russell standish wrote:
> 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.

No need to do it.  Even more telling experiments have already been done in 
the "measurement" was just the unrecorded IR radiation from buckyballs. 
Buckyballs which were sufficiently cold showed the 2-slit interference pattern 
in a Young's slit type experiment.  But when they were warm enough to emit IR 
radiation that, if detected, could have localized them, the interference 
disappeared.  So it is not only a matter of the experimenter not looking at the 
result, the rest of the universe has to not look too.


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