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? 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]. > 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]. > 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. 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