Many-worlds true quantum event generator

[Dmitry67]

Just guessing but you would need the whole energy of our universe to create an alternative one right?

No
http://www.hedweb.com/manworld.htm#ockham's

Q22 Does many-worlds violate conservation of energy?
First, the law conservation of energy is based on observations within each world. All observations within each world are consistent with conservation of energy, therefore energy is conserved.
Second, and more precisely, conservation of energy, in QM, is formulated in terms of weighted averages or expectation values. Conservation of energy is expressed by saying that the time derivative of the expected energy of a closed system vanishes. This statement can be scaled up to include the whole universe. Each world has an approximate energy, but the energy of the total wavefunction, or any subset of, involves summing over each world, weighted with its probability measure. This weighted sum is a constant. So energy is conserved within each world and also across the totality of worlds.

One way of viewing this result - that observed conserved quantities are conserved across the totality of worlds - is to note that new worlds are not created by the action of the wave equation, rather existing worlds are split into successively "thinner" and "thinner" slices, if we view the probability densities as "thickness".

 

[ExecNight]

So there is a thick arrow of space-time. And this is only getting sliced by probabilities.

Any thought experiment about what happens when split two probabilities again connect with each other after a certain amount of time then? Be it 10 years or 10 nanoseconds i don't know. 10 years seem absurd but well just for brainstorming.

 

[rodsika]

I already told you I don't think there'd be a clearly-defined set of "worlds" in the most common version of the MWI. If you just use "world" as a sort of shorthand for aspects of the superposition that would be visibly different to observers like ourselves, I suppose however many distinct ways the particle can hit the screen that your detector will differentiate between (both all the different spatial positions it could be detected at, and all the different times the detection could happen), that would be the number of "worlds" defined directly by the detection-event, although things like random vibrations in the particles making up the equipment could (I would think) also lead to other macro-differences due to the butterfly effect.

No, I already said in post #3 that it's not just quantum experiments that lead to multiple outcomes but the quantum nature of all physical systems, and I know you read that post because you responded in post #6, so I don't really understand why you would ask this question.

Sure. Forget the MWI for a second, suppose we had a mega-computer that could simulate the evolution of the wavefunction of an isolated Solar system for 100 years, starting from a state where the positions of all the particles were fairly narrowly defined (not necessarily a position eigenstate since we may not want huge uncertainty in their momenta either), so at a macroscopic level we could say we were starting with a single "world", do you doubt that after 100 years the calculated wavefunction would be a superposition which would assign significant amplitudes to position eigenstates with very different configurations of particles on the simulated Earth, say an eigenstate where Jerry had 2 sons and another where he had 3? Consider my comment about Schroedinger's cat in post #26:

Do you disagree that this is what standard non-MWI QM would predict about the evolution of the wavefunction of any chaotic macroscopic system, if we could do the calculation?

I don't know what you mean by "produce billions and billions of galaxies", both before and after the experiment there's a single universal wavefunction which can be broken down into a superposition of vast number of position eigenstates (or whatever basis you like) each of which features different configurations of particles in galaxies. Do you find the quantum rules for wavefunction evolution to be "absurdity"?

Again I don't know what you mean by "produce". If you don't do the double slit experiment the particles that would have been used in the experiment are still around and in a superposition of different possible states, so if we just define "worlds" loosely as macroscopically distinguishable possibilities, it's not clear that the choice of whether to use those particles in a specific experiment or just leave them lying around in a junk heap makes any difference to the total number of "worlds".

I've been thinking about this over and over again all day and re-reading the thread and other references. I think knowing what are branches and worlds is vitally important and we seem to have different ideas here. First.. based on a website you shared:

"Q19 Do worlds differentiate or split?
Can we regard the separate worlds that result from a measurement-like interaction (See "What is a measurement?") as having previous existed distinctly and merely differentiated, rather than the interaction as having split one world into many? This is definitely not permissible in many-worlds or any theory of quantum theory consistent with experiment. Worlds do not exist in a quantum superposition independently of each other before they decohere or split. The splitting is a physical process, grounded in the dynamical evolution of the wave vector, not a matter of philosophical, linguistic or mental convenience (see "Why do worlds split?" and "When do worlds split?") If you try to treat the worlds as pre-existing and separate then the maths and probabilistic behaviour all comes out wrong."

Anyway. I'm still a bit confused by what constitute a world. Let me give an example.

1. When the atoms in my body produce choices.. diverging of worlds occur.. so are those worlds only in my body atom vicinity.. or do they travel or expand and to what extend?

2. In the above site you gave... splitting is mentioned which means no longer in superposition.. but splitting doesn't necessary mean there are not clearly differentiated worlds as you emphasized. It means other components of the superposition forming branches and diverging. Now say the atoms in my body is diverging into "worlds". How long before me as a person diverge into two copies or branches and how far will it encompass?

3. Now most important. Supposed I'm diverging into 2 copies or branches/worlds.. and you are also diverging into two or more copies. And supposed we are going to meet physically tomorrow at Madison Square Garden.. which one of our bodies/branches are going to meet? Is this what you mean there are no clearly defined worlds.. because it's mixed up? Any of our branches can cross each other? something like that? But how could this be.. how do worlds merge or blend into each other? This is the consequence if branches don't form parallel world but intermingle. This is the part I don't understand quite well.

