rodsika said:Hi, what cheap device is available where a quantum choice can be made..
JesseM said: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.
Momentum and position eigenstates are axes in Hilbert space, each one forming a different "basis". It's like how in 3D space you can have coordinate system #1 made up of x-y-z axes, as well as coordinate system #2 made up of x'-y'-z' axes pointing in different directions, and you can use either coordinate system to describe points and vectors in that space.rodsika said:I've read the threads you mentioned. But Collin Bruce seems to be describing it differently in Schroedinger Rabbit. He seemed to be saying that the problem of preferred basis is how to map the Hilbert space to the geometry of our own space-time. What has this got to do with momentum? Anyway he said (he was describing the Hilbert Space):
"... How to decide which way to draw the axes needed? Why should the directions of the various axes we chose correspond in any way to the directions of our particular three-dimensional space?
If two observables commute (like position and spin), then one meaning of that is that in terms of the Hilbert space, you can find a set of basis vectors such that each vector is an eigenvector of both those observables. If they don't commute, then an eigenvector of one will be a superposition of different eigenvectors of the other, and vice versa. So, another way of stating the preferred basis problem is that you have to pick a complete set of commuting observables as your basis, if the vectors are position eigenvectors (definite position states) then they won't be momentum eigenvectors (each vector will be a superposition of different momentum states) and vice versa.rodsika said:What do you mean by commute and what has this got to do with mapping Hilbert space to the geometry of our own space-time?
JesseM said:Momentum and position eigenstates are axes in Hilbert space, each one forming a different "basis". It's like how in 3D space you can have coordinate system #1 made up of x-y-z axes, as well as coordinate system #2 made up of x'-y'-z' axes pointing in different directions, and you can use either coordinate system to describe points and vectors in that space.
If two observables commute (like position and spin), then one meaning of that is that in terms of the Hilbert space, you can find a set of basis vectors such that each vector is an eigenvector of both those observables. If they don't commute, then an eigenvector of one will be a superposition of different eigenvectors of the other, and vice versa. So, another way of stating the preferred basis problem is that you have to pick a complete set of commuting observables as your basis, if the vectors are position eigenvectors (definite position states) then they won't be momentum eigenvectors (each vector will be a superposition of different momentum states) and vice versa.
A more intuitive physical meaning of commuting vs. not commuting is that that if two observables commute, you can measure one without disturbing the value of the other--if you measure position, then immediately after that (a negligible time interval) measure spin, then immediately after that measure position again, then if the time between measurements is arbitrarily small the second position measurement will be arbitrarily close to the first one (in the limit as the time goes to infinity the change in position goes to zero). But if you measure position, then immediately measure momentum, then immediately measure position again, then no matter how small the time intervals the probability distribution for position will be significantly changed, by an amount which can be calculated from the position/momentum uncertainty relation.
Dmitry67 said:1. My hope has some foundation. For example, most of the scientific community agree on Block Time, hence there is nothing special in the moment of time called "NOW". The "NOW" phenomenon is not explained by physics, but is moved the the realm of the yet-to be-explained consciousness.
2. When I google
Jeffrey A Barrett mwi relativity
I find this thread and few links to Barrett works
what exactly are you talking about
Could you provide a description of that "problem"?
Fyzix said:Those who favor a decoherence account of splitting worlds sometimes seem to imagine some sort of “unzipping” of spacetime that occurs along the forward light cone of the spacetime region that contains the measurement interaction. While decoherence effects can be expected to propagate along the forward light cone of the region that contains the interaction event between the measuring device and the object system, and while there is no problem describing the decoherence effects themselves in a way that is perfectly compatible with relativity, there is a problem in imagining that such a splitting process somehow physically copies the systems involved. A strong picture of spacetime somehow unzipping into connected spacetime regions along the forward light cone of the measurement event, would not be compatible with special relativity insofar as relativity presupposes that all events occur on the stage of Minkowski spacetime. And if we give up this assumption, then it is unclear what the rules are for compatibility with special relativity.
