On Sunday, August 19, 2018 at 11:36:47 AM UTC, Bruce wrote: > > From: Bruno Marchal <[email protected] <javascript:>> > > On 19 Aug 2018, at 09:36, Bruce Kellett <[email protected] > <javascript:>> wrote: > > From: Bruno Marchal <[email protected] <javascript:>> > > You do seem to have got yourself into a bit of a tangle, Bruno. > > What I still do not understand in your view is how can you interpret > > |psi> = (|u>|d> - |d>|u>)/sqrt(2) > > as a unique superposition. It seems to me you can do that because Alice > and Bob have prepared that state, but that state represents also another > superposition, like |psi> = (|u'>|d'> - |d'>|u'>)/sqrt(2). Why would |psi> > denotes a superposition of |u>|d> and |d>|u> and not |u'>|d'> and > |d'>|u’>. It seems to me that you choose a particular base, when Everett > makes clear that this would lead to nonsense. The physical state represent > by |psi> must be the same whatever base is chosen. > > > Of course. When Have I ever said otherwise? Let me spell it out for you. > The basis vectors |u> and |d> are just examples -- place holders if you > like -- for whatever basis vectors are most convenient for your purposes. > Given the expression in terms of |u> and |d>, we can always rotate to > another basis by applying the formulae for the rotation of spinors that I > gave in my paper: > > |u> = cos(theta/2)|u'> + sin(theta/2)|d'>, > |d> = -sin(theta/2)|u'> + cos(theta/2)|d'>. > > Substitute these expressions in the above, and you will get the state in > terms of the rotated spinors: > > psi = (|u>|d> - |d>|u>)/sqrt(2) = (|u'>|d'> - |d'>|u'>)/sqrt(2). > > That is what is meant by rotational symmetry, and that is all there is to > it. Nothing could be simpler. > > > No problem with this. > > > Maybe you just need to apply this insight a little more carefully. > > That leads to considering that psi describes not one superposition, but > many superposition. That get worse with GHZ and n-particles state, and that > is why I have often (in this list or on the FOR list of Deutsch) explained > why the multiverse is a multi-multi-multi-… multi-verse. I don’t insist too > much because more careful analysis would require a quantum theory of > space-time, and the Everett theory will certainly needs some improvement. > > > |psi> does not describe just one superposition > > > Good. That is the key point. > > > You jump in too quickly with your typical misunderstanding. Read the rest > of the sentence/paragraph before you jump to conclusions. > > -- by rotation the spinors we can go to any basis whatsoever. You > certainly do not get many superpositions, one for each possible basis. Let > me spell out in detail how superpositions arise in Everettian quantum > mechanics. You start with a state |psi>, which is just a vector in the > appropriate Hilbert space. The Hilbert space is spanned by a complete set > of orthonormal eigenvectors for each operator in that space. Again, the > basis is not unique, so we can perform an arbitrary rotation in the Hilbert > space to any other set of vectors that span the space. But this is rather > beside the point, because we usually choose a basis because it is useful, > not just because it is possible. (This relates to the preferred basis > problem, which I prefer not to got into at the moment.) > > > Yes. My feeling is that you do introduce some preferred base. > > > Yes, your feelings are very much at fault here. If you thought a bit > rather than go with feelings, we might be better off. I do not introduce a > preferred basis. Where do you think I do that? You argue against a straw > man, as usual. A typical base is not a preferred base. >
*Since you could have chosen u - d and u + d as the basis, cannot u and d be considered a preferred basis? AG * > > Given a basis, the state |psi> can be expanded in terms of these basis > vectors: > > |psi> = Sum_i c_i |a_i>, > > where we the basis we have chosen is the set of eigenvectors for some > operator A and labelled them by the corresponding eigenvalues. This > expansion is the basis of the superposition, and of the formation of > relative states (or parallel universes, or the many worlds of Everett.) We > operate on the vector |psi> with the operator A, which gives > > A|psi> = A(Sum_i c_i|a_i>) = Sum_i c_i a_i |a_i> > > where |c_i|^2 is the probability that we will be in the state relative to > the observed eigenvalue, a_i. We could continue the operation of the > Schrödinger equation to include the apparatus for operator A, the observer, > and the rest of the environment, but you should be able to do this for > yourself. > > The point is that this is the only way in which superpositions can be > formed, and from those superpositions, the many worlds or relative states > of Everett develop by normal Schrödinger evolution. But you do not have > such a superposition for the different possible orientations of > eigenvectors for the singlet state. > > > ? (That seems to contradict what you just show above). > > > You deliberately misunderstand me. There is no grand superposition of > possibles bases. Choose a base, then you can express a superposition. That > is all there is to it. Only one superposition for the chosen (typical) > basis. > > > Nor do you have an operator in some Hilbert space that picks out the angle > in which a measurement is to be made. > > > That is correct, but if Alice can choose her spin direction, a choice is > made on the way to partition the multiverse, or better the multi-multiverse. > > > But there is no multiverse to partition unless there is a superposition of > these separate universes that make up the multiverse. But there is no such > superposition. You have just made it up. > > > So the "many superpositions" that you posit are entirely arbitrary, pulled > out of the air without any justification. > > > If she measure u, Bob get d. But is she measure u’, Bob get d’ (with > certainly, if they have decided to measure in the same base u’d’ before). > To account for that, obviously maintaining locality, we must take into > account the initial uncertainty, due to psi = (|u>|d> - |d>|u>)/sqrt(2) = > (|u'>|d'> - |d'>|u'>)/sqrt(2). > > > You cannot assume locality when locality is the issue in question. If the > measurements are in the same direction, then Bob's direction must rotate > with Alice's. There is no prior partitioning of anything. There is no > uncertainty due to rotational symmetry. That symmetry is broken by the > choice of measurement direction. And that is a choice, not the result of a > measurement that locates the observer in some branch of a superposition, > because there is no relevant superposition. > > > They clearly do not form any part of