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 which
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.
Brent
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Received on Sun Mar 15 2009 - 22:06:10 PDT