> On 9 Aug 2019, at 13:09, Jason Resch <[email protected]> wrote: > > > > On Fri, Aug 9, 2019 at 3:22 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > >> On 8 Aug 2019, at 17:41, Jason Resch <[email protected] >> <mailto:[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 > > > Thank you Bruno for your explanation and references.
Y’re welcome. > 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. Yes, There is no HTML page for the long text. But you can consult also my paper: Marchal B. The Universal Numbers. From Biology to Physics, Progress in Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381. https://www.ncbi.nlm.nih.gov/pubmed/26140993 You will still need some background in quantum logic, like the paper by Goldblatt which makes the link between minimal quantum logic and the B modal logic. There is also a paper by Rawling and Selesnick which shows how to build a quantum NOT gate, from the Kripke semantics of the B logic. It is not entirely clear if this can be used in arithmetic, because we loss the necessitation rule in “our” B logic. Open problem. A positive solution on this would be a great step toward an explanation that the universal machine has necessarily a quantum structure and can exploit the “parallel computations in arithmetic” in the limit of the 1p indeterminacy.. Rawling JP and Selesnick SA, 2000, Orthologic and Quantum Logic: Models and Computational Elements, Journal of the ACM, Vol. 47, n° 4, pp. 721-T51. Ask question, online or here. It *is* rather technical at some point. Bruno > > 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] > <mailto:[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 > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgiWHfT%2Bbivr0L-3o53RLXp4CaiUGipvhFV6knbrTiE3w%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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3BACC2E1-7FD2-4260-8635-441D4F72A239%40ulb.ac.be.
