipative. I try to understand you post #1 in the light of this and your explanations in #78.

a "world" is a term in the superposition I wrote down in the OP; i.e., each of the terms |$1>|U>$ and $|2>|D>$ is a "world". So "worlds" are picked out by the interaction between the measured system and the measuring apparatus and how the two become entangled.

This means that your worlds are not features of the (objective) universal wave function alone, but mathematical artifacts defined for the special purpose of analyzing a particular experiment. The worlds are created when the experiment is set up (the first moment where one can distinguish measured system and detector), and they are destroyed once the experiment is finished and something else is measured. [But your universe in #1 is exceedingly simple, having only 2*3 dimensions, with a fixed tensor product basis, from which one infers that there is no ''something else''. (I guess this is what you mean by ''highly schematic''.) ]

During the time where the experiment can faithfully be simplified to your setting, the number of worlds remains constant (2 in your case), and only the states in these worlds (R,U,D) evolve. Thus the resulting worlds are dynamical in time.

Note that nothing splits during the experiment, the splitting happens when the experiment is set up, where one world for each possible measurement result is created. The measurement result is therefore determined in advance by the world the detector is in, independent of the dynamics of the state, and independent of the interaction. In particular, the measurement says nothing about the state of the measured system, only something about the world in which the measurement happens. Moreover, the dynamics in each world is open since the future of world 1 depends also on the present state of world 2, and vice versa. In a sense, the other worlds serve as a reservoir of hidden variables of some kind for the dynamics of a given world.

Nothing about my surprising conclusions significantly changes in a more complex world, where R,U,D are replaced by highly complex states encoding the detector, any observers, and the environment.

My analysis differs significantly from the answers you gave in #78, so please correct me where I made an assumption not intended by you, or a logical error.

Let me also note that in quantum mechanics applied to the real world, there should be something objective about what is measured by what. Since everything objective is in MWI encoded into the state of the universe, the tensor product basis should be determined intrinsically by the state of the universe. Apparently it isn't - but this criticism is unrelated to your question.

 

[A. Neumaier]

So if I'm reading this right, you're basically saying that the interaction I described in the OP can't be realized by a unitary operator if there is more than one possible result?

Well, my answer (given in #93) turned out to say something quite different. If I understood your setting correctly, it has nothing to do with the notion of ''good observation'' I criticized in Everett.

 

[romsofia]

A lot of questions can be answered by reading this paper by the great Bryce DeWitt "Quantum mechanics and reality":
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.729.5437&rep=rep1&type=pdf

Honestly, his papers are the ones to read in regards to this issue.

 

[PeterDonis]

Unitary evolution, postulated in MWI, implies that the wave function is that of the universe, since the universe is the only isolated system that exists

Yes, agreed. And one issue with any actual description of a quantum experiment in terms of the MWI is that nobody actually writes down the wave function for the entire universe; they write down "highly schematic" abbreviated wave functions that only describe the very, very tiny portion of the universe that they are picking out as relevant to the experiment. For purposes of this discussion, I'm not raising that issue; I'm assuming that, for purposes of discussion, we can usefully talk about highly schematic wave functions like the one I wrote down in the OP as wave functions of a "system" whose evolution can be usefully modeled as unitary. But I agree that some people might think that eliminates too much.

During the time where the experiment can faithfully be simplified to your setting, the number of worlds remains constant (2 in your case), and only the states in these worlds (R,U,D) evolve. Thus the resulting worlds are dynamical in time.

Hm, yes, I see what you mean; there are two terms in the superposition both before and after the interaction. Which means that the definition of "worlds" I gave before--worlds are terms in the superposition--can't be the one that MWI advocates normally use, since MWI advocates describe the process I described in the OP as one world splitting into two.

For the process I described in the OP, I think an MWI advocate would say that "worlds" are defined by the "apparatus" kets; there is one world before the interaction because the state only contains $|R>$, one apparatus ket, and there are two worlds after the interaction because the state has two apparatus kets, $|U>$ and $|D>$. Or perhaps a better way of saying it is that the state before the interaction is separable, and the part describing the apparatus is in a single eigenstate; but after the interaction, the state is entangled and the apparatus by itself does not have a definite state; its state is entangled with that of the measured system, and that entanglement interaction is the "splitting" of one world into two. But because that interaction is unitary, nothing is actually being "created"; it's just a unitary process that entangles two subsystems.

So with this alternate definition of "worlds", what determines how many worlds there are is the apparatus: whatever basis is picked out by the physical configuration of the apparatus is the one that is used to determine how many "worlds" there are. I take it that this would be an MWI advocate's answer to the "preferred basis" problem (what picks out the basis in which the "worlds" are counted).

My analysis differs significantly from the answers you gave in #78, so please correct me where I made an assumption not intended by you, or a logical error.

