Hello Eric,
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.
Decoherence is said to occur when two waves (or wavefunctions) which
were initially in phase (or having a constant or well-defined phase
difference) are no longer in phase. This can be for a variety of
reasons. Typically, this is cited as occurring due to interactions with
large numbers of particles (or a single interaction with one particle
that goes on to affect a large number of particles). In this case the
fact that these particles have a large number of internal states means
that it is unlikely that the two waves remain in phase.
Another example of decoherence would be in light from a regular
light-bulb. The polarization of the light is subject to rapid and
random changes in direction (due to emission of individual photons by
the bulb), so that while the horizontal and vertical components of the
light are instantaneously coherent, they rapidly decohere from each
other to give some other value of polarization. The fact that at any
particular instant there is a well defined but random value of
polarization for regular light is what allows us to do Young's Double
Slits with unpolarized light, as at any point on the screen the light
arriving from either slit shares the same polarization, even though the
value of this polarization is subject to rapid fluctuations.
In answer to your second question, the loss of interference (at least in
the Copenhagen Interpretation) is due to the collapse of the
wavefunction, from a superposition of different possibilities to one
actuality. The Copenhagen Interpretation really does not say anything
about what causes this collapse (apart from the nebulously defined
notion of observation). Decoherence has been invoked as one possible
explanation for this loss of interference, specifically that once a
large number of particles are involved in the quantum system, it is
unlikely that any of them will be in phase enough for us to be able to
see interference in practice.
In the Many Worlds Interpretation, it is not necessarily decoherence,
but the linearity of the Schroedinger Wave Equation that makes
interference disappear. Specifically, once an observer (or any other
system for that matter) interacts with a superposed wavefunction, that
system's wavefunction is also put into a superposition of relative
states. The relative states are all separately solutions of the SWE, so
linearity prevents them from directly interacting ( = exchanging energy)
or subjectively noticing each other through interference, in the same
way as ripples on a pond are capable of moving through each other.
Decoherence comes into the MWI explanation of (apparent) wavefunction
collapse once a second observer (or system) interacts with the
superposed system. Let's say our first observer/system has interacted
with the particle on its way from the double slits to the screen in such
a way that that observer/system knows (or has an unambiguous record of)
which slit the particle went through. Now a second observer is going to
record the position the photon strikes the screen. Under MWI, the
particle is *still* in a superposition of states when it reaches the
screen. However, it has also interacted with the first observer system,
which for the sake of argument we shall assume consists of a large
number of particles. Because of the interaction with the first
observer, the second observer is not just interacting with the
wavefunction of the particle that went through the slits, but also with
the superposed relative state wavefunctions of the first observer(s).
These two relative states are highly unlikely to be in phase because of
the large number of particles involved. Therefore, the second observer
is also highly unlikely to observe an interference pattern at the screen
when the experiment is repeated many times.
Note that in MWI the second observer's wavefunction is also split into
two relative states by watching the screen, and so she may obtain a
result indicating that the particle went through either slit regardless
of the first observer's result (who is actually in a superposition of
having got both results). Linearity of the SWE ensures that the second
observer's result will always agree with the first observer's result
should they compare notes later in that particular branch of the multiverse.
This is also how the MWI preserves locality in the EPR paradox/Aspect
experiments, which I think is an important experimental vindication of MWI.
>Take the a double-slit-like experiment. A particle can take
>two paths, A and B. We can in principle detect which path
>the particle went through.
>
>Suppose we can make the detecting apparatus 'non-interfering'
>enough so that the particle is not grossly deflected by the
>detection, but can still reach the screen. We know that the
>result of this thought-experiment is that interference does not
>happen.
>
>The first answer is that the paths have 'decohered'. But what
>exactly does that mean? In a MWI perspective, I like the
>explanation that the two universes A and B are different by a
>large number of particles: the electrons in a wire, which carry
>the amplified pulse of the detector, which then reach a
>computer, and such and such. Something of the order of 10^23
>particles have changed state.
>
>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).
Hope this helps,
Matt.
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When God plays dice with the Universe, He throws every number at once...
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Received on Tue Nov 18 2003 - 13:36:24 PST
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