### Re: MWI, Copenhage, Randomness (fwd)

On 09-Sep-02, Bruno Marchal wrote: Jesse Mazer wrote: Bruno Marchal wrote: Jesse Mazer wrote Ok, I think I see where my mistake was. I was thinking that decoherence just referred to interactions between a system and the external environment, but what you seem to be saying is that it can also refer to an internal effect where interactions among the components of a system with many degrees of freedom cause interference terms to become negligible. If that's correct, then when Wigner decided that interference would cause the wavefunction of the cat or Wigner's friend to collapse even before the box or the room was opened, then he was probably referring to this sort of internal effect, so my argument about using quantum computers to simulate truly impenetrable boxes would not make a difference. BM: decoherence refers to anything interacting with what you are, as observer, describing by a wave function, and which is not currently described by your wave function. (- need of a tensor product). IMO, it has been discovered by Everett and it explained why we don't feel the split or the differentiation. Decoherence is just entanglement with the the environment, it is the contagion of the superposition state, the linearity of the tensor product. JM: I probably need to read up on the actual mathematics behind decoherence before I can discuss it very intelligently. Brent Meeker seemed to say that even in the case of an isolated system whose wavefunction we know completely, if it has many degrees of freedom there will be an effect which approximates wavefunction collapse in which interference terms become neglible. Presumably this does not collapse the wavefunction onto any one particular classical state (dead cat vs. live cat), but by eliminating interference terms you get something similar to classical probabilities, where you're free to assume the cat is really in some state all along and your measurement just reveals that preexisting state (interference is the reason you get into trouble thinking that way about the quantum world, as is shown most clearly by the Bell inequality). I don't know whether this diagonalization effect in an isolated system would normally be called decoherence or if some other term would be used. I'd guess that they're two sides of the same coin, since if you knew the wavefunction for system + external environment it would itself have a large number of degrees of freedom, so the principle is probably the same. Also, I don't know whether Wigner was referring to an internal diagonalization effect or to entanglement with the outside environment when he argued that decoherence shows that the act of opening the box and observing the cat has no particular importance. BM: I don't see how the internal interaction could leads to decoherence, unless the information is not available to the observer. If a cat is in the (a + d) state in the box, and if we know the state of each air molecules in the box, we can in principle observe macro cat interferences. Obviously we cannot keep track of all those molecules and that's why in practice, even if the box completely isolates the cat and the air molecules we will not be able to see the interferences. So Brent is practically right, but the we loose the ability of witnessing interferences just if the cat interact with *any* particle we didn't keep track of, whether that particle was inside the box or not. Right. Because we cannot construct an appratus that measures an operator corresponding to determing the state of the cat and all the particles the cat interacts with and which constitute the cat, we cannot observe the interference between the very complicated dead-subspace and live-subspace. However while this is a limitation in practice and not in the mathematics, it is more than *merely* practical. We, or anything exhibiting intelligence, must have memory, i.e. irreversible encoding of some past events/experience. This implies that we, and our instruments, must be macroscopic, quasi-classical things. So it is impossible that we, or other intelligent beings, can experience the interference effects. I suspect that this is a counter-argument to Deutsche's AI quantum computer that experiences interference, but I haven't worked it through. ... JM: Maybe since this is a computer simulation where we know the dynamical rules and initial state precisely, we would know just where to look for even the smallest interference effects, unlike in an ordinary macroscopic system where we don't have such detailed information. Also, we could run such a simulation over and over again from the same initial conditions, which would also help to detect small statistical deviations from classical predictions. I once read a comment by Deutch about decoherence where he said something like (paraphrasing) saying the interference terms are 'almost' zero is like saying someone is a

