Re: (De)coherence

From: Eric Cavalcanti <eric.domain.name.hidden>
Date: Tue, 18 Nov 2003 17:53:32 -0200

Hi Matt,

----- Original Message -----
From: "Matt King" <m.domain.name.hidden>

> Just my tuppenceworth...
>
> Eric Cavalcanti wrote:
>
> >I think this discussion might have already took place
> >here, but I would like to take you opinions on this.
> >
> >How do we define (de)coherence? What makes interference
> >happen or be lost?
> >
> >
> First, these are two separate questions.

(...)

> This is also how the MWI preserves locality in the EPR paradox/Aspect
> experiments, which I think is an important experimental vindication of
MWI.

Thanks for this first part. Some stuff could clarify my thoughts.

(...)

> >Now suppose we use some kind of very slow detector. The
> >detection is made by, say, a very slow process such that not
> >many particles (suppose only one particle, even though I don't
> >know how to make that detector) change their state before the
> >interfering particle reaches the screen. After that, we can amplify
> >this information and know which path the particle went through.
> >Again, I believe interference would not be possible. But it is a
> >little harder to say why.
> >
> >
> I'm not sure I can answer this question with certainty. I think it
> depends on how many possible internal states the recording
> particle/system may have; the more states, the more decoherence, and the
> less likely it is that interference will be seen by the second
> observer. If the detector had only two possible internal states, I
> think it is indeed possible for the screen observer to see some
> interference if the experiment were repeated many times.
>
> I don't think the Copenhagen Interpretation was designed to include
> single particles as observers; rather one would include them in the
> wavefunction of the total system. Consider as an example Helium. You
> could think of one electron as being the observer of the other electron;
> under CI both are included in the wavefunction nonetheless. I think
> that the CI would therefore make different predictions whether or not
> one assumes that the recording particle qualifies as an observer. I'm
> not aware of anything in the CI framework which would help you choose
> which assumption to make; rather you'd do this retroactively depending
> on which results you got. I know that the logical inconsistencies in
> the CI when more than one observer are included are exactly what led
> Everett to develop MWI in the first place; if anyone has any specific
> information about what these inconsistencies were, I'd be very excited
> to hear about it.
>
> In the MWI, there is no distinction between observers and other systems,
> even single particles, and I'm pretty sure that it would predict that
> the second observer would see some interference in this case, with the
> amount of interference smoothly (and exponentially rapidly) decreasing
> with increasing number of internal states of the first observing system
> (due to decoherence).

How do you express that mathematically?
On another thought, wouldn't that lead to an inconsistency? No matter
how small the detector is, if in principle we could read the result and
know what path the particle went through, how could the other path
have interfered?

> Hope this helps,

Yes, it did. Thanks.

-Eric.
Received on Fri Nov 21 2003 - 05:11:20 PST