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: Duplication Thought Experiment Involving Complementarity
Russell Standish wrote: [EMAIL PROTECTED]"> George Levy wrote:...As it stand, the comp hypothesis is only a philosophical exercise because it does not reproduce the same phenomenon as QM in particular the phenomenon of complementarity. Therefore, to establish a meaningful relevance between comp and QM we must show that such phenomena can be incorporated in comp.The following thought experiment is an attempt to illustrate how complementarity can be incorporated into a duplication experiment. This experiment raises some interesting questions regarding the relationship between the scientific MW and the philosopical plenitude.Thought Experiment: QuestionsThis thought experiment, attempt to provide a model of how MW relates to the Comp hypothesis. Many questions arise.1) Why is it that the Plenitude is not directly accessed by QM as explained by comp. Why is there a need for an intermediate MW characterized by complementarity?2) Why is complementarity two-dimensional? Could it be three-dimentional? or higher?3) Is the two-dimensionality of complementarity fact-like? Are there other worlds in the Plenitude which have a complementarity with a higher dimensionality?4) Is the MW only one instance in the Plenitude? How many levels do we have to go from the scientifically determined MW to the philosophically determined Plenitude?5) Is complementarity anthropically necessary?This is only a feable attempt in the generation of a physical model to relate comp to the MW. I hope that we can improve on it through our discussions.Geor ge I would like to point out that my "Why Occam's Razor" paper answersabout 90% of your question (with the other 10% being the mostdifficult bit, or course :).Complementarity is a property of any two quantum operators that arerelated by the Fourier transform (x - id/dx). The proof is wellknown, and can be found (eg) in Shankar's book. Come on! This is circular reasoning. Conventional QM complementarity requires 2D Fourier. Therefore 2D Fourier must describe complementarity. True for conventional QM. I was talking about other MWs within the Plenitude. Could their complementarity be described by Hadamar transforms for example? [EMAIL PROTECTED]"> That momentum is represented by derivative operator (P=id/dx) iscalled the correspondence principle, and is usually given as an axiom(see Shankar). Henry gave a "derivation" of this correspondenceprinciple about 10 years ago, (Bruno kindly sent me a copy), but Ibelieve his derivation is faulty. To date, I still gregard thecorrespondence principle as a mystery.The other "axioms" of quantum mechanics can be derived from a simplemodel of observation (set out in Why Occams razor). Observers selectan observation purely at random from an ensemble of choices, subjectto the anthropic constraint. This is analogous to Darwinian evolution,where natural selection selects from natural variation. It is mysupposition that this generalized evolutionary process is the onlypossible creative process - the only means of generating the complex(information rich) structures from the simple ones that are favoured int he Schmidhuber ensemble.It is the anthropic principle that requires us to live in aninformation rich world. The AP is a mystery - one that I believe to beequivalent to the famous "mind-body" problem, ie why should we observea correspondence between our mind and a a complex structure called thebrain?So to answer your dot points:1) The above mechanism is why we need an intermediate Multiverse.2) The complementarity is 2D because the Fourier transform is its owninverse. I don't agree with this reasoning. It is circular. [EMAIL PROTECTED]"> A 3D complementarity relationship would require a 3-cycletransformation between operators: X--Y ^ /\v Z(ASCII characters are _so_ limited...)To fully answer this question requires answering "Why the correspondenceprinciple?"3) appears to be related to 2) ...?4) The Multiverse appears to be the only one containing consciousobservers (subject to the above model of consciousness being necessary).5) I believe yes (subject to an adequate derivation of thecorrespondence principle existing). Interesting but you haven't convinced me. George
Re: Duplication Thought Experiment Involving Complementarity
jamikes wrote: George Levy wrote a comprehensive thought experiment with a major flaw: 6.6257 square miles arenot interchangeable to 6.6257 sqare kilometers. There was indeterminacy in the units. But the number is real and does correspond to a natural constant. ;-) George
Re: Duplication Thought Experiment Involving Complementarity
Bruno Marchal wrote: George Levy wrote: Bruno Marchal wrote: George Levy asks recently Could somebody incorporate complementarity in a thought experiment in the style of Bruno's duplication experiment? This is an interesting proposal and I would be glad if someone manage to present one. Just that it is *because* duplication-like experiment leads quickly to obscurities and misleading intuitions, *that* modal logic appears to be a fruitful investment, even if it is not the only one. GL: As it stand, the comp hypothesis is only a philosophical exercise because it does not reproduce the same phenomenon as QM in particular the phenomenon of complementarity. BM: Do you mean it does not reproduce the same phenomenon as QM, or do you mean that we have not yet understood how it could reproduce the same ph enomenon as QM? I don't know enough to be certain about either possibility. But if comp is true, it is not intuitive how it can explain QM. There is a need for a thought experiment that would connect the two. I will not bore you with technics buts complementarity can be handled in Z1* (extract from comp) although there are still open problems. If you could construct a thought experiment using Z1, it would certainly stengthen the argument for comp as a potential explanation for QM.