### Re: MWI, Copenhage, Randomness

Jesse Mazer wrote: Bruno Marchal wrote: Jesse Mazer wrote Ok, I think I see where my mistake was. I was thinking that decoherence just referred to interactions between a system and the external environment, but what you seem to be saying is that it can also refer to an internal effect where interactions among the components of a system with many degrees of freedom cause interference terms to become negligible. If that's correct, then when Wigner decided that interference would cause the wavefunction of the cat or Wigner's friend to collapse even before the box or the room was opened, then he was probably referring to this sort of internal effect, so my argument about using quantum computers to simulate truly impenetrable boxes would not make a difference. BM: decoherence refers to anything interacting with what you are, as observer, describing by a wave function, and which is not currently described by your wave function. (- need of a tensor product). IMO, it has been discovered by Everett and it explained why we don't feel the split or the differentiation. Decoherence is just entanglement with the the environment, it is the contagion of the superposition state, the linearity of the tensor product. JM: I probably need to read up on the actual mathematics behind decoherence before I can discuss it very intelligently. Brent Meeker seemed to say that even in the case of an isolated system whose wavefunction we know completely, if it has many degrees of freedom there will be an effect which approximates wavefunction collapse in which interference terms become neglible. Presumably this does not collapse the wavefunction onto any one particular classical state (dead cat vs. live cat), but by eliminating interference terms you get something similar to classical probabilities, where you're free to assume the cat is really in some state all along and your measurement just reveals that preexisting state (interference is the reason you get into trouble thinking that way about the quantum world, as is shown most clearly by the Bell inequality). I don't know whether this diagonalization effect in an isolated system would normally be called decoherence or if some other term would be used. I'd guess that they're two sides of the same coin, since if you knew the wavefunction for system + external environment it would itself have a large number of degrees of freedom, so the principle is probably the same. Also, I don't know whether Wigner was referring to an internal diagonalization effect or to entanglement with the outside environment when he argued that decoherence shows that the act of opening the box and observing the cat has no particular importance. BM: I don't see how the internal interaction could leads to decoherence, unless the information is not available to the observer. If a cat is in the (a + d) state in the box, and if we know the state of each air molecules in the box, we can in principle observe macro cat interferences. Obviously we cannot keep track of all those molecules and that's why in practice, even if the box completely isolates the cat and the air molecules we will not be able to see the interferences. So Brent is practically right, but the we loose the ability of witnessing interferences just if the cat interact with *any* particle we didn't keep track of, whether that particle was inside the box or not. JM: But this makes me wonder about the thought-experiment by David Deutsch which Hal Finney brought up, in which interference shows that an isolated A.I. was splitting into multiple versions which experienced different outcomes. Presumably a simulation of an intelligence would have a lot of degrees of freedom too, so why wouldn't decoherence ruin things? Ok, but then SWE is wrong at some point. Where do you think? What does SWE stand for? Sorry. It is Schroedinger Wave Equation. JM: Maybe since this is a computer simulation where we know the dynamical rules and initial state precisely, we would know just where to look for even the smallest interference effects, unlike in an ordinary macroscopic system where we don't have such detailed information. Also, we could run such a simulation over and over again from the same initial conditions, which would also help to detect small statistical deviations from classical predictions. I once read a comment by Deutch about decoherence where he said something like (paraphrasing) saying the interference terms are 'almost' zero is like saying someone is a little bit pregnant. His argument would probably be that although decoherence may explain why the world looks approximately classical in the many-worlds framework, it doesn't remove to postulate those other worlds in the first place. BM: I don't understand your last sentence. What I meant was although in practice decoherence might seem to solve the measurement problem and remove the need for other worlds, in

