On Tuesday, December 5, 2017 at 5:35:37 AM UTC, Bruce wrote: > > On 5/12/2017 4:00 pm, Brent Meeker wrote: > > On 12/4/2017 7:23 PM, Bruce Kellett wrote: > >> On 5/12/2017 2:03 pm, Russell Standish wrote: > >>> On Tue, Dec 05, 2017 at 12:18:02PM +1100, Bruce Kellett wrote: > >>>> Randomness in the sense that I am using it arises in deterministic > >>>> systems > >>>> from lack of knowledge of the initial conditions. As in the coin > >>>> toss, in > >>>> general you do not know the initial conditions with sufficient > >>>> accuracy to > >>>> predict the outcome with certainty. What other type of randomness is > >>>> relevant in classical situations? Thermal motions are sufficiently > >>>> random > >>>> FAPP. > >>> And thermal motions are amplified from more minor uncertainties in the > >>> molecular scattering process, which are quantum in nature ISTM. > >> > >> It is my contention that any addition randomization from this source > >> is effectively irrelevant. The momentum involved in thermal motions > >> at room temperature is such that the uncertainty in momentum due to > >> the UP in the wave packet describing the quantum particle is > >> completely negligible, FAPP. > >> > >>> If lack of knowledge in initial conditions were all there is, then the > >>> state of the coin (or dice) is completely determined by the initial > >>> conditions (just unknown), in which case they're not exactly a random > >>> device, just (possibly) pseudorandom. In such a case, there will not > >>> be two universes, one with heads and one with tails, just one universe > >>> with one or the other outcome. > >> > >> That is, in fact, the point I was originally trying to make. It > >> seemed to me that Bruno was suggesting that the coin toss produced a > >> split in the world, where one branch got heads and the other branch > >> got tails. Bruno was suggesting that a random shaking of the coin, > >> prior to the toss, would amplify quantum indeterminacies to the > >> extent that the coin itself was put into a quantum superposition of > >> head-vs-tail outcomes. I contended, and still contend, that this is > >> impossible. Random shaking of the coin cannot produce a superposition > >> -- for many reasons, but the most important is that the original > >> indeterminacies are incoherent, whereas the superposition required > >> for a quantum world split is completely coherent. No amount of > >> shaking can make an incoherent mixture a coherent pure state. That is > >> where the Poincare recurrence time came from -- the time it takes a > >> fully decohered state to recohere, if left to its own devices. > > > > This seems to raise and interesting question. As Russell has agreed, > > flipping a coin isn't a good example of quantum randomness because we > > know that with sufficient care we can make it deterministic, i.e. the > > randomness just came from our ignorance of the initial conditions. > > My contention is that for a macroscopic object, such as the coin, the > randomness is always deterministic, and due to our lack of knowledge of > the initial conditions. Classical probability theory arose from such > cases, as in card games or the roulette wheel and other games of chance. > The argument is as to whether there is such a thing as pure classical > probability, or do quantum effects always (or sometimes) dominate. I > tend to the view that decoherence is universal, and an effective > classical world does emerge from the quantum, so that quantum effects > are no longer relevant in this emergent classical world. > > > But between flipping a coin and flipping an electron spin, there is a > > range of cases. That means there are some which sorta, partially, > > maybe split the world?? How quantum must the randomness be for > > Everett to apply. Must it be a pure state or can it be partly mixed? > > Splitting of worlds is a consequence of Schrodinger evolution of the > wave function. You start with a pure quantum state, viz., one which can > be represented as a vector or ray in the appropriate Hilbert space, and > evolve it according to the interaction Hamiltonian. Expressing this in > the einselected stable basis, we are led to a separate world for each > basis vector
*How do we get to separate worlds? I just don't see it. AG* > . Everything else becomes entangled with these stable basis > vectors. It seems to me that this is an all-or-nothing process: if the > initial state cannot be expressed as a pure state, a vector in the > appropriate Hilbert space, then there is no single set of basis vectors, > and world splitting cannot be defined. > > In other words, the randomness must be purely quantum for Everettian > splitting to occur -- the apparent randonmness arises as a result of the > splitting, it was not present before in any sense since the SE is > deterministic. > > Incidentally, what is a partly mixed state? A mixed state is a > probabilistic mixture of pure states, and can only be represented as a > density matrix, not as a vector in a Hilbert space, so it cannot lead to > splitting of worlds. > > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