I think the error was mine, in giving an incorrect definition (from the MWI advocate's perspective) of "worlds". I don't know if the alternate definition I gave above changes anything substantive about your criticism, though. It is still true that the "worlds" are determined by the apparatus (although I don't think it is true that the state of the apparatus in each "world", under my new definition, gives no information about the state of the measured system).

the dynamics in each world is open since the future of world 1 depends also on the present state of world 2, and vice versa.

I don't think this is true (even on my original wrong definition of "worlds"). Each term in the superposition evolves independently of the others. That's why we can use "effective collapse" in the math of QM to ignore all the other terms once we've observed a particular measurement result.

To be clear, I am not considering cases where the two terms will be made to interfere later; in the highly schematic picture I've been using, any later interference would be part of the "measurement interaction" (the $\rightarrow$ in the OP). The final state would be the one after all such interactions have been completed (and everything has been allowed to decohere).

 

[Derek P]

To be clear, I am not considering cases where the two terms will be made to interfere later; in the highly schematic picture I've been using, any later interference would be part of the "measurement interaction" (the $\rightarrow$ in the OP). The final state would be the one after all such interactions have been completed (and everything has been allowed to decohere).

Which is why some people say the idea of worlds should only be applied after decoherence. I guess that ties in with @stevendaryl's point. But in the end the process is clear enough - if you can call decoherence theory "clear"... which I suppose you can in an A level thread. But where in the process you say "here be worlds" is somewhat arbitrary. Rather like trying to say when "life begins" from a biological PoV. There was a time when I definitely didn't exist but I definitely do exist now. I think.

So with this alternate definition of "worlds", what determines how many worlds there are is the apparatus: whatever basis is picked out by the physical configuration of the apparatus is the one that is used to determine how many "worlds" there are. I take it that this would be an MWI advocate's answer to the "preferred basis" problem (what picks out the basis in which the "worlds" are counted).

I think the "preferred basis" is coarse-grained though I'm open to correction about that. Otherwise every particle could be an apparatus. @bhobba will know :)

 

[bhobba]

We seem to be getting caught up in measurements here. Decoherent histories only has them indirectly - specifically in that interpretation QM is a stochastic theory of histories:
https://arxiv.org/abs/quant-ph/0504155

Gell-Mann's point is that one can consider instead of one particular history existing then all can in separate worlds with one overall wave-function.

I still like the simple idea a world is the element of a mixed state after decoherence - but its not the only way of looking at it.

Thanks
Bill

 

[A. Neumaier]

a world is the element of a mixed state after decoherence

What is an ''element of a mixed state''?

 

[A. Neumaier]

the definition of "worlds" I gave before--worlds are terms in the superposition--can't be the one that MWI advocates normally use, since MWI advocates describe the process I described in the OP as one world splitting into two.

For the process I described in the OP, I think an MWI advocate would say that "worlds" are defined by the "apparatus" kets; there is one world before the interaction because the state only contains $|R>$, one apparatus ket, and there are two worlds after the interaction because the state has two apparatus kets, $|U>$ and $|D>$. Or perhaps a better way of saying it is that [...] entanglement interaction is the "splitting" of one world into two.

This does not change my conclusions: Separability is lost immediately after the experiment is set up (since even at a distance, the interactions are present though tiny).

Each term in the superposition evolves independently of the others.

No. The unitary evolution introduces terms in the other worlds, since the eigenstates 1 and 2 are not eigenstates of the interacting Hamiltonian (if it were, measurement would be impossible).

 

[Derek P]

This does not change my conclusions: Separability is lost immediately after the experiment is set up (since even at a distance, the interactions are present though tiny).

No. The unitary evolution introduces terms in the other worlds, since the eigenstates 1 and 2 are not eigenstates of the interacting Hamiltonian (if it were, measurement would be impossible).

Surely they are eigenstates of the total interaction including interaction with the "environment"? The states are already superposed and therefore evolving independently before decoherence starts. Or maybe I'm just not getting the point.

 

[A. Neumaier]

Surely they are eigenstates of the total interaction including interaction with the "environment"?

No. Why should they be? There is only one Hamiltonian, that for the whole universe, and there is no reason at all why this Hamiltonian should have separable eigenstates. Almost no Hamiltonians, except very simple contrived ones, have this property.

 

[Derek P]

No. Why should they be? There is only one Hamiltonian, that for the whole universe, and there is no reason at all why this Hamiltonian should have separable eigenstates. Almost no Hamiltonians, except very simple contrived ones, have this property.

Sure. Even Zurek has said that MWI may need to postulate that "there are systems". The model of detection begins with a microscopic interaction that is then amplified and decohered. If the universe can't be modeled this way then pretty well all of science falls apart.

 

[A. Neumaier]

Sure. Even Zurek has said that MWI may need to postulate that "there are systems". The model of detection begins with a microscopic interaction that is then amplified and decohered. If the universe can't be modeled this way then pretty well all of science falls apart.

