Many-worlds true quantum event generator

[rodsika]

Does Al-khalili say specifically that he is talking about DeWitt's version of the MWI and not other versions? As I said in [post=3236959]post #28[/post], I thought DeWitt's version was just about picking a preferred basis and saying every possible eigenstate in that basis with nonzero amplitude would be a separate "world", so the whole issue of decoherence should have nothing to do with the number of worlds, whereas Al-khalili seems to say decoherence determines the number of distinct worlds in the quote above (this seems more in line with the idea I referred to earlier that we can only talk about 'worlds' in an approximate sense, with different worlds being differentiable at a macroscopic coarse-grained level, which I think is the same idea discussed in this section of an online Everett FAQ).

In post #28 I quoted from a Stanford Encyclopedia article as a basis for my understanding of DeWitt, which was also written by a philosopher of science, http://www.lps.uci.edu/barrett/ , and the other Stanford Encyclopedia article I quoted in the same post was written by a physicist (Lev Vaidman) and said in section 6:

The level of discussion in those articles is typically a bit more rigorous than what you find in a typical pop physics book aimed at a broad audience (does Al-khalili talk about the preferred basis problem, for example?) If Al-Khalili says he is talking specifically about DeWitt's version and not some other version, please quote the section where he says so.

No. Jim Al-Khalili didn't emphasize what he mentioned is DeWitt's version. He just mixed them up. He said:

"Back to Everett. His interpretation has since spawned a number of variants. While his original idea is now known as the many-worlds interpretation, there is also the multiverse interpretation, the many-histories interpretation and the many-minds interpretation. I quick like the first, do not really understand the second, and am not at all keen on the third"

Looking at the Index. Dewitt is only mentioned in one sentence where he mentioned:
"Interest in his work was revived in the late 1960s by Bryce DeWitt who coined the term 'many-worlds interpretation'."

So I guess Jim Al-Khalili just mixed Everett with Dewitt and make them one. I think he can be forgiven because the book is pop-sci account of the quantum and Many worlds is just mentioned in two page. He didnt mention about preferred basis problem. Maybe he doesnt
even know what it is. The book has so many colorful illustrations. In the one describing Many Worlds. He wrote something beside the illustration I still can't fully understand after years of reading it. He said:

"The many-worlds explanation: all possible realities co-exist. The atom goes through a different slit in each universe and the two universes overlap only at the level of the single atom. In each universe, the atom feels the presence of its parallel self which has gone through the other slit. The superposition, and hence interference, is the result of superposition of universes."

Let's put it in the context of Dewitt Splitting, There is some sense I can't understand.
Let's analyze this step by step. As the emitter sends off the atom. It begins to split into two atoms in each world. Now does each atom still behave as a wave? I wonder what the above means by the atom feeling the presence of its parallel self and interfering. We know the empty part of the interference at the detector is where there is 180 degrees out of phase in the wave from each slit. Now replacing it with atoms. In what sense can the atoms feel the other's presence and know they are 180 degrees out of phase and cause destructive interference? Unless the atom is still behaving as wave and it is the wave that interferes? If not. Does it mean when the atoms are in the same space, destructive inference is what results and both of the atoms shifted their positions from the null area? Also both atoms are supposed to be in their own worlds. How can they still feel each other's presence?*

Again we are talking about the version of Dewitt Splitting. But I think I prefer Everett original version as Dewitt Splitting is so ridicuous as one atom in your body can spaw billions of big bangs but I have to understand Dewitt's first before fully concentrating on Everett version which I think is the one you like and prefer.

 

[JesseM]

So I guess Jim Al-Khalili just mixed Everett with Dewitt and make them one.

Why do you think he mixed them up? Again, the description of "splitting" you gave didn't sound like DeWitt's version at all, since DeWitt's version shouldn't depend on decoherence for splitting.

He wrote something beside the illustration I still can't fully understand after years of reading it. He said:

"The many-worlds explanation: all possible realities co-exist. The atom goes through a different slit in each universe and the two universes overlap only at the level of the single atom. In each universe, the atom feels the presence of its parallel self which has gone through the other slit. The superposition, and hence interference, is the result of superposition of universes."

Let's put it in the context of Dewitt Splitting, There is some sense I can't understand.
Let's analyze this step by step. As the emitter sends off the atom. It begins to split into two atoms in each world.