My belief previously in 10 years of my study of quantum mechanics is that when worlds split, a separate parallel universe forms that extend to the cosmos.. but this seems to be wrong idea that I'm still analyzing. And this is the main source of confusion in Many Worlds. If you know of web sites that have illustrations of how worlds blend or merge and split and all those going on simultaneously. Pls. share it as I want to imagine how it all happen. Many thanks.

 

[JesseM]

Anyway. I'm still a bit confused by what constitute a world. Let me give an example.

1. When the atoms in my body produce choices.. diverging of worlds occur.. so are those worlds only in my body atom vicinity.. or do they travel or expand and to what extend?

2. In the above site you gave... splitting is mentioned which means no longer in superposition.. but splitting doesn't necessary mean there are not clearly differentiated worlds as you emphasized. It means other components of the superposition forming branches and diverging. Now say the atoms in my body is diverging into "worlds". How long before me as a person diverge into two copies or branches and how far will it encompass?

3. Now most important. Supposed I'm diverging into 2 copies or branches/worlds.. and you are also diverging into two or more copies. And supposed we are going to meet physically tomorrow at Madison Square Garden.. which one of our bodies/branches are going to meet? Is this what you mean there are no clearly defined worlds.. because it's mixed up? Any of our branches can cross each other? something like that? But how could this be.. how do worlds merge or blend into each other? This is the consequence if branches don't form parallel world but intermingle. This is the part I don't understand quite well.

My belief previously in 10 years of my study of quantum mechanics is that when worlds split, a separate parallel universe forms that extend to the cosmos.. but this seems to be wrong idea that I'm still analyzing. And this is the main source of confusion in Many Worlds. If you know of web sites that have illustrations of how worlds blend or merge and split and all those going on simultaneously. Pls. share it as I want to imagine how it all happen. Many thanks.

Well, again a "split" based on decoherence can only be an approximate matter, but the FAQ I linked to suggests that when one object "splits" due to decoherence, other objects around it "split" along the future light cone of the first object's splitting, due to actual causal influences from one version or another of the first object. From Q12, Is Many-Worlds a local theory?:

Macrostates descriptions of objects evolve in a local fashion. Worlds split as the macrostate description divides inside the light cone of the triggering event. Thus the splitting is a local process, transmitted causally at light or sub-light speeds. (See "Does the EPR experiment prohibit locality?" and "When do worlds split?")

 

[rodsika]

Well, again a "split" based on decoherence can only be an approximate matter, but the FAQ I linked to suggests that when one object "splits" due to decoherence, other objects around it "split" along the future light cone of the first object's splitting, due to actual causal influences from one version or another of the first object. From Q12, Is Many-Worlds a local theory?:

So in split caused by decoherence, the newly created branch in my atoms would form its own world that includes another version of you there.. this means the new branch would not be able to blend into this world and meet you here.. right?
It is stuff like this that makes it hard to believe in Many worlds. A single Ant has billions of atoms in his bodies and any random process can create branches that would include another version of Earth and the galaxies and the universe. This is absurdity to the max. How can you accept this thought?

Are you saying that split not by decoherence but by DeWitt Preferred basis won't cause the branch creation of an entire universe?
But Decoherence is tied up with Many Worlds. This is because if wave function doesn't collapse. Then one have Decoherence. Or are you saying that collapse and decoherence can both not exist, but how could that it.. they are the only possible occurences to wave function. Since Many Worlds don't have collapse, it automatically have Decoherence. No?

 

[JesseM]

So in split caused by decoherence, the newly created branch in my atoms would form its own world that includes another version of you there.. this means the new branch would not be able to blend into this world and meet you here.. right?

I think that's right, although as I said I don't understand the technical details. My understanding is that if you "split" into multiple versions, then a short time after, causal influences between you and me will cause a corresponding "split" in me so that after that point it's in some sense predetermined which version of me will encounter which version of you from that original split (though there will of course be plenty of subsequent splits in both of us)

It is stuff like this that makes it hard to believe in Many worlds. A single Ant has billions of atoms in his bodies and any random process can create branches that would include another version of Earth and the galaxies and the universe. This is absurdity to the max. How can you accept this thought?

Counter-intuitiveness is not really much of an argument--it may seem strange, but it doesn't lead to any predictions which conflict with our ordinary experience, and there are plenty of other aspects of modern physics that are also pretty counter-intuitive like the notion of "curved spacetime". Also, I've often seen MWI advocates use quantum computing as a way of supporting this picture--quantum computers would be able to perform certain kinds of calculations quickly that might take an ordinary computer billions of years or something, this is easier to understand conceptually in a picture where the computer effectively splits the task up into a vast number of different "worlds" and then merges them again (a quantum computer would be designed so that it would not include any thermodynamically irreversible 'splits' in its operations).

Are you saying that split not by decoherence but by DeWitt Preferred basis won't cause the branch creation of an entire universe?

I think the DeWitt version would involve a vast number of different "worlds" at any given moment, but I'm not sure about how temporal evolution works in this picture--how you would justify saying that basis vector A at time t0 is part of the "same history" as basis vector B at a later time t1. I suppose you could look at whether the records in B are consistent with A, but it seems like that would only be approximate, there wouldn't be any definitive way to decide whether B was a possible future of A or if B was more like a future of a different "world" that had already diverged from A's "world" prior to t0. So I don't know how the concept of "splitting" would apply in DeWitt's version, but I think the number of "worlds" at any given time should be defined merely by the number of vectors assigned a nonzero amplitude in the preferred basis, I don't see why decoherence would enter into it.