I don't really have a detailed understanding of decoherence and its relation to the MWI, so take what I say with a large grain of salt, but from what I've read if you have the wavefunction for some quantum subsystem and a larger "environment" which interacts thermally with it, then if you calculate the wavefunction of the whole system and use it to figure out what happens to the component of the wavefunction dealing only with the small subsystem alone (not the environment), then interaction with the environment tends to drive the wavefunction of the subsystem into something close to a mixed state, a classical statistical ensemble of different eigenstates in some basis determined "naturally" by the decoherence process, rather than a "pure state" which is just a single quantum state vector that will be a superposition of different eigenstates, different from a statistical ensemble of them (in a statistical ensemble there is no interference, you're free to imagine it's definitely in one of the eigenstates and you're just uncertain about which it is). One problem here is that it only works for the wavefunction of the subsystem, the full wavefunction of the whole system composed of both the subsystem and its "environment" does not approach a mixed state (so this suggests some difficulties in using decoherence to explain how the whole universe ends up as a collection of "worlds", since the universe has no external environment...I don't really understand the "decoherent histories" approach though, maybe it has something to say about this issue). The other problem is that while the subsystem approaches something very close to a mixed state via decoherence, it doesn't do so exactly, the interference terms don't quite go to zero. Here's a quote on this from one of the most prominent MWI advocates today, David Deutsch, quoted on p. 332 of the book Minds, Machines and the Multiverse:rodsika said:Ok. After continuous reading of many references. I came across this paper by Maximilian Schlosshauer "Decoherence, the measurement problem, and interpretations of quantum mechanics":".. the results thus far suggest that the selected properties are in agreement with our observation: for mesoscopic and macroscopic objects the distance-dependent scattering interaction with surrounding air molecules, photons, etc., will in general give rise to immediate decoherence into spatially localized wave packets and thus select position as the preferred basis. On the other hand, when the environment is comparably "slow," as is frequently the case for microscopic systems, environment-induced superselection will typically yield energy eigenstates as teh preferred states."
So Environmental Superselection is the key to the Prefered Basis Problem. So what's the mystery left to solve? Pls. give an example of the subtle problem, thanks.
There's also a good discussion of how decoherence relates to Everett interpretations in section 4.3 of this Stanford Encyclopedia article...on the specific subject of the preferred basis problem, they say:From the point of view of the interpretation of quantum mechanics, I think decoherence is almost completely unimportant. That's because decoherence is a quantitative matter. The interference phenomena never completely vanish; they only decrease exponentially until you can't be bothered to measure them anymore. The question of what the [interference] terms mean is still there, even if the coefficient in front of them is very small. It's like being a little pregnant. Those terms, however small, raise the same problem. If the argument is supposed to be that superpositions occur at a microscopic level but not to macroscopic objects, that's a bit like saying that you believe your bank is honest at the level of pennies but is cheating you at the level of pounds. It just doesn't make sense. It can't be that there are multiple universes at the levels of atoms but only a single universe at the level of cats.
The most useful application of decoherence to Everett, however, seems to be in the context of the problem of the preferred basis. Decoherence seems to yield a (maybe partial) solution to the problem, in that it naturally identifies a class of ‘preferred’ states (not necessarily an orthonormal basis!), and even allows to reidentify them over time, so that one can identify ‘worlds’ with the trajectories defined by decoherence (or more abstractly with decoherent histories).[21] If part of the aim of Everett is to interpret quantum mechanics without introducing extra structure, in particular without postulating the existence of some preferred basis, then one will try to identify structure that is already present in the wave function at the level of components (see e.g., Wallace, 2003a). In this sense, decoherence is an ideal candidate for identifying the relevant components.