Re: R: Duplication Thought Experiment Involving Complementarity
scerir wrote: 002401c25780$ce1358c0$f0c7fea9@scerir"> George Levy: 5) Is complementarity anthropically necessary? I may be wrong but it seems to me that complementarity is nothing more, and nothing less than a consequence of the finiteness of (quantum) information. I don't understand. 002401c25780$ce1358c0$f0c7fea9@scerir"> It seems also that the complementarity principle is a "smooth" principle. Yes, this is a difference between the thought experiment and nature. Or is it? The fact that we haven't been able to show discreteness in QM indeterminacy is no proof that there isn't. 002401c25780$ce1358c0$f0c7fea9@scerir"> When we say, i.e. following von Weizsaeker, that localization and superposition are complementary, we mean that the predictability of the path plus the visibility of the interference fringes (in the double slit experiment)equals a certain constant. There is a "smooth" transition between the wave-like behavior and the particle-like behaviour. Wootters and Zurek [see "Complementarity in the Double- Slit Experiment: Quantum Nonseparability and a Quantitative Statement of Bohr's Principle", in Physical Review, D19, (1979)] showed that a photon still has a wave-like behaviour even if the path (the which way in a double-slit experiment) is predicted almost certainly. Their gedanken experiment is very simple: a single-slit + a double-slit + a screen. Thus to me the question "Is complementarity anthropically necessary?" means "Can *we* get infinite information from a single quantum?" This would be a great feature for quantum computers. But I don't understand how you arrive to this conclusion. George 002401c25780$ce1358c0$f0c7fea9@scerir">
Re: Duplication Thought Experiment Involving Complementarity
George Levy wrote: Complementarity is a property of any two quantum operators that are related by the Fourier transform (x - id/dx). The proof is well known, and can be found (eg) in Shankar's book. Come on! This is circular reasoning. Conventional QM complementarity requires 2D Fourier. Therefore 2D Fourier must describe complementarity. True for conventional QM. I was talking about other MWs within the Plenitude. Could their complementarity be described by Hadamar transforms for example? Not sure - the Hadamard transform is defined on a 2D vector space, and is equivalent to rotations by 45 degrees. This is rather restrictive. However, you could make your point with other transforms perhaps a Laplace transform, or wavelets. I suspect that the proper transform to use depends on what are the natural boundary conditions, ie if your wavefunctions are elements of L^2, then the Fourier transform is the only transform that makes sense. In more general terms, a Heisenberg uncertainty relation of the form \Delta X \Delta Y = const must hold if [X,Y]=const Of course, in general [X,Y] is an operator, not a number. Can there be 3-way complementary structure? What if [X,[Y,Z]]=const? What does it all mean? The mathematics of 3D rotations (or equivalently Quarternions) has some interesting properties, which could be important in all this. Cheers A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: Duplication Thought Experiment Involving Complementarity
On 10-Sep-02, George Levy wrote: Complementarity is a property of any two quantum operators that are related by the Fourier transform (x - id/dx). The proof is well known, and can be found (eg) in Shankar's book. Come on! This is circular reasoning. Conventional QM complementarity requires 2D Fourier. Therefore 2D Fourier must describe complementarity. True for conventional QM. I was talking about other MWs within the Plenitude. Could their complementarity be described by Hadamar transforms for example? Observables come in complementary pairs (instead of triples or something else) because the laws of physics are 2nd order (partial) differential equations. Hence a position has a canonically conjugate momentum and vice versa. The reason they are related by a Fourier transform is that the action of a wave in the Hamilton-Jacobi form of classical mechanics has the products of the conjugate variables in the exponent. See Goldstein, section 10-8. ... Brent Meeker Pluralitas non sunt ponenda sine necessitate --- William of Ockham
