From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Tue May 07 2002 - 16:08:07 MDT
Ah, it looks like I wrote the message asking that question about quantum
ansibles, then left it in my Drafts folder. Anyway, as you can see, the
question that's been bugging me is almost exactly the same one raised in
this paper, and if there's a known flaw in this, I really wish someone would
point it out.
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
attached mail follows:
As long as the Extropian list is discussing this, I'd like to ask a
physics question that's been bugging me for the last eight years or so.
We all know that quantum entanglement can't be used to transmit useful
information by performing two measurements in different places, say on
both sides of the Atlantic, because you need to compare the measurements
in order to prove that information transmission has taken place. I think
John K Clark summarized it best when he said that if you flip a coin and
get HTHHHTH, and I flip a coin and get THTTTHT, it's clear that some kind
of information must have been shared, but it's not useful information
until we compare strings, which has to happen at the ordinary speed of
light. This I understand.
However, the classic two-slit experiment shows that the presence or
absence of a "measurement" can produce qualitatively different behavior; a
wave distribution versus two clusters. In the two-slit experiment, you
send a stream of photons at a barrier with two slits, A and B. If you
measure which slit the photon went through, then each photon will appear
to pass through either one slit or the other, and will hit the target in
an area clustered directly behind the slits. If you don't measure which
slit a photon goes through, the photon goes through both slits, interferes
with itself, and ends up with a wavelike probability distribution of
hitting any of the points behind the barrier. This, too, I understand.
Another classic quantum experiment uses a half-silvered mirror. You send
a photon through a half-silvered mirror at A; it splits and goes both
ways, bounces off one fully silvered mirror at B or bounces off another
fully silvered mirror at C depending on which path it took (an entangled
photon will take both paths), recombines at a half-silvered mirror at D,
and goes on from there to either target E or target F, depending on which
path it took originally and whether it bounced off the half-silvered
mirror at D. If no measurements are performed during this operation, the
photon has a 100% chance of winding up at E. If you measure whether the
photon bounced off B or C, the photon has a 50% chance of winding up at
either E or F. Again, this is all perfectly straightforward in terms of
probability amplitudes.
Here's the part I don't understand.
Now let's suppose that you use any of the quantum-cloning or
quantum-teleportation techniques to produce two entangled photons. I
transmit one photon to Boston and the other photon to London. Now I take
the photon in Boston and send it through the second quantum experiment; I
send it through a half-silvered mirror at A, let it possibly bounce off
mirror B and mirror C, but now instead of mirror B and mirror C both
sending the photon to recombine at half-silvered mirror D, mirror B and
mirror C both send the photon bouncing back and forth along a long
corridor of mirrors - long enough that there's a quarter second before the
photon recombines at half-silvered mirror D.
During this quarter second, the experimenters in London choose whether or
not to perform a measurement on their photon - the photon that's entangled
with the one in Boston. If they perform a measurement at this point, then
as I understand quantum physics, both photons - the one in London and the
one in Boston - should undergo a collapse of the wavefunction. If the
photon in Boston undergoes a collapse of the wavefunction, it will have an
equal chance of hitting target E or target F. If the photon in London is
not measured, and the photon in Boston is thus not collapsed during that
quarter second, the photon in Boston will hit target E with 100%
probability.
If so, it allows for nonlocal transmission of information - a quantum
ansible. Note that the information is *not* transmitted through the
requirement that two measurements be consistent in some way. The
information transmitted is simply whether or not a measurement has taken
place; the actual results of the measurement are completely irrelevant to
the transmission of this information.
The interval before recombination, a quarter second, was selected not to
raise Special Relativity space-of-simultaneity issues between London and
Boston, but the issues are obviously there.
What's wrong with this picture?
-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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