But Decoherence is tied up with Many Worlds. This is because if wave function doesn't collapse. Then one have Decoherence.

Sure, even in the Copenhagen interpretation you could have decoherence if you could keep a sufficiently complex system consisting of both a subsystem and its "environment" in isolation for a little while, so there'd be no external system to "collapse" it (like Schroedinger's cat, or a simulation on a large quantum computer). I'm not saying there isn't such a thing as decoherence in the DeWitt version, just that I don't think it has anything to do with the number of "worlds" or their contents at any given time.

 

[yoda jedi]

So there seems to be two versions of Many Worlds, Everett original and DeWitt splitting? If so, it is not wrong to think in terms of DeWitt, isn't it? Then my questions above has to do with DeWitt version. Pls re-answer them in the context of DeWitt version just as Jim described. I'll read more of Everett original version as I reflect on your words about it. But Dewitt version is distinct from it. Thanks.

MWI is realist, deterministic and local theory.
there are various versions of MWI, DeWitt, Deustch, Zurek, Polley etc

 

[rodsika]

I think that's right, although as I said I don't understand the technical details. My understanding is that if you "split" into multiple versions, then a short time after, causal influences between you and me will cause a corresponding "split" in me so that after that point it's in some sense predetermined which version of me will encounter which version of you from that original split (though there will of course be plenty of subsequent splits in both of us)

Counter-intuitiveness is not really much of an argument--it may seem strange, but it doesn't lead to any predictions which conflict with our ordinary experience, and there are plenty of other aspects of modern physics that are also pretty counter-intuitive like the notion of "curved spacetime". Also, I've often seen MWI advocates use quantum computing as a way of supporting this picture--quantum computers would be able to perform certain kinds of calculations quickly that might take an ordinary computer billions of years or something, this is easier to understand conceptually in a picture where the computer effectively splits the task up into a vast number of different "worlds" and then merges them again (a quantum computer would be designed so that it would not include any thermodynamically irreversible 'splits' in its operations).

I think the DeWitt version would involve a vast number of different "worlds" at any given moment, but I'm not sure about how temporal evolution works in this picture--how you would justify saying that basis vector A at time t0 is part of the "same history" as basis vector B at a later time t1. I suppose you could look at whether the records in B are consistent with A, but it seems like that would only be approximate, there wouldn't be any definitive way to decide whether B was a possible future of A or if B was more like a future of a different "world" that had already diverged from A's "world" prior to t0. So I don't know how the concept of "splitting" would apply in DeWitt's version, but I think the number of "worlds" at any given time should be defined merely by the number of vectors assigned a nonzero amplitude in the preferred basis, I don't see why decoherence would enter into it.

Sure, even in the Copenhagen interpretation you could have decoherence if you could keep a sufficiently complex system consisting of both a subsystem and its "environment" in isolation for a little while, so there'd be no external system to "collapse" it (like Schroedinger's cat, or a simulation on a large quantum computer). I'm not saying there isn't such a thing as decoherence in the DeWitt version, just that I don't think it has anything to do with the number of "worlds" or their contents at any given time.

We must know the tecnnical details so we can know whether the whole idea can be refuted by nonsolvable conflicts.

Anyway. If I split into multiple versions. You website says "Thus the splitting is a local process, transmitted causally at light or sub-light speeds." so it means my other copy (a branch) would have its reality expanding at the speed of light. Supposed you are in Alpha Centauri 4.37 light years away.* It would take 4.37 years for the branch to include you?* Or instantaneously? Supposed halfway you got a transgender operation and became a female. Would my branch included you as the new female or the original male?* Previously I thought Alpha Centauri is copied instantaneously but now I think the branch expanding has to travel as the speed or sublight speed.

Well. The whole idea is beyond science fiction that is why I have to go back to interpretations where Many worlds don't exist. Let's go back to pure Copenhagen.

In the buckyball with 430 atoms sent as a quantum particle in the double slit. Supposed you are the buckyball and sent off. Would you still feel the same where you either go to the left or right slit.. or would you experience superposition?* This wouldn't require any Many Worlds. But it's not hard to imagine you can experience superposition, isn't it. So I guess if I were the buckyball, I'd experience superposition or like a ghost. Why is this not possible. When object is in coherence, there is no classical state.

Let's go to the Schroedinger Cat. Supposed it could be isolated in a box (let's ignore gravity for now). Then the Schroedinger Cat is in pure state. This means it's entire body is in coherence, right? Or can pure state occur without Coherence? Anyway. Supposed the cat is in coherence, then we can assume that whenever an object is in coherence, it loses all classical state or positions. So the cat should experience superposition itself. This would avoid any Many Worlds. If one can accept the multiciplicity of worlds as default. Why not accept that superposition is also default mode. Meaning classical positions are abnormal things. Superposition is the norm. This would remove the need of Many Worlds.