### Re: MWI, Copenhage, Randomness

### Re: MWI, Copenhage, Randomness

Jesse Mazer wrote Ok, I think I see where my mistake was. I was thinking that decoherence just referred to interactions between a system and the external environment, but what you seem to be saying is that it can also refer to an internal effect where interactions among the components of a system with many degrees of freedom cause interference terms to become negligible. If that's correct, then when Wigner decided that interference would cause the wavefunction of the cat or Wigner's friend to collapse even before the box or the room was opened, then he was probably referring to this sort of internal effect, so my argument about using quantum computers to simulate truly impenetrable boxes would not make a difference. decoherence refers to anything interacting with what you are, as observer, describing by a wave function, and which is not currently described by your wave function. (- need of a tensor product). IMO, it has been discovered by Everett and it explained why we don't feel the split or the differentiation. Decoherence is just entanglement with the the environment, it is the contagion of the superposition state, the linearity of the tensor product. But this makes me wonder about the thought-experiment by David Deutsch which Hal Finney brought up, in which interference shows that an isolated A.I. was splitting into multiple versions which experienced different outcomes. Presumably a simulation of an intelligence would have a lot of degrees of freedom too, so why wouldn't decoherence ruin things? Ok, but then SWE is wrong at some point. Where do you think? Maybe since this is a computer simulation where we know the dynamical rules and initial state precisely, we would know just where to look for even the smallest interference effects, unlike in an ordinary macroscopic system where we don't have such detailed information. Also, we could run such a simulation over and over again from the same initial conditions, which would also help to detect small statistical deviations from classical predictions. I once read a comment by Deutch about decoherence where he said something like (paraphrasing) saying the interference terms are 'almost' zero is like saying someone is a little bit pregnant. His argument would probably be that although decoherence may explain why the world looks approximately classical in the many-worlds framework, it doesn't remove to postulate those other worlds in the first place. I don't understand your last sentence. Bruno

### Re: MWI, Copenhage, Randomness

Bruno Marchal wrote: Jesse Mazer wrote Ok, I think I see where my mistake was. I was thinking that decoherence just referred to interactions between a system and the external environment, but what you seem to be saying is that it can also refer to an internal effect where interactions among the components of a system with many degrees of freedom cause interference terms to become negligible. If that's correct, then when Wigner decided that interference would cause the wavefunction of the cat or Wigner's friend to collapse even before the box or the room was opened, then he was probably referring to this sort of internal effect, so my argument about using quantum computers to simulate truly impenetrable boxes would not make a difference. decoherence refers to anything interacting with what you are, as observer, describing by a wave function, and which is not currently described by your wave function. (- need of a tensor product). IMO, it has been discovered by Everett and it explained why we don't feel the split or the differentiation. Decoherence is just entanglement with the the environment, it is the contagion of the superposition state, the linearity of the tensor product. I probably need to read up on the actual mathematics behind decoherence before I can discuss it very intelligently. Brent Meeker seemed to say that even in the case of an isolated system whose wavefunction we know completely, if it has many degrees of freedom there will be an effect which approximates wavefunction collapse in which interference terms become neglible. Presumably this does not collapse the wavefunction onto any one particular classical state (dead cat vs. live cat), but by eliminating interference terms you get something similar to classical probabilities, where you're free to assume the cat is really in some state all along and your measurement just reveals that preexisting state (interference is the reason you get into trouble thinking that way about the quantum world, as is shown most clearly by the Bell inequality). I don't know whether this diagonalization effect in an isolated system would normally be called decoherence or if some other term would be used. I'd guess that they're two sides of the same coin, since if you knew the wavefunction for system + external environment it would itself have a large number of degrees of freedom, so the principle is probably the same. Also, I don't know whether Wigner was referring to an internal diagonalization effect or to entanglement with the outside environment when he argued that decoherence shows that the act of opening the box and observing the cat has no particular importance. But this makes me wonder about the thought-experiment by David Deutsch which Hal Finney brought up, in which interference shows that an isolated A.I. was splitting into multiple versions which experienced different outcomes. Presumably a simulation of an intelligence would have a lot of degrees of freedom too, so why wouldn't decoherence ruin things? Ok, but then SWE is wrong at some point. Where do you think? What does SWE stand for? Maybe since this is a computer simulation where we know the dynamical rules and initial state precisely, we would know just where to look for even the smallest interference effects, unlike in an ordinary macroscopic system where we don't have such detailed information. Also, we could run such a simulation over and over again from the same initial conditions, which would also help to detect small statistical deviations from classical predictions. I once read a comment by Deutch about decoherence where he said something like (paraphrasing) saying the interference terms are 'almost' zero is like saying someone is a little bit pregnant. His argument would probably be that although decoherence may explain why the world looks approximately classical in the many-worlds framework, it doesn't remove to postulate those other worlds in the first place. I don't understand your last sentence. What I meant was although in practice decoherence might seem to solve the measurement problem and remove the need for other worlds, in principle even tiny interference effects are just as much in need of an explanation as large ones, and decoherence will not make interference disappear completely (as I argued above, we should be able to detect tiny interference effects in simulations of macroscopic systems on a quantum computer, unlike in ordinary macroscopic systems where we don't have enough information to know where to look for such tiny effects). If you view the universe as a giant computation, the only way to duplicate interference effects precisely is to compute all those other histories--I think this is the point you were making about Bohm and his rejection of COMP, since computing the behavior of the pilot wave would probably be equivalent to computing all possible histories of the system you are

