On Tue, Aug 6, 2019 at 7:23 PM Bruno Marchal <[email protected]> wrote:
> On 6 Aug 2019, at 10:28, Bruce Kellett <[email protected]> wrote: > > > 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. > > > You are a bit too much fuzzy for me. I don’t see how a rotating ray in an > Hilbert space fail to described superposition states, and without wave > collapse the local (partial trace description) of the situation above makes > the superposition of the observer states not eliminable. > I do not understand your objections here. They make no sense. All I am claiming is some basic facts about vector spaces. If you have a vector space, you can form an arbitrary number of sets of basis vectors that span the space. Any vector in the space can be described in terms of its projections onto these basis vectors. Correspondingly, any set of values along the basis vectors can be summed to give a single vector (or ray) in the space. Any change to either the basis vector components, or the vector itself, is reflected in the other representation. In other words, change the vector and you change the projections on to the basis. Or change these basis components and you change the vector. In the case of a quantum computer, description of the calculation in terms of some set of basis vectors is completely captured in the corresponding changes to the summation vector. Consequently, the description of the QC action in terms of some set of basis vectors is entirely unnecessary -- the same action of the QC is entirely captured by the unitary rotations of the summation vector in the Hilbert space. That is all that there is to it. The advantage of the vector description is that such a description is independent of the chosen basis -- what happens to the vector can be described in terms of any one of the infinite number of possible alternative bases. This is the basis ambiguity, or problem of a preferred basis. To pick out one set of base vectors and claim that these vectors represent a set of parallel worlds in which the computations actually occur, is simply unnecessary -- description in terms of the single summation vector eliminates this stupidity. Maybe you can tell me what happens in that situation. Note that even after > measurement, we can get back the interference effect by erasing the > memorised outcome of the result. Without collapse pure state remains pure, > and decoherence is relative to each “copies” of the observer in the terms > of the (universal) > These observations are entirely beside the point. You cannot erase the memory of the result because memory is intrinsically irreversible. Quantum erasure is a technical matter that occurs only in highly constrained situations. I think you should catch up on some recent work on quantum foundations, in which Everett does not necessarily require the continuing purity of the quantum state. Measurement changes the pure state into a mixture. Zureck has made considerable progress in this direction in recent years. Quantum foundations has moved on since 1957. 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%3DGGLH2OrucwT5_C%3DxpxrBRQt0BE1aQmbess6CvMkL4Q%40mail.gmail.com.
