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.
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
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