On 5/12/2017 3:15 am, Bruno Marchal wrote:
On 01 Dec 2017, at 01:49, Bruce Kellett wrote:
On 1/12/2017 8:57 am, Bruce Kellett wrote:
On 1/12/2017 4:21 am, Bruno Marchal wrote:
On 29 Nov 2017, at 23:16, Bruce Kellett wrote:
On 30/11/2017 2:24 am, Bruno Marchal wrote:
On 29 Nov 2017, at 04:59, Bruce Kellett wrote:
I would suggest that there is no such world. Whether a coin
comes up head or tails on a simple toss is not a quantum event;
it is determined by quite classical laws of physics governing
initial conditions, air currents and the like.
It depends. If you shake the coin long enough, the quantum
uncertainties can add up to the point that the toss is a quantum
event. With some student we have evaluate this quantitavely (a
long time ago) and get that if was enough to shake the coin less
than a minute, but more than few seconds ... (Nothing rigorous).
That is a misunderstanding of quantum randomness. For the outcome
of a coin toss to be determined by quantum randomness, we would
have to have a single quantum event where the outcome was
amplified by decoherence so that it was directly entangled with
the way the coin landed. Schematically:
|quantum event>|coin> = (|outcome A> + |outcome B>)|coin>
= (|outcome A>|coin heads> + |outcome B>|coin tails>)
The coin is quantum.
The coin is classical, consisting of something of the order of 10^22
atoms. Indeterminacy in position as given by the Heisenberg
Uncertainty Principle, is undetectably small.
I think it is worth while to put some (approximate) numbers around
this. The reduced Planck constant, h-bar, is approximately 10^{-27}
g.cm^2/s. The Uncertainty Principle is
delta(x)*delta(p) >= h-bar/2.
For a coin weighing approximately 10 g and moving at 1 cm/s, the
momentum is mv = 10 g.cm/s. Taking the momentum uncertainty to be of
this order, the uncertainty in position, delta(x) is of the order of
10^{-28} cm. A typical atom has a diameter of about 10^{-8} cm, so
the uncertainty in position is approximately 20 orders of magnitude
less than the atomic diameter.
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.
That is why quantum uncertainties are irrelevant for macroscopic
objects. Uncertainties do not add up coherently for macroscopic
objects --
Sure they do, unless you add continuous collapse, or something.
decoherence is only entanglement with the environment, that is
"contagion of the superposition".
You are talking rubbish. As above, the uncertainties are not coherent so
they cannot add up to form a superposition. Collapse has nothing to do
with it. Decoherence is unitary interaction with the environment, so
that the environment becomes entangled with the original superposition,
but you have to start with a superposition -- that process does not make
one!
macroscopic objects act as a unit, and the HUP is irrelevant, even
for small coins.
I am not yet convinced.
Bruno
I think there are some basics of quantum mechanics over which you are
very confused.
Bruce
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