Why two? I would think in DeWitt's version, if the preferred basis vectors are position eigenvectors, the number of "worlds" would become infinite immediately after emission since there is a continuous infinity of distinct possible positions for the atom and the wavefunction assigns each one some nonzero amplitude (though perhaps in relativistic QM it would only assign nonzero amplitude to positions which were inside the future light cone of the event of the emitter sending the atom). I suppose in quantum gravity space might be quantized so the range of possible positions wouldn't be truly infinite, still very large. And it's also possible the preferred basis wouldn't be position eigenvectors, but in that case I would think in DeWitt's version you couldn't talk about "worlds" where the particle has a precise position at any time (perhaps each basis vector would at least confine the particle's position to a narrow possible range).

 

[rodsika]

Why do you think he mixed them up? Again, the description of "splitting" you gave didn't sound like DeWitt's version at all, since DeWitt's version shouldn't depend on decoherence for splitting.

Why two? I would think in DeWitt's version, if the preferred basis vectors are position eigenvectors, the number of "worlds" would become infinite immediately after emission since there is a continuous infinity of distinct possible positions for the atom and the wavefunction assigns each one some nonzero amplitude (though perhaps in relativistic QM it would only assign nonzero amplitude to positions which were inside the future light cone of the event of the emitter sending the atom). I suppose in quantum gravity space might be quantized so the range of possible positions wouldn't be truly infinite, still very large. And it's also possible the preferred basis wouldn't be position eigenvectors, but in that case I would think in DeWitt's version you couldn't talk about "worlds" where the particle has a precise position at any time (perhaps each basis vector would at least confine the particle's position to a narrow possible range).

Wait. When you speak about "worlds", are you talking about parallel universes where there is a duplicate milky way and everything in the universe, or just in the measurement setting? Anyway. This is the complete statements of Jim's to get the whole context across:

"The basic idea is the following: When a quantum system is faced with a choice of alternatives such as a particle going through one of two or more slits then, rather than the wave function entering a superposition, we think of it, and the Whole Universe along with it, as splitting into a number of realities equal to the number of options available. These different worlds/universes/branches will be identical to each other apart from the different option chosen by the particle: in one universe it has gone through the upper slit, in the other it has gone through the lower slit. The universes overlap, only in that region where interference is taking place, until decoherence sets in. This then causes them to separate into non-interacting independent realities. That is it. There is no measurement process any more and the wavefunction never needs to 'collapse'. Schrodinger's cat will end up dead in one universe and alive in the other. We, as observers, will also split and so only ever see the outcome of our branch. But there will be other copies of us in parallel universe for whom the alternative outcomes are realized."

So you see. Any atomic process in our body can spawn new worlds.. meaning new universes. This is what I mean when I said that just doing one double slit experiment can create a duplicate of everything with a duplicate United States, duplicate solar system, dupicate galaxy, duplicate billions of galaxies and duplicate universe. This is possible because if there are two copies of us in parallel universe as Jim said, then there is duplicate Universes with billions of galaxies. Since atomic processes occur naturally in our body atoms and everything. Then in one second billions of universe and billions of galaxies are spawned. This is why I can't accept it all these years. Now you are saying this is not the correct idea and Jim is just hyperbolating or exagerating when he says there are other copies of us in parallel universes?

 

[JesseM]

Wait. When you speak about "worlds", are you talking about parallel universes where there is a duplicate milky way and everything in the universe, or just in the measurement setting?

In DeWitt's version as I'm understanding it there'd be no restriction to measuring instruments, you take the wavefunction of the entire universe, use a preferred basis to express it as a vast sum of basis vectors (if the preferred basis is position, each vector in the sum would be a distinct configuration of positions for the entirety of all the particles in the universe), and treat each of these basis vectors as a distinct "world".

"The basic idea is the following: When a quantum system is faced with a choice of alternatives such as a particle going through one of two or more slits then, rather than the wave function entering a superposition, we think of it, and the Whole Universe along with it, as splitting into a number of realities equal to the number of options available. These different worlds/universes/branches will be identical to each other apart from the different option chosen by the particle: in one universe it has gone through the upper slit, in the other it has gone through the lower slit. The universes overlap, only in that region where interference is taking place, until decoherence sets in. This then causes them to separate into non-interacting independent realities. That is it. There is no measurement process any more and the wavefunction never needs to 'collapse'. Schrodinger's cat will end up dead in one universe and alive in the other. We, as observers, will also split and so only ever see the outcome of our branch. But there will be other copies of us in parallel universe for whom the alternative outcomes are realized."