### Re: MWI, Copenhage, Randomness

On 04-Sep-02, Tim May wrote: On Wednesday, September 4, 2002, at 02:44 PM, Hal Finney wrote: Tim May wrote: In weaker forms of the MWI, where it's the early state of the Big Bang (for example) which are splitting off into N universes, De Witt and others have speculated (as early as around 1970) that we may _possibly_ see some evidence consistent with the EWG interpretation but NOT consistent with other interpretations. I'm not familiar with the details of this. But I know that much of the impetus for increased acceptance of MWI models comes from the cosmologists. It was in DeWitt's article, Quantum mechanics and reality, Physics Today, September 1970, reprinted in the collection The Many-Worlds Interpretation of Quantum Mechanics, edited by Bryc DeWitt and Neill Graham, 1973. Moreover a decision between the two interpretations may ultimately be made on grounds other than direct laboratory experimentation. For example, in the very early moments of the universe, during the cosmological Big Bang, the universal wave function may have possessed an overall coherence as yet unimpaired by condensation into non-interfering branches. Such initial coherence may have testable implications for cosmology. (p. 165 of the reprint volume). But to maintain strictly unitary evolution the branches are only non-intefering when measured by macroscopic operators. For some (impossible to realize operators) there will still be cross terms. By the way, issues of observers and measurements are obviously fraught with Chinese boxes types of problems. In the Schrodinger's Cat pedantic example, if the cat alive or cat dead measurement is made at the end of one hour by opening the sealed box, what if a video camera had been also sealed inside the box, and had seen the cat breathe in the cyanide gas at 10 minutes into the experiment? Does this imply the wave function collapsed at the time of the measurement by the human observers, at the one hour point, or at the time the video camera unambiguously recorded the cat's death? Alive and dead are very macroscopic operators (average of lots of micro-states) and so the cats interaction with it's environment (the box) will very quickly diagonalize the Alive X Dead density matrix. To introduce observers as having a special effect seems to introduce an aphysical mysticism. One could arrange a thought experiment involving literally a series of boxes within boxes, each being opened at, say, one minute intervals after the cyanide was released or not released. One set of observers sees the cat either alive or dead at the end of the canonical one hour period. But they are sealed inside a box. After one minute, their box is opened, and the observers in the next-larger box then see the collapse of the wave function at the 61-minute point. After another minute, their box is opened and a new set of observer sees the collapse of the wave function at the 62-minute point. And so on. (I don't know if I'm just reinventing a thought experiment someone developed many decades ago...it seems like a natural idea.) Seen this way, the collapse of the wave function in the Schrodinger's Cat thought experiment is seen as a problem of knowledge, not something quasi-mystical about an instantaneous collapse of some psi-squared function. (More interesting are the delayed choice experiments.) In Bohm's QM the universal wave function determines everything and the apparent randomness we see it just like the randomness of statistical mechanics, it comes from our inability to take into account all the non-local effects of all the rest of the universe. It solve the collapse of the wave function problem as you suggest by making it a collapse of our uncertainity and it's perfectly understandable then that different observers collapse it at different times. The problem is that BQM isn't Lorentz invariant - but people are working on that. ... Brent Meeker The concept of 'measurment' becomes so fuzzy on reflection that it is quite suprising to have it appear in physical theory at the most fundamenatal level. -- J. S. Bell