You may argue that the entire universe is in pure state. Why do we not experience Superposition. Let's pretend for now that there is something out there that observe us, let's say God which collapse the universe wave function. If God removed his influenced on us. Then we will all experience superposition. Why not? But ignore this paragraph and arguments for now. Let's just deal with the Schroedinger Cat in the paragraphs prior to this. Many thanks.

 

[ExecNight]

Noting about what happens when,

There are two probabilities, A and B.
Both A and B have the same outcome C after 10 nanoseconds.
It is a closed system and doesn't affect the universe at all.

How does this work? Are they still split?

Or when we make an experiment to observe how C happened do we find both A and B as the answer?

 

[JesseM]

In the buckyball with 430 atoms sent as a quantum particle in the double slit. Supposed you are the buckyball and sent off. Would you still feel the same where you either go to the left or right slit.. or would you experience superposition?* This wouldn't require any Many Worlds. But it's not hard to imagine you can experience superposition, isn't it. So I guess if I were the buckyball, I'd experience superposition or like a ghost. Why is this not possible. When object is in coherence, there is no classical state.

Let's go to the Schroedinger Cat. Supposed it could be isolated in a box (let's ignore gravity for now). Then the Schroedinger Cat is in pure state. This means it's entire body is in coherence, right? Or can pure state occur without Coherence? Anyway. Supposed the cat is in coherence, then we can assume that whenever an object is in coherence, it loses all classical state or positions. So the cat should experience superposition itself. This would avoid any Many Worlds. If one can accept the multiciplicity of worlds as default. Why not accept that superposition is also default mode. Meaning classical positions are abnormal things. Superposition is the norm. This would remove the need of Many Worlds.

You may argue that the entire universe is in pure state. Why do we not experience Superposition. Let's pretend for now that there is something out there that observe us, let's say God which collapse the universe wave function. If God removed his influenced on us. Then we will all experience superposition. Why not? But ignore this paragraph and arguments for now. Let's just deal with the Schroedinger Cat in the paragraphs prior to this. Many thanks.

This is getting rather philosophical, but my question here would be, what does it mean to "experience" superposition? Suppose we replace Schroedinger's cat with an intelligent being capable of communication (perhaps a person, but slightly more realistically it could be an A.I. running on a quantum computer), and instead of the random radioactive decay either killing them or letting them live, the outcome of the decay just determines which of two hidden photographs will be uncovered and shown to this being. The subject of the photos isn't known in advance to the being and they could be absolutely anything, perhaps one is a photo of a painting of George Washington and the other is a photo of a duck. So would "experiencing" superposition of (left photo uncovered, right photo remains hidden) and (right photo uncovered, left photo remains hidden) involve being aware of what was in both photos at once? The problem is, suppose we ask this being to then write down a story about whatever it is he has seen...obviously we'll get a superposition of stories, and significant amplitude will be assigned to both stories involving George Washington and stories involving ducks, but the amplitude assigned to stories that actually involve George Washington interacting with a duck will be totally negligible (perhaps not exactly zero since a person who just sees a picture of George Washington might by chance happen to write a story which also involves a duck and vice versa, but the amplitude to "George Washington interacts with a duck" stories shouldn't be any less negligible than "George Washington interacts with a tiger" or any other random animal). So, if you claim that this individual has "experienced" a superposition of George Washington and a duck, it seems like you have to say that somehow the individual can't act on this composite knowledge when writing a story (or superposition of stories), which seems to indicate a radically dualistic view of the relation between their "experience" and the actual behavior caused by their physical brain.

 

[rodsika]

No, the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI.

You could take a look at this thread, and there's some discussion of the preferred basis problem starting on p. 9 of this paper. But you can find more references just by typing the words "preferred basis everett" (not in quotes) into google scholar or google books.

Hi JesseM, I'm reading old archive about the preferred basis problem and I came across the following post by Fredrik/wolverine in 2009. He said:
"There are always infinitely many bases to choose from. What decoherence does is (among other things) to single out one of them as "special"."
He said "infinite many bases". You mentioned only position and momentum. What others, how can it reach infinite? what weird combination is possible that can make it so numerous? pls give 10 examples of other bases beside our usual observables. Thanks

The following is from A. Neumaier site, one of the critique of Many Worlds. He wrote (what do
you think?):
"
Q8 When does Schrodinger's cat split?
******** As the cyanide/no-cyanide interacts with the cat the cat
******** is split into two states (dead or alive). From the surviving
******** cat's point of view it occupies a different world from its
******** deceased copy. The onlooker is split into two copies only
******** when the box is opened and they are altered by the states
******** of the cat.
Indeed, this confirms that splitting is a subjective process not
affecting the world at large. Otherwise the number of worlds could not
depend on the point of view? Or is it to be understood as follows:
As the cyanide/no-cyanide interacts with the cat the world is split
into two, one containig a dead cat and the other one that is alive?
And each of these two worlds splits again as the onlooker opens the box?
But then we have 4 worlds, two of which corresponding to nonexistent
possibilities (e.g., the world with the dead cat which is found alive
on opening the box). Thus only one split should have occured, and the
`explanation' is nonsense."