A justification for this identification can then be variously given by suggesting that a ‘world’ should be a temporally extended structure and thus reidentification over time will be a necessary condition for identifying worlds, or similarly by suggesting that in order for observers to evolve there must be stable records of past events (Saunders 1993, and the unpublished Gell-Mann & Hartle 1994 (see the Other Internet Resources section below), or that observers must be able to access robust states, preferably through the existence of redundant information in the environment (Zurek's ‘existential interpretation’, 1998).
In alternative to some global notion of ‘world’, one can look at the components of the (mixed) state of a (local) system, either from the point of view that the different components defined by decoherence will separately affect (different components of the state of) another system, or from the point of view that they will separately underlie the conscious experience (if any) of the system. The former sits well with Everett's (1957) original notion of relative state, and with the relational interpretation of Everett preferred by Saunders (e.g., 1993) and, it would seem, Zurek (1998). The latter leads directly to the idea of many-minds interpretations (see the entry on Everett's relative-state interpretation and the website on ‘A Many-Minds Interpretation of Quantum Theory’ referenced in the Other Internet Resources). If one assumes that mentality can be associated only with certain decohering structures of great complexity, this might have the advantage of further reducing the remaining ambiguity about the preferred ‘basis’.
The idea of many minds was suggested early on by Zeh (2000; also 1995, p. 24). As Zeh puts it, von Neumann's motivation for introducing collapse was to save what he called psycho-physical parallelism (arguably supervenience of the mental on the physical: only one mental state is experienced, so there should be only one corresponding component in the physical state). In a decohering no-collapse universe one can instead introduce a new psycho-physical parallelism, in which individual minds supervene on each non-interfering component in the physical state. Zeh indeed suggests that, given decoherence, this is the most natural interpretation of quantum mechanics.[22]
In Copenhagen the choice of what to measure determines what basis the quantum state will "collapse" onto a basis vector of. In Bohmian mechanics it's assumed at the outset that position has a special role, all particles have definite positions at all times and the way the positions evolve is determined by the "pilot wave", all other types of measurements are derived from the positions of "pointers" of measuring devices (see this article for more on Bohmian mechanics).rodsika said:Also is this just particulars to Many World? Preferred basis problem also exist in pure Copenhagen and Bohmian Mechanics and other interpretations because Decoherence is the general mechanism that replaces wavefunction collapse.
JesseM said:The other problem is that while the subsystem approaches something very close to a mixed state via decoherence, it doesn't do so exactly, the interference terms don't quite go to zero.
As I understand it, it's not a matter of them having any "influence", it's more that their presence makes the notion of dividing the system's wavefunction into distinct "worlds" with distinct probabilities somewhat ill-defined conceptually.Dmitry67 said:I don't understand why it is important. I've heard that these terms vanish to about 10^-20 in nanoseconds, when we deal with big macroscopic systems.
The probability of having any influence of such terms is lower that to observe an violation of the second law of thermodynamics. In practice we assume that 2nd law is right, even is not "exactly" right. But who cares? The same for decoherence...
Dmitry67 said:Wait, wait... He explicitly admits, that MWI *IS* compatible with relativity! The only problem for him is (bold part) *imagining* this process!
LOL!
It is like saying that "While GR is perfectly consistent with the observations, there is a problem in imagining that spacetime is not Euclidean" :)
there is no problem describing the decoherence effects themselves in a way that is perfectly compatible with relativity, there is a problem in imagining that such a splitting process somehow physically copies the systems involved
Dmitry67's comment seems accurate to me, Schlosshauer's main criticism is that he personally finds it counterintuitive that systems would constantly be "copied" (and I think he's taking 'copying' too literally, it's just a metaphor for the different elements in the superposition), not that this would be incompatible with any known physical principles: "there is a problem in imagining that such a splitting process somehow physically copies the systems involved." His other criticism is that "A strong picture of spacetime somehow unzipping into connected spacetime regions along the forward light cone of the measurement event, would not be compatible with special relativity insofar as relativity presupposes that all events occur on the stage of Minkowski spacetime", but this is a strawman since the MWI does not offer such a "strong picture" picture of spacetime "unzipping", it says that there are superpositions of different macroscopic states in the same spacetime (though this would become trickier if we tried to incorporate different curvatures of spacetime in general relativity...without a theory of quantum gravity, what the MWI says about spacetime curvature is bound to be speculative though)Fyzix said:I have to ask... Are you stupid?
