On 05 Dec 2017, at 01:26, Bruce Kellett wrote:
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.
Not coherent can only be a relative point of view brought by the first
person indeterminacy. In the 3p perspective coherence never disappear,
and once a particle is in a superposition state, it remains so forever
(in QM without collapse). Look at Everett's explanation of why
coherence explains the appearance of decoherence and collapse.
You just assume collapse. You assume the SWE is wrong somewhere. Where?
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
They look that way, but it is only because we get eventually entangled
with the coin (here).
so they cannot add up to form a superposition.
The heisenberg uncertainty is due to a superposition existing at the
start.
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!
It starts with one. Any position and momentum are superposition of
each other. They behave as gaussian packet, each being a Fourier
transform of the other.
Bruno
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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