 

[JesseM]

Hi JesseM, I'm reading old archive about the preferred basis problem and I came across the following post by Fredrik/wolverine in 2009. He said:
"There are always infinitely many bases to choose from. What decoherence does is (among other things) to single out one of them as "special"."
He said "infinite many bases". You mentioned only position and momentum. What others, how can it reach infinite? what weird combination is possible that can make it so numerous? pls give 10 examples of other bases beside our usual observables. Thanks

'
Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example. To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

The following is from A. Neumaier site, one of the critique of Many Worlds. He wrote (what do
you think?):
"
Q8 When does Schrodinger's cat split?
******** As the cyanide/no-cyanide interacts with the cat the cat
******** is split into two states (dead or alive). From the surviving
******** cat's point of view it occupies a different world from its
******** deceased copy. The onlooker is split into two copies only
******** when the box is opened and they are altered by the states
******** of the cat.
Indeed, this confirms that splitting is a subjective process not
affecting the world at large. Otherwise the number of worlds could not
depend on the point of view? Or is it to be understood as follows:
As the cyanide/no-cyanide interacts with the cat the world is split
into two, one containig a dead cat and the other one that is alive?
And each of these two worlds splits again as the onlooker opens the box?
But then we have 4 worlds, two of which corresponding to nonexistent
possibilities (e.g., the world with the dead cat which is found alive
on opening the box). Thus only one split should have occured, and the
`explanation' is nonsense."

I think a more mathematical analysis than I know how to do would be required to address this. If you think in terms of my comments on the other thread about macrostates vs. microstates, it might for example be that if you just consider the macrostates of the cat they have already decohered before the box is opened (interference between live cat macrostate and dead cat macrostate has become negligible), but that if you considered the macrostates of the cat + experimenter system than interference would still be significant until the box was opened, so that this could be the basis for talking about an initial split in the cat and a later split in the experimenter when he opens the box. But I can't definitely say that this is how it works since I don't know enough about how to do the math.

 

[rodsika]

'
Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example. To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

I think a more mathematical analysis than I know how to do would be required to address this. If you think in terms of my comments on the other thread about macrostates vs. microstates, it might for example be that if you just consider the macrostates of the cat they have already decohered before the box is opened (interference between live cat macrostate and dead cat macrostate has become negligible), but that if you considered the macrostates of the cat + experimenter system than interference would still be significant until the box was opened, so that this could be the basis for talking about an initial split in the cat and a later split in the experimenter when he opens the box. But I can't definitely say that this is how it works since I don't know enough about how to do the math.

Let's talk about Hilbert Space.
Let's say you have w,x,y,z axis.
You make axis w as momentum, x as position, y as spin, z as charge. Then you only need one vector to characterize the whole system.
I think you refer to the w, x, y, z axis as basis vector. But you said "the basis vectors could each involve a superposition of multiple positions and multiple momenta for example". You are saying we need to put more axis like u and v to Hilbert Space and make it a superposition of multiple momentum? I thought the 4 axis for example can characterize a system based on its position, momentum, spin and charge. But by adjusting the main vector, one can change the value of the momentum.* Is it standard practice to put more axis to Hilbert Space to character superposition of momentum for example?

 

[JesseM]

Let's talk about Hilbert Space.
Let's say you have w,x,y,z axis.
You make axis w as momentum, x as position, y as spin, z as charge. Then you only need one vector to characterize the whole system.

No, each possible momentum eigenstate is a separate vector orthogonal to all the others, same with position etc. So if you want use basis where the vectors are each position eigenstates, you need a separate basis vector for positions x1, x2, x3, etc. Since some observables like position and momentum have a continuous range of possible values, the full Hilbert space must be infinite-dimensional.

 

[bg032]

Let \Psi(t)=U(t)\Psi_0 be the universal wave function. According to de Witt, at every t there is a (approximately defined) preferred decomposition of \Psi(t) into the sum of orthogonal vectors (worlds):

<br /> \Psi(t)=\Psi_1 + \ldots + \Psi_{n_t}.<br />​

The problem of how to define this decomposition is referred to as the preferred basis problem. However I find this term misleasing, because, in order to define the above decomposition there is no need to define a basis for the whole Hilbert space of the universe. The name preferred decomposition would be more appropriate.

 

[Dmitry67]

Why should there be a preferred decomposition? Such claim is equivalent to a claim that cat is *not* in a superposition before opening a box. Also, in other 'alternatives' the very number of objects (an elements of decomposition) might be different (say, there is no life on Earth).

It does not make any sense to me. "Preferred" to who? Based on what criteria? It is an attempt to drag into MWI framework some "objective" view of the Universe. The only 'objective' view is universe wavefunction itself. Like in relativity we can't ask 'does it move' without specifying 'relative to what', in 'pure' MWI we can't ask 'what happens' without specifying 'relative to what basis/observer'.

When such 'preferred' stuff is forced into MWI, we get such weird artefacts like 'preferred basis problem' or 'splitting is not lorentz-invariant, because preferred basic exists in preferred frame' etc

 

[JesseM]

Well, the preferred basis issue is part of DeWitt's version of the MWI. The advantage is that it allows you to state precisely what the different "worlds" are at any given moment (and their respective probabilities if you also assume the Born rule). The disadvantage, as you say, is that it seems a bit arbitrary and sort of messes with the elegance of the "the wavefunction is all there is" version of the MWI. That "wavefunction is all there is" version is probably more popular, with the "worlds" just being distinguished by decoherence, but the disadvantage of that version is that there is no precise and rigorous definition of what the worlds or branches are, when there has been "enough" decoherence for worlds to become differentiated, etc. See John Bell's criticisms of the non-precise "for all practical purposes" (FAPP) definition of worlds in http://duende.uoregon.edu/~hsu/blogfiles/bell.pdf.

