> On 19 Aug 2018, at 09:36, Bruce Kellett <bhkell...@optusnet.com.au> wrote: > > From: Bruno Marchal <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>> > > 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. > >> 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. > -- 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. > > 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). > 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. > 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). > 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. 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 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. > 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. > >> (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. 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. > >> 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. > 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). > 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. > 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. Bruno > > Dreaming up multiple imaginary superpositions or multi-multi-verses is not > going to change this result. > > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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 everything-list+unsubscr...@googlegroups.com. 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