On Tue, Aug 6, 2019 at 6:05 PM Bruno Marchal <[email protected]> wrote:
> On 5 Aug 2019, at 15:12, Bruce Kellett <[email protected]> wrote: > > 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.”. > > > Maybe in some dualist theory of mind. I am just using the idea that O(a+b) > = Oa + Ob, where O is an observer not interacting with a superposition > state. > No, you are just attempting to divert attention away from the fact that you have no answer to my original argument that a quantum computer can quite reasonably do the calculation by rotating the state vector in Hilbert space, and consequently, there is no need to imagine a large number of parallel worlds in which the calculations are performed by a series of clunky linear processing Turing machines. The hypothetical observer is entirely irrelevant. > In that state, O has still the choice to look at this in the {a, b} base, > or in the {a+b, a-b} base. In the first, the universal ray will describe > ((O seeing a) a + (O seeing b) b) (well normalised), > A change of base does not make the idea that there are parallel worlds any more convincing. Again, this is just a diversionary tactic. 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/CAFxXSLS%2BGA6gk%3D%3Dd%3Dez0zduiqboWo960rSEXKY-v4H4bL%2B-gxA%40mail.gmail.com.
