On Wednesday, October 9, 2019 at 1:28:38 AM UTC-5, Brent wrote: > > > > On 10/8/2019 9:20 PM, Alan Grayson wrote: > > I've argued this before, but it's worth stating again. It's a > > misintepretation of superposition to claim that a system described by > > it, is in all the component states simultaneously. As is easily seen > > in ordinary vector space, an arbitrary vector has an uncountable > > number of different representations. Thus, to claim it is in some > > specific set of component states simultaneously, makes no sense. Thus > > evaporates a key "mystery" of quantum theory, inclusive of S's cat and > > Everett's many worlds. AG > > No. It changes the problem to the question of why there are preferred > bases. > > Brent > >
On the preferred-basis problem and its possible solutions arXiv:1008.3708 The preferred basis problem is mentioned in the literature in connection with the measurement problem and with the Many World Interpretation. It is argued that this problem actually corresponds to two inequivalent problems: (i) the preferred-decomposition problem, i.e., what singles out a preferred decomposition of a suitable state vector of a system as the sum of a finite or countable set of vectors?, and (ii) the preferred-representation problem, i.e., what singles out a preferred representation for the Hilbert space of a system? In this paper the preferred-decomposition problem is addressed and two processes, namely decoherence and permanent spatial decomposition (PSD), are examined and compared as possible solutions to this problem. It is shown that, perhaps contrary to common belief, in realistic situations decoherence is not sufficient to solve the preferred-decomposition problem. PSD is the (hypothesized) tendency of the wave function of the universe to decompose into permanently non-overlapping wave packets. Three phases can be roughly identified as composing PSD: Microscopic decomposition, amplification, and interaction with the environment. Decoherence theory considers only the interaction with the environment and ignores the first two phases. For this reason PSD is fundamentally different from decoherence and, unlike decoherence, provides a simple and non-elusive solution to the preferred-decomposition problem. No Quantum Process Can Explain the Existence of the Preferred Basis: Decoherence Is Not Universal Journal of Quantum Information Science Vol.06 No.03 (2016) Environment induced decoherence, and other quantum processes, have been proposed in the literature to explain the apparent spontaneous selection―out of the many mathematically eligible bases―of a privileged measurement basis that corresponds to what we actually observe. This paper describes such processes, and demonstrates that―contrary to common belief―no such process can actually lead to a preferred basis in general. The key observation is that environment induced decoherence implicitly assumes a prior independence of the observed system, the observer and the environment. However, such independence cannot be guaranteed, and we show that environment induced decoherence does not succeed in establishing a preferred measurement basis in general. We conclude that the existence of the preferred basis must be postulated in quantum mechanics, and that changing the basis for a measurement is, and must be, described as an actual physical process. @philipthrift -- 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/3a2b2714-d106-43aa-96c2-8b0426595bbd%40googlegroups.com.
