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.
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.
This direct entanglement is not reproduced by the sum over many
random quantum events where the ensuing entanglement is extremely
complicated, with no direct connection between a quantum outcome and
the result of the toss.
Why? It looks you make QM wrong for the coin.
The coin is quantum at the atomic level, but classical (or
pseudo-classical) at the macro level of the coin itself. You do wrong if
you confuse these levels of description.
Such accumulation of quantum uncertainties is similar to simple
thermal noise, and could not be distinguished from it.
I agree. In no worlds there will be able to distinguish the MW from
some UM, but that was not the point. Yet, it seems to me that with the
quantum (the real) coin, the Heisenberg uncertainties on the position
grows with shaking leading after some times to an infinity of
universes, having different results, but with the right classical
statistics (1/2). It is just that decoherence is almost at speed c
that at no time we can detect intermediate interference, and then, as
usual, we don't feel the split.
Quantum uncertainties do not grow in this way for macrosopic objects.
The Heisenberg uncertainty on the coin is given by the uncertainty on
the coin as a whole. And for an object as massive as a coin this is
indiscernible. I can't remember the details of the calculation or the
numbers, but I may come across it again sometime. The world does not
split on a coin toss because that is a classical event, the SE is not
approprate. I call on quantum mechanics for quantum objects, but I do
not call on a quantum mechanic to fix my car.
Bruce
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