Since there didn't seem to be objections to the last bit of formalism, let me take the next step. I would like to consider a system of two spin 1/2 particles produced from a spin 0 state. As an aside, actual experiments that have been conducted are a bit more complicated than this idealized experiment. But, this simplified example is useful in the same sense that examples of perfectly elastic collisons are useful in understanding classical mechanics.
QM describes two spin 1/2 particles coming out a spin zero state as a superpositon: (|+-> + |-+>)/sqrt(2). |+-> is defined as particle 1 with spin up and particle 2 with spin down |-+> is defined as particle 1 with spin down and particle 2 with spin up. One thing we can immediately see is that if one particle is measured up, the other one should be measured down. This makes sense, if both of them were up in the same direction, angular momentum would not be a conserved quantity, since we would have a spin zero state turning into either a plus 1 or a minus 1 state. And, we can do the experiment, and find that, to within experimental errors, there is 100% anti-correlation between the spin of these particles. Fairly early on, by the mid-30s, the fact that these correlations, according to the formalism of QM, could be spaceline. Einstein Podanski and Rosen pointed this out in their 1935 paper...and arrieved at conclusions concerning the completeness of QM. This work has been generalized, and called the EPR paradox. The paper itself can be found (as .jpg files from scanning) at http://www.burgy.50megs.com/epr.htm It's a bit hard to read, but I was able to go through it. As the paper states, Einstein thought this showed the incompleteness of QM. But, the work of Bell and the experimental work of Aspect and the other experimentalists who have found spacelike correlations show that the spacelike collapse of the wavefunction into eigenstates is not evidence for the incompleteness of QM. Rather, it is an experimentally testable prediction of QM. Experimental observations have been made confirming the predictions obtained when the QM formalism of the spacelike* collapse of the wavefunction occures. But, before going on with that, I'd like to stop again and be sure that Warren, Ray and others who are following along agree with my explaination of this. I'd appreciate a short yes or no on this. Dan M. ** Spacelike is a term that refers to two events in space and time that cannot be connected by a signal. For example, let's say Cassia is suppose to fire it's engines to enter Saturn's orbit at time t. On earth, we cannot know whether this happened before t+d/c, where d is the distance from Saturn to the earth. If d/c is 30 minutes, then the event of the firing/non fireing of the engine and the event of the observer listening to telemetry are spacelike....it is impossible to send a signal from one to the other. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
