On 5/14/2022 3:55 PM, Bruce Kellett wrote:
On Sun, May 15, 2022 at 1:17 AM smitra <smi...@zonnet.nl> wrote:
On 13-05-2022 21:59, Brent Meeker wrote:
> Right CI doesn't explain the collapse and MWI doesn't explain the
> collapse either but assumes it can be explained without new
physics.
> I hypothesize (not assume) that CI+ <non-zero minimum
probability> can
> explain the collapse. I don't see any big advantage for MWI here.
The big advantage is that decoherence is a well researched area of
(mathematical) physics, results like the density matrix becoming
approximately diagonal, and relations between decoherence to entropy
increase making it effectively irreversible are all rigorous results
that are uncontroversial.
But it is more than "effectively" irreversible because decohering
information spreads at the speed of light, and in an expanding universe
cannot be captured and reversed. This why I think there is some
relation between the holographic principle, expansion of the universe,
Hawking-Bekenstien entropy, and a non-zero minimum probability.
Brent
People may still have objections against the
MWI, but they'll still accept these results on decoherence.
Yes. And decoherence says that with time, the off-diagonal elements of
the density matrix become arbitrarily small. If there is a smallest
non-zero probability, then eventually these off-diagonal elements
become zero. This reduces the pure state to a mixture. Which is to say
that there is a collapse; unitary evolution ceases, and we have
reached a classical world.
Non-zero minimum probability on its own, however, does not cause a
system to evolve in a non-unitary way.
It does when decoherence is taken into account. See the above
explanation. Bruce has not omitted anything.
Bruce
Bruce is omitting something here,
perhaps some limits in which the time evolution operator becomes
degenerate or something like that. But a product of two unitary
transforms is a unitary transform, so the nth power of a unitary
transform is also a unitary transform. There is no ay you can get
anything non-unitary out of this, unless possibly in the limit of
n to
infinity.
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