> On 8 Aug 2019, at 17:41, Jason Resch <[email protected]> wrote: > > > > On Thu, Aug 8, 2019, 5:51 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > >> On 8 Aug 2019, at 11:56, Bruce Kellett <[email protected] >> <mailto:[email protected]>> wrote: >> >> On Thu, Aug 8, 2019 at 7:21 PM Bruno Marchal <[email protected] >> <mailto:[email protected]>> wrote: >> On 8 Aug 2019, at 02:23, Bruce Kellett <[email protected] >> <mailto:[email protected]>> wrote: >>> On Wed, Aug 7, 2019 at 11:30 PM Bruno Marchal <[email protected] >>> <mailto:[email protected]>> wrote: >>> On 7 Aug 2019, at 14:41, Bruce Kellett <[email protected] >>> <mailto:[email protected]>> wrote: >>>> >>>> Superpositions are fine. It is just that they do not consist of "parallel >>>> worlds”. >>> >>> But then by QM linearity, it is easy to prepare a superposition with >>> orthogonal histories, like me seing a cat dead and me seeing a cat alive, >>> when I look at the Schoredinger cat. Yes, decoherence makes hard for me to >>> detect the superposition I am in, but it does not make it going away >>> (unless you invoke some wave packet reduction of course) >>>> >>>> “Parallel worlds/histories” are just a popular name to describe a >>>> superposition. >>>> >>>> In your dreams, maybe. There is a clear and precise definition of separate >>>> worlds: they are orthogonal states that do not interact. The absence of >>>> possible interaction means that they are not superpositions. >>> >>> That is weird. >>> The branches of a superposition never interact. The point is that they can >>> interfere statistically, if not there is no superposition, nor >>> interference, only a mixture. >>> >>> There some to be some fluidity is the concepts of superposition and basis >>> vectors inherent in this discussion. Any vector space can be spanned by a >>> set of orthogonal basis vectors. There are an infinite number of such >>> bases, plus the possibility of non-orthogonal bases given by any set of >>> vectors that span the space. If the basis vectors are orthogonal, these >>> basis vectors do not interact. But any general vector can be expressed as a >>> superposition of these orthogonal basis vectors. (Orthonormal basis for a >>> normed Hilbert space.) >>> >>> So the question whether the branches of a superposition can interact >>> (interfere) or not is simply a matter of whether the branches are >>> orthogonal or not. If we have a superposition of orthogonal basis vectors, >>> then the branches do not interact. However, if we have a superposition of >>> non-orthogonal vector, then the branches can interact. >>> >>> For example, the wave packet for a free electron is a superposition of >>> momentum eigenstates (and position eigenstates). These momentum eigenstates >>> are orthogonal and do not interact. The overlap function <p|p'> = 0 for all >>> p not equal to p'. This is the definition of orthogonal states. But this >>> does not mean that the wave packet of the electron is a mixture: It is a >>> pure state since there is a basis of the corresponding Hilbert space for >>> which the actual state is one of the basis vectors. (We can construct an >>> orthonormal set of basis vectors around this vector.) On the other hand, >>> the two paths that can be taken by a particle traversing a two-slit >>> interference experiment are not orthogonal, so these paths can interact. So >>> when the quantum state is written as a superposition of such paths, there >>> is interference. >>> >>> Orthogonality is the key difference between things that can interfere and >>> those that cannot. So if separate worlds are orthogonal, there can be no >>> interference between them, and the absence of such interaction defines the >>> worlds as separate. >> >> What I use is the fact that when we have orthogonal states, like I0> and >> I1>, I can prepare a state like (like I0> + I1>), and then I am myself in >> the superposition state Ime>( I0> + I1>), Now, in that state, I have the >> choice between measuring in the base {I0>, I1>} or in the base {I0> + I1>, >> I0> - I1>). In the first case, the “parallel” history becomes indetectoble, >> but not in the second case, so we have to take the superposition into >> account to get the prediction right in all situations. >> >> I don't think this is actually correct. Take a concrete example that we all >> understand. If we prepare a silver atom with spin 'up' in the x-direction, >> then a measurement in the x direction does not produce a superposition -- >> the answer is 'up' with 100% certainty. But is we measure this state in the >> transverse, y-direction, the result is either 'up-y' or 'down-y' with equal >> probabilities. This is because the initial state 'up-x' is already a >> superposition of 'up-y' and 'down-y'. When we measure this in the >> x-direction, there is no parallel history. When we measure in the >> y-direction, we get either 'up-y' or 'down-y'. MWI says that for either >> result, the alternative occurs in some other world. And that alternative >> result is just as undetectable as the 'down-x' result for the x-measurement. > > > The pure state up-x is the same state as the superposition of up-y and > down-y. > Me in front of up-x and Me in front of up-y + down-y are only different > description of the same state. When measuring that state in the x-direction, > I don’t made that y-superposition disappears. > > > >> >> The point being that whatever measurement we perform, we get only one >> result, and the alternative results that may or may not have been possible >> are undetectable. > > Yes, that is why we can exploit the parallel worlds (aka superposition of > states relative to me) only by isolating the computer from from me, so that I > don’t get entangled with it. > > > >> >> However, it is interesting how this discussion has morphed. We started with >> the observation that a quantum computer does not demonstrate the existence >> of parallel worlds because its operation