Again, the fact that he is talking about decoherence being needed to differentiate worlds suggests to me he is not talking about DeWitt's version, which just seems to treat each basis vector as a distinct "world" regardless of decoherence. Did you read this entry of the Everett FAQ I linked to earlier? It seems like it's talking about the same sort of idea as in the quote above. In both cases I think the "worlds" are only approximate, there are no clear precise criteria for when a sufficient "amount" of decoherence has occurred for a "split", though after sufficient time the interference terms will have become so tiny that we can ignore them "for all practical purposes" (a commonly-used phrase in papers about the measurement problem thanks to John Bell's abbreviation "FAPP" in his 1990 paper Against Measurement).

Now you are saying this is not the correct idea and Jim is just hyperbolating or exagerating when he says there are other copies of us in parallel universes?

I'm saying the "parallel universes" aren't differentiated by any totally clear-cut criteria, they're just an approximate way about talking about different elements of the single universal wavefunction, but certainly the universal wavefunction contains a superposition of different versions of the Earth (different position eigenstates for all the particles making up the Earth and its inhabitants, say) with different versions of you that have recorded different experiences in their brains and in other records they leave such as internet postings.

 

[JesseM]

Did Everett mention specifically that there aren't really clearly-differentiated worlds??

I don't think he specifically said that, but I also don't think he specifically said there are clearly-differentiated worlds, which has led to a lot of different interpretations of what he meant, see the Stanford Encyclopedia page on Everett's formulation of QM. This bit of section 5 may be relevant:

One problem is simply interpretational: it is unclear that Everett himself had a physical splitting of observers in mind. Perhaps Everett's most careful explanation of how pure wave mechanics accounts for determinate experience is found in a footnote to his extended presentation.

At this point we encounter a language difficulty. Whereas before the observation we had a single observer state afterwards there were a number of different states for the observer, all occurring in a superposition. Each of these separate states is a state for an observer, so that we can speak of the different observers described by the different states. On the other hand, the same physical system is involved, and from this viewpoint it is the same observer, which is in different states for the different elements of the superposition (i. e., has had different experiences in the separate elements of the superposition). In this situation we shall use the singular when we wish to emphasize that a single physical system is involved, and the plural when we wish to emphasize the different experiences for the separate elements of the superposition. (1973, 68 footnote)

On the face of it, this seems perfectly clear. There is exactly one post-measurement physical observer and multiple classical states simultaneously obtain for the one physical observer. It remains to explain how it is possible for multiple, classically incompatible, states each to obtain determinately for a single physical system in a way that does not require physical splitting. But it does seem, at least here, that for Everett there is no physical splitting of observers or any other physical systems.

Also, looking on google books at p. 158 of a biography of Everett, I see he emphasized the reversibility of the evolution of the universal wavefunction, suggesting he didn't believe in any irreversible "splits" between worlds:

Linking entropy, information, and probability in his long thesis, Everett showed that the universal wavefunction is intrinsically reversible (time can flow backwards, broken eggs reverse trajectories to reunite yolk and shell). But for us, the motion through time appears to be irreversible, said Everett:

Macroscopically irreversible phenomena are common to both classical and quantum mechanics, since they arise from our incomplete information concerning a system, not from any intrinsic behavior of the system.

And in the handwritten draft:

Thus the apparent irreversibility of natural processes is understood also as a subjective phenomena, relative to observers who lose information in an essential manner, still within a determinate framework which is overall reversible (in which total information is conserved).

So, even though the universal wave function allows information to be transferred to a scientist who does not stand outside the system observed, his perspective is limited:

These are, therefore, fundamental restrictions to the knowledge that an observer can obtain about the state of the universe...Any single observer can therefore possesses knowledge only of relative state function (relative to his state) of any systems, which is in any case all that is of any importance to him.