### Re: MWI, Copenhage, Randomness

Brent Meeker wrote: On 04-Sep-02, Tim May wrote: By the way, issues of observers and measurements are obviously fraught with Chinese boxes types of problems. In the Schrodinger's Cat pedantic example, if the cat alive or cat dead measurement is made at the end of one hour by opening the sealed box, what if a video camera had been also sealed inside the box, and had seen the cat breathe in the cyanide gas at 10 minutes into the experiment? Does this imply the wave function collapsed at the time of the measurement by the human observers, at the one hour point, or at the time the video camera unambiguously recorded the cat's death? Alive and dead are very macroscopic operators (average of lots of micro-states) and so the cats interaction with it's environment (the box) will very quickly diagonalize the Alive X Dead density matrix. To introduce observers as having a special effect seems to introduce an aphysical mysticism. But even if one understands that conscious observers are not necessary to collapse the wave function, Tim's questions do not go away. One could always imagine that the box in the Schroedinger's cat experiment was made of some super-material that blocked interaction between the inside and the outside so effectively that decoherence was completely eliminated, so from the outside the cat would have to be treated as being in a macroscopic superposition until the box was opened, even though the cat (or a video camera inside the box) would remember having been in a single definite state all along. One could arrange a thought experiment involving literally a series of boxes within boxes, each being opened at, say, one minute intervals after the cyanide was released or not released. One set of observers sees the cat either alive or dead at the end of the canonical one hour period. But they are sealed inside a box. After one minute, their box is opened, and the observers in the next-larger box then see the collapse of the wave function at the 61-minute point. After another minute, their box is opened and a new set of observer sees the collapse of the wave function at the 62-minute point. And so on. (I don't know if I'm just reinventing a thought experiment someone developed many decades ago...it seems like a natural idea.) Yes, this is similar to the Wigner's friend thought-experiment. The physics dictionary entry on Schrodinger's cat at http://physics.about.com/library/dict/bldefschrdingerscat.htm describes it briefly: Wigner's friend is a variation of the SchrĂ¶dinger's cat paradox in which a friend of the physicist Eugene Wigner is the first to look inside the vessel. The friend will find a live or dead cat. However, if Professor Wigner has both the vessel with the cat and the friend in the closed room, the state of the mind of the friend (happy if there is a live cat but sad if there is a dead cat) cannot be determined in Bohr's interpretation of quantum mechanics until the professor has looked into the room although the friend has already looked at the cat. These paradoxes indicate the absurdity of the overstated roles of measurement and observation in Bohr's interpretation of quantum mechanics. By the way, anyone interested in the measurement problem and interpretations of QM might want to take a look at the book Foundations and Interpretations of Quantum Mechanics by Gennaro Auletta...I haven't read it, just browsed it (it's a bit over my head for now), but it looks like a very comprehensive phone-book sized reference on these issues, with a lot of discussion of new interesting experiments probing quantum weirdness. There's a brief description and a table of contents at http://www.wspc.com/books/physics/4194.html --Jesse _ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

### Re: MWI, Copenhage, Randomness

Yes, this is similar to the Wigner's friend thought-experiment. Wigner later (1983) changed opinion and wrote that decoherence forbids superposition of states like c1 |s 1 |friend 1 + c2 |s 2 |friend 2 After that in QM the conscious being - i.e. the friend who tells that he already knows whether the outcome is |s 1 or |s 2 - plays no role. Von Neumann, London, Bauer, Wigner thought (and many more still think) that consciousness was able to collapse a superposition (E.P.W., Collected Papers, VI, pages 225-244) s.

