On 6/12/2017 6:13 am, Brent Meeker wrote:
On 12/4/2017 9:35 PM, Bruce Kellett wrote:
In other words, the randomness must be purely quantum for Everettian
splitting to occur -- the apparent randonmness arises as a result of
the splitting, it was not present before in any sense since the SE is
deterministic.
Incidentally, what is a partly mixed state? A mixed state is a
probabilistic mixture of pure states, and can only be represented as
a density matrix, not as a vector in a Hilbert space, so it cannot
lead to splitting of worlds.
Pure/mixed is not a binary attribute. If the trace of the density
matrix squared is 1.0 then it's a pure state. If it's 1/N where N is
the Hilbert space dimension it's a maximally mixed state. In between
it's a partially mixed state.
Can you give reference where this is spelled out? It does not seem right
to me. My understanding of pure/mixed states is along the lines of the
Wikipedia article I referenced:
https://en.wikipedia.org/wiki/Quantum_state
The pure state is one which can be expressed as a sum of the basis
vectors of some Hilbert space. If a state cannot be so represented, then
it is mixed. Sounds like a binary attribute to me, and the idea of a
partially mixed state is incoherent -- that would just be a mixed state.
Sometimes pure states, since they can be represented as density
matrices, are said to be a special type of mixed state, but I do not
find that idea helpful. Representing a pure state as a density matrix is
also unhelpful because the same density matrix can be a mixed as well as
a pure state: the density matrix representation is not definitive of a
pure state.
Bruce
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