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. That is why quantum uncertainties are
irrelevant for macroscopic objects. Uncertainties do not add up
coherently for macroscopic objects -- macroscopic objects act as a unit,
and the HUP is irrelevant, even for small coins.
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.
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