all, this is a question of causality in special relativity, and could be considered purely classically.
Suppose two travelers originating atπ^0 are each given a ball. Both travelers know that the ball
given to one of them is black, while the ball given to the otheris white, but they do not know
whether the ball each one received is black or white. They nowtravel apart for a long long time,
until one of the travelers decides to open his present and finds out this his ball is black. He then
instantaneously knows that the other guy’s ball is white. Nonetheless, no information has really
traveled faster than light, and again, this is not the key problem in the EPR paradox. After all, if
bothAandBonly measure along commuting observables, such asSzaandSbz, their measurements
are analogous to classical ones.
The real distinction brought by quantum behavior is that onecan make measurements along
Szaor alongSxa, for example, and these operators do not commute. It is this realization that was
new in Bell’s work. If we allow for these observables to be measured, then the possible outcomes
are as given in Table 1 below.
spin component result spin component result
measured by A measured by B
z + z −
z − z +
z + x +
z + x −
z − x +
z − x −
x + x −
x − x +
x + z +
x + z −
x − z +
x − z −
For example,
- If bothAandBmeasureSzor both measureSx, the spins measured are opposite;
- IfAmakes no measurement, then the measurements ofBare 50% spin + ̄h/2 and 50% spin
− ̄h/2; - IfAmeasuresSazandBmeasuresSxb, there is completely random correlation between the
two measurements. Even ifSazis measured to be + ̄h/2, the measurement ofSxb will yield
50% spin + and 50% spin−.
Thus, the outcome of the measurements ofBdepend on what kind of measurementAdecides to
perform. AndAcan decide to orient his measurement directionnlong after the two particles have
separated. It is as though particlebknows which spin component of particleais being measured.