Thanks very much Jesse!
You answered the question I *would have* asked had I rememberd my quantum
physics better ;-)
I think your answer is related to a paradox a friend mentioned to me.
The paradox is as follows:
"One does the EPR thing of creating two particles with opposite spin. Send
one far away to Alpha Centauri and send the other through a
Stern-Gerlach magnet and let the spin up and spin down outputs
interfere to form a double slit. If the far away particle is measured
up vs. down, our local particle must definitely go through the up hole
or the down hole and we get no interference pattern. If he measures
the far away particle sideways we get a superposition of states and we
get interference. Thus by rotating his measurement he should be able
to communicate to us faster than the speed of light. We should see our
pattern blinking between interference and not. What's wrong with that
argument?"
Along the lines of your solution to my other, related puzzle, I'll try to
analogize a solution to this puzzle.
I guess the idea must be: there is no "change" to what a particular particle
does
when you observe its faraway coupled pair in a certain way. Its individual
results do not visibly
change from non-interference to interference. (If that did happen,
you'd have the basis for a faster than light communicator, as you say.)
Instead, when you observe some of the particles sideways and some
vertically,
you must be creating "correlational information" that exists only
statistically
as a correlation between that's happening in Alpha Centauri and what's
happening locally.
So, maybe there is some weird cancellation here, like in the case you
described in your email.
Perhaps, if one restricts attention to the cases where
the faraway particle is measured "right" then interference is seen, and if
one restricts
attention to the cases where the faraway particle is measured "left" then
interference
is seen; but if one looks across all cases where the faraway particle is
measured
sideways, then the peaks and troughs of the different cases might cancel out
and
you'd get no interference?
-- Ben
> 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 - 18:05:22 PDT