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

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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 modelled this way then pretty well all of science falls apart.
 

A. Neumaier

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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 modelled 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.
 
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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)?
 
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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

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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.
 
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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

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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

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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).
 
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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.
 
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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.
 
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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." :H
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.
 
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stevendaryl

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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

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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.
 
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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.
 
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A. Neumaier

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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.
 
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

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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.
 

Mentz114

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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.
 
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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.
 
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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.
No, the split is the decoherence of some subsystems as a result of interaction with others.
 
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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.
I think you may be confusing worlds with universes. Unless you're harking back to the OP and simply saying "no it does not" :)
 

Mentz114

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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.
Where does 'copying' or 'splitting' come in ?
I have to admit that I don't know ( or I cannot accept) what you are saying.

No, the split is the decoherence of some subsystems as a result of interaction with others.
At which time t a copy is made ?
I think you may be confusing worlds with universes. Unless you're harking back to the OP and simply saying "no it does not" :)
Are the 'worlds' contained in 'universes' ?

Of course, the computing analogy breaks down because it requires a computer to do the eveolution and splitting.
Is the Hamiltonian the 'computer' ? Since it is required to perform the evolution.
 
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Where does 'copying' or 'splitting' come in ?
There is no copying. "Splitting", as I think @A. Neumaier clarified very well in his subthread with me, is not really well defined by MWI proponents, but basically it amounts to picking a basis that reflects the eigenstates of the measuring apparatus, and calling each term in a superposition of product states of the measured system and measuring apparatus eigenstates in that basis a "world". My OP to this thread described such a state; the ##|U>## and ##|D>## kets in that state describe eigenstates of the measuring apparatus, and the final state described therefore has two "worlds" in it. Then an interaction that takes a state like the initial state in my OP, which is separable, into an entangled superposition of multiple "worlds" as just defined, is what is meant in the MWI by "splitting" into multiple worlds.
 

Mentz114

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There is no copying. "Splitting", as I think @A. Neumaier clarified very well in his subthread with me, is not really well defined by MWI proponents, but basically it amounts to picking a basis that reflects the eigenstates of the measuring apparatus, and calling each term in a superposition of product states of the measured system and measuring apparatus eigenstates in that basis a "world". My OP to this thread described such a state; the ##|U>## and ##|D>## kets in that state describe eigenstates of the measuring apparatus, and the final state described therefore has two "worlds" in it. Then an interaction that takes a state like the initial state in my OP, which is separable, into an entangled superposition of multiple "worlds" as just defined, is what is meant in the MWI by "splitting" into multiple worlds.
Can what you are saying be expressed mathematically ? I really can't see where the splits come from or end up.
Until there are equations in which all the 'splits' are explicit surely MWI is just handwaving.

A superposition of observable states is already splittable. But it's only meaningful to call them worlds when their interaction with the detector and the environment has created a superposition of global states each of which is consistent with one of the observed outcomes i.e. an improper mixture.

The physics of MWI is just unitary QM.
The usual postulate of QM says that we will get an eigenfunction ##m## of the operator with probability ##|\alpha_m|^2##. There is nothing about splitting.
I presume that the wave function of the universe ##\psi_\Omega## must satisfy something like ##\hat{H}_\Omega \psi_\Omega = C\psi_\Omega## where ##C## is a constant. There two things in that equation.

Thanks for the responses.
 

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