 

[bg032]

Why should there be a preferred decomposition? ...

My position is that the universal wave function has a pattern which strongly suggests a preferred decomposition. Suppose for example that \Psi(t) is the sum of spatially well separated (in 3N configuration space) wave packets which remains separated under time evolution. Bohm has extensively studied this situation. For me it is obvious that such a pattern strongly suggests the preferred decomposition in which every element is a single wave packet. This decomposition is evident even though it cannot be exactly defined, because the boundaries between the wave packets cannot be exactly defined.

Of course, the fact that the universal wave function posseses such a pattern has to be proved. Note however that the presence of such a pattern is not matter of interpretation or of taste. At least in principle, it can be proved or disproved by calculating Schroedinger's evolution of a wave function with reasonable (not conspirative) initial conditions.

Another example: the clouds in the sky derive from a pattern of the density \rho(x) of water vapor. We cannot exactly define the boundary of a cloud. Nevertheless for us clouds are existing objects, and if the pattern of \rho(x) is appropriate, you can distinguish and count the clouds.

Why should there be a preferred decomposition? Such claim is equivalent to a claim that cat is *not* in a superposition before opening a box. Also, in other 'alternatives' the very number of objects (an elements of decomposition) might be different (say, there is no life on Earth).

I am not sure to understand this. Assuming that the wave functions |cat alive> and |cat dead> are spatially separated in configuration space, the wave function of the cat (and therefore of the universe) is already decomposable according the above criterion before opening the box.

 

[Dmitry67]

bg032, ok, slightly different version.

Say, I have an emitter of 'wave packets'. When it emits a wave packet, it becomes 'spacially separated' from it. It is programmed to emit it when radioactive atom decays. There are 100 atoms.

After a while, there is a superposition of emitter plus from 0 to 100 wavepackets. From 1 to 101 spacially separated subsystems. How do you decompose such system?

I agree with you: in *some* cases the pattern is clear, but it is not a universal rule.

 

[bg032]

Well, the preferred basis issue is part of DeWitt's version of the MWI. The advantage is that it allows you to state precisely what the different "worlds" are at any given moment (and their respective probabilities if you also assume the Born rule). The disadvantage, as you say, is that it seems a bit arbitrary and sort of messes with the elegance of the "the wavefunction is all there is" version of the MWI. That "wavefunction is all there is" version is probably more popular, with the "worlds" just being distinguished by decoherence, but the disadvantage of that version is that there is no precise and rigorous definition of what the worlds or branches are, when there has been "enough" decoherence for worlds to become differentiated, etc. See John Bell's criticisms of the non-precise "for all practical purposes" (FAPP) definition of worlds in http://duende.uoregon.edu/~hsu/blogfiles/bell.pdf.

JesseM, in my previous post (posted I think at the same time of yours) is explained why I have no problem with approximately defined branches. For me branches are patterns of the wave function, and patterns may be evident even though vaguely defined. Branches are like clouds in a sky with well defined clouds: they cannot be exactly defined but nevertheless they exist and are evident.
On the contrary, I am totally unsatisfied by the mechanism based on decoherence for giving rise to the branches, which I find confused and elusive. In the paper of Wallace you cited you can read:

“Worlds” are mutually dynamically isolated structures instantiated within the quantum state, which are structurally and dynamically “quasiclassical”.

What does this mean? What are mutually dynamically isolated structures? I do not understand...


Dmitry67: certainly you can built situations in which the decomposition into separated wavepackets is not possible. However my opinion is that at the macroscopic level the universal wave function has a strong tendency to decompose into permanently non-overlapping wave packets. The reason of this is basically the form of the potential of the hamiltonian + the process of macroscopic amplification and the interaction with the environment. The splitting into non-overlapping parts arises at the microscopic level in the scattering processes, and than it is amplified and made permament by the interaction with the environment. See for example chapters 5 and 6 in the book of Bohm: The Undivided Universe.
However I know that this opinion would have to be better proved, and it is largely minority in the physics community, which is mainly oriented towards the decoherence mechanism.

 

[JesseM]

In the paper of Wallace you cited you can read:

“Worlds” are mutually dynamically isolated structures instantiated within the quantum state, which are structurally and dynamically “quasiclassical”.

What does this mean? What are mutually dynamically isolated structures? I do not understand...

I think he probably means that if you consider the reduced density matrix for "the structure" (whether the structure refers to a subsystem of some larger system, or to a set of coarse-grained macrostates of a given system which omit a lot of microscopic detail), then decoherence has dynamically caused the off-diagonal interference terms to have a very tiny amplitude, so that it is approximately correct to just see it as a classical statistical ensemble of the diagonal terms in the density matrix, each of which could be seen as a version of the structure in a different "world".

 

[rodsika]

No, each possible momentum eigenstate is a separate vector orthogonal to all the others, same with position etc. So if you want use basis where the vectors are each position eigenstates, you need a separate basis vector for positions x1, x2, x3, etc. Since some observables like position and momentum have a continuous range of possible values, the full Hilbert space must be infinite-dimensional.