### Re: MWI, Copenhage, Randomness

scerir wrote: Wigner later (1983) changed opinion and wrote that decoherence forbids superposition of states like c1 |s 1 |friend 1 + c2 |s 2 |friend 2 After that in QM the conscious being - i.e. the friend who tells that he already knows whether the outcome is |s 1 or |s 2 - plays no role. But can decoherence really forbid macroscopic superpositions in principle, or only in practice? To build quantum computers, people have to figure out clever tricks to keep fairly large systems in quantum coherence, even though under normal circumstances decoherence would prevent this. Is there a limit to how far we could take this? If quantum computing follows something like Moore's law, it seems concievable that we could eventually simulate something as complex as a cat-in-a-box, which we'd have to treat as being in a superposition of states as long as coherence was maintained among the elements of the computer itself. And we don't need something so complex to get these sorts of paradoxes--at the bare minimum, we just need a system complex enough to keep internal records of its own state (analogous to the cat's brain or the videocamera in the box) so that we must treat the system as being in a superposition as long as coherence is maintained, but once coherence breaks down we can look at the internal records and see that the system *appears* to have been in a definite state all along (Is there any well-defined notion of what it means for a system to keep records of its own history, BTW? Maybe this is related to Maxwell's demon and the thermodynamics of computation?) Then we could then extend this to a nested-box scenario where one subsystem is in coherence relative to a larger system, which is itself in coherence relative to the outside world, and then decoherence occurs between the system and the subsytem while the system as a whole remains in coherence from an outside point of view (which would be like Wigner's friend looking in the box while both the box and the friend were still sealed in a room). Von Neumann, London, Bauer, Wigner thought (and many more still think) that consciousness was able to collapse a superposition (E.P.W., Collected Papers, VI, pages 225-244) Did Wigner only believe this until his change of opinion in 1983, or did he continue to think this way afterwards? --Jesse _ Join the worldÂ’s largest e-mail service with MSN Hotmail. http://www.hotmail.com

### Re: MWI, Copenhage, Randomness

Jesse Mazer wrote: But can decoherence really forbid macroscopic superpositions in principle, or only in practice? To build quantum computers, people have to figure out clever tricks to keep fairly large systems in quantum coherence, even though under normal circumstances decoherence would prevent this. Is there a limit to how far we could take this? If quantum computing follows something like Moore's law, it seems concievable that we could eventually simulate something as complex as a cat-in-a-box, which we'd have to treat as being in a superposition of states as long as coherence was maintained among the elements of the computer itself. David Deutsch took this idea farther, I think in his 1985 paper. He proposed the following experiment: 1. Create a large quantum computer 2. Create a conscious AI program 3. Run the AI on the QC 4. Let the AI make a two-way quantum observation 5. Keep the AI in a superposition of the two states a la Schrodinger's cat 6. The AI announces that it has made a definite, precise observation 7. Recombine the two states and reveal interference This shows that the conscious mind of the AI was in two states, and both were equally real. Hence one of the following must be true: A. Consciousness doesn't collapse the wave function B. AI's aren't conscious C. QM is wrong and more generally we get a choice between: A. MWI is wrong B. QM is wrong People like Penrose believe that QM is wrong, that there is a yet-unknown law called objective reduction which makes state function collapse an objectively real phenomenon and determines when and how it happens. But if you're not willing to go that far, it is hard to deny the force of Deutsch's thought experiment. Hal Finney