can be understood completely in >> terms of unitary rotations of the state vector in the one world of Hilbert >> space. > > Unitary rotations conserves the superposition (and the relative > probabilities). > > > > >> Now we seem to have ended up with a discussion of the nature of >> superpositions, and the idea that unobserved outcomes from experiments have >> to be taken into account. How they are to be taken into account is never >> made clear. > > > I don’t know why you say this. We need to take the superposition into account > to get the probabilities right for arbitrary possible measurements. > > > >> They are orthogonal, in fact, and cannot interact with the observed result. >> Parallel worlds, whether they "exist" or not, have no consequences for >> physics or experimental results. So Everett and MWI are otiose -- they have >> no conceivable effects, particularly in quantum computers, so they are >> irrelevant. > > If the superposition are not relevant, then I don’t have any minimal physical > realist account of the two slit experience, or even the stability of the > atoms. > > My goal is not in finding working theory, just to see if the current modern > theory given by the physicists is consistent with digital mechanism, and > indeed, its MWI aspect is the easiest prediction of mechanism. Then the math > suggest we get also the negative interference and that QM confirms Digital > Mechanism, unless we add the collapse postulate, which indeed is an option > for the non-computationalist. But the collapse itself is not something that > we can detect or observe in any way. > > Bruno, > > Forgive me if I have asked this before, but can you elaborate on the how/why > the math suggests negative interference? > > I currently have no intuition for why this should be. > > I recall reading something on continuous probability as being more natural > and leading to something much like the probability formulas in quantum > mechanics. Is that related?
It is not intuitive at all. With the UDA, we can have have the intuition coming from the first person indeterminacy on all all computational continuation in arithmetic, but in the AUDA (the Arithmetical UDA), the probabilities are constrained by the logic of self-reference G and G*. So the reason why we can hope for negative amplitude of probability comes from the fact that modal variant of the first person on the (halting) computations, which is given by the arithmetical interpretation of: []p & p or []p & <>t or []p & <>t & p With, as usual, [] = Beweisbar, and p is an arbitrary sigma_1 sentences (partial computable formula). They all give a quantum logic enough close to Dalla Chiara’s presentation of them, to have the quantum features like complimentary observable, and what I have called a sort of abstract linear evolution build on a highly symmetrical core (than to LASE: the little Schroeder equation: p -> []<>p, which provides a quantisation of the sigma_1 arithmetical reality. It is mainly the presence of this quantisation which justify that the probabilities behave in a quantum non boolean way, but this is hard to verify because the nesting of boxes in the G* translation makes those formula … well, probably in need of a quantum computer to be evaluated. But normally, if mechanism (and QM) are correct this should work. This is explained with more detail in “Conscience et Mécanisme”. Bruno > > Jason > > > We cannot detect even one world. “World” are metaphysical notion. The old > dream argument made this clear since long. > > > > >> >> >> When I talk about some pure state, I mean it as an object considered before >> we male a measurement on it. And I *assume* QM (without collapse) to be >> correct. >> >> That is not necessarily a pure state. You can also prepare a mixed state >> before you make any measurement on it. A pure state is a state that can act >> as a basis vector in the relevant Hilbert space. > > I don’t contest this, albeit I doubt there is any real mixture in nature, > just a pure universal state starting (say) at the Big Bang, but that’s not > relevant here. > > > >> QM without collapse might be correct, but you can never demonstrate this, >> because whether it is correct or not has no observable consequences. MWI is >> an interpretation of QM, not an alternative theory. > > QM is an alternative to QM + collapse. Those are different theories. Both > have their interpretation problem. But only QM confirms Digital Mechanism, > and if someone was able to detect the collapse, he would give a real evidence > against the mechanist hypothesis. > > I don’t defend any theory. I only study their logical compatibility or > inter-dependencies. Digital mechanism and QM are allies. Non-Mechanism and > QM+collapse are allies. > > Now, this list is founded on the idea that everything is simpler to assume > than any particular thing, and both Digital Mechanism and QM belongs to that > type. QM+collapse and non-mechanism are of the type of assuming particular > things. > > Bruno > > > > > > >> >> 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] >> <mailto:[email protected]>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/CAFxXSLTaUDpo7GnwEndzwsxO_hMbbscYEANC%2BjktRfgXZvF_1A%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/everything-list/CAFxXSLTaUDpo7GnwEndzwsxO_hMbbscYEANC%2BjktRfgXZvF_1A%40mail.gmail.com?utm_medium=email&utm_source=footer>. > > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/4C971303-9A3F-495C-89A0-B9120265FBD2%40ulb.ac.be > > <https://groups.google.com/d/msgid/everything-list/4C971303-9A3F-495C-89A0-B9120265FBD2%40ulb.ac.be?utm_medium=email&utm_source=footer>. > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUju9yE0fAd022_EdFp43xtkXqBZhbkshsdj_ZHaDhRseQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUju9yE0fAd022_EdFp43xtkXqBZhbkshsdj_ZHaDhRseQ%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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