Re: entanglement question

From: John Denker (jsd_at_av8n.com)
Date: 09/13/04 

Date: 13 Sep 2004 17:34:33 GMT

Paul Kelly wrote:
> from a humble chemist; as I understand it, if you have two entangled
> particles (a) and (b) and measure a property of particle (a) this
> instantaneously, and "spookily", determines the property of particle (b), no
> matter how far away it is. Measurement of (b)'s property would confirm
> this.
> But what if the two measurements - of particle (a) and particle(b) - were
> done instantaneously? (a) and (b) would both try to exert a spooky action at
> once...

A refinement: If you want to keep the nitpickers at bay, you
shouldn't say "instantaneous". Instead say "at a spacelike
separation" ... which means sufficiently quickly and sufficiently
far apart that no signal from one measurement-site can arrive in
time to influence the other measurement, because of the limitations
of relativistic causality, i.e. no signals can travel faster
than the speed of light.

Subject to that emendation, the question is an excellent one.
A lot of very sharp physicists have asked the question, and
some even did the experiment to check whether the theory gave
the right answer. (Spoiler: it does.)

What you find is that the theory does not predict that any
"action" is "exerted". Instead the theory predicts a slightly
spooky _correlation_. The correlation is enforced even across
spacelike separations.

Here's the classical analogy. (The quantum refinement will
follow). Roll a die. The number on top is random. The
number on the bottom is also random. They are however
correlated. (They always add up to 7, in case you hadn't
noticed.) The top-number is just as random as the bottom
number. Classically, you can see how the correlation is
enforced: the top of the die is locked to the bottom of
the die, and if grab one side of the die and try to flip
it to a new number, the other side will find out about it
at the speed of sound if not faster.

You can also set up partial correlations. For instance the
number on the north side of the die is partially correlated
with the number on the top of the die.

For the corresponding QM experiment, the "top" number is
entirely random, and the "bottom" number is also entirely
random ... but they are correlated. Under ideal conditions
you can have 100% correlation, or you can arrange partial
correlation if you want (like the top/north correlation
exhibited by the die).

One somewhat-spooky thing is that the correlations are
enforced even under conditions where no signal can flow
from one measurement-site to the other

NOTE: This does not violate a properly-formulated notion
of relativisitic causality, because we have only
correlation at a distance, not action at a distance. The
effect cannot be used to transmit information across the
gap from one measurement to the other. One guy sees a
random number. The other guy sees a random number. The
numbers are correlated, but neither side can control
which number appears, so the theory about correlations does
not (at the time) tell them anything they didn't already
know... which is the key to making this not really very
spooky. The only way they can confirm that the numbers
are correlated is to write them down and communicate them
(via ordinary causal communiation channels) to the other
guy. Then using 20/20 hindsight they can confirm that
the measurements were correlated. This means that the
two observers, if they ever manage to interact through
causal channels, can _recognize_ each other as having
been the participants in this particular experiment, but
that's about all it's good for.

A more detailed analysis shows that this sort of correlation
would be very hard to explain by any classical phenomenon,
such as e.g. the presence of a pool of correlated pseudo-
random numbers (which the two observers hypothetically
inherited from some common ancestor).

The experiment has been done, and agrees with the QM predictions.
Alain Aspect's group did some of the earliest experiments:
   http://atomoptic.iota.u-psud.fr/EnMain.htm

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