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates? It doesn't. Only the initial state may be assumed (by preparation) to be separable. Apart from that, system, detector and environment are represented as terms in the total Hamiltonian, but the existence of interaction terms makes it very unlikely that the eigenstates of the total Hamiltonian are separable.

You are far too vague for a serious discussion. You neither define your terms nor point to sources where they are clearly defined.

 

[PeterDonis]

the eigenstates 1 and 2 are not eigenstates of the interacting Hamiltonian

In the model I was describing, the Hamiltonian is time-dependent; the interaction term is only "turned on" for a short period (while the particle is inside the apparatus). Before and after that, there is no interaction term in the Hamiltonian, so the kets I wrote down should be eigenstates during those times.

This is similar, as I understand it, to the way scattering experiments are modeled. Are you saying that this can only be an approximation (similar to the way you have to take the times to minus or plus infinity, heuristically speaking, to get definite "in" and "out" states in scattering--at any finite time there is still a nonzero interaction)?

 

[Derek P]

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates? It doesn't. Only the initial state may be assumed (by preparation) to be separable. Apart from that, system, detector and environment are represented as terms in the total Hamiltonian, but the existence of interaction terms makes it very unlikely that the eigenstates of the total Hamiltonian are separable.

You are far too vague for a serious discussion. You neither define your terms nor point to sources where they are clearly defined.

Yeah, you're probably right. Ta-ta!

 

[A. Neumaier]

the interaction term is only "turned on" for a short period (while the particle is inside the apparatus). Before and after that, there is no interaction term in the Hamiltonian, so the kets I wrote down should be eigenstates during those times.

This still doesn't change my analysis; it just restricts it to the short period where the interaction is on. Afterwards the system is stationary so nothing changes.

This is similar, as I understand it, to the way scattering experiments are modeled. Are you saying that this can only be an approximation (similar to the way you have to take the times to minus or plus infinity, heuristically speaking, to get definite "in" and "out" states in scattering--at any finite time there is still a nonzero interaction)?

Indeed, it is only an approximation. But even when the interaction time is taken to be finite, the analysis still leads to the same strange result. Separability is lost once the interaction is turned on, hence (in microscopic terms) long before the measurement is completed. Thus with your revised definition, the worlds split at the moment the measurement begins, and the result in each world is predetermined.

Moreover, if one thinks of reversing the situation (unitary dynamics is reversible), worlds should disappear (merge) whenever two states of the detector happen to become equal. This is quite unreasonable from a formal point of view. The natural thing to expect is that the two worlds were always there, and will always be there, which is the reversible situation. The other, even more natural interpretation is that the worlds are an artifact of imposing a particular tensor product basis on the universe, and appear and disappear together with the coordinate system. This is what I had in mind when asking about the ''point of view'' interpretation.

Note also that nothing is said by this version of the MWI about how the worlds are selected by a real observer - they all have fully democratic existence of the same kind. Labeling them by a formal number called probability is of course possible, but nothing explains why this formal label actually has the property of an observed relative frequency by an observer moving along a particular (coarse-grained) world line.

 

[PeterDonis]

The natural thing to expect is that the two worlds were always there, and will always be there, which is the reversible situation. The other, even more natural interpretation is that the worlds are an artifact of imposing a particular tensor product basis on the universe, and appear and disappear together with the coordinate system.

For purposes of this discussion, given its title question, I think both of these alternatives support the answer "no"; the MWI does not create worlds.

 

[A. Neumaier]

For purposes of this discussion, given its title question, I think both of these alternatives support the answer "no"; the MWI does not create worlds.

With the meaning of the terms implied by our discussion, this is a fair conclusion.

 

[Mentz114]

With the meaning of the terms implied by our discussion, this is a fair conclusion.

Thank you for your contribution to this thread. Also @PeterDonis and others.
Even for someone acutely sceptical about MWI it has been instructive (and entertaining).

 

[romsofia]

Sure. Even Zurek has said that MWI may need to postulate that "there are systems".

That is a postulate of MWI.

"Everett, Wheeler and Graham (EWG) postulate that the real world, or any isolated part of it one may wish for the moment to regard as the world, is faithfully represented solely by the following mathematical objects: a vector in a Hilbert space; a set of dynamical equations (derived from a variational principle) for a set of operators that act on the Hilbert space, and a set of commutation relations for the operators (derived from the Poisson brackets of the classical theory by the quantization rule, where classical analogs exist). Only one additional postulate is then needed to give physical meaning to the mathematics. This is the postulate of complexity: The world must be sufficiently complicated that it be decomposable into systems and apparatuses."

As far as I am aware, you need branches (worlds) for MWI to work. That's just how it is set up. To me though, MWI is just a causal interpretation of QM.

