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

[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.

 

[PeterDonis]

is the universe not considered to be a closed system in MWI

Yes, in the sense that it's in a pure state.

and so it cannot gain or lose energy

It's quite possible that MWI proponents assume that. I don't know if it's actually required for consistency of the model.

 

[Mentz114]

Yes, in the sense that it's in a pure state.
[..]
It's quite possible that MWI proponents assume that. I don't know if it's actually required for consistency of the model.

Thanks, Peter. My ignorance about MWI is showing.

About the independence of the Hamiltonian and universal WF - it seems the Hamiltonian must have the whole future of the UWF encoded in it.

I have to log off for a while now.

 

[A. Neumaier]

the split is the decoherence of some subsystems as a result of interaction with others.

This is very vague and probably meaningless. Decoherence is a continuous process that happens to the density operator, while a split is by its nature something instantaneous.

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.

Yes. And this happens whenever there are interactions. Thus the unsplit world exists only for a moment of infinitesimal length.

the interpretation explicitly says that all of the outcomes occur.

Does it? The interpretation explicitly says that there are worlds for each possible outcome. But since a world is not ''the universe'', and ''outcome'' is never defined, it doesn't really say anything about outcomes. The latter should be what comes actually out, which is a single result.

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.

This is certainly wrong, as it would mean that the wave function doesn't evolve in time.

if the Hamiltonian and the wave function contain exactly the same information.

No. The wave function contains the information about the state at a particular time, and the Hamiltonian tells how it changes with time.

is the universe not considered to be a closed system in MWI

This only implies that the expectation value of the Hamiltonian is constant.

it seems the Hamiltonian must have the whole future of the UWF encoded in it.

The Hamiltonian provides the evolution equation, and the wave function at a fixed time provides the initial condition. Both are needed to fix the future of the wave function.

 

[Derek P]

This is very vague and probably meaningless.

Yeah, strange how I keep coming up with vague and meaningless statements.

Decoherence is a continuous process that happens to the density operator

Correct.

a split is by its nature something instantaneous.

If you assume that then you will find yourself having a long tedious and unproductive argument on PhysicsForums trying to pin down the exact moment that the split occurs. Good luck with that.

 

[A. Neumaier]

If you assume that then you will find yourself having a long tedious and unproductive argument on PhysicsForums trying to pin down the exact moment that the split occurs. Good luck with that.

Please tell me how something can split without a discrete moment where the split happens. If you split a plank into two there is a moment where the plank gets disconnected, i.e., is split. The discreteness is in the notion itself, independent of the application.

But apparently nothing ever splits in MWI, and ''split'', like ''world'', is a misnomer.

 

[Derek P]

Please tell me how something can split without a discrete moment where the split happens. If you split a plank into two there is a moment where the plank gets disconnected, i.e., is split. The discreteness is in the notion itself, independent of the application.

Yes, I have come across the phenomenon of splitting planks. Also of splitting hairs. Last time I looked it was a continuous process of fibre rupture and then separation of molecules held together by Van de Waals forces. So no exact moment. It's the same with worlds splitting. It is a continuous process quite easily described as the diagonalization of the density matrix through decoherence. So it can be quantified, leaving it as a function of time which is asymptotically zero in time past and asymptotically100% in time future. The only remaining arbitrariness is deciding what level of diagonalization is "complete for all practical purposes".

But apparently nothing ever splits in MWI, and ''split'', like ''world'', is a misnomer.

Then you have been misinformed.

 

[lukesfn]

I've been curious about a similar question to the OP which this thread has been circling around.

I'm quite ignorant compared to most posters here though so please forgive imprecise use of words.

(btw, because I always hear comments worlds splitting in MWI, it leads me to believe the worlds in MWI as usually referred to, must be distinguishable worlds. Alternatively you could imagine many extra indistinguishable worlds that rather then spit, become distinguishable. Probabilities may be more intuitive interpreting this way)

Anyway, my question is that if the universe is in equilibrium, then wouldn't we think that MWI doesn't even lead to an increase in distinguishable worlds? Worlds would merge at the same rate the spit?

Similar to the OP, I see a lot of people making prediction of infinite future increase in worlds in MWI, but it would seem not necessarily so.

 

[johnkclark]

The key is what "collapse of the wave function" means physically, I think it means there is something special about one particular state of that function. The Many World's Interpretation says no state is special, nothing collapses, and everything that can happen does happen. This is how I think the MWI would describe several variations of the two-slit experiment:

In the usual experiment the universe splits when it passes the two slits because the 2 worlds are different, but when the photons hit the film and they no longer exist in either world so the 2 worlds are identical once more and the universes fuse back together again. Looking back from that fused world we find evidence that the photon went through slit X only and evidence it went through slit Y only and this causes an interference pattern. There is nothing special about an observer in this, the same thing would happen if nobody looked at the film, or even if you used a brick wall instead of film, because the important thing is not that the photon makes a record (whatever that is) but simply that it is destroyed. Mind has nothing to do with any of this so unlike the Copenhagen interpretation the MWI doesn't need to explain it, or explain what “measurement" means, or “record", or “observation", or “consciousness". That is a very very big advantage! The key point is that worlds split when they become different and merge when they become the same.

Now do the two-slit experiment again but instead of using film to stop the photon after it passes the slits, let it head out into infinite space. If Many Worlds is correct then the entire universe splits into 2 when the photon hit's the 2 slits and never recombines. There is nothing special about you the observer, you split just like everything else, you know that the photon went through one and only one slit, but of course you have no way of knowing which one.

It's more difficult to do but the 2 slit experiment can be set up in such a way that you can tell which slit the photon went through, but if you do that then the photons will not produce an interference pattern on the film. This is because even after the photon hits the film in both worlds and is destroyed the worlds remain different, in one the physical memory pattern in my brain encodes that the photon went through slot X and in the other slot Y, so the worlds don’t merge back together and no interference pattern is seen in either world.

Separate worlds only emerge if there is a difference between them, if the worlds evolve in such a way that the difference disappears then re-coherence occurs. For obvious reasons re-coherence can only occur if the 2 worlds are only very slightly different and have only been separated for a short time, and that is why experiments of this sort are difficult and it explains why in our everyday world we don’t see macro objects becoming entangled and even atoms aren’t usually entangled for long at room temperatures.

John K Clark

 

[A. Neumaier]

worlds splitting. It is a continuous process quite easily described as the diagonalization of the density matrix through decoherence. So it can be quantified, leaving it as a function of time which is asymptotically zero in time past and asymptotically100% in time future. The only remaining arbitrariness is deciding what level of diagonalization is "complete for all practical purposes".

This is the first time you provide substance to the discussion. Please add a bit of detail by telling us what in the decoherence process are the worlds, and when, "for all practical purposes", there is only one world and when there are several. Or are there from the beginning infinitely many worlds?

 

[PeterDonis]

it seems the Hamiltonian must have the whole future of the UWF encoded in it.

Since unitary evolution is deterministic, yes, knowing the state vector at any time and knowing the Hamiltonian means that you know the entire history of the state vector.