I think the emphasis on defining observations relative to the state of observers also suggests he wasn't thinking of complete "worlds", just of a universal superposition which contains different versions of any given observer having different experiences. This fits pretty well with the version of the many-worlds interpretation discussed in this Stanford Encyclopedia article, where for example the author writes:

Another concept (considered in some approaches as the basic one, e.g., in Saunders 1995) is a relative, or perspectival, world defined for every physical system and every one of its states (provided it is a state of non-zero probability): I will call it a centered world. This concept is useful when a world is centered on a perceptual state of a sentient being. In this world, all objects which the sentient being perceives have definite states, but objects that are not under her observation might be in a superposition of different (classical) states. The advantage of a centered world is that it does not split due to a quantum phenomenon in a distant galaxy, while the advantage of our definition is that we can consider a world without specifying a center, and in particular our usual language is just as useful for describing worlds at times when there were no sentient beings.

The concept of "world" in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) in describing our experience. When we refer to the "definite classically described state" of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is maximally specified according to our ability to distinguish between the alternatives and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world.[2]

Also see sections 3.4 and 6.2 which talk more about this observer-centered perspective on the MWI, which seems to me to be closest to what Everett had in mind.

 

[JesseM]

How many percentage of physicists do you think believe in clearly differentiated world than those who do not?

No idea.

For this idea of clearly differentiated world. Can a Universal Wavefunction able to produce a billion duplicate universes spawned by say atomic processes in the atoms of the bodies of an ant? But what would happen if a second ant spawed another billion duplicate universes. And millions of ants spawning billions and billions and billions of duplicate universes. Do they fall under one Universal Wavefunction common to all the ants? Or does each ant has its own Universal Wavefunction it can split separate from others? This concept is for those who believe in clearly differentiated worlds. And scientists like Nick Herbert believes in this.

"Universal wavefunction" means the wavefunction of the entire universe considered as a single system, it doesn't make any sense to talk about different parts of the universe having their "own Universal Wavefunction".

 

[rodsika]

In DeWitt's version as I'm understanding it there'd be no restriction to measuring instruments, you take the wavefunction of the entire universe, use a preferred basis to express it as a vast sum of basis vectors (if the preferred basis is position, each vector in the sum would be a distinct configuration of positions for the entirety of all the particles in the universe), and treat each of these basis vectors as a distinct "world".

Again, the fact that he is talking about decoherence being needed to differentiate worlds suggests to me he is not talking about DeWitt's version, which just seems to treat each basis vector as a distinct "world" regardless of decoherence. Did you read this entry of the Everett FAQ I linked to earlier? It seems like it's talking about the same sort of idea as in the quote above. In both cases I think the "worlds" are only approximate, there are no clear precise criteria for when a sufficient "amount" of decoherence has occurred for a "split", though after sufficient time the interference terms will have become so tiny that we can ignore them "for all practical purposes" (a commonly-used phrase in papers about the measurement problem thanks to John Bell's abbreviation "FAPP" in his 1990 paper Against Measurement).

I think Decoherence applied MWI is more natural than needing special preferred basis. Have you read this paper by Maximilian Schlosshauer called "Decoherence, the measurement problem, and interpretations of quantum mechanics"?

http://arxiv.org/abs/quant-ph/0312059

It says (page 23):

"There are several advantages in a decoherence-related approach to selecting the preferred Everett bases: First, no a priori existence of a preferred basis needs to be postulated, but
instead the preferred basis arises naturally from the physical criterion of robustness. Second, the selection will be likely to yield empirical adequacy, since the decoherence program is derived solely from the well-confirmed Schr¨odinger dynamics (modulo the possibility that robustness may not be the universally valid criterion). Lastly, the decohered components of the wave function evolve in such a way that they can be reidentified over
time (forming "trajectories" in the preferred state spaces) and thus can be used to define stable, temporally extended Everett branches. Similarly, such trajectories can be used to ensure robust observer record states and/or environmental states that make information about the state of the system of interest widely accessible to observers (see, for example, Zurek’s "existential interpretation," outlined in Sec. IV.C.3 below)."

