On 13/12/2017 2:12 am, smitra wrote:
On 12-12-2017 12:33, Bruce Kellett wrote:
On 12/12/2017 9:46 pm, smitra wrote:
Yes, it's only an estimation but it yields a good order of magnitude
estimate for the center of mass. What the calculation shows is that
quantum superpositions do exists at the macroscopic level and these
can then be amplified by chaotic dynamics. Of course, it then
becomes incoherent, but in the MWI that's besides the point.
MWI splitting depends on coherence, so it is certainly not beside the
point for the coin toss.
It doesn't depend on coherence. Why would it matter if the state of
the coin gets entangled with a zillion other environmental degrees of
freedom? The dynamics according to unitary time evolution leads toa
superposition, no matter how many degrees of freedom are involved in
the entanglement.
You are missing the point. Splitting according to the Schrödinger
equation does depend on coherence. The decoherence that entangles the
coin with a zillion other environmental degrees of freedom occurs after
the splitting. Given decoherence, the process is irreversible FAPP,
which means that there is no practical way, by design or chance, that a
decohered state can recohere. Sure, in the many worlds of MWI the
superposition, if it once existed, is still intact. But if no such
superposition ever existed, then it can't be created from non-coherent
interactions.
So Schrödinger's cat was once a coherent state of a cat in a box, and
the splitting occurs with the decay of a nucleus; decoherent
entanglement then leads to the splitting of worlds FAPP. But given an
arbitrary coin, it is already non-coherently entangled with many
environmental degrees of freedom, but there is no state that can lead to
{heads>+|tails>} in a unitary manner, so there is no state that can then
evolve into a splitting and decoherence into worlds distinguished by
either |heads> or |tails>. If you think that there is, write out the
schematic sequence of states evolving under the SE that leads to this
result.
The only relevant issue here is if you then become different due to
such an entanglement such that even before you make a measurement, you
will already feel subjectively different in the two sectors.
What you feel subjectively is irrelevant to the existence or
non-existence of splitting. In the Cat scenario, you don't know the
result until you open the box, but the split occurred long before that,
and the cat was dead in one world but still alive in the other long
before the observer became aware of it.
Otherwise you have an exact copy as far as your subjective feelings
are concerned, so before measurement you can end up in both sectors.
You are in both sectors even after the split -- it is just that the
"you" in one world exist alongside a live cat, and in the other world
you exist alongside a dead cat. However, in the case of the coin toss,
there is no splitting due to the toss -- so if there is splitting caused
by some other adjacent quantum event, then you exist in each of the
consequent worlds in the same state viv a vis the coin; i.e., it is
either heads in all the worlds, or tails in all the worlds.
MWI mumbo jumbo and appeals to "entanglement" magic cannot get you out
of the clear results of quantum evolution.
Bruce
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