scerir wrote:
>
> A single particle is prepared in a (weird) superposition.
> The superposition consists in being in three boxes.
>
> The initial state is |psi_1>
> |psi_1> = 3 ^ (-1/2) ( |A> + |B> + |C> )
>
> and the final state is |psi_2>
> |psi_2> = 3 ^ (-1/2) ( |A> + |B> - |C> )
>
> where A, B and C are the three boxes.
>
> If you search, in the intermediate time, in the box A
> you'll find the particle. Otherwise the state would be
> |psi_huh> = 2 ^ (-1/2) ( |B> + |C> ) which is forbidden
> being orthogonal to the final state.
>
> If you search, in intermediate time, in the box B
> you'll find the particle. Otherwise the state would be
> |psi_hoh> = 2 ^ (-1/2) ( |A> + |C> ) which is forbidden
> being orthogonal to the final state.
>
> Then the single particle is in the box A (searching in A)
> and in the box B (searching in B).
>
> What about searching in A *and* B? I don't know.
> And it's too late now. And QM is a nasty trick.
I can't tell whether or not this is a serious description of quantum
physics, but I'm guessing that this is actually one of those transparently
flawed thought experiments - the reason being that if this is true, it's
obviously easy to build a quantum ansible. Send box A to London, send box
B to Boston. London chooses whether or not to perform a measurement at
4:00 and Boston measures at 4:01. If London measures, Boston will never
find the particle; if London does not measure, Boston will always find the
particle.
The flaw, I think, is that any measurement of A collapses the complete
state - if the particle is not found in A, that does not just eliminate
the portion of the particle's position function which was in A; it
collapses the state completely. So if the measurement shows the particle
is not in box A, the resulting quantum state is either 1 * |B> or 1 * |C>
- not 2 ^ (-1/2) ( |B> + |C> ). Thus, the particle is not forced to be in
A.
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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