From: Mitchell Porter (mitchtemporarily@hotmail.com)
Date: Wed May 07 2003 - 02:10:11 MDT
D. Goel said:
> [ |x=2>|you_2> + 0.5* |x=1>|you_2> ] + [ |x=1> |you_1> - 0.5*
>|x=1>|you_2> ]
(I've corrected the last ket.)
These terms factorize into
(|x=2>+0.5*|x=1>)|you_2> + |x=1>(|you_1>-0.5*|you_2>)
There are two observations to make here:
* If the basis is arbitrary, system state doesn't have to match observer
state (in the lefthand term, observer state is "2" but system state is a
superposition).
* If we treat observer states as quantum states, the superposition
principle implies the existence of observer states which don't make
any subjective sense (observer state in righthand term).
>why do you always observe the
>particle at a particular position instead of a mixture?
>
>The answer to this, iiuc is that the above division is "not stable" to
>wavefunction evolution. Only certian divisions turn out to be
>"stable" as the Schr. eqn. progresses. And this phenomenon is called
>decoherence.
[...]
>When i say "unstable" to wavefunction evolution, i meant that the
>complex coefficients in front of the various parts of the wavefunction
>(which i omitted above) evolve differently with time, rendering the
>division impossible within an epsilon second.
Well, the coefficients of "mismatch states" like |x=1>|you=2> should
become very small, compared to those of "veridical states" like
|x=1>|you=1>. But I don't see how that addresses the basis problem.
The state that you started with... |x=1>|you=1> + |x=2>|you=2>...
has no mismatch component at all, but you can still change the basis.
So I still think you need an extra postulate in MWI, in order to single
out a basis.
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