On Fri, Aug 9, 2019 at 3:22 AM Bruno Marchal <[email protected]> wrote:
> > On 8 Aug 2019, at 17:41, Jason Resch <[email protected]> wrote: > > > > On Thu, Aug 8, 2019, 5:51 AM Bruno Marchal <[email protected]> wrote: > >> >> On 8 Aug 2019, at 11:56, Bruce Kellett <[email protected]> wrote: >> >> On Thu, Aug 8, 2019 at 7:21 PM Bruno Marchal <[email protected]> wrote: >> >>> On 8 Aug 2019, at 02:23, Bruce Kellett <[email protected]> wrote: >>> >>> On Wed, Aug 7, 2019 at 11:30 PM Bruno Marchal <[email protected]> wrote: >>> >>>> On 7 Aug 2019, at 14:41, Bruce Kellett <[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 > > Thank you Bruno for your explanation and references. Regarding “Conscience et Mécanisme”, is there a web/html or English version available? Unfortunately my browser cannot do translations of PDFs but can translate web pages. If not don't worry, I can copy and paste into a translator. Jason -- 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgiWHfT%2Bbivr0L-3o53RLXp4CaiUGipvhFV6knbrTiE3w%40mail.gmail.com.
