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. 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/CAFxXSLQZsVrxu2oxRmfEw83Apfo3%3DTFB6xkVV2yUnBLG2LmigQ%40mail.gmail.com.
