Re: Why does EPR need two observables?
- From: a student <of_1001_nights@xxxxxxxxxxx>
- Date: Fri, 17 Feb 2006 00:04:11 +0000 (UTC)
Vonny N. wrote:
Einstein's main point in his EPR thought-experiment was that under
Bohr's 'measurement=meaning' interpretation of the quantum formalism,
one could show that a measurement in one part of space must
instantaneously influence the results of a measurement performed in
another part of space. As is well known, this argument makes use of a
pair of non-commuting observables for each of two entangled systems.
But it seems to me that only *one* observable is required to establish
Einstein's thesis. If, for example, one takes a pair of entangled
particles with total momentum equal to zero, then the results of the
measurement of one immediately imply the result of a subsequent
measurement performed on the other. Who needs a second observable
(position, say) for this argument to have force?
The main point of the EPR paper was not to show that a measurement
instantaneously influences results elsewhere (indeed, the converse is
assumed in the paper). Further, even if a measurement on one particle
may imply the result of a measurement on a distant particle, there need
be no instantaneous influence involved - if two billiard balls collide,
I can work out the momentum of one from the momentum of the other
without anything non-local going on.
The EPR paper assumed that (i) NO instantaneous influence of
measurements, and (ii) a perfect pre-existing correlation between
distant particles implies that the correlated observables have
pre-existing values (otherwise how would one particle "know" how to
output the correct correlated value, given assumption (i)?). Here
"pre-existing" denotes "after preparation and before measurement".
But quantum mechanics allows perfect correlations between pairs of
non-commuting observables (position and momentum in the EPR paper, Bohm
later gave the spin example). The EPR paper therefore concludes that
(a) in such cases these observables must have pre-existing values, and
hence that (b) since quantum mechanics does not (and cannot) prescribe
such values, it must be incomplete.
Thus, noncommuting observables are needed, as the validity of (b)
depends on the non-existence of simultaneous eigenstates of such
observables.
Many people (particularly after the glorious sharpening by Bell, and
subsequent experiments by Aspect), regard the "locality" assumption (i)
above as suspect. However, given that no measurable non-local
influence is detectable (according to quantum mechanics), one can as
well suspect the "reality" assumption (ii). Some people also note
that the root of the trouble might be the implicit use of a third
"non-conspiracy" assumption, that experimenters have free choice in
what they are going to measure.
.
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