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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
