Theorthodox quantum interpretationof this situation is as follows. We must accept that when
Aperforms a measurement on the spin of one of the particles, this is really a measurement on the
entire system, even though it would appear thatAis making a measurement on only part of the
system (namely only one of the two particles). IfAmakes a measurement ofSza, then the act of
performing the measurement will select an eigenstate ofszaout of the full state|Φ〉. Depending on
the eigenvalue ofSazobserved, the state selected will be
Sza= +̄h
2
|z+;z−〉Sza=−
̄h
2|z−;z+〉 (17.36)This then explains why measuring thenSbzgives perfectly anti-correlated outcomes, and why mea-
suringSbxgives 50% spin + and 50% spin−.
The real novelty in EPR is that the measurement atAchanges the whole state and in particular
the state asBwill measure it.
17.8 Einstein’s locality principle
Einstein Podolsky and Rosen could not accept as part of a complete theory the fact that a mea-
surement atAcould change the state as measured byBin violation of macroscopic causality. To
quote them
If, without in any way disturbing a system, we can predict with certainty (i.e. with
probability equal to unity) the value of a physical reality,then there exists an element
of physical reality corresponding to this physical quantity.and also
The real factual situation of the systemBis independent of what is done with the
systemA, which is spatially separated fromB.The first principle led totheories with hidden variables, in which the measured values ofSbxin an
eigenstate ofSazactually have a physical reality, but this reality remains hidden from us, and we
can probe these deterministic hidden variables only in a statistical sense. Hidden variable theories
seemed so generally possible that it seemed always possibleto mimic the predictions of quantum
mechanics (and their experimental verifications) by introducing some extra degrees of freedom of
this type.
17.9 Bell’s inequalities
The situation changed dramatically in 1964, when John Bell made verifiable and falsifiable predic-
tions that could distinguish between quantum mechanics andtheories of hidden variables.^15 The
key is to trigger on these entanglements typical of quantum theory.
(^15) J.S. Bell, Physics 1 (1964) 195;Speakable and unspeakable in quantum mechanics, Cambridge, 1991.