Does the MWI require "creation" of multiple worlds?

[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.

 

[Derek P]

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.

 

[Derek P]

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]

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.

 

[PeterDonis]

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]

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.

 

[stevendaryl]

Can what you are saying be expressed mathematically ? I really can't see where the splits come from or end up.

That's because there are no splits. What is sometimes picturesquely described as the world splitting is that if the universe is initially in a state in which a macroscopic property has a definite value, then interactions will lead to a state in which it does not have a definite value.

We can make this concrete by fine-graining. Let's pick some partitioning of the universe into little cubes of size maybe 1 cubic millimeter. Pick some indexing scheme so that each cube is defined by three integer indices $i, j, k$. Then we can define a set of observables:

$\vec{E}_{ijk}$ = the average electric field in cube number $i,j,k$
$\vec{B}_{ijk}$ = the average magnetic field in that cube.
$U_{ijk}$ = the total energy within the cube.
$Q_{ijk}$ = the total charge within the cube.

So we can (I assume) describe the Hilbert space of the universe using a basis of eigenstates of our countably many operators (they will approximately commute). (In general, there will be many eigenstates with the same values for those 4 operators).

So the phenomenon that might be described as "splitting" is that in certain circumstances, an eigenstate of our macroscopic operators may evolve into a state that is a superposition of different values for those macroscopic operators.

 

[PeterDonis]

Can what you are saying be expressed mathematically ?

Have you looked at the OP of this thread?

 

[PeterDonis]

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.

That is saying that the wave function of the universe must be an eigenstate of the universal Hamiltonian. Why would that have to be the case?

 

[Mentz114]

Have you looked at the OP of this thread?

Will do so again.

That is saying that the wave function of the universe must be an eigenstate of the universal Hamiltonian. Why would that have to be the case?

I did qualify this with 'something like'.

The point is, does $\hat{H}_\Omega$ have an independent existence from $\psi_\Omega$ ?

 

[Mentz114]

That's because there are no splits. What is sometimes picturesquely described as the world splitting is that if the universe is initially in a state in which a macroscopic property has a definite value, then interactions will lead to a state in which it does not have a definite value.
[..]
So the phenomenon that might be described as "splitting" is that in certain circumstances, an eigenstate of our macroscopic operators may evolve into a state that is a superposition of different values for those macroscopic operators.

Cute reply. I will take a while to absorb this and maybe write equations.

 

[PeterDonis]

does $\hat{H}_\Omega$ have an independent existence from $\psi_\Omega$ ?

$\psi$ is the state and $\hat{H}$ governs its dynamical evolution in time. I'm not sure whether that makes the answer to this "yes" or "no".

 

[Stephen Tashi]

The common interpretation of a probabilistic situation is that there are several "possible" outcomes and only one of them "actually' occurs. In the MWI (and other interpretations of QM that do not allow collapse of wave functions) is such an interpretation possible?

If so, what kind of events are the "possible" outcomes - of which only one "actually" occurs?

If not, then what is the physical interpretation of probability?

 

[PeterDonis]

In the MWI (and other interpretations of QM that do not allow collapse of wave functions) is such an interpretation possible?

No; the interpretation explicitly says that all of the outcomes occur. (More precisely, it says that unitary evolution is always valid, which obviously implies that all outcomes occur.)

If not, then what is the physical interpretation of probability?

As I understand it this is one of the key unresolved issues with the MWI.

 

[Mentz114]

$\psi$ is the state and $\hat{H}$ governs its dynamical evolution in time. I'm not sure whether that makes the answer to this "yes" or "no".

I don't know either.

if $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ then $\hat{H}_\Omega\psi_\Omega=\psi_\Omega$ and $\hat{H}_\Omega$ depends on the basis selected for $\psi_\Omega$. Is that right ? In which case they are not independent.

 

[PeterDonis]

if $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ then $\hat{H}_\Omega\psi_\Omega=\psi_\Omega$

Yes. In this special case, the universal wave function would be constant in time (since it is an eigenstate of the Hamiltonian). But there is nothing that requires this to be the case.

and $\hat{H}_\Omega$ depends on the basis selected for $\psi_\Omega$. Is that right ?

No. The equation $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ is basis independent. Equivalently, whether a particular state vector is an eigenvector of a particular operator is basis independent.

 

[Mentz114]

Yes. In this special case, the universal wave function would be constant in time (since it is an eigenstate of the Hamiltonian). But there is nothing that requires this to be the case.

So the universal wave function may depend on time ? And
$\hat{H}_\Omega(t,x)=|\psi_\Omega\rangle \langle \psi_\Omega|$

No. The equation $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ is basis independent. Equivalently, whether a particular state vector is an eigenvector of a particular operator is basis independent.

OK, thanks.

I still can't work out if the Hamiltonian and the wave function contain exactly the same information.

 

[PeterDonis]

So the universal wave function may depend on time ?

I don't see what would rule out such a model.

And
$\hat{H}_\Omega(t,x)=|\psi_\Omega\rangle \langle \psi_\Omega|$

No. If $|\psi_\Omega\rangle$ depends on time, then it's not an eigenstate of $\hat{H}_\Omega$, which means $\hat{H}_\Omega \neq |\psi_\Omega\rangle \langle \psi_\Omega|$.

Having $\hat{H}$ itself depend on time is something different.

 

[PeterDonis]

I still can't work out if the Hamiltonian and the wave function contain exactly the same information.

One is a state and the other is the operator you apply to states to see how they evolve in time. To me that means they don't contain the same information.

 

[Mentz114]

I don't see what would rule out such a model.

I could be wrong but is the universe not considered to be a closed system in MWI and so it cannot gain or lose energy.
I ought to look this up.

No. If $|\psi_\Omega\rangle$ depends on time, then it's not an eigenstate of $\hat{H}_\Omega$, which means $\hat{H}_\Omega \neq |\psi_\Omega\rangle \langle \psi_\Omega|$.

Having $\hat{H}$ itself depend on time is something different.

Yes, sorry I'm a bit rusty but its coming back ...

One is a state and the other is the operator you apply to states to see how they evolve in time. To me that means they don't contain the same information.

OK, I'll think about that.

 

[kith]

If not, then what is the physical interpretation of probability?

There have been attempts to use a decision theoretic approach, i.e. probabilities are related to how a rational agent would need to act in order to maximize his utility. The current state of affairs seems to be the 2009 paper "A formal proof of the Born rule from decision-theoretic assumptions" by David Wallace.