lew@ihuxr.UUCP (06/06/83)
This is a sequel to my article "Bell's theorem and the Soma cube", but doesn't really depend on it except for the statement of Bell's theorem. One can actually perform an experiment that can be described roughly as follows. A particle decay occurs that results in two spin-1/2 particles flying off in opposite directions. The decay mode is such that the particles always have opposite spin, measured along any axis perpendicular to their line of flight. So far this is easy to picture classically. We just imagine the particles' spins being set oppositely at the the time of decay. Note though, that the spin measurement is quantized along ALL axes, so we have to imagine an extensive agreement, as it were, between the particles as to what measurement to give (plus or minus) when measured along any axis. The question is, can we imagine such an agreement being made which will give results consistent with QM. Here is how Bell's theorem gives a negative answer. Consider three axes: X, Y, and D. X and Y are perpendicular and D is diagonal between them. QM predicts that measurements along X and Y will be uncorrelated, but that measurements along D will be strongly correlated with both X and Y. Bell's theorem shows that the strength of this correlation is too great for the X and Y measurements to remain uncorrelated in any preset agreement. Since a measurement of one particle along any axis tells us what the measurement along the same axis of the other particle must yield, we can express all measurements with respect to one particle. If we look at the statistical mix of the X, Y, and D measurements, Bell's theorem tells us: N( X- Y+ ) <= N( X- D+ ) + N( Y+ D- ) N() means the fraction of all measurements having the given value pair. Since X and Y are uncorrelated N( X- Y+ ) is 1/4. The terms on the right can be calculated by QM (I can still do this!) Each is the probability of measuring a spin value at 135 degrees to a prepared spin, times the 1/2 probability of the first spin having the given value. This value is .073223 for a total of .146447 ... much less than the required .25 . (These numbers are mine and so are not above suspicion, but the idea is at least right.) Lew Mammel, Jr. ihuxr!lew