On Mon, Aug 5, 2019 at 10:37 PM Bruno Marchal <[email protected]> wrote:
> On 5 Aug 2019, at 14:13, Bruce Kellett <[email protected]> wrote: > > On Mon, Aug 5, 2019 at 6:07 PM Bruno Marchal <[email protected]> wrote: > >> On 5 Aug 2019, at 03:27, Bruce Kellett <[email protected]> wrote: >> >> On Sat, Aug 3, 2019 at 10:52 AM Jason Resch <[email protected]> wrote: >> >>> On Fri, Aug 2, 2019 at 7:33 PM 'Brent Meeker' via Everything List < >>> [email protected]> wrote: >>> >>>> On 8/2/2019 5:12 PM, Jason Resch wrote: >>>> >>>> On Fri, Aug 2, 2019 at 6:51 PM 'Brent Meeker' via Everything List < >>>> [email protected]> wrote: >>>> >>>> >>>> Wherever it happens, it's one world. Worlds are things things that are >>>> orthogonal on to one another so that's why they're separate. I don't know >>>> what Deutsch believes. >>>> >>>> In any case, you have still managed to avoid the question of the >>>>> reality of the 10^1000 intermediate computational states. I won't press >>>>> for an answer if you don't have one. >>>>> >>>>> >>>>> I already gave the answer. There is only one intermediate state. It >>>>> just happens to have lots of components in the basis you used to express >>>>> it. >>>>> >>>> >>>> And each of those components represents a trace of a computation >>>> performed on one of the many possible values of the input qubits, do they >>>> not? >>>> >>>> >>>> That's one way of representing them. Just as citing the Fourier >>>> components of a firecracker going off shows the many components of the >>>> sound. >>>> >>> >>> That would be a convincing counterpoint, except here this "way of >>> looking at the many components" performs a computation that would not >>> otherwise be possible if all the atoms of the universe were mustered to >>> perform the computation. >>> >> >> The fact is that it is possible. The 2^n dimensions of the Hilbert space >> for n qbits is ample space for the computations. The trouble with looking >> to parallel worlds to do the computations is that there are an uncountable >> infinity of possible bases for the Hilbert space. What picks out just one >> base to represent all these parallel worlds? That is the real problem. You >> are ignoring the basis problem, just as Deutsch does. You naively assume >> that the computational base that you used to set up you quantum computer in >> the first instance is the only possible basis in which to view it. If you >> take the view that the single ray in Hilbert space represents all that is >> possible to know about the QC, and that computations are nothing more than >> rotations of this state ray in the space, then all these silly notions of >> parallel worlds evaporate. >> >> >> But then the interference between different branch of the universal ray, >> whatever base is used to describe it, will disappear. >> > > No they won't. […] The rotations in this space cause exactly the necessary > interferences. > > > It is a functional space, the ray describes all relative histories, and in > the case of an observer looking a a superposition, the ray describes the > observer being superposed itself. Shor algorithm exploits this. > That is a really weird thing to say. The ray in Hilbert space is a concise description over the basis vectors. Whatever you do in some basis is reflected exactly in the ray representing the state. Conversely, whenever the state vector is rotated, the representation in terms of the basis vectors is changed correspondingly. They are not two distinct things. The point of thinking in terms of the state vector is that this is independent of the base chosen, so is a more objective way of looking at things. Think of a simple example. In general relativity we have the static spacetime given by Schwarzschild solution which describes a black hole. In the standard Schwarzschild metric, there is a 1/(r - 2M) term, so it appears that there is a singularity at the horizon (r = 2M). Eventually it was realised that this is merely an artefact of the coordinate system -- the horizon is not really singular, as can be shown by going to Kruskal or Eddington-Finkelstein coordinates, which are both smooth at the horizon. Working in a particular coordinate system (or set of basis states) is always fraught with ambiguity (the 'preferred basis' problem), so the actual situation is best represented by the state vector itself. The thing about the Hilbert space vector describing the quantum computer is that there is no observer involved. Since, in order to maintain coherence, there cannot be any external observer. So it is just meaningless to claim that "in the case of an observer looking a a superposition, the ray describes the observer being superposed itself.". 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/CAFxXSLQ0Mf53Q68Ri%3DXcXG3pECyCVhX5mawfhqJPFTbYQ19BCg%40mail.gmail.com.