Let's take the case of an electron. The projection of the state vector on each axis is a measure of the possibility of an electron being at a particular position. That's why one has, as you said, to use separate vector orthogonal to all the others for each value. However, earlier you said:

"Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example."

I thought each basis (meaning located in the axis) vector represent one value. But you said it could involve superposition of multiple positions? How could one value becomes a superposition of values?

Second let's take the case of Hydrogen atom with nucleus composed of 3 quarks and electron around it. When putting it in Hilbert Space. Do you use an axis or basis vector for each value of each position, momentum, etc. of the up quark, down quark and electron?

 

[JesseM]

Let's take the case of an electron. The projection of the state vector on each axis is a measure of the possibility of an electron being at a particular position.

Only if you use a basis where the basis vectors are position eigenstates. If the basis vectors are momentum eigenstates, each basis vector represents a quantum state that's a superposition of different possible positions. And you are free to pick a set of basis vectors that aren't eigenstates of position or momentum or any other observable, each of which is a distinct quantum state that represents a different superposition of positions/momenta/etc.

I thought each basis (meaning located in the axis) vector represent one value.

No, that's only true if the basis vectors are eigenstates of an observable, but the definition of "basis" has nothing to do with the notion that each vector should be a value of some observable. Reread what I said in post #72:

To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

So if you have some set S of quantum state vectors, such that any possible new state vector you could come up with can be expressed as a weighted some of the vectors in S, and such that none of the vectors in S can be expressed as a weighted some of the other vectors in S, then S is a valid basis.

 

[rodsika]

Only if you use a basis where the basis vectors are position eigenstates. If the basis vectors are momentum eigenstates, each basis vector represents a quantum state that's a superposition of different possible positions. And you are free to pick a set of basis vectors that aren't eigenstates of position or momentum or any other observable, each of which is a distinct quantum state that represents a different superposition of positions/momenta/etc.

No, that's only true if the basis vectors are eigenstates of an observable, but the definition of "basis" has nothing to do with the notion that each vector should be a value of some observable. Reread what I said in post #72:

So if you have some set S of quantum state vectors, such that any possible new state vector you could come up with can be expressed as a weighted some of the vectors in S, and such that none of the vectors in S can be expressed as a weighted some of the other vectors in S, then S is a valid basis.

Ok.

Earlier in the thread you said "the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI."

Why.. what would it looks like if other MWI branches only have momentum basis? Can you please describe what that world would be like? For example. A ball rolling on the floor. If momentum basis only is chosen, what would happen. Or since preferred basis in other branches can be any basis in Hilbert space, (right?) Let's say the preferred basis chosen is charge. What would happen if a ball is rolling on the floor in that branch.. or do you mean to say the branch where charge is the preferred basis won't have moving objects but everything static?

 

[JesseM]

Ok.

Earlier in the thread you said "the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI."

Why.. what would it looks like if other MWI branches only have momentum basis?

What do you mean "other MWI branches"? The idea of DeWitt's version is that you pick a single set of basis vectors for the whole universal wavefunction, not that each branch has its own basis. I don't know what the worlds would "look like" if you used a momentum basis, would it even make sense to talk about distinct brain states of observers if each particle's position was maximally uncertain? It seems to me that this is another aspect of the preferred basis problem, that it's hard to make sense of what it would even mean to choose a basis where the positions of particles weren't confined to a sufficiently narrow range to be able to talk about brain structures, measurement records etc.

 

[rodsika]

What do you mean "other MWI branches"? The idea of DeWitt's version is that you pick a single set of basis vectors for the whole universal wavefunction, not that each branch has its own basis. I don't know what the worlds would "look like" if you used a momentum basis, would it even make sense to talk about distinct brain states of observers if each particle's position was maximally uncertain? It seems to me that this is another aspect of the preferred basis problem, that it's hard to make sense of what it would even mean to choose a basis where the positions of particles weren't confined to a sufficiently narrow range to be able to talk about brain structures, measurement records etc.

I thought it was like the concept of Inflationary Bubble Universes where there are different constants of nature in each parallel universe, or the concept of Superstring Landscape where there are different laws of physics in each landscape universe. Similary. I thought different Many Worlds or Branches have different Preferred Basis chosen such that we can have one branch where charge or spin is the preferred basis. But is this impossible. So if one basis is chosen in the Universal Wavefunction, all the billions of worlds or branches would choose the same basis. Is this a definite certainty or can Hilbert Spaces be doctored to produce different Preferred Basis for each branch? What's the proof it can't? Remember decoherence divide the worlds.. so if our world has position as preferred basis. What would stop other branches to have spin as preferred basis? Why does the mathematics of Hilbert Space prevent that?

Btw just curious. Are you a physicist? What is your specialization?

 

[JesseM]

I thought it was like the concept of Inflationary Bubble Universes where there are different constants of nature in each parallel universe, or the concept of Superstring Landscape where there are different laws of physics in each landscape universe. Similary. I thought different Many Worlds or Branches have different Preferred Basis chosen such that we can have one branch where charge or spin is the preferred basis. But is this impossible. So if one basis is chosen in the Universal Wavefunction, all the billions of worlds or branches would choose the same basis. Is this a definite certainty or can Hilbert Spaces be doctored to produce different Preferred Basis for each branch? What's the proof it can't? Remember decoherence divide the worlds.. so if our world has position as preferred basis. What would stop other branches to have spin as preferred basis? Why does the mathematics of Hilbert Space prevent that?

