On 5/12/2017 10:20 pm, smitra wrote:
On 05-12-2017 04:23, 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.
It seems that you were talking about the time for quantum uncertainty
to influence thermal motions. That is a completely different issue,
and we may have been talking at cross purposes.
Bruce
Bruno is right and the article itself makes this claim explicitly.
Even if one can write down a state that does contain sufficient
information, this wouldn't be relevant. In the MWI all the alternative
branches also exist and the observer cannot distinguish between one
branch and an infinitesimally different micro-branch, and the outcome
of the coin toss is going to be different between those branches.
But the observer cannot switch between branches. So in the branch in
which he makes the toss, there is only one outcome, no further split.
Bruce
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