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?
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
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.
Before anyone says that *some* other particle has changed
state, and that should be enough for the decoherence, suppose
now an experiment with a charged particle, say, an electron.
We make it go through paths A and B by steering it with
magnetic fields. Certainly, it has interacted with *something*,
ot it could not be steered. It interacted with the photons of the
EM field, or in last analysis, with the electrons that are
generating it. We could use electric fields, so that the interaction
is more evident. On the other hand, a photon being reflected
by a mirror is also interacting with something, but that does
not prevent the interference from happening, as is well known.
Therefore interaction by itself does not cause decoherence.
And if it is just a large number of particles changing state that
does, then what is the threshold? Would an experiment with a
few-particle-delayed-detector as described above allow
interference? Or is it the 'information' that causes decoherence?
If that is the case, how does one define 'information'?