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 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. 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. 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. 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. 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. 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. 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.