Are we still talking about DeWitt's version? The "preferred basis" is a basis for splitting the entire universal wavefunction into a set of different "worlds", I don't even understand what it would mean for different branches to have their own basis. I will say that since there is no requirement that the basis vectors all be eigenvectors of the same observable, I think you could probably have a single basis where some of the basis vectors were position eigenvectors, some were momentum eigenvector, etc. (by the way spin commutes with both position and momentum, see [post=2676394]here[/post], so you could have a basis where every vector was both a position eigenvector and a spin eigenvector, meaning every particle would have both a precise position and a precise spin, or a basis where every vector was both a momentum eigenvector and a spin eigenvector).

Btw just curious. Are you a physicist? What is your specialization?

No, I got my undergraduate degree in physics and still read about physics-related stuff a fair amount on my own, but that's the extent of my training.

 

[rodsika]

Are we still talking about DeWitt's version? The "preferred basis" is a basis for splitting the entire universal wavefunction into a set of different "worlds", I don't even understand what it would mean for different branches to have their own basis. I will say that since there is no requirement that the basis vectors all be eigenvectors of the same observable, I think you could probably have a single basis where some of the basis vectors were position eigenvectors, some were momentum eigenvector, etc. (by the way spin commutes with both position and momentum, see [post=2676394]here[/post], so you could have a basis where every vector was both a position eigenvector and a spin eigenvector, meaning every particle would have both a precise position and a precise spin, or a basis where every vector was both a momentum eigenvector and a spin eigenvector).

No, I got my undergraduate degree in physics and still read about physics-related stuff a fair amount on my own, but that's the extent of my training.

I'm not referring to any particular version. You mean the idea of Preferred basis is different in different versions of quantum interpretations like Bohmian, etc.?

Also you mean Preferred Basis can change? Or is it fixed. If fixed. What Prefered basis is chosen to explain our classical world? How many set of preferred basis are there. Like...

1st Preferred Basis is: Position

2nd Preferred Basis: Position + Spin,

3rd Preferred Basis: Position not commuted with Momentum, etc.

I mean. What are the exact Preferred Basis chosen for our universe?

Hmm.. I thought anyone who has undergraduate degree in physics is automatically a physicist? why not?

 

[JesseM]

I'm not referring to any particular version. You mean the idea of Preferred basis is different in different versions of quantum interpretations like Bohmian, etc.?

The function of the preferred basis in DeWitt's version is to define the set of worlds, what would you need a preferred basis for in Bohmian mechanics? There aren't multiple worlds there, and every particle has a hidden position variable at all times. And in non-DeWitt MWI decoherence is supposed to define what observable the environment is effectively "measuring", I think one of the papers linked on this thread said it normally be position but for small systems interacting more slowly/weakly with the environment it could be energy.

Also you mean Preferred Basis can change? Or is it fixed.

Change over time, you mean? I don't know what DeWitt's version would say about that.

If fixed. What Prefered basis is chosen to explain our classical world? How many set of preferred basis are there. Like...

1st Preferred Basis is: Position

2nd Preferred Basis: Position + Spin,

3rd Preferred Basis: Position not commuted with Momentum, etc.

How is "position not commuted with momentum" different than "position"? There's no such thing as position that does commute with momentum, it's an inherent property of the two observables that they don't commute. And I don't think position alone would suffice as a basis, if you want a basis made up of eigenvectors of observables I think you need a complete set of commuting observables to span the Hilbert space. Anyway, as I said the arbitrariness of choosing the basis is exactly why the preferred basis issue is a problem for DeWitt's version of the MWI.

 

[rodsika]

The function of the preferred basis in DeWitt's version is to define the set of worlds, what would you need a preferred basis for in Bohmian mechanics? There aren't multiple worlds there, and every particle has a hidden position variable at all times. And in non-DeWitt MWI decoherence is supposed to define what observable the environment is effectively "measuring", I think one of the papers linked on this thread said it normally be position but for small systems interacting more slowly/weakly with the environment it could be energy.

Change over time, you mean? I don't know what DeWitt's version would say about that.

How is "position not commuted with momentum" different than "position"? There's no such thing as position that does commute with momentum, it's an inherent property of the two observables that they don't commute. And I don't think position alone would suffice as a basis, if you want a basis made up of eigenvectors of observables I think you need a complete set of commuting observables to span the Hilbert space. Anyway, as I said the arbitrariness of choosing the basis is exactly why the preferred basis issue is a problem for DeWitt's version of the MWI.

Why do you put so much weight on DeWitt. Maybe we should just reject DeWitt version because he didn't give any explanation why or how the Preferred Basis is chosen at all.. just a priori... In Everett original formula, he used the concept of "Relative state" as shown in the Stanford website which was incomplete. Therefore why can't we just accept the Decoherence version of MWI as it needs the environment to define the Preferred basis. Now in pure Decoherence version (without DeWitt Adhoc ness), is it possible other branches would have other environments (akin to parallel worlds with different laws of nature) such that the environment there with constants of nature that don't admit positions to have charge as the preferred basis? Or do you mean Many Worlds only work within our Spacetime with our given Constants of Nature??