On Tuesday, December 5, 2017 at 7:13:23 PM UTC, Brent wrote: > > > > On 12/4/2017 9:35 PM, Bruce Kellett 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. 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. > > Yes, that would seem to be the Everett math. But in practice we can > never know that we have a pure state to start with. > > > > > 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. > > Pure/mixed is not a binary attribute. If the trace of the density > matrix squared is 1.0 then it's a pure state. If it's 1/N where N is > the Hilbert space dimension it's a maximally mixed state. In between > it's a partially mixed state. >
Not easy to understand. A pure state is a state a system is definitely in, a vector in the appropriate Hilbert space. OTOH, mixed states represent different probabilities of possible states. So, having both types represent the same system at the same time sort-of defies conceptualization. AG > > Brent > > > > > 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.
