Re: Simulating the Schrödinger Equation

From: Marchal <marchal.domain.name.hidden>
Date: Fri Oct 26 06:28:02 2001

Saibal Mitra wrote


>We get an interesting paradox if we try to simulate the time evolution
>according to the schrödinger equation on a classical machine.

>Consider
>simulating an observer measuring the z-component of a spin in the state:
>
>a ¦up> + b ¦down>,
>
>where ¦a¦ is not equal to ¦b¦.
>
>The classical computer will end up simulating the states of the observer
>having measured spin up and spin down. The probability for the observer in
>any of these states is 1/2 irrespective of a and b.


Maudlin said something similar, but it seems to me that this paradox
is solved in Everett long paper.


>Therefore from the first person's perspective the laws of quantum
>mechanics are violated.


No more than it seems QM is violated each times we makes observations.
But Everett (+decoherence) explain why the illusion of collapse is
just natural for the machine trying to see the split.

The clearer explanation for the probabilities is the one by
Hartle, or the one by Graham, although I believe Gleason theorem
could makes things conceptually simpler.

Deutsch wrote a (not so easy) paper justifying the quantum probabilities
(for the observer) without using "frequencies" like Hartle.

If you emulate a "[up> + b [down> + your observer", with 'a not equal to 'b
and, I add, irrational, you must dovetail among 2^aleph_O up and down,
which makes many observers. 'course the UD makes that "all the time", from
all "angles".


Bruno
Received on Fri Oct 26 2001 - 06:28:02 PDT