Re: Duplication Thought Experiment Involving Complementarity
Brent Meeker wrote: On 10-Sep-02, George Levy wrote: Complementarity is a property of any two quantum operators that are related by the Fourier transform (x - id/dx). The proof is well known, and can be found (eg) in Shankar's book. Come on! This is circular reasoning. Conventional QM complementarity requires 2D Fourier. Therefore 2D Fourier must describe complementarity. True for conventional QM. I was talking about other MWs within the Plenitude. Could their complementarity be described by Hadamar transforms for example? Observables come in complementary pairs (instead of triples or something else) because the laws of physics are 2nd order (partial) differential equations. Hence a position has a canonically conjugate momentum and vice versa. The reason they are related by a Fourier transform is that the action of a wave in the Hamilton-Jacobi form of classical mechanics has the products of the conjugate variables in the exponent. See Goldstein, section 10-8. ... Brent Meeker Pluralitas non sunt ponenda sine necessitate --- William of Ockham But that just begs the question of why classical dynamics is 2nd order (or iow why Newtons 2nd law). Vic Stengar seems to have an answer to this. Indeed classical dynamics is 1st order in phase space (2nd order only in real space). So it comes down to extra meaning attached to the variable x p. Cheers A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: Duplication Thought Experiment Involving Complementarity
On 10-Sep-02, Russell Standish wrote: Brent Meeker wrote: On 10-Sep-02, George Levy wrote: Complementarity is a property of any two quantum operators that are related by the Fourier transform (x - id/dx). The proof is well known, and can be found (eg) in Shankar's book. Come on! This is circular reasoning. Conventional QM complementarity requires 2D Fourier. Therefore 2D Fourier must describe complementarity. True for conventional QM. I was talking about other MWs within the Plenitude. Could their complementarity be described by Hadamar transforms for example? Observables come in complementary pairs (instead of triples or something else) because the laws of physics are 2nd order (partial) differential equations. Hence a position has a canonically conjugate momentum and vice versa. The reason they are related by a Fourier transform is that the action of a wave in the Hamilton-Jacobi form of classical mechanics has the products of the conjugate variables in the exponent. See Goldstein, section 10-8. ... Brent Meeker Pluralitas non sunt ponenda sine necessitate --- William of Ockham But that just begs the question of why classical dynamics is 2nd order (or iow why Newtons 2nd law). Vic Stengar seems to have an answer to this. Vic's working on a book, tentatively called Why There is Something Rather Than Nothing in which he shows that all fundamental physics, i.e. QM, GR, and the Standard Model, can be derived from gauge+broken symmetry. From that standpoint physics is described by 2nd order PDE's because the two symmetries we observe are space-time translation and space-time rotation (i.e. Lorentz boosts). Vic argues that these are inherent symmetries of the void, but as to why there aren't other symmetries I think must be left to empirical determination. I do urge you to join Vic's avoid-l mailing list. I'm sure he would appreciate your well informed comments. Brent Meeker Ms Schroedinger: What did you do to that poor cat? It looks half dead. Erwin: I don't know. Ask Wigner's friend.