### Re: MWI, Copenhage, Randomness

J. Mazer [about Wigner and consciousness] Did Wigner only believe this until his change of opinion in 1983, or did he continue to think this way afterwards? Wigner wrote (Nov. 18, 1978) ... ... as far as living organism of any complexity are concerned, the same initial state hardly can be realized several times. There are no two identical people and if we repeat the same experiment on the same individual the initial conditions are no longer the same - the individual will remember at the second experiment the event of the first one - his mental outlook will have changed thereby. This means that the relevant statements of the theory encompassing life will be terribly different from those of the present natural sciences. and also ... I do not believe there are two entities: body and soul. I believe that life and consciousness are phenomena which have a varying effect on the event around us - just as light pressure does. Under many circumstances, those with which present-day physics is concerned, the phenomenon of life has an entirely negligible influence. There is then a continuous transition to phenomena, such as our own activities, in which this phenomenon has a decisive influence. Probably, the behaviour of viruses and bacteria could be described with a high accuracy with present theories. Those of insects could be described with a moderate approximation, those of mammals and men are decisively influenced by their minds. For these, present physical theory would give a false picture even as far as their physical behavior is concerned. E. P. Wigner, Philosophical Reflections and Syntheses, Springer, 1995, page 272

### Re: MWI, Copenhage, Randomness

J. Mazer: But can decoherence really forbid macroscopic superpositions in principle, or only in practice? Well, experiments have been done many times, showing the effect of decoherence on (macroscopic) quantum superpositions http://physicsweb.org/article/world/13/8/3/1 http://physicsweb.org/article/news/4/7/2/1 http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v406/n6791/abs/4 06043a0_fs.html

### Re: MWI, Copenhage, Randomness

Brent Meeker wrote: OK, consider a single excited hydrogen atom in a perfectly reflecting box. Has it emitted a photon or not? QM will predict a superposition of photon+H and H-excited in which the amplitude for H-excited decays exponentially with time. But the exponential decay is only approximate it actually decays, not to zero, but to a small value corresponding the an equilibrium state in which the probability of the photon being emitted is balanced by the probability of it being reabsorbed. So is what is in the box - photon+H or H-excited? The answer is, in effect, both. What's in the box is the wave-function that describes the superposition. You can't get the paradox back by supposing there's a video camera watching the state, because the video camera is a macroscopic object with so many degrees of freedom that when it detects the photon the system (camera + H + photon) will go into a superposition of states which, when projected onto (emitted, not-emitted) will be essentially diagonal, i.e. the wave-function will be collapsed. Ok, I think I see where my mistake was. I was thinking that decoherence just referred to interactions between a system and the external environment, but what you seem to be saying is that it can also refer to an internal effect where interactions among the components of a system with many degrees of freedom cause interference terms to become negligible. If that's correct, then when Wigner decided that interference would cause the wavefunction of the cat or Wigner's friend to collapse even before the box or the room was opened, then he was probably referring to this sort of internal effect, so my argument about using quantum computers to simulate truly impenetrable boxes would not make a difference. But this makes me wonder about the thought-experiment by David Deutsch which Hal Finney brought up, in which interference shows that an isolated A.I. was splitting into multiple versions which experienced different outcomes. Presumably a simulation of an intelligence would have a lot of degrees of freedom too, so why wouldn't decoherence ruin things? Maybe since this is a computer simulation where we know the dynamical rules and initial state precisely, we would know just where to look for even the smallest interference effects, unlike in an ordinary macroscopic system where we don't have such detailed information. Also, we could run such a simulation over and over again from the same initial conditions, which would also help to detect small statistical deviations from classical predictions. I once read a comment by Deutch about decoherence where he said something like (paraphrasing) saying the interference terms are 'almost' zero is like saying someone is a little bit pregnant. His argument would probably be that although decoherence may explain why the world looks approximately classical in the many-worlds framework, it doesn't remove to postulate those other worlds in the first place. --Jesse _ Chat with friends online, try MSN Messenger: http://messenger.msn.com