Hal Finney wrote:
>
>Ben Goertzel writes:
> > Hal,
> > > It won't make any difference, because the CC is not used in the way
>you
> > > imagine. It doesn't have to produce a record and it doesn't have to
>erase
> > > any records.
> >
> > OK, mea culpa, maybe I misunderstood the apparatus and it was not the CC
> > that records
> > things, but still the records
> > could be kept somewhere, and one can ask what would happen if the
>records
> > were
> > kept somewhere else (e.g. in a macroscopic medium). No?
>
>I don't think this makes sense, at least I can't understand it.
I think Ben's question here does make sense. See below...
>
>
> > > The point is, there is no change to the s photon when we put the
>polarizer
> > > over by p. Its results do not visibly change from non-interference
> > > to interference, as the web page might imply. (If that did happen,
> > > we'd have the basis for a faster than light communicator.) No, all
> > > that is happening is that we are choosing to throw out half the data,
> > > and the half we keep does show interference.
> >
> > Yes but we are choosing which half to throw out in a very peculiar way
>--
> > i.e. we are throwing it out by "un-happening" it after it happened,
> > by destroying some records that were only gathered after the events
> > recorded in the data already happened...
>
>You have to try to stop thinking of this in mystical terms. IMO people
>present a rather prosaic phenomenon in a misleading and confusing way,
>and this is giving you an incorrect idea. Nothing is un-happening.
>No records are destroyed after they were gathered.
Although it may be true that no records are destroyed after they're
gathered, what is true is that an *opportunity* to find out retroactively
which path the "signal" photon took is eliminated when you choose to combine
the paths of the "idler" photons instead of measuring them. For reference,
look at the diagram of the setup in fig. 1 of this paper:
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047.pdf
In this figure, pairs of entangled photons are emitted by one of two atoms
at different positions, A and B. The signal photons move to the right on the
diagram, and are detected at D0--you can think of the two atoms as
corresponding to the two slits in the double-slit experiment, while D0
corresponds to the screen. Meanwhile, the idler photons move to the left on
the diagram. If the idler is detected at D3, then you know that it came from
atom A, and thus that the signal photon came from there also; so when you
look at the subset of trials where the idler was detected at D3, you will
not see any interference in the distribution of positions where the signal
photon was detected at D0, just as you see no interference on the screen in
the double-slit experiment when you measure which slit the particle went
through. Likewise, if the idler is detected at D4, then you know both it and
the signal photon came from atom B, and you won't see any interference in
the signal photon's distribution. But if the idler is detected at either D1
or D2, then this is equally consistent with a path where it came from atom A
and was reflected by the beam-splitter BSA or a path where it came from atom
B and was reflected from beam-splitter BSB, thus you have no information
about which atom the signal photon came from and will get interference in
the signal photon's distribution, just like in the double-slit experiment
when you don't measure which slit the particle came through. Note that if
you removed the beam-splitters BSA and BSB you could guarantee that the
idler would be detected at D3 or D4 and thus that the path of the signal
photon would be known; likewise, if you replaced the beam-splitters BSA and
BSB with mirrors, then you could guarantee that the idler would be detected
at D1 or D2 and thus that the path of the signal photon would be unknown. By
making the distances large enough you could even choose whether to make sure
the idlers go to D3&D4 or to go to D1&D2 *after* you have already observed
the position that the signal photon was detected, so in this sense you have
the choice whether or not to retroactively "erase" your opportunity to know
which atom the signal photon came from, after the signal photon's position
has already been detected.
This confused me for a while since it seemed like this would imply your
later choice determines whether or not you observe interference in the
signal photons earlier, until I got into a discussion about it online and
someone showed me the "trick". In the same paper, look at the graphs in
Fig. 3 and Fig. 4, Fig. 3 showing the interference pattern in the signal
photons in the subset of cases where the idler was detected at D1, and Fig.
4 showing the interference pattern in the signal photons in the subset of
cases where the idler was detected at D2 (the two cases where the idler's
'which-path' information is lost). They do both show interference, but if
you line the graphs up you see that the peaks of one interference pattern
line up with the troughs of the other--so the "trick" here is that if you
add the two patterns together, you get a non-interference pattern just like
if the idlers had ended up at D3 or D4. This means that even if you did
replace the beam-splitters BSA and BSB with mirrors, guaranteeing that the
idlers would always be detected at D1 or D2 and that their which-path
information would always be erased, you still wouldn't see any interference
in the total pattern of the signal photons; only after the idlers have been
detected at D1 or D2, and you look at the *subset* of signal photons whose
corresponding idlers were detected at one or the other, do you see any kind
of interference.
So, my guess is that something similar would be true if you created a more
complicated type of quantum-eraser experiment along the lines of what Ben is
suggesting. For example, imagine something like the double-slit experiment
with an electron, except that the slits are on one side of a closed box
whose insides resemble a cloud chamber, with the electron gun on the inside
of the box on the opposite side. Imagine that this box is an idealized one
that can perfectly isolate the inside from any interactions with the outside
world, along the lines of the box in the Schrodinger's cat
thought-experiment (perhaps the only way to realize this practically would
be to simulate the insides of the box on a quantum computer). Now, if an
electron comes out of the slits and hits a screen, then if we immediately
open the box and look inside, we'll probably still be able to see the path
the electron took through the cloud chamber, and thus we'll know which slit
it went through. On the other hand, if we wait for a long time before
opening the box, the insides will have gone back to equilibrium and we'll
have no way of telling which slit the electron went through. In analogy with
the quantum-eraser experiment, no matter which we do, I don't think you'll
see an interference pattern in the total pattern of electrons on the screen.
But, again in analogy with the quantum-eraser experiment, if you were to
look at all possible outcomes of measuring the exact quantum state of the
inside of the box in the case where you wait a large time t to open it (and
the number of possible distinct quantum states would be huge, because of the
number of particles making up a cloud chamber), and then you performed the
experiment an equally huge number of times so you could look at the subset
of trials where the box was found in a particular quantum state X, then in
that subset, my guess is that you'd see an interference pattern in the
position that the electron was detected on the screen. But if you add up all
the different subsets involving each possible quantum state for the inside
of the box, my guess is that just as in Fig. 3 and Fig. 4, the peaks and
troughs of all the various subsets would add together so the total
distribution of the electron's position would show no interference. And on
the other hand, if you opened the box immediately instead of waiting a large
amount of time, then most of the exact states you would find when you open
the box would show clearly which path the electron took, so that even if you
looked at a subset of trials where the box was found in a particular quantum
state Y, you'd still see no interference pattern in the electron, just like
you don't see an interference pattern in Fig. 5 of the paper which looks
only at the subset of trials where the idler ended up at D3 and thus was
known to have come from atom A.
And of course, instead of just having the inside of the box contain a cloud
chamber, you could have it contain some even more complicated macroscopic
recording device, like a cloud chamber *and* a little man who can see the
condensation track in the cloud chamber and remember it, and then you could
choose whether to open the box and measure the state of the system inside
while the man's memory was still intact, or after a bomb had gone off inside
the box and made the information impossible to recover even in principle
from a measurement of the state. The basic idea here should be the
same--you'll never see interference in the total pattern of electrons, but
if you repeat this experiment some vast amount of times and look only at the
subset of trials where the inside of the box was found in a particular
precise quantum state, then you may see interference in that subset, in the
cases where the information has been erased (in this example, the cases
where you wait until after the bomb has blown the man and his memories to
smithereens).
Jesse
Received on Wed Oct 12 2005 - 16:45:22 PDT