Brent Meeker wrote:
>OK, consider a single excited hydrogen atom in a perfectly
>reflecting box. Has it emitted a photon or not? QM will
>predict a superposition of photon+H and H-excited in which
>the amplitude for H-excited decays exponentially with time.
> But the exponential decay is only approximate it actually
>decays, not to zero, but to a small value corresponding the
>an equilibrium state in which the probability of the photon
>being emitted is balanced by the probability of it being
>reabsorbed. So is what is in the box - photon+H or
>H-excited? The answer is, in effect, both. What's in the
>box is the wave-function that describes the superposition.
>You can't get the paradox back by supposing there's a video
>camera watching the state, because the video camera is a
>macroscopic object with so many degrees of freedom that
>when it detects the photon the system (camera + H + photon)
>will go into a superposition of states which, when
>projected onto (emitted, not-emitted) will be essentially
>diagonal, i.e. the wave-function will be "collapsed".
Ok, I think I see where my mistake was. I was thinking that "decoherence"
just referred to interactions between a system and the external environment,
but what you seem to be saying is that it can also refer to an internal
effect where interactions among the components of a system with many degrees
of freedom cause interference terms to become negligible. If that's correct,
then when Wigner decided that interference would cause the wavefunction of
the cat or Wigner's friend to "collapse" even before the box or the room was
opened, then he was probably referring to this sort of internal effect, so
my argument about using quantum computers to simulate truly impenetrable
boxes would not make a difference.
But this makes me wonder about the thought-experiment by David Deutsch which
Hal Finney brought up, in which interference shows that an isolated A.I. was
splitting into multiple versions which experienced different outcomes.
Presumably a simulation of an intelligence would have a lot of degrees of
freedom too, so why wouldn't decoherence ruin things? Maybe since this is a
computer simulation where we know the dynamical rules and initial state
precisely, we would know just where to look for even the smallest
interference effects, unlike in an ordinary macroscopic system where we
don't have such detailed information. Also, we could run such a simulation
over and over again from the same initial conditions, which would also help
to detect small statistical deviations from classical predictions. I once
read a comment by Deutch about decoherence where he said something like
(paraphrasing) "saying the interference terms are 'almost' zero is like
saying someone is a little bit pregnant." His argument would probably be
that although decoherence may explain why the world looks approximately
classical in the many-worlds framework, it doesn't remove to postulate those
other worlds in the first place.
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