EPR, Bell, and FTL Bandwidth

[Eric Cordian <emc@wire.insync.net>]

Steve Schear writes"
 
> Why aren't the coding techniques commonly used in telecom and disk
> data encoding adequate to both synchonize and convey data?
 
Think of the classical case.  I bake two fortune cookies, one with
"FOO" written on the slip of paper inside, and the other reading
"BAR." I then put them in a box and shake it for quite a while, until
the final state has chaotic dependence upon initial conditions, and
cannot be predicted.  I then keep one fortune cookie, and mail the
other one to Lucky Green in Tonga.
 
Someday in the future, I open my cookie, and instantly know what Lucky
will see when he opens his.  In doing so, I have created a
"instantaneous" correlation between two things separated by a vast
distance, which were in an identical state of ambiguity prior to one
of them being examined.
 
I am sure we will agree that there was no genuine faster-then-light
communication of information in this case.
 
In quantum mechanics, pairs of observables may have the property that
both of them may not be known precisely for a physical system.  The
Heisenberg Uncertainty principle states this for position and
momentum. Similar relationships exist for energy and time,
polarization or angular momentum measured with respect to different
axes, and various other things.  In addition, measuring a physical
system for one such variable always changes its wavefunction into one
for which the value of that variable is precisely specified, and the
value of the other "non-commuting" variable is not.
 
You can see this easily with three polarizing filters.  If you shine a
light through two of them at right angles to each other, it will be
completely blocked.  But it you insert third filter at a 45 degree
angle, some light will get through.  This is because light whose
polarization is known to be vertical or horizontal is in a mixed state
with respect to its polarization rotated 45 degrees.
 
It is therefore tempting to think that perhaps the miracle of quantum
mechanics could be employed in our fortune cookie experiment for the
transmission of information.  I generate many pairs of cookies, with
random but identical polarization, keeping one of each pair for
myself, and sending the other to Lucky.  I then encode a stream of
bits by measuring the polarization of 100 cookies, vertically if I
wish to transmit a "0", and at a 45 degree angle if I choose to
transmit a "1".  I then know Lucky's corresponding cookie to be in an
exact state with respect to one of these observables, and in a mixed
state with respect to the other, and if Lucky measures the vertical
polarization of his groups of cookies, there should be a correlation
between his results and mine which can only be explained by non-local
communication of my choice, on the fly, of which way I measured the
polarization, to his apparatus.
 
Now here we have good news and bad news.  The good news is that when
we do such an experiment, precisely enough to know for sure that there
is a spacelike separation between the two measurement events, we do
indeed see the correlation predicted by quantum mechanics.  The bad
news is that either end of the experiment, by itself, cannot see this
correlation without knowing what results were obtained by the person
at the other end. The correlation is between both ends.  There is no
experiment that can be done by either end alone which will turn out
differently depending upon what the guy at the opposite end is doing.
 
Thus, while such experiments involve non-local communication between
two locations separated by a spacelike distance, such communication is
obvious only to someone able to see what is going on in both places at
once, but not to either isolated experimenter. Hence, the non-local
collapse of quantum mechanical wavefunctions cannot be employed for
the transmission of information.
 
A similar argument applies to quantum teleporation, in which the value
of some measurable variable is transferred from a dynamical system to
one of two particles in correlated but unknown quantum states, causing
the particle's twin to take on an identical value.  Again, a person
able to view both systems can see that non-local communication has
taken place, but there is nothing either end can do by itself to learn
what has transpired at the other end.  This is because the correlation
which proves non-local communication is present only in combined data
from both ends of the experiment, but not in data from either end
alone.

-- 
Eric Michael Cordian 0+
O:.T:.O:. Mathematical Munitions Division
"Do What Thou Wilt Shall Be The Whole Of The Law"