Read again, then reply...
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.rodsika said:JesseM,
1. In a double slit experiment.. how many worlds are there.. just 2 corresponding to the 2 slit choices or thousands corresponding to the numerous dots in the interference patterns?
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.rodsika said:2. Supposed there are 2 worlds corresponding to each slit or 1000 worlds from the dots or other similar quantum divergence. Would ALL events in the world outside the device be identical after 100 years.
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:rodsika said:or are histories random such that after 100 years.. America conquered the Arabs in one world, and the Arabs occupied American in the second world (with the initial difference among them just slits in the double slit experiment) or Jerry has 2 sons in one world and 3 sons in the second world?
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?You're talking about the Copenhagen interpretation, not the MWI. But we can still discuss the issue of chaotic systems in this context, as long as we are willing to have a thought-experiment like Schroedinger's cat where a large macroscopic system can remain totally isolated for a while, until it is finally observed and "collapses". My assertion would be that if the cat's brain is sufficiently chaotic for sensitive dependence on initial conditions to apply (plausible given how many nonlinear effects there are in brains), then even if the experiment is not specifically designed so the cat lives or dies based on the decay of a radioactive particle, it would still be true that if enough time is left between the moment the cat is sealed in the box and the moment it's opened, then at the moment before the box is opened and the cat's wavefunction is collapsed, according to QM the cat would be in a superposition of macroscopically distinct states, like "sitting in North corner", "sitting in South corner", "walking in the middle of the box", "sleeping in the middle", etc.
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"?rodsika said:3. Say there are billions and billions of galaxies. And you do a single double slit experiment. Would the billions and billions of galaxies in the 2 world exist after you do the experiment versus not existing if you don't do it? I think this is what is too much in Many Worlds. Just doing a double split experiments can produce billions and billions of galaxies and if the bubble inflation is true that each bubble produce new Big Bang, then a single double slit experiments can literally produce billions of big bangs in the 2nd copy world. This is near absurdity.. maybe it's just easier to believe in Santa Clause.. :)
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".rodsika said:But you mentioned ealier in the thread "There aren't really clearly-differentiated "worlds" as I understand it, just a single wavefunction for the entire universe which can be seen (in the same way as any normal quantum wavefunction) as a superposition of different position states, a superposition of different momentum states, etc."
But if you don't do the double slit experiment. You won't produce 2 worlds.
JesseM said: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".
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).rodsika said:In the above questions. I'm asking in the context of DeWitt version of MWI where splitting occurs. In Jim Al-khalili Quantum: Guide to the Perplexed. It is mentioned in page 146 (where he is describing Many Worlds):"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."
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:rodsika said:Note Jim Al-Khalili is a theoretical physicist.
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.Barrett uses the name "MWI" for the splitting worlds view publicized by De Witt 1970. This approach has been justly criticized: it has both some kind of collapse (an irreversible splitting of worlds in a preferred basis) and the multitude of worlds.
JesseM said: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.
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.rodsika said:So I guess Jim Al-Khalili just mixed Everett with Dewitt and make them one.
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 said: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.
JesseM said: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).
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".rodsika said: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?
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).rodsika said:"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."
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.rodsika said: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 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:rogerl said:Did Everett mention specifically that there aren't really clearly-differentiated worlds??
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: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.
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.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)
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: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:
And in the handwritten draft: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.
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: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).
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.
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.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]
No idea.rogerl said:How many percentage of physicists do you think believe in clearly differentiated world than those who do not?
"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".rogerl said: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.
JesseM said: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).
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:rodsika said: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
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
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.(. . . ) 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.