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.
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".
macroscopic objects act as a unit, and the HUP is irrelevant, even
for small coins.
I am not yet convinced.
Bruno
Bruce
The quantum event is given by its position, the Heisenberg
uncertainty makes it diffusing rapidly (at the speed of light) and
decoherence is only local contamination of the superposition of
the "gaussian" position, this evolves in infinity of (gigantic
number of universe) with the coin landing on tail or head about
one halve the contexts.
No, you only get splitting of worlds when quantum events are
amplified to macroscopic levels. Otherwise the concept of a "world"
as closed to interaction from outside, loses all meaning.
--
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.
http://iridia.ulb.ac.be/~marchal/
--
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.