I'm not going to attempt to make points in regards to MWI better than Bryce DeWitt, so start with the article I linked in post 95, but here is a more readable version: http://cqi.inf.usi.ch/qic/deWitt1970.pdf I will address issues with regards to this, but I can't be bothered going through this whole thread as I joined the discussion too late.

If you can't find his paper "The Everett-Wheeler Interpretation of Quantum Mechanics," I can try and get a photo copy of it from my library in the next few days.

 

[PeterDonis]

I can try and get a photo copy of it from my library in the next few days.

Unfortunately we can't post scans of library copies here, due to copyright issues. Many older papers are available online now.

 

[Derek P]

That is a postulate of MWI.
Only one additional postulate is then needed to give physical meaning to the mathematics. This is the postulate of complexity: The world must be sufficiently complicated that it be decomposable into systems and apparatuses."

I think Zurek's point was a bit different from that but it doesn't matter now as I'm "far too vague for a serious discussion."

As far as I am aware, you need branches (worlds) for MWI to work.

They exist in the maths, which is postulated to be ontic. You don't need to postulate them twice.

 

[stevendaryl]

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates?

What does "separable eigenstates" mean here? Are you talking about being able to write the total wave function as a product?

 

[stevendaryl]

Surely they are eigenstates of the total interaction including interaction with the "environment"? The states are already superposed and therefore evolving independently before decoherence starts. Or maybe I'm just not getting the point.

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

 

[Derek P]

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

Well it's not very clear to me either.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

Yes. That's what we want isn't it?
But frankly I'm tired of this discussion. Either you can write the state as a sum of products using THREE kets each and allow the second two to interact later, or you can't. If you can't then MWI and most of measurement theory is junk. But I can't for the life of me see why you shouldn't.

 

[A. Neumaier]

What does "separable eigenstates" mean here? Are you talking about being able to write the total wave function as a product?

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

Separable state = product state.

 

[ronronron3]

My impression has been that the 'many-worlds' interpretation is, at present, at best a metaphor based on an analogy with unix processes as below. Just the sort of thing that might turn out to be true or at least illuminating of course.

From http://www.csl.mtu.edu/cs4411.ck/www/NOTES/process/fork/create.html

"System call fork() is used to create processes. It takes no arguments and returns a process ID. The purpose of fork() is to create a new process, which becomes the child process of the caller. After a new child process is created, both processes will execute the next instruction following the fork() system call. Therefore, we have to distinguish the parent from the child. This can be done by testing the returned value of fork():

• If fork() returns a negative value, the creation of a child process was unsuccessful.
• fork() returns a zero to the newly created child process.
• fork() returns a positive value, the process ID of the child process, to the parent. The returned process ID is of type pid_t defined in sys/types.h. Normally, the process ID is an integer. Moreover, a process can use function getpid() to retrieve the process ID assigned to this process.

Therefore, after the system call to fork(), a simple test can tell which process is the child. Please note that Unix will make an exact copy of the parent's address space and give it to the child. Therefore, the parent and child processes have separate address spaces."

 

[Mentz114]

My impression has been that the 'many-worlds' interpretation is, at present, at best a metaphor based on an analogy with unix processes as below. Just the sort of thing that might turn out to be true or at least illuminating of course.

From http://www.csl.mtu.edu/cs4411.ck/www/NOTES/process/fork/create.html

"System call fork() is used to create processes. It takes no arguments and returns a process ID. The purpose of fork() is to create a new process, which becomes the child process of the caller. After a new child process is created, both processes will execute the next instruction following the fork() system call. Therefore, we have to distinguish the parent from the child. This can be done by testing the returned value of fork():

• If fork() returns a negative value, the creation of a child process was unsuccessful.
• fork() returns a zero to the newly created child process.
• fork() returns a positive value, the process ID of the child process, to the parent. The returned process ID is of type pid_t defined in sys/types.h. Normally, the process ID is an integer. Moreover, a process can use function getpid() to retrieve the process ID assigned to this process.

Therefore, after the system call to fork(), a simple test can tell which process is the child. Please note that Unix will make an exact copy of the parent's address space and give it to the child. Therefore, the parent and child processes have separate address spaces."

I think this is off-topic but the anaology does not hold because the wave function of the universe does not contain enough to make the split. Therefore an outside agency is required, which contradicts the postulate that the WF is all that exists.

 

[PeterDonis]

the wave function of the universe does not contain enough to make the split

Why not?

 

[Mentz114]

Why not?

In what little I've read about MWI this has not been made explicit. I can't find anything that could correspond to a creation operator for a universe in the standard formalism.

 

[PeterDonis]

I can't find anything that could correspond to a creation operator for a universe in the standard formalism.

There isn't one. The total quantum state of the universe in the MWI is just a pure state that evolves by unitary evolution. You can't create or annihilate it.