standard quantum mechanics, because > the account of superpositions and Schrödinger evolution to many worlds that > I have given above is the only way in which these can be formed in quantum > mechanics. > > It is also why I prefer to describe the “many-worlds” as a many relative > states, (or even many histories), and you are right, they are not all > reflecting simply the superpositions, but different partitions of the > multiverse. > > > You just made this up. It is not part of quantum mechanics. > > > When Alice choses a direction for measuring her particle’s spin, she > choose the partition, and enforced “her” Bob, that is the Bob she can meet > in the future, to belong to that partition, wth the corresponding spin. But > she could have used another direction, and they both would be described > (before the measurement), by a different (locally) superposition, despite > it describing the same state. > > > That is nonsense, because it does not correspond to anything that can be > derived from the Schrödinger equation acting on a state vector in Hilbert > space. > > That is where you are completely wrong. This is not how the singlet state > is treated in quantum mechanics. > > > Everett is still ambiguous. I argue this is the way to get the closer to > Everett local relative state theory. Unfortunately Everett is quick, even > in his long text, on the EPR-Bell issue. > > > So you know better that Everett did, or any other advocates of many worlds > theory do? It seems from what you say that Everett didn't really get to > grips with the entangled state. He eliminated collapse for simple states, > but the entangled state defeated him. That is not surprise -- it has > defeated many. Because you can't eliminate the collapse of a non-separable > state occasioned by interaction with any part of that state. > > > Alice could measure the same state in a different direction simply by > rotating her basis to the new angle at which her magnet is set. Nothing > mysterious, no waving of your magical Everettian wand to produce more > superpositions from thin air. > > > Those superpositions exist, as you show it yourself. > > > They do not pre-exist. There is a difference between the superposition of > the rotated state and rotating into a pre-existing superposition. Your > error is in thinking, without any justification, that these superpositions > all exist before Alice chooses her measurement direction. That is just > nonsense. > > > > (You were right that it is different from the position of the electron in > the orbital). > > So if you can clarify your view of the MW-description of the equality > between (|u>|d> - |d>|u>)/sqrt(2) and (|u'>|d'> - |d'>|u'>)/sqrt(2), it > could be helpful. > > > Done above. > > > I don’t see it. I see two different superposition, describing the same > unique psi state, but describing different relative state according to > Alice’s choice. > > > But these do not exist until Alice makes her choice. > > The two different superposition are supposed to give exactly the same > prediction, but this entails (by locality, I agree) that Alice and Bob are > indetermined on the many correlated worlds right at the start. > > > You cannot assume locality as part of your argument when locality is the > issue in question. The rest of your comment here is wrong. > > > It seems to me that the “many-worlds” are not dependent of the choice of > the base |u>,|d> or |u'>,|d’>. I mean, unlike Deustch (initially) and some > many-worlders, the whole multiverse has to be the same physical object > whatever base we are using. > > > Sure, physics has to be independent of the base. But that does not mean > that some bases are not more useful that others. > > > Locally yes, but that should not change the basic ontology which has to be > base independent. > > > Where has it been claimed otherwise? > > Or that one cannot pick out a typical basis vector, or branch of the wave > superposition, to argue that anything proved in that branch, and does not > depend on the particular branch chosen, must apply equally to every branch, > and so to the superposition as a whole. This is the basis of my proof that > quantum mechanics is non-local, > > > Yes. I begin to see that you do accept in the MWI some FTL influence (as > opposed to FTL information transfer). > > > Forget FTL. You are obsessed with FTL. The non-local influence occasioned > by interacting with a non-separable state may be instantaneous, but that > means FTL only on some models of space-time. You might have heard of the > EPR = ER conjecture. That is the idea that the entangled particles are > linked by a worm hole (ER = Einstein-Rosen bridge), so that space is > bypassed in the instantaneous interaction. There might be other models of > space in which the instantaneous connection does not involve any FTL > communication. For example, the Relativistic Flashy GRW model introduced by > Tumulka and supported by Maudlin in the 3rd edition of his book: "The > essential new feature is that if our pair of particles starts off in an > entangled state, like the singlet state, then the collapse of the > wave-function associated with a flash on one particle can change the > probability distribution for the location of flashes of the other particle, > even if it happens to be at space-like separation. So a pair of entangled > "particles" in flashy relativistic GRW can exhibit behaviour that violates > Bell's inequality for experiments at space-like separation, even though the > theory only makes use of the relativistic space-time structure in > specifying its dynamics." (p.246f) > > Your horizons are too limited, Bruno. > > > even in the many-worlds interpretation. Bell's theorem proves non-locality > in a typical branch. > > > The violation of Bell’s inequality proves this, indeed. But with the > many-world, you need to favour some base to get the FTL influence. > > > No, you might need some particular model of space-time structure, but that > is a different thing. > > > That non-locality does not depend on the eigenvalue measured in that > branch (in other words, the proof is branch-independent), so non-locality > is proved for the singlet state as a whole. And since for the singlet > state, for the universal wave function as a whole. > > > OK. But the FTL influence associated to non-locality is based on the > choice of some base. > > > No, it is base-independent because it is branch-independent and applies to > the wave function as a whole. It might depend on other things, but it does > not depend on the choice of basis vectors. > > Bruce > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. 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