Why does EPR need two observables?



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?

Obviously, two observables are necessary to get Bell's inequalities,
and also to discuss Heisenberg's Uncertainty Principle, but why are
they needed to establish Einstein's conclusion.

Vonny N.

.



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