I'll read the paper in its entirely tomorrow as well as check out Maximilian book in the library. I can't believe that watching the movie Source Code to give me relaxation just ignites my interests in the Many Worlds and the ensuing headache this study can cause. :( :)

 

[JesseM]

I think Decoherence applied MWI is more natural than needing special preferred basis. Have you read this paper by Maximilian Schlosshauer called "Decoherence, the measurement problem, and interpretations of quantum mechanics"?

http://arxiv.org/abs/quant-ph/0312059

Haven't read it, but looks like an excellent resource, thanks. Skimming it over, I see that on p. 24 he discusses the concept that decoherence gives only an approximate basis, and therefore only an approximate decomposition of the universal wavefunction into "worlds", though he doesn't see this as a problem:

The approach of using environment-induced superselection and decoherence to define the Everett branches has also been critized on grounds of being “conceptually approximate,” since the stability criterion generally leads only to an approximate specification of a preferred basis and therefore cannot give an “exact” definition of the Everett branches (see, for example, the comments of Kent, 1990; Zeh, 1973, and also the well-known “anti-FAPP” position of Bell, 1982). Wallace (2003a, pp. 90–91) has argued against such an objection as

(. . . ) arising from a view implicit in much discussion of Everett-style interpretations: that certain concepts and objects in quantum mechanics must either enter the theory formally in its axiomatic structure, or be regarded as illusion. (. . . ) [Instead] the emergence of a classical world from quantum mechanics is to be understood in terms of the emergence from the theory of certain sorts of structures and patterns, and . . . this means that we have no need (as well as no hope!) of the precision which Kent [in his (1990) critique] and others (. . . ) demand.

Accordingly, in view of our argument in Sec. II.B.3 for considering subjective solutions to the measurement problem as sufficient, there is no a priori reason to doubt that an “approximate” criterion for the selection of the preferred basis can give a meaningful definition of the Everett branches—one that is empirically adequate and that accounts for our experiences.

 

[Dmitry67]

Interesting. Many of the articles about MWI were written in pre-decoherence era. I believe, before the discovery of the decoherence MWI looked very artificial. Decoherence had created a solid ground for it. Were scientists thinking that Everett was crazy in 195x-196x?

 

[ExecNight]

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

 

[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??

 

[JesseM]

Why do you put so much weight on DeWitt.

I don't, but the problem of needing to find a preferred basis seems specific to DeWitt's version, so since you were asking questions about how to pick it I figured you were asking about that version.

Therefore why can't we just accept the Decoherence version of MWI as it needs the environment to define the Preferred basis.

Right, but with the decoherence version there is no precise definition of "worlds" and decoherence only approximately forces various subsystems into a mix of eigenstates of some observable like position, the interference terms don't entirely disappear and the whole business also depends on how you divide "subsystem" and "environment".

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?

We have to assume the same basic laws apply to all "worlds" in the MWI because you have to be able to represent the wavefunction of the universe as a single state vector evolving according to the Schroedinger equation. The paper you linked to earlier by Schlosshauer says that decoherence tends to drive subsystems towards an ensemble of position eigenstates, though in some cases it can be energy eigenstates instead, see page 14:

In general, three different cases have typically been
distinguished (for example, in Paz and Zurek, 1999) for
the kind of pointer observable emerging from an interaction
with the environment, depending on the relative
strengths of the system’s self-Hamiltonian bHS and of the
system-environment interaction Hamiltonian bHSE :

(1) When the dynamics of the system are dominated
by bHSE , i.e., the interaction with the environment,
the pointer states will be eigenstates of bHSE (and
thus typically eigenstates of position). This case
corresponds to the typical quantum measurement
setting; see, for example, the model of Zurek (1981,
1982), which is outlined in Sec. III.D.2 above.

(2) When the interaction with the environment is weak
and bHS dominates the evolution of the system (that
is, when the environment is “slow” in the above
sense), a case that frequently occurs in the microscopic
domain, pointer states will arise that are energy
eigenstates of bHS (Paz and Zurek, 1999).

(3) In the intermediate case, when the evolution of
the system is governed by bHSE and bHS in roughly
equal strength, the resulting preferred states will
represent a “compromise” between the first two
cases; for instance, the frequently studied model
of quantum Brownian motion has shown the emergence
of pointer states localized in phase space,
i.e., in both position and momentum (Eisert, 2004;
Joos et al., 2003; Unruh and Zurek, 1989; Zurek,
2003b; Zurek et al., 1993).

(again, look at the actual paper to see the notation rendered correctly, I didn't feel like translating the various Hamiltonian symbols into LaTeX)

 

[Dmitry67]

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.

This is true only when Universe had cooled enough. In early Universe (quagma state) or even just an ordinary plasma matter was too hot, so no separate structures existed, and even more, no structures with any sort of "memory" were possible.

