On 5/12/2017 11:53 am, Russell Standish wrote:
On Tue, Dec 05, 2017 at 11:26:53AM +1100, Bruce Kellett wrote:
On 5/12/2017 3:15 am, Bruno Marchal wrote:
I think that is enough to get the macroscopic superposition, as, like I
explained, you have to take into account not just the quantum
indeterminacy, + the classical chaos. You might need to shake for some
minutes.
You could shake for longer than the age of the universe and you will still
not convert quantum uncertainties and classical thermal motions into a
macroscopic superposition. Do you know nothing about coherence? And the fact
that coherent phases between the components are what separates a
superposition from a mixture? Random quantum uncertainties and thermal
motions are not coherent, so cannot form superpositions.
To repeat - coherence and superposition are orthogonal concepts. A
fully decohered multiverse is still in a superposition.
But that superposition is only of the whole multiverse, and we do not
have access to that. The concepts are not orthogonal, because any finite
physical system will not, in general, be in a superposition of any kind.
The distinction between pure states -- coherent superpositions -- and
mixed states is fairly fundamental if you want to make any progress in
fundamental physics.
Re the length of time for quantum uncertainty to affect macroscopic
state, much less than the age of the universe is required.
The Poincaré recurrence time for the general decohered state is
certainly of the order of the age of the universe. Quantum uncertainties
can affect the macroscopic state in some circumstances -- particular
when there is a clear route for amplification of the quantum effects, as
in most quantum experiments. It has been suggested that the chaotic
rotation of Saturn's moon Hyperion is related to quantum effects, but
that is a particularly unstable system.
Whilst the StosszahlAnsatz will be strictly speaking incorrect, as I
understand it it is very approximately true. This will entail that quantum
randomness will affect classical randomness on about the same
timescale as the mean free time of molecules in a gas at room
temperature, or about 0.1 ns.
I think this remains to be proved for the general case.
Unless you are proposing some other source of randomness that is not
quantum? Then I'm all ears. Classical physics doesn't have it, it is
deterministic.
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.
BTW - as Brent pointed out, coin tosses many not actually be a good
example of chaotic inflation of quantum uncertainty, and aren't
actually a good source of randomness - fine, but clearly such systems
do exist, eg lava lamps.
Is that quantum randomness? -- it is chaotic motion certainly, but of
purely thermal origin.
Bruce
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