On Sun, Mar 15, 2009 at 11:06:42AM -0700, Brent Meeker wrote:
>
> Saibal Mitra wrote:
> > If we consider measuring the spin of a particle, you could also say that the
> > two possible outcomes just exist and thatthere are two possible future
> > versions of me. There is no meaningful way to associate myself with either
> > of the two outcomes.
> >
> > But then, precisely this implies that after a measurement and forgetting
> > about the result will yield a version of me who is in a similar position as
> > that earlier version of me who had yet to make the measurement. If one could
> > perform measurements in a reversible way, this would be possible to
> > experimentally confirm, as David Deutsch pointed out. You can start with a
> > spin polarized in the x direction. Then you measure the z-component. There
> > then exists a unitary transformation which leads to the observer forgetting
> > about the outcome of the measurement and to the spin to be restored in the
> > original state. The observer does remember having measured the z-component
> > of the spin.
> >
> > Then, measuring the x-component again will yield "spin-up" with 100%
> > probability, confirming that both branches in which the observer measured
> > spin up and spin down have coherently recombined. This then proves that had
> > the observer measured the z-component, the outcome would not be a priori
> > determined, despite the observer having measured it earlier. So, both
> > branches are real. But then this is true in general, also if the quantum
> > state is of the form:
> >
> > |You>[|spin up>|rest of the world knows the spin is up> + |spin down>|rest
> > of the world knows spin is down>]
>
> You're contemplating reversing three different things:
>
> 1) Your knowledge, by forgetting a measurement result. Something that's easy to do.
>
> 2) The spin state of a particle.
>
> 3) The state of what the rest of the world knows.
>
> Because of the entanglement, I don't think you can, in general, reverse the spin
> state of the particle without reversing what is known about it by "the rest of
> the world".
> If it was a known state (to someone) the particle can easily be put back in that
> state. But to do so for a general, unknown state, after a measurement would
> require invoking time-reversal invariance of the state of whole universe (or at
> least all of it entangled with the particle spin via the measuring apparatus).
>
> Brent Meeker
>
By contrast, I think this line of reasoning can be used to create an
experiment that tests a couple of different versions of MWI.
Consider a Stern-Gerlach experiment where a particle is prepared in
the x+ state. Then measure the state of the particle's spin along the
z-axis, but _do not_ record the result. Finally measure the spin along
the x-axis.
According to Saibal's interpretation (which accords with my own
intuition), the result should be spin up (x+) always. According to the
interpretation you're suggesting Brent (the decoherence of the
environment to contain a memory of whether the spin was z+ or z- -
which I think accords with David Deutch's intuition), the final result
should be x+ or x- with 50% probability. It may be important to send
the result of the intervening measurement to a memory store somewhere
else that the experimenter does not look at.
This should be a doable experiment, and in fact may already have been
done. It is similar in some respects to a version of the two-slit
experiment performed a couple of years ago that generated a spark of
interest.
--
----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Sun Mar 15 2009 - 21:57:15 PDT