Of course, we are free to pick any basis, including "this area of quagma", but the result does not have a lot of sense, like the famous "photon perspective" question.

 

[bg032]

This is true only when Universe had cooled enough. In early Universe (quagma state) or even just an ordinary plasma matter was too hot, so no separate structures existed, and even more, no structures with any sort of "memory" were possible.

Of course, we are free to pick any basis, including "this area of quagma", but the result does not have a lot of sense, like the famous "photon perspective" question.

I agree, but I do not see problems; now the universe is cooled and now we observe a quasi-classical realm.

 

[woolyhead]

Hi. Can I say it seems to me that none of the standard or non standard explanations are very true. I think they are the best theories we can come up with in the hope that they will somehow spawn a better predictive capability but in another sense they are all just attempts to cover the fact that we just don't know, while giving us some sort of picture of what happens, based on our experience of the world around us and how she works. I agree that what "makes sense" to us may not be any sort of reality in the "absolute sense" Our mathematical analyses are based on having some sort of image in our minds about how maths should work, but although it seems to work out in practice most of the time, we shouldn't start to believe too much in the maths either. At root nature is a mystery.

 

[Fyzix]

Hi. Can I say it seems to me that none of the standard or non standard explanations are very true. I think they are the best theories we can come up with in the hope that they will somehow spawn a better predictive capability but in another sense they are all just attempts to cover the fact that we just don't know, while giving us some sort of picture of what happens, based on our experience of the world around us and how she works. I agree that what "makes sense" to us may not be any sort of reality in the "absolute sense" Our mathematical analyses are based on having some sort of image in our minds about how maths should work, but although it seems to work out in practice most of the time, we shouldn't start to believe too much in the maths either. At root nature is a mystery.

I agree with you about this.
It seems a lot of people who are MWI proponents value math over observed reality.



Dmitry67,

So you are admitting that the Dewitt Many Worlds with real splitting of worlds are in violation with relativity, correct?
So you are also agreeing that since that MWI version cannot make sense of probability and has problems with relativity, it's basically worse than Bohm which can atleast get probability right?

So you are a proponent of the "pure wave mechanics" which has no relativity problem, but still can't make sense of probability without additional postulates?

 

[Fyzix]

JesseM, you seem to be pretty knowledgeable in this subject.
Are you a proponent of MWI or just playing Devil's Advocate?

 

[JesseM]

JesseM, you seem to be pretty knowledgeable in this subject.
Are you a proponent of MWI or just playing Devil's Advocate?

Insofar as there's any "real truth" about what's going on with QM my hunch is that the truth would a) not involve anything special happening during "measurement", since measuring devices are just large collections of particles which should follow the same laws as smaller collections, and b) not involve any violation of relativistic locality. So given Bell's theorem I think something along the lines of the MWI is the best option, but I hold out hope that in the future someone may find a new formulation of a "many-worlds-like" interpretation that doesn't have the preferred basis problem of DeWitt's version or the ambiguity about how to derive probabilities of the "pure wavefunction" version.

 

[Fyzix]

Well the thing is, DeWitt MWI got problems with relativity, Bohm got problems with relativity, Bohm derive Born Rule.

So Bohm is the obvious choice between the two, but personally I struggle with accepting problems with relativity.

If we discard both of those and move onto the "pure wavemechanics", we are still stuck with the Probability problem.
It seems that a lot of people don't really recognize the severity of the probability problem, it's flat out disproving MWI at this point.
It's saying "MWI DOES NOT FIT REALITY", so how may one go about solving it?

Well one is definitely forced to add postulates, which most MWI adherents are now starting to slowly accept... Such as either particles (Many Bohmian Worlds) or some other selection process, either way, "PURE" MWI is disproved.
(Unless you manage to fool yourself into believing that consciousness somehow solves it all...)

By the way, there seems to be some problems with decoherence too, that it alone isn't enough to account for our experience in "pure wave mechanics"

See here:
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.1926v1.pdf


Not to mention that others such as Tim Maudlin also has critized this "pure wave mechanics decoherence approach).

I think it's safe to conclude that these 2 approaches (in their current forms) have been thoroughly refuted.

 

[JesseM]

If we discard both of those and move onto the "pure wavemechanics", we are still stuck with the Probability problem.
It seems that a lot of people don't really recognize the severity of the probability problem, it's flat out disproving MWI at this point.

How does it "disprove" it? It's not that the "pure wavemechanics" version gives incorrect probabilities, it's just that it's not clear how to get any probabilities from it (some MWI advocates claim that arguments from decision theory are sufficient), but I don't see why we can't hope that new insights might appear in the future. For example, one interesting suggestion I saw here was that one might describe the evolution of the universal wavefunction in computational terms, and somehow treat classical observers as sub-computations, so the computation required to compute the evolution of the universal wavefunction might naturally lead to a probability measure on different possible sub-computations. Another speculation I've seen is mangled worlds though I don't really understand this proposal very well. And there's the interesting result of http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf showing that if you model the state vector of an idealized observer performing an infinite series of measurements in some quantum experiment, as the number of experiments go to infinity the state will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts", even with no assumption of anything like the Born rule.

By the way, there seems to be some problems with decoherence too, that it alone isn't enough to account for our experience in "pure wave mechanics"

See here:
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.1926v1.pdf

But it depends what you mean by "account for our experience", for example the author of that problem has some philosophical (not technical) objections to the idea of using coarse-graining to define macroscopic "worlds", but if you define the range of possible "experiences" we could have as some collection of coarse-grained descriptions of our lab equipment or brain states, then decoherence could (I think) explain why we don't see interference between different possible coarse-grained macrostates. So it becomes a philosophical question of whether you think this is a good enough way of accounting for the apparent classical macro-world or whether you're bothered by the lack of any totally well-defined formula for what the most "natural" choice of coarse-graining would be, there's no debate about the technical details of what decoherence says or doesn't say. Personally I find such an approach unsatisfying, but to make definitive statements like this:

I think it's safe to conclude that these 2 approaches (in their current forms) have been thoroughly refuted.

...is just silly. For something to be "thoroughly refuted" in physics there needs to be some undeniable technical critique that causes the approach to fall apart, not just verbal philosophical objections.

 

[Fyzix]

First let's take the standard DeWitt MWI approach, I would say that YES, unless we are willing to let go of relativity, this approach is refuted by relativity...

How does it "disprove" it? It's not that the "pure wavemechanics" version gives incorrect probabilities

Well, it sort of does...
Take a simple experiment where QM predicts 0.1% chance of X occurring and 0.9% of Y occurring.
We repeat this ten times and always get 1 X and 9 Y's, according to MWI this "probability" would always go to 50/50 as the universe branch into 2 branches.
So infact it does give us probabilities that are in direct conflict with reality...

(some MWI advocates claim that arguments from decision theory are sufficient)

Yes a few people do, but these are a minority of people who has just decided that they believe in MWI and therefore do not really care too much.
There are quite a few papers that adresses this decision theory approach and shows why it's wrong... I guess you are aware of these papers.

but I don't see why we can't hope that new insights might appear in the future.

Sure we can hope, but hoping isn't science, then we might as well hope for a interpretation that doesn't have any of these problems resulting from progress in ToE...

For example, one interesting suggestion I saw here was that one might describe the evolution of the universal wavefunction in computational terms, and somehow treat classical observers as sub-computations, so the computation required to compute the evolution of the universal wavefunction might naturally lead to a probability measure on different possible sub-computations.

Yes, I've been in contact with the author of this paper discussing MWI before.
He himself doesn't seem overly enthusiastic about it, giving MWI without modification less than 25% of being correct in the end...
That says a lot when the author of the paper admits it's in serious problems (which I admire him for).

Another speculation I've seen is mangled worlds though I don't really understand this proposal very well.

I'm aware of this approach, interestingly enough the previous author you mentioned has given a clear and simple critique of the Mangled Worlds theme right here:

http://onqm.blogspot.com/2009/09/decision-theory-other-approaches-to-mwi.html

And there's the interesting result of http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf

I haven't checked this out yet, but I've been in contact with Jeff Barrett and while he has faith in pure wave mechanics, it's not done like he said.
Bohmian Mechanics is also something he considers "pure wave mechanics" (although he is not particulary fond of Bohmian mechanics), but in his view Pure wave mechanics does not have to imply all outcomes, which changes the game quite a bit...

As for the problems with decoherence, I will try to dig up Tim Maudlin's objections too so you can see that there are infact technical and philosophical reasons for not